ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8

Seismic design of steel building accordance to

Eurocode 3 and 8

Valentinos Neophytou BEng, MSc

JULY 2013

-‐Worked examples – Hand calculations

ETABS manual

ABOUT THIS DOCUMENT

This publication provides a concise compilation of selected rules in the Eurocode 8, together

with relevant Cyprus National Annex, that relate to the design of common forms of concrete

building structure in the South Europe. It id offers a detail view of the design of steel framed

buildings to the structural Eurocodes and includes a set of worked examples showing the

design of structural elements with using software (CSI ETABS). It is intended to be of

particular to the people who want to become acquainted with design to the Eurocodes. Rules

from EN 1998-1-1 for global analysis, type of analysis and verification checks are presented.

Detail design rules for steel composite beam, steel column, steel bracing and composite slab

with steel sheeting from EN 1998-1-1, EN1993-1-1 and EN1994-1-1 are presented. This

guide covers the design of orthodox members in steel frames. It does not cover design rules

for regularities. Certain practical limitations are given to the scope.

Due to time constraints and knowledge, I may not be able to address the whole issues.

Please send me your suggestions for improvement. Anyone interested to share his/her

knowledge or willing to contribute either totally a new section about Eurocode 8 or within

this section is encouraged.

For further details:

My LinkedIn Profile:

http://www.linkedin.com/profile/view?id=125833097&trk=hb_tab_pro_top

Email: [email protected]

Slideshare Account: http://www.slideshare.net/ValentinosNeophytou

List of contents

1.1 DESIGN AND ANALYSIS EXAMPLE OF STEEL FRAME WITH CONCENTRIC BRACING ................................................................................................................................. 7

1.1 LAYOUT OF STRUCTURE ............................................................................................... 7

1.2 PRELIMINARY DESIGN................................................................................................... 9

1.2.1 PRELIMINARY DESIGN OF COLUMNS AND BEAMS ............................................ 9

1.3 MATERIAL PROPERTIES .............................................................................................. 11

1.3.1 MATERIAL PROPERTIES OF CONCRETE ............................................................... 11

1.3.2 MATERIAL PROPERTIES OF STEEL ........................................................................ 12

1.3.3 MATERIAL PROPERTIES OF STEEL AND CONCRETE AS DEFINE IN ETABS 13

1.3.4.1 MODELING REQUIREMENTS OF EC8 FOR CONCRETE MEMBERS ............... 15

1.3.4.2 MODELING REQUIREMENTS OF EC8 FOR FLOOR DIAPHRAGMS ................ 15

1.3.4.3 MESHING OF SLABS ................................................................................................ 16

1.4 JOINT MODELING (EN1993-1-1,CL.5.1.2) ................................................................... 17

2.0 MODAL RESPONSE SPECTRUM ANALYSIS ............................................................. 20

2.1 STRUCTURAL TYPES AND BEHAVIOR FACTOR ACCORDING TO EN1998-1-1,CL.6.3 ................................................................................................................................... 20

2.2 DEFINE DESIGN HORIZONTAL RESPONSE SPECTRUM ........................................ 24

2.2.1 VERTICAL RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.3) ................................ 24

2.2.2 HORIZONTAL RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.5) .......................... 24

2.2.3 PARAMETERS OF ELASTIC RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.5) .. 25

2.2.3.1 GROUND INVESTIGATION CONDITIONS ........................................................... 29

2.2.3.2 IMPORTANCE FACTOR ........................................................................................... 29

2.2.3.3 DUCTILITY CLASS ................................................................................................... 30

2.3 ANALYSIS TYPES .......................................................................................................... 31

2.3.1 MODAL RESPONSE SPECTRUM ANALYSIS .......................................................... 31

2.3.1.1 ACCIDENTAL ECCENTRICITY .............................................................................. 32

2.3.2 LATERAL FORCE ANALYSIS REQUIREMENTS .................................................... 34

2.3.4 ESTIMATION OF FUNDAMENTAL PERIOD T1 ...................................................... 35

2.3.5 AUTOMATIC LATERAL FORCE ANALYSIS USING ETABS ................................ 36

2.3.6 USER LOADS - LATERAL FORCE ANALYSIS USING ETABS ............................. 38

2.3.7 TORSIONAL EFFECTS ................................................................................................ 45

2.3.8 SUMMARY OF ANALYSIS PROCESS IN SEISMIC DESIGN SITUATION ........... 46

3.0 DEFINE STATIC LOADS ................................................................................................ 47

4.0 SEISMIC MASS REQUIREMENTS ACCORDING TO EC8 ......................................... 48

4.1 MASS SOURCE OPTION ................................................................................................ 49

5.0 WIND LOADING ON STRUCTURE (EN1991-1-4:2004) .............................................. 51

5.1 CALCULATION OF WIND LOAD ACCORDING TO EN1991-1-4:2004 .................... 51

5.2 APPLICATION OF WIND LOADING USING ETABS ................................................. 54

6.0 LOAD COMBINATION ................................................................................................... 59

7.0 DESIGN PREFERENCES ................................................................................................ 61

8.0 ANALYSIS AND DESIGN REQUIREMENTS FOR CONCENTRICALLY BRACED FRAMES ACCORDING TO EN1998-1-1,CL.6.7.2 .............................................................. 64

8.1 STEPS OF THE DESIGN DETAIL OF CONCENTRIC STEEL FRAMES ................... 65

8.2 CLASSIFICATION OF STEEL SECTIONS .................................................................... 66

8.3 DESIGN OF COMPOSITE SLAB UNDER GRAVITY LOADS .................................... 68

8.4 DESIGN OF COMPOSITE BEAM (WITH STEEL SHEETING) UNDER GRAVITY LOADS .................................................................................................................................... 72

8.5 DETAIL DESIGN OF STEEL COLUMNS UNDER GRAVITY LOADS ...................... 79

8.6 DETAIL DESIGN RULES OF STEEL CONCENTRIC BRACED FRAMES (CBF) ACCORDING TO EUROCODE 8 .......................................................................................... 87

8.6.1 DETAIL DESIGN RULES OF STEEL BRACING ACCORDING TO EUROCODE 8.................................................................................................................................................. 87

8.7 DETAIL DESIGN RULES OF STEEL COLUMNS AND BEAMS ACCORDING TO EUROCODE 8 ......................................................................................................................... 88

8.8 DETAIL DESIGN RULES OF STEEL COMPOSITE MEMBERS ACCORDING TO EUROCODE 8 ......................................................................................................................... 89

8.9 DETAIL DESIGN RULES OF STEEL MOMENT RESISTANCE FRAMES (MRF) ACCORDING TO EUROCODE 8 .......................................................................................... 90

8.9.1 DETAIL DESIGN RULES FOR MRF - DESIGN CRITERIA .................................... 90

8.9.2 DETAIL DESIGN RULES OF STEEL BEAM FOR MRF ........................................... 90

8.9.3 DETAIL DESIGN RULES OF STEEL COLUMN FOR MRF ..................................... 91

9.0 DESIGN OF STEEL FRAMES ......................................................................................... 92

9.1 DESIGN OF STEEL MEMBER OVERWRITES DATA ................................................. 92

9.2 DESIGN OF COLUMNS / BEAMS USING ETABS – GRAVITY LOAD ANALYSIS ONLY ...................................................................................................................................... 97

9.3 DESIGN OF STEEL COLUMN (GRAVITY DESIGN SITUATION) – HAND CALCULATIONS ................................................................................................................. 105

9.4 DESIGN OF STEEL COLUMN (SEISMIC DESIGN SITUATIONN) ......................... 118

9.4.1 DESIGN OF STEEL COLUMN (SEISMIC DESIGN SITUATION – HAND CALCULATION) .................................................................................................................. 124

9.5 DESIGN OF COMPOSITE BEAMS - HAND CALCULATIONS ................................ 128

9.5 DESIGN OF STEEL BRACING ..................................................................................... 145

9.5.1 MAIN CONFIGURATION OF DESIGN OF STEEL BRACING .............................. 145

9.5.2 SIMPLIFIED DESIGN OF FRAMES WITH X BRACING (EXTRACT FROM DESIGN GUIDANCE TO EC8) ........................................................................................... 147

9.5.3 MODEL IN ETABS ..................................................................................................... 148

9.5.4 DESIGN OF STEEL BRACING (GRAVITY/SEISMIC DESIGN SITUATION) – HAND CALCULATION ....................................................................................................... 156

10.0 MODAL RESPONSE SPECTRUM ANALYSIS ......................................................... 170

10.1 SET THE ANALYSIS OPTIONS ................................................................................. 170

10.2 EVALUATE THE ANALYSIS RESULTS OF THE STRUCTURE ACCORDING TO THE MODAL ANALYSIS REQUIREMENTS ................................................................... 171

10.2.1 ASSESS THE MODAL ANALYSIS RESULTS BASED ON THE EN1998 ........... 172

11.0 SECOND ORDER EFFECTS (P – Δ EFFECTS) ACCORDING TO EN1998-1-1,CL.4.4.2.2 ........................................................................................................................... 173

11.1 DISPLACEMENT CALCULATION ACCORDING TO EN1998-1-1,CL.4.4.2.2 ..... 174

11.2 INTERSTOREY DRIFT ................................................................................................ 174

11.3 CALCULATION OF SECOND ORDER EFFECT USING ETABS ........................... 175

11.3.1 INTERSTOREY DRIFT DISPLACEMENT ............................................................. 176

11.3.2 TOTAL GRAVITY LOAD PTOT ................................................................................ 178

11.3.2 TOTAL SEISMIC STOREY SHEAR VTOT ............................................................... 180

12.0 DAMAGE LIMITATION ACCORDING TO EN1998-1-1,CL.4.4.3 .......................... 184

12.1 CALCULATION OF DAMAGE LIMITATION .......................................................... 185

ANNEX - A .......................................................................................................................... 186

ANNEX A.1 - ASSUMPTIONS MADE IN THE DESIGN ALGORITHM (MANUAL OF ETABS – EC3 & EC8) .......................................................................................................... 186

A1.1:LIMITATION MADE IN THE DESIGN ALGORITHM (MANUAL OF ETABS – EC3&EC8) ............................................................................................................................. 187

ANNEX –B: STEEL DESIGN FLOWCHARTS .................................................................. 188

1.1 Design and analysis example of steel frame with concentric bracing

1.1 Layout of structure

Figure 1.1: Plan view

Figure 1.2: Side Elevation (4) & (1)

Figure 1.3: Side Elevation (A) & (D)

Table 1.1: Dimensions of the building

Dimensions Symbol Value Units

Storey height h 3.0 m

Total height of the building H 9.0 m

Beam length in X-direction lx 5.0 m

Beam length in Y-direction ly 5.0 m

Building width in X-direction Lx 15.0 m

Building width in Y-direction Ly 15.0 m

1.2 Preliminary design

Table 1.2: Seismic design data

Data Symbol Value Units

Seismic zone - 3 -

Reference peak ground acceleration on type A ground, agR.

agR 0.25 m/s2

Importance class γI 1.0 -

Design ground acceleration on type A ground ag 0.25 m/s2

Design spectrum - Type 1 -

Ground type - B -

Structural system Steel frame with concentric bracing

Behavior factor q 4.0 -

1.2.1 Preliminary design of columns and beams

Preliminary design of steel beam

Design data:

Span of beam

Bay width

Overall depth of slab

Loading data:

Density of concrete

Loads of floor per meter

Live load

Live load per meter

Partial factor for actions:

Safety factor are obtain from Table A.1(2)B EN1990 Permanent actions, γ G

Variable actions, γ Q

Total load

Lx 5000mm:=

wbay 5000mm:=

h 130mm:=

γ c 25kNm 3−⋅:=

gfloor γ c h⋅ Lx⋅ 16.25 kNm 1−⋅⋅=:=

qoffice 2kNm 2−⋅:=

qservice qoffice Lx⋅ 10 kNm 1−⋅⋅=:=

γG 1.35:=

γQ 1.5:=

Ed γG gfloor⋅ γQ qservice⋅+ 36.94 kNm 1−⋅⋅=:=

Material properties:

Young Modulus of Elasticity

Structural steel (clause 6.1(1) EN 1993 1-1)

Structural steel properties:

Yield strength, fy

Ultimate strength, fu

Yield strength of reinforcement, fyk

Deflection limitation:

Deflection limit - General purpose

Second moment area required

Second moment area provided (IPE240)

Moment resistance check:

Design moment (Fixed end)

Plastic modulus required

Plastic modulus provided (IPE240)

Weak Beam - Strong column -Capacity design:

Plastic modulus of column required

Plastic modulus of column provided (HE220A)

Es 210kNmm 2−⋅:=

γM0 1.0:=

fy 355N mm 2−⋅:=

fu 450N mm 2−⋅:=

fyk 500N mm 2−⋅:=

FLx300

:=

Ireq300 Ed⋅ Lx

3⋅

384 Es⋅1.718 103× cm4⋅=:=

Iprov 3892cm4:=

Check_1 if Iprov Ireq> "OK", "NOT OK", ( ):=

Check_1 "OK"=

MEdEd Lx

2⋅

1276.953kNm⋅⋅=:=

Wpl.y.reqMEdfy

216.769cm3⋅=:=

Wpl.y 324.4cm3:=

Check_2 if Wpl.y Wpl.y.req> "OK", "NOT OK", ( ):=

Check_2 "OK"=

Wpl.y.c.req 1.3Wpl.y⋅ 421.72cm3=:=

Wpl.y.c 515cm3:=

Check_3 if Wpl.y.c Wpl.y.c.req> "OK", "NOT OK", ( ):=

Check_3 "OK"=

1.3 Material properties

ETABS: Define > Material properties

1.3.1 Material properties of concrete

Design requirement Poisson ratio is equal to v = 0 (cracked concrete) and v = 0.2 (un-cracked concrete) as

(EN1992-1-1,cl.3.1.3).

Table 1.3: Concrete properties (EN 1992, Table 3.1)

Property Data for concrete

C16/20

(N/mm2)

C20/25

(N/mm2)

C25/30

(N/mm2)

C30/37

(N/mm2)

Mass per unit Volume 2,5E-09 2,5E-09 2,5E-09 2,5E-09

Weight per unit volume 2,5E-05 2,5E-05 2,5E-05 2,5E-05

Modulus of Elasticity 29000 30000 31000 33000

Poisson’s Ratio (cracked concrete) 0 0 0 0

Coeff. of thermal expansion 10E-06 10E-06 10E-06 10E-06

Charact. ConcCyl. Strength, fck 16 20 25 30

Bending Reinf. Yield stress, fyk 500 500 500 500

Shear Reinf. Yield stress, fyk 500 500 500 500

1.3.2 Material properties of steel

Table 1.4: Material properties of steel

Material Properties Symbol Value Units References

Mass per unit Volume γs 7.85E-09 kg/mm3 EN1991-1-1,table A.4

Weight per unit Volume

γs 7.70E-05 N/mm3 EN1991-1-1,table A.4

Modulus of Elasticity Es 210,000 N/mm2 EN1993-1-1,cl.3.2.6(1)

Poisson’s ratio ν 0.3 - EN1993-1-1,cl.3.2.6(1)

Coeff of Thermal Expansion (Steel structures)

α 1.2x10-5 per K (for T ≤ 100oC) K EN1993-1-1,cl.3.2.6(1)

Coeff of Thermal Expansion (Composite Concrete-Steel structures)

α 1.2x10-5 per K (for T ≤ 100oC) K EN1993-1-1,cl.3.2.6(1)

Shear Modulus G ≈81,000 N/mm2 EN1993-1-1,cl.3.2.6(1)

Characteristic yield strength of steel profile

fy 275 N/mm2 EN1993-1-1,table 3.1

Ultimate strength fu 430 N/mm2 EN1993-1-1,table 3.1

Table 1.5: Strength vales of steel sections (EN1993-1-1,table 3.1)

Steel grade

Nominal thickness of the element t (mm)

t ≤ 40mm 40mm < t ≤ 80mm Grade

reference fy (N/mm2) fu (N/mm2) fy (N/mm2) fu (N/mm2)

S235 235 360 215 360 EN 10025-2

S275 275 430 255 410 EN 10025-2

S355 355 510 335 470 EN 10025-2

S450 440 550 410 550 EN 10025-2

Note: You may use the product standard instead of those given in EN1993-1-1

1.3.3 Material properties of steel and concrete as define in ETABS

Figure 1.4: Material properties of concrete (C25/30)

Figure 1.5: Material properties of steel (S275)

1.3.4 Slab modeling

Table 1.6: Slab properties


Slab depth hs 170 mm

Diameter of stud d 19 mm

Height of stud haw 152 mm

Tensile strength of stud fu 430 N/mm2

ETABS: Define > Wall/Slab/Deck Sections/Add new deck

Figure 1.6: Deck section properties

Press “Set Modifier” in order to modify the slab properties

1.3.4.1 Modeling requirements of EC8 for concrete members

1. Unless a more accurate analysis of the cracked elements is performed, the elastic

flexural and shear stiffness properties of concrete and masonry elements may be taken

to be equal to one-half of the corresponding stiffness of the un-cracked elements

(EN1998-1-1,cl.4.3.1(7)).

Figure 1.7: Modified “Stiffness Modifiers”

1.3.4.2 Modeling requirements of EC8 for floor diaphragms

ETABS: Select > Wall/Slab/Deck section > Select Deck

ETABS: Define > Diaphragms

ETABS: Select “D1” (Rigid diaphragms)

2. When the floor diaphragms of the building may be taken as being rigid in their planes,

the masses and the moments of inertia of each floor may be lumped at the centre of

gravity (EN1998-1-1,cl.4.3.1(4)).

1.3.4.3 Meshing of slabs

ETABS: Select > Wall/Slab/Deck section > Select Deck

ETABS: Assign > Shell area > Auto Object Auto mesh option

When you have a composite beam floor system, ETABS, by default, automatically meshes

(divides) the deck at every beam and girder. This allows ETABS to automatically distribute

the loading on the deck to each beam or girder in an appropriate manner.

Figure 1.8: Meshing of composite slab

Figure 1.9: Meshing of normal slab

1.4 Joint modeling (EN1993-1-1,cl.5.1.2)

(1) The effects of the behavior of the joints on the distribution of internal forces and

moments within a structure, and on the overall deformations of the structure, may

generally be neglected, but where such effects are significant (such as in the case of

semi-continuous joints) they should be taken into account, see EN 1993-1-8.

(2) (2) To identify whether the effects of joint behavior on the analysis need be taken into

account, a distinction may be made between three joint models as follows, see EN

1993-1-8, 5.1.1:

– simple, in which the joint may be assumed not to transmit bending

moments.

– continuous, in which the behavior of the joint may be assumed to have no

effect on the analysis.

– semi-continuous, in which the behavior of the joint needs to be taken into

account in the analysis.

Table 1.7: Example of joint types

Simple joint Continuous Fixed joint Semi- continuous joint

ETABS: Pin joint in ETABS The pin-joint in ETABS can be achieved by selecting the members that you assumed to be

pinned in the analysis process. This can be done as follow:

Select member > Assign > Frame/Line > Frame Releases Partial Fixity

Figure 1.10: Pinned joint (both ends)

ETABS: Fixed joint in ETABS The fixed-joint in ETABS can be achieved by selecting the members that you assumed to be

fixed in the analysis process. This can be done as follow:

Select member > Assign > Frame/Line > Frame Releases Partial Fixity

Figure 1.11: Fixed joint

2.0 Modal Response Spectrum Analysis

2.1 Structural types and behavior factor according to EN1998-1-1,cl.6.3

Table 2.1: Structural types and behavior factor

Structural Type q-factor DCM DCH

Moment resisting frames (MRF)

αu/ α1 =1.1 αu/ α1 =1.2 (1 bay) αu/ α1 =1.3 (multi-bay)

dissipative zones in beams and column bases

4 5αu/ α1

Concentrically braced frames (CBF)

Dissipative zones in tension diagonals

4 4

V-braced frames (CBF)

2 2.5

Dissipative zones in tension and compression diagonals

Frames with K-bracing (CBF)

Not allowed in dissipative design

Eccentrically braced frame (EBF)

αu/ α1 =1.2 dissipative zones in bending or shear links

4 5αu/ α1

Inverted pendulum system

αu/ α1 =1.0 αu/ α1 =1.1

dissipative zones in column base, or column ends (NEd/Npl,Rd < 0.3)

2 2αu/ α1

Moment-resisting frames with concentric bracing (MRF) + (CBF)

4 4αu/ α1

αu/ α1 =1.2

dissipative zones in moment frame and tension diagonals Moment frames with infills

Unconnected concrete or masonry infills,

in contact with the frame

2 2

Connected reinforced concrete

Infills

See EN1998-1-1,table 5.1

Infills isolated from moment frame

4 5αu/ α1

Structures with concrete cores or walls

See EN1998-1-1,table

5.1

Note: If the building is non-regular in elevation (see EN1998-1-1,cl.4.2.3.3) the upper limit values of q listed above should be reduced by 20 %

Table 2.2: Values of behavior factor for regular and irregular structure

Structural type Regular in plan

and elevation

Irregular in

plan / Regular

in elevation

Regular in plan

/ Irregular in

elevation

Irregular in

plan &

elevation

Irregular in

plan / Regular

in elevation

Regular in plan

/ Irregular in

elevation

Irregular in

plan &

elevation

DCM DCH DCM DCM DCM DCH DCH DCH

Moment resisting frame

Single storey portal 4.0 5.5 3.2 3.2 3.2 5.25 4.4 4.2

One bay multi-storey 4.0 6.0 3.2 3.2 3.2 5.5 4.8 4.4

Multi-bay, multi-storey 4.0 6.5 3.2 3.2 3.2 5.75 5.2 4.6

Concentrically braced frame

Diagonal bracing 4.0 4.0 3.2 4.0 4.0 4.0 3.2 3.2

V-bracing 2.0 2.5 1.6 2.5 2.5 2.5 2.0 2.0

Frame with masonry infill

panels 2.0 2.0 1.6 2.0 2.0 2.0 1.6 1.6

2.2 Define design horizontal response spectrum

2.2.1 Vertical response spectrum (EN1998-1-1,cl.3.2.2.3)

The vertical component of the seismic action should be taken into account if the avg>0.25g

(2.5m/s2) in the cases listed below:

• for horizontal structural member spanning 20m or more,

• for horizontal cantilever components longer than 5m,

• for horizontal pre-stressed components,

• for beams supporting columns,

• in based-isolated structures.

2.2.2 Horizontal response spectrum (EN1998-1-1,cl.3.2.2.5)

For the horizontal components of the seismic action the design spectrum, Sd(T), shall be

defined by the following expressions:

0 ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙!!+ !

!!∙ !.!

!− !

!(ΕΝ1998-1-1,Eq. 3.13)

𝑇! ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙!.!!

(ΕΝ1998-1-1,Eq. 3.14)

𝑇! ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙2.5𝑞

𝑇!𝑇

≥ 𝛽 ∙ 𝑎! (ΕΝ1998-1-1,Eq. 3.15)

𝑇! ≤ 𝑇 ≤ 4𝑠: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙!.!!

!!!!!!

≥ 𝛽 ∙ 𝑎! (ΕΝ1998-1-1,Eq. 3.5)

Design ground acceleration on type A ground: ag=γIagR

Lower bound factor for the horizontal spectrum: β=0.2

Note: the value of q are already incorporate with an appropriation value of damping viscous,

however the symbol η is not present in the above expressions.

2.2.3 Parameters of elastic response spectrum (EN1998-1-1,cl.3.2.2.5)

Table 2.3: Parameters of Type 1 elastic response spectrum (CYS NA EN1998-1-1,table

3.2)

Ground

Type

S TB (s) TC (s) TD (s)

A 1.0 0.15 0.4 2.0

B 1.2 0.15 0.5 2.0

C 1.15 0.20 0.6 2.0

D 1.35 0.20 0.8 2.0

E 1.4 0.15 0.5 2.0

Note: For important structures (γI>1.0), topographic amplification effects should be taken

into account (see Annex A EN1998-5:2004 provides information for topographic

amplification effects).

ETABS: Define > Response spectrum function

1. Peak ground acceleration agR=0,25g,

2. Type C or D for building within category of importance I and II,

3. Define two response spectrum cases if the factor q is different in each direction,

Select EUROCODE8 Spectrum

Add New Function

4. Modify the existing values of elastic response spectrum case in order to change it into

the design response spectrum.

Figure 2.1: Response Spectrum to EC8

PERIOD ACCELERATION g = 9.81 m/sec2

T Sd(T) β = 0.2 -‐

0.0000 0.2000 SoilType = B -‐

0.1000 0.1917 q = 4.00 -‐

0.1500 0.1875 αgR = 0.25 -‐

0.2000 0.1875 S = 1.20 -‐

0.4000 0.1875 TB = 0.15 sec

0.6000 0.1563 TC = 0.50 sec

0.8000 0.1172 TD = 2.00 sec

1.0000 0.0938 T = 0.50 sec

1.5000 0.0625 2.0000 0.0469 Data for soil type -‐ Type Spectrum 1 2.5000 0.0300 index Soil Type S TB TC TD 3.0000 0.0500 1 A 1 0.15 0.4 2 4.0000 0.0500 2 B 1.2 0.15 0.5 2 5.0000 0.0500 3 C 1.15 0.2 0.6 2 6.0000 0.0500 4 D 1.35 0.2 0.8 2 8.0000 0.0500 5 E 1.4 0.15 0.5 2 10.0000 0.0500

Convert the existing elastic response spectrum case to design response

spectrum case

Figure 2.2: Amendment Response spectrum (q = 4)

2.2.3.1 Ground investigation conditions

Table 2.4: Geological studies depend on the importance class (CYS NA EN1998-1-1, NA

2.3 / cl.3.1.1 (4))

Importance class of buildings

Ground

Type

I II III IV

A NRGS NRGS RGS RGS

B NRGS NRGS RGS RGS

C NRGS NRGS RGS RGS

D NRGS NRGS RGS RGS

E NRGS NRGS RGS RGS

NRGS: Not required geological studies

RGS: required geological studies if there is not adequate information

2.2.3.2 Importance factor

Table 2.5: Importance classes for buildings (ΕΝ1998-1-1,table.4.3 and CYS NA EN1998-

1-1,cl NA2.12)

Importance

class

Buildings Important

factor γI

Consequences

Class

I Buildings of minor importance for public

safety, e.g. argricultural buildings, etc. 0.8 CC1

II Ordinary buildings, not belonging in the other

categories. 1.0 CC2

III

Buildings whose seismic resistance is of

importance in view of the consequences

associated with a collapse, e.g. schools,

assembly halls, cultural institutions etc.

1.2 CC3

IV

Buildings whose integrity during earthquakes

is of vital importance for civil protection, e.g.

hospitals, fire stations, power plants, etc.

1.4 CC3

CC1: Low consequence for loss of human life, and economic, social or environmental

consequences small or negligible.

CC2: Medium consequence for loss of human life, economic, social or environmental

consequences considerable.

CC3: High consequence for loss of human life, or economic, social or environmental

consequences very great

2.2.3.3 Ductility class

Table 2.6: Requirement for importance class relate to ductility class (CYS NA EN1998-

1-1,cl NA2.16 & cl.5.2.1(5))

Importance

class Zone 1 Zone 2 Zone 3

I DCL DCL DCL

II DCM/DCH DCM/DCH DCM/DCH

III DCM/DCH DCM/DCH DCM/DCH

IV DCH DCH DCH

DCL: Ductility class low.

DCM: Ductility class medium.

DCH: Ductility class high.

2.3 Analysis types

2.3.1 Modal Response spectrum analysis

Table 2.7: Requirements of modal response spectrum analysis according to Eurocode 8

Requirements Values References

Regular in plan YES / NO ΕΝ1998-1-1,table 4.1

Regular in elevation NO ΕΝ1998-1-1,table 4.1

Sum of the effective

modal masses

≥ 90% EN1998-1-1,cl.4.3.3.1(3)

≥ 5% of total mass

Minimum number of

modes

k ≥3.√n

k: is the number of modes

n: is the number of storey

EN1998-1-1,cl.4.3.3.1(5)

Behaviour factor q

Tk ≤ 0.20sec

Tk: is the period of vibration of

mode k.

EN1998-1-1,cl.4.3.3.1(5)

Fundamental period Tj ≤ 0.9 Ti SRSS

EN1998-1-1,cl.4.3.3.2.1(2) Tj ≥ 0.9 Ti CQC

Accidental eccentricity See section 2.1.1.1 EN1998-1-1,cl.4.3.2

1. Independently in X and Y direction,

2. Define design spectrum,

3. Use CQC rule for the combination of different modes (EN1998-1-1,cl.4.3.3.3.2(3))

4. Use SRS rule for combined the results of modal analysis for both horizontal directions

(EN1998-1-1,cl.4.3.3.5.1(21)).

5. Modal Combination: “Complete Quadratic Combination” (CQC) can be used if the Tj

≤ 0,9 Ti (EN1998-1-1,cl.4.3.3.3.2(3)P).

2.3.1.1 Accidental eccentricity

Accidental eccentricity of each storey cause of uncertainties location of masses have been

taken into account 5% (EN1998-1-1,cl.4.3.2). Moreover, if there are masonry infills with a

moderately irregular and asymmetric distribution in plan, is doubled further in Eurocode 8

(i.e., to 10% of the storey orthogonal dimension in the baseline case, or 20% if accidental

torsional effects are evaluated in a simplified way when using two separate 2D models).

Table 2.8: Summary of accidental eccentricity

Percentage of

accidental

eccentricity

Geometry

of model

(3D/2D)

Asymmetric

distribution of mass

(Regular/Irregular)

Masonry infills

(Regular/Irregular)

5% 3D Regular Regular

10% 3D Irregular Irregular

20% 2D - -

Note: Accidental eccentricity is automatically included during response-spectrum analysis in

ETABS, though equivalent static-load procedures are also available for manual evaluation.

Note that floor diaphragms must be rigid, otherwise torsional effects are not substantial.

ETABS implements an efficient and practical approach while formulating dynamic response

from accidental eccentricity. After the response-spectrum load case is run, the X and Y

acceleration at each joint location is determined, then multiplied by the tributary mass and the

diaphragm eccentricity along either Y or X. The larger absolute value of these resultant

moments (m*Xacc*dY or m*Yacc*dX) is then applied as torsion about the joint location.

Static response is then added to response-spectrum output to account for the additional design

forces caused by accidental eccentricity.

Define > Response spectrum cases

Note: Add two response spectrum cases: EQX and EQY as showing below (figure 9).

Figure 2.3: Response Spectrum case Data for EQY& EQX

2.3.2 Lateral force analysis requirements

Table 2.9: Requirements of lateral force analysis according to Eurocode 8

Requirements Values References

Regular in plan YES / NO ΕΝ1998-1-1,table 4.1

Regular in elevation YES ΕΝ1998-1-1,table 4.1

Ground acceleration 0.10-0.25g CYS NA EN1998-1-

1:Seismic zonation map

Spectrum type 1 EN1998-1-1,cl.3.2.2.2(2)P

Ground type

A,B,C,D,E

Normally type B or C can be used

normal condition

EN1998-1-1,cl.3.1.2(1)

Lower bound factor for

the horizontal design

spectrum

λ = 0.85 if T1 ≤ 2TC and more than

2 storey

λ=1.0 in all other case

EN1998-1-1,cl.4.3.3.2.2(1Ρ)

Behaviour factor q

Concrete DCM q= 1.5 – 3.90 EN1998-1-1,cl.5.2.2.2(2)

Concrete DCH q= 1.6 – 5.85 EN1998-1-1,cl.5.2.2.2(2)

Steel DCM q= 2.0 – 4.00 EN1998-1-1,cl.6.3.2(1)

Steel DCH q= 2.0 – 5.85 EN1998-1-1,cl.6.3.2(1)

Fundamental period T1≤4Tc

T1≤2,0s EN1998-1-1,cl.4.3.3.2.1(2)

Accidental eccentricity See section 2.1.1.1 EN1998-1-1,cl.4.3.2

Table 2.10: Equivalent Static Force Case

Load case name Direction and Eccentricity % Eccentricity

EQXA X Dir + Eccen. Y 0.05

EQYA X Dir – Eccen. Y 0.05

EQXB Y Dir + Eccen. X 0.05

EQYB Y Dir – Eccen. X 0.05

2.3.4 Estimation of fundamental period T1

Table 2.11: Estimation of fundamental period T1

Reference structure Period T1

Exact formula for Single Degree of Freedom

Oscillator. Mass M lumped at top of a vertical

cantilever of height H. Cantilever mass MB = 0. 𝑇! = 2𝜋

𝑀𝐻!

3𝐸𝐼


Oscillator. Vertical cantilever of height H and of

total mass MB. 𝑇! = 2𝜋

0.24𝑀!𝐻!

3𝐸𝐼


Oscillator. Mass M lumped at top of a vertical

cantilever of height H and of total mass MB. 𝑇! = 2𝜋

𝑀 + 0.24𝑀! 𝐻!

3𝐸𝐼

Approximate Relationship (Eurocode 8).

Ct = 0,085 for moment resisting steel space frames

Ct = 0,075 for eccentrically braced steel frames

Ct = 0,050 for all other structures

𝑇! = 𝐶!𝐻!/!

H building height in m measured from

foundation or top of rigid basement.

Approximate Relationship (Eurocode 8).

d : elastic horizontal displacement of top of

building in m under gravity loads applied

horizontally.

𝑇! = 2 𝑑

2.3.5 Automatic Lateral force analysis using ETABS

ETABS: Define > Static load cases

Figure 2.4: Apply the Equivalent Static Force Case

Figure 2.5: Modify the Equivalent Static Force Case

Note: The seismic forces should be applied only above the top of the basement

Fundamental period (EN1998-1-1,Eq.4.6) T1=CtH3/4 (For heights up to 40m)

Value of Ct(EN1998-1-1,cl.4.3.3.2.2(3)) Ct = 0.085 (for moment resisting steel frames) Ct= 0.075 (for moment resisting concrete frames) Ct= 0.05 (for all other structures) (EN 1998-1-1:2004, cl. 4.3.3.2.2(3)) Ct= 0.075/√ΣAc(for concrete/masonry shear wall structures) (EN 1998-1-1:2004, Eq. 4.7) Ac= Σ[Ai·(0,2+(lwi/H2))] (EN 1998-1-1:2004, Eq. 4.8)

Fundamental period requirements (EN1998-1-1,Eq.4.6)

T1≤4TCT1≤2sec IF this

YES

LATERAL FORCE

ANALYSIS

RESPONSE SPECTRUM ANALYSIS

Correction factor λ(EN1998-1-

1,cl.4.3.3.2.2(1Ρ)) λ=0.85 if T1≤2TC and more than 2 storey λ=1.0 in all other case

Design spectrum Sd(T)(EN1998-1-

1,cl.3.2.2.5) 0≤T≤TB

TB≤T≤TcTC≤T≤TD

TD≤T

Seismic mass(EN1998-1-1,cl.3.2.4)

ΣGk,j/g”+”ΣψE,i.Qk,i/g (EN 1998-1-1:2004, Eq.3.17)

Base shear(EN1998-1-1,cl.4.3.3.2.2) Fb=Sd(T1).m.λ

(EN 1998-1-1:2004, Eq. 4.5)

Horizontal seismic forces (according to displacement of

the masses)

F! = F! ∙s! ∙m!

s! ∙m!

(EN 1998-1-1:2004, Eq. 4.10)

Horizontal seismic forces (according to height of the

masses)

F! = F! ∙z! ∙m!

z! ∙m!

(EN 1998-1-1:2004, Eq. 4.11)

NO

2.3.6 User loads - Lateral force analysis using ETABS

Geometrical data

Span of the longitutinal direction Span of the transverse direction

Span of each beam

Span of each bracing

Height of each column

Total heigh of building

Area of floor for each storey

Number of floors

Number of beams IPE240 at each floor

Number of beams IPE180 at each floor

Number of columns HE280A at each floor

Number of TUBE sections D127-4 at each floor

Lx 15m:=

Ly 15m:=

Lb 5m:=

Lt 5.831m:=

hc 3m:=

H 9m:=

Af Ly Lx⋅ 225m2=:=

Nf 3:=

Nb 24:=

Ns 9:=

Nc 16:=

Nt 8:=

Dead load

Weight of steel column HE280A

Weight of primary beams IPE240

Weight of secondary beams IPE180

Weight of steel beams TUBE-D127-4

Slab thickness

Weigth of concrete

Weight of slab

Weigth of finishes

Total dead load

Total dead load

Live load

Combination coefficient for variable action

Live load

Total live load

Total gravity load per storey (EN1998-1-1,cl.3.2.4(2)P)

Total gravity load per storey (EN1998-1-1,cl.3.2.4(2)P)

Seismic mass

gc 76.4kg m 1−⋅:=

gp 30.7kg m 1−⋅:=

gs 18.8kg m 1−⋅:=

gt 12.38kg m 1−⋅:=

hs 170mm:=

γ c 25kNm 3−⋅:=

gslab γ c hs⋅ 4.25 kNm 2−⋅⋅=:=

gfin 1kNm 2−⋅:=

Gk.storey gc Nc⋅ hc⋅ gp Nb⋅ Lb⋅+ gs Ns⋅ Lb⋅+ gt Nt⋅ Lt⋅+( )g gslab Af⋅+ gfin Af⋅+⎡⎣ ⎤⎦ 1.267 103× kN⋅=:=

Gk gc Nc⋅ hc⋅ gp Nb⋅ Lb⋅+ gs Ns⋅ Lb⋅+ gt Nt⋅ Lt⋅+( )g gslab Af⋅+ gfin Af⋅+⎡⎣ ⎤⎦ Nf⋅ 3.802 103× kN⋅=:=

ψEi 0.3:=

qk 2kN m 2−⋅:=

Qk qk Af⋅ 450 kN⋅=:=

FEd.storey Gk.storey ψEi Qk⋅( )+ 1.402 103× kN⋅=:=

FEd Gk ψEi Qk⋅( ) Nf⋅+ 4.207 103× kN⋅=:=

S_massFEdg

4.29 105× kg=:=

Horizontal design response Spectrum (EN1998-1-1,cl.3.2.2.5)

Behaviour factor q (EN1998-1-1,cl.6.3)

Lower bound factor (EN1998-1-1,cl.3.2.2.5(4)P)

Seismic zone (CYS NA EN1998-1-1, zonation map)

Importance factor (CYS NA EN1998-1-1,cl. NA2.12)

Design ground acceleration on type A (EN1998-1-1,cl.3.2.1(3))

Value of Ct (EN1998-1-1,cl.4.3.3.2.2(3))

Fundamental period of vibration (EN1998-1-1,cl.4.3.3.2.2(3))

Type of soil (EN1998-1-1,cl.3.1.2(1))

Value of parameters describing the Type 1 elastic response spectrum (EN1998-1-1,table 3.2)

Soil factor, S

q 1.5:=

β 0.2:=

Seismic_zone "3":=

agR 0.15g Seismic_zone "1"if

0.2g Seismic_zone "2"if

0.25g Seismic_zone "3"if

2.452m

s2=:=

Importance_factor "II":=

γ I 0.8 Importance_factor "I"if

1.0 Importance_factor "II"if

1.2 Importance_factor "III"if

1.4 Importance_factor "IV"if

1=:=

ag γ I agR⋅ 2.452m

s2=:=

Value_Ct "OTHER":=

Ct 0.085 Value_Ct "MRSF"if

0.075 Value_Ct "MRCF"if

0.05 Value_Ct "OTHER"if

0.05=:=

T1 CtH

m

⎛⎜⎝

⎞⎟⎠

3

4

⋅

⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦s 0.26s=:=

Soil_type "B":=

S 1.0 Soil_type "A"if

1.2 Soil_type "B"if

1.15 Soil_type "C"if

1.35 Soil_type "D"if

1.2=:=

Lower limit of the period, TB

Upper limit of the period, TC

Constant displacement value, TD

Corection factor λ (EN1998-1-1,cl.4.3.3.2.2(1)P)

Check the fundamental period of vibration requirements (EN1998-1-1,cl.4.3.3.2.1(2))

Design spectrum for elastic analysis (EN1998-1-1,cl.3.2.2.5(4)P)

TB 0.15s Soil_type "A"if

0.15s Soil_type "B"if

0.20s Soil_type "C"if

0.20s Soil_type "D"if

0.15s=:=

TC 0.40s Soil_type "A"if




0.5s=:=

TD 2.0s Soil_type "A"if




2s=:=

λ 0.85 T1 2TC≤ Nf 2>∧if

1 otherwise

0.85=:=

Check_1 if T1 4TC≤ T1 2s≤∧ "Lateral force analysis", "Response spectrum analysis", ( ):=

Check_1 "Lateral force analysis"=

S1e T1( ) ag S⋅23

T1TB

2.5q

23

−⎛⎜⎝

⎞⎟⎠

⋅+⎡⎢⎣

⎤⎥⎦

⋅:= S1e 0( ) 1.961 m s 2−⋅⋅=

S2e T1( ) ag S⋅2.5q

⋅:= S2e TB( ) 4.903m s 2−⋅⋅=

S3e T1( ) ag S⋅2.5q

⋅TCT1⋅ ag S⋅

2.5q

⋅TCT1⋅ β ag⋅≥if

β ag⋅( ) β ag⋅ ag S⋅2.5q

⋅TCT1⋅≥if

:= S3e TC( ) 4.903m s 2−⋅⋅=

S4e T1( ) ag S⋅2.5q

⋅TC TD⋅

T12

⋅⎛⎜⎜⎝

⎞⎟⎟⎠

ag S⋅2.5q

⋅TC TD⋅

T12

⋅ β ag⋅≥if

β ag⋅( ) ag S⋅2.5q

⋅TC TD⋅

T1( )2⋅ β ag⋅≤if

:=

Design spectrum acceleration

Seismic base shear (EN1998-1-1,cl.4.3.3.2.2(1))

Seismic base shear on each bracing Note: 2 bracing on each direction

S4e T1( ) 72.642m

s2=

Se T( ) if T TB< S1e T( ), if T TC< S2e T( ), if T TD< S3e T( ), S4e T( ), ( ), ( ), ( ):=

T 0.01sec 0.02sec, 4sec..:=

0 1 2 3 40

2

4

6

8

Se T( )

T

Se S1e 0( ) 0 T1≤ TB≤if

S2e TB( ) TB T1≤ TC≤if

S3e TC( ) TC T1≤ TD≤if

S4e T1( ) TD T1≤ 4s≤if

4.903m

s2=:=

Fb S_mass Se⋅T1s

⋅ λ⋅ 464.519kN⋅=:=

Fb.bracingFb2

232.259kN⋅=:=

Table 2.12: Summary table of the lateral force results

StoryHeigth

zi (m)

Mass mi (kN)

zi*miFb (kN)

F=Fb(zi*mi)/Σzi*mi

Moment M=F*zi (kNm)

Length of floor Lx=Ly

Accidental eccentricity ei=0.05L

Torsional moment M=F*ei (kNm)

Moment due to SRSS

MSRS=√Mx^2+My^2 (kNm)

STORY1 9 1402 12618 464.52 232.26 2090.34 15 0.75 174.195 246.3489315STORY2 6 1402 8412 464.52 154.84 929.04 15 0.75 116.13 164.232621STORY3 3 1402 4206 464.52 77.42 232.26 15 0.75 58.065 82.1163105

TOTAL 4206 25236 464.52 3251.64

Mass per storey

Heigth at roof level

Heigth at level 2

Heigth at level 1

Total mass:

Lateral force at roof level (EN1998-1-1,Eq.4.11)

Lateral force at level 2 (EN1998-1-1,Eq.4.11)

Lateral force at level 1 (EN1998-1-1,Eq.4.11)

Check lateral force per storey

mi FEd.storey 1.402 103× kN=:=

z3 9m:=

z2 6m:=

z1 3m:=

Σmi_zi FEd.storey z3⋅ FEd.storey z2⋅+ FEd.storey z1⋅+ 2.524 104× kNm⋅=:=

F3mi z3⋅

Σmi_ziFb⋅ 232.259kN⋅=:=

F2mi z2⋅

Σmi_ziFb⋅ 154.84kN⋅=:=

F1mi z1⋅

Σmi_ziFb⋅ 77.42kN⋅=:=

F F3 F2+ F1+ 464.519kN=:=

Check_2 if F Fb≠ "OK", "NOT OK", ( ):=

Check_2 "OK"=

ETABS: Define > Static load case >

Figure 2.6: Define manually the lateral forces

Figure 2.7: Define manually the lateral forces/moments per storey

2.3.7 Torsional effects

FLOW CHART OF TORSIONAL EFFECTS

Carry out Lateral force analysis/ Response spectrum analysis

𝑀! = 𝑒!𝐹!

𝑀! = 𝑒!𝐹!

𝑒! = −0.05 ∗ 𝐿!

𝑒! = +0.05 ∗ 𝐿!

𝑒! = +0.05 ∗ 𝐿!

𝑒! = −0.05 ∗ 𝐿!

SRSS rule

𝑀!"!! = 𝑀!! +𝑀!

!

2.3.8 Summary of analysis process in seismic design situation

Importance class/Ductility class

I II III IV

DCL DCM DCH

DCM DCH

DCH

Ignore “topographic amplification effects”

Consider “topographic amplification effects”

IF Slopes <15o Cliffs height

<30m

Slopes <15o Cliffs height

<30m

Ignore Consider

Regular in plan: YES Regular in elevation YES

Regular in plan: NO Regular in elevation YES

Regular in plan: YES Regular in elevation NO

Regular in plan: NO Regular in elevation NO

Type of soil: A , B ,C ,D, E, S1, S2

Type 1 elastic response spectrum

0≤T≤TB

TB≤T≤TC

TC≤T≤TD TD≤T≤4s

LATERAL FORCE

MODAL ANALYSIS

Displacement ds=qd·de

P-Δ effects θ≤0.1 – Ignore

0.1≤θ≤0.2 Consider 0.2≤θ≤0.3 Consider θ≥0.3 Not Permitted

Interstorey drift drv≤0.005h - Brittle

drv≤0.0075h - Ductile drv≤0.010h - Other

Frame joint ΣMRC≥1.3ΣMRB

Storey ≥ 2

3.0 Define static loads

Here define as many load cases for your model as you need e.g. dead loads, live loads, wind

loads, seismic loads, thermal loads etc. To be simple define only one dead load with self

weight multiplier 1(including finishes, dead, walls etc) and one live load.

Figure 3.1: Static load cases

4.0 Seismic mass requirements according to EC8

Combination of the seismic action with other actions (EN 1998-1-1,cl.3.2.4):

1. Define the category of building (EN 1991,Table 6.1),

2. Define the reduce factor (EN 1991, Table A.1.1).

Combination of seismic mass

𝐆𝐤,𝐣 + 𝛙𝐄𝐢𝐐𝐤,𝐢 (ΕΝ1998-1-1,Eq. 3.17)

Combination coefficient for variable action is: ψ!" = ϕ ∙ ψ!" (ΕΝ1998-1-1,Eq. 4.2)

Table 4.1: Values of φ for calculating 𝛙𝐄𝐢 (CYS NA EN1998-1-1:2004)

Type of Variable

action

Storey φ

Categories A-C1

Roof

Storeys with correlated occupancies

Independently occupied storeys

1,0

0,8

0,5

Categories A-F1 1.0

Table 4.2: Values of ψ coefficients

Category Specific Use ψο ψ1 ψ2

A Domestic and residential 0.7 0.5 0.3

B Office 0.7 0.5 0.3

C Areas for Congregation 0.7 0.7 0.6

D Shopping 0.7 0.7 0.6

E Storage 1.0 0.9 0.8

F Traffic < 30 kN vehicle 0.7 0.7 0.6

G Traffic < 160 kN vehicle 0.7 0.5 0.3

H Roofs 0.7 0 0

Snow, altitude < 1000 m 0.5 0.2 0

Wind 0.5 0.2 0

4.1 Mass Source Option

In ETABS, the user has the option of choosing one of three options for defining the source of

the mass of a structure. Click the Define menu > Mass Source command to bring up the

Define Mass Source form. The following options appear on the form:

1. From Self and Specified Mass:

Each structural element has a material property associated with it; one of the items specified

in the material properties is a mass per unit volume. When the ‘From Self and Specified

Mass’ box is checked, ETABS determines the building mass associated with the element

mass by multiplying the volume of each structural element times it’s specified mass per unit

volume. This is the default. It is also possible to assign additional mass to account for

partitions and cladding, etc. ETABS adds any additional mass assignments to the element

mass to derive a total mass. You cannot have a negative mass in ETABS.

2. From Loads:

This specifies a load combination that defines the mass of the structure. The mass is equal to

the weight defined by the load combination divided by the gravitational multiplier, g. This

mass is applied to each joint in the structure on a tributary area basis in all three translational

directions.

3. From Self and Specified Mass and Loads:

This option combines the first two options, allowing you to consider self- weight, specified

mass, and loads in the same analysis.

It is important to remember when using the ‘From Self and Specified Mass and Loads’

option, NOT to include the Dead Load Case in the ‘Define Mass Multiplier for Loads’

box. This will account for the dead load of the structure TWICE.

Figure 4.1: Seismic source

5.0 Wind loading on structure (EN1991-1-4:2004)

5.1 Calculation of Wind load according to EN1991-1-4:2004

Step by step procedure

Figure 5.1: Fundamental Basic wind velocity, vb,0

(CYS NA EN1991-1-4,Fig.1)

Season factor (CYS EN1991-1-4,NA 2.4)

cseason=1.0

Directional factor (CYSEN1991-1-4,NA 2.4)

cdir=1.0 (Conservative value for all direction)

Basic wind velocity (EN1991-1-4, Eq. 4.1)

vb=cdir.cseasonvb,0

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�-*'�'��+��'%%",,�� '�� (*"$��

Figure 1 Isotach contours of the fundamental value of the basic wind velocity v

�� $"��'��%��'��!��#��%�#��#�

b,0

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Table 5.1: Terrain category and terrain parameters (EN1991-1-4, Tab.:4.1) Terrain category

Description z0 (m) zmin(m)

0 Sea, costal area exposed to the open sea. SEA 0.003 1

I Lakes or area with negligible vegetation and without obstacles.

COUNTRY

0.01 1

II

Area with low vegetation such as grass and isolated obstacles trees, buildings) with separations of at least 20 obstacle height.

0.05 2

III

Area with regular cover of vegetation or buildings or woth isolatd obstacles with seperations of maximum 20 obstacle height (such as villages, suburban terrain, permanent forest). TOWN

0.3 5

IV* Area in which at least 15% of the surface is covered with building and their average height exceeds 15m.

1.0 10

* For buildings in terrain category IV, displacement height hdis should be consider and information can be found in Aneex A.5 of EN1991-1-4:2005.

Roughness factor, cr(z) (EN1991-1-4,Eq.4.3-4.5)

cr(z)=kr . ln(z/z0) for zmin≤z≤zmax

cr(z)=cr . (zmin) for z≤zmin z0: is the roughness length

Maximum height, zmax (EN1991-1-4, cl. 4.3.2)

zmax=200m Orography factor co(z)

co(z)=1

Terrain factor, (EN1991-1-4,cl.4.4) kr=0.19(z0/z0,II)0.07

Mean wind velocity, vm(z) (EN1991-1-4 cl.4.3.1 )

vm(z)=cr(z).co(z).vb

Wind turbulence, Iv(z) (EN1991-1-4,Eq.4.7)

Iv(z)=σv/vm(z)=kl/co(z)ln(z/z0) for zmin≤z≤zmax Iv(z)=Iv(zmin) for z≤zmin Turbulence factor: kl=1.0 (NA CYS EN1991-1-4, cl. NA 2.10) Note: for co(z)=1 Iv(z) is not important

Peak velocity pressure, qpeak(z) (EN1991-1-4 Eq.4.8 )

qpeak(z)=[1+7 Iv(z)]0.5ρ vm2

(z)=ce(z)·0.5·ρ·vb2

Air density:ρ=1.25kg/m3

Table 5.3: Values of external pressure coefficient for vertical walls of rectangular plan building

(EN1991-1-4, Tab.:4.1)

ZONE A B C D E

h/d cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

5 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.7 1 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.5

≤0.25 -1.2 -1.4 -0.8 -1.1 -0.5 +0.7 +1.0 -0.3 Note: Values for cpe,1 are intended for the design of small elements and fixings with an element of 1m2 or less such as cladding elements and roofing elements. Values for cpe,10 may be used for the design of the overall load bearing structure of buildings. The external pressure coeffiecient cpe,1 and cpe,10 is using for loadaded area of 1m2 and 10m2 respectively.

Key for vertical walls – Flat Roof (EN1991-1-4, Fig.7.5)

Key for vertical walls –Mono&dual pitch Roof

(EN1991-1-4, Fig.7.5)

Pressure on surface &Wind force (EN1991-1-4, Eq. 5.1&5.5) we=qp(ze).(cpe +cpi) & Fw=cscd·Σwe·Aref

Table 5.2: Reference height ze, depending on h and b, and corresponding velocity pressure profile (EN1991-1-4, Fig. 7.4)

5.2 Application of wind loading using ETABS

Table 5.4: Wind load assumptions


Basic wind velocity vb,0 24 m/s

Terrain category - II -

Structural factor cscd 1 -

Turbulence factor kl 1 -

Orography factor co(z) 1 -

ETABS: Clink on

ETABS: Select from first drop-down menu

ETABS: Click on select “NONE” and draw rectangular cover all side of plan view

Draw walls in plan

ETABS: Select the area of elevation A-A

ETABS: Assign > Shell/Area loads > Wind pressure coefficients

Figure 5.2: Wind load areas

Table 5.5: Wind pressure coefficient applied on walls

Wind pressure coefficient for load case WINDX

Windward load “Area D” Leeward load “Area E”

Side load “Area A & B” Side load “Area A & B”

Wind pressure coefficient for load case WINDY

Windward load “Area D” Leeward load “Area E”

Side load “Area A & B” Side load “Area A & B”

WIND LOADING ACCORDING TO EN1991-1-4:2005

Job No.:

Sheet No.: Date: December 2012 Check by:

CALCULATION OF WIND LOADING TO EN 1991-1-4:2005. Loading available for rectangular, clad buildings with flat roofs only.

Obstruction height, have = 7.5 m Distance to nearest adjacent building, x = 50 m Height of building, h = 9 m Longitudinal length of the building ,

d = 15 m

Transverse length of the building, b = 15 m Edge distance, (Wind direction - θ=90°) e = 15 Basic Wind Velocity, Vbo = 24 m/s ( Figure1)

Season Factor, Cseason = 1.0 (cl.NA2.4)

Directional Factor, Cdir = 1.0 (cl.NA2.4)

Basic Wind Velocity, Vb0=CdirCseasonVb,o Vb = 24 m/s (Eq.4.1)

Structural factor, CsCd = 1.0 (cl.6.2)

Orography factor, Co(z) = 1.0 cl.4.3.1(1))

Turbulence factor, kI = 1.0 (cl.NA2.10)

z0 zmin (Τable 4.1)

Terrain Category Define terrain category II 0.05 2

Max heigh, zmax = 200 m (cl. 4.3.2)

Height above ground, z = 100 m

Dispacement height, hdis = 4.5 m (Annex A.5)

Clear height of building,

h-hdis = 4.5

Define height z

5

External Pressure Coefficients Walls Cpe

Wind direction θ=0°

Width b = 15 m Height h = 9 m Depth d = 15 m Edge distance, (Wind direction - θ=0°) e = 15 m Actual h/b (For zone D -‐ windward face) h/b = 0.60

Length in Zone A

Zones A & B exist

3 m

Length in Zone B

12 m

Length in Zone C

0 m

Wind direction θ=90°

Width b = 15 m

Height h = 9 m

Depth d = 15 m

Edge distance, (Wind direction - θ=90°) e = 15 m

Actual h/b (For zone D -‐ windward face) h/b = 0.60

Length in Zone A

Zones A & B exist

3 m

Length in Zone B

12 m

Length in Zone C

0 m

Table 7.1 values of Cpe for wind on

Front (θ=90°) Front (θ=0°) Zones (θ=90°) Zones (θ=0°)

D 0.747 0.747 A 3 m A -‐1.2 m E -‐0.567 -‐0.567 B 12 m B -‐0.8 m A -‐1.2 -‐1.2 C 0 m C 0 m

B -‐0.8 -‐0.8 C 0 0

6.0 Load combination

Table 6.1: Load combination factors and coefficients

Data Symbol Value Reference

Permanent action γG 1.35 EN1990,cl.6.4.3.2

Variable action γQ 1.5 EN1990,cl.6.4.3.2

Office areas (Type B), ψ0 0.7 CYS NA EN1990:2002, Table A1.1

Roofs ψ0 0.7 CYS NA EN1990:2002, Table A1.1

Wind loads ψ0 0.5 CYS NA EN1990:2002, Table A1.1

Persistent and transient design situation – STR/GEO Equation 6.10 Ed=ΣγG Gk +γQ Qk1 + γQ ψ0,2 Qk2

Ultimate limit state (ULS)

Static load combination

STATIC 2. 1.35DL + 1.5LL STATIC 3. 1.35DL + 1.5LL + 0.75WINDX STATIC 4. 1.35DL + 1.5LL - 0.75WINDX STATIC 5. 1.35DL + 1.5LL + 0.75WINDY STATIC 6. 1.35DL + 1.5LL - 0.75WINDY STATIC 7. 1.35DL + 1.5WINDX + 1.05LL STATIC 8. 1.35DL - 1.5WINDX – 1.05LL STATIC 9. 1.35DL + 1.5WINDY + 1.05LL STATIC 10. 1.35DL - 1.5WINDY – 1.05LL

Seismic load combination for “Modal Analysis”

SEISMIC 2. DL + 0.3LL + EQX + 0.3EQY SEISMIC 3. DL + 0.3LL + EQX – 0.3EQY SEISMIC 4. DL + 0.3LL - EQX + 0.3EQY SEISMIC 5. DL + 0.3LL - EQX – 0.3EQY SEISMIC 6. DL + 0.3LL + EQY + 0.3EQX SEISMIC 7. DL + 0.3LL + EQY – 0.3EQX SEISMIC 8. DL + 0.3LL - EQY + 0.3EQX SEISMIC 9. DL + 0.3LL - EQY – 0.3EQX

Seismic load combination for “Lateral force Analysis”

SEISMIC 10. DL + 0.3LL + EQXA + 0.3EQYA SEISMIC 11. DL + 0.3LL + EQXA – 0.3EQYA SEISMIC 12. DL + 0.3LL - EQXA + 0.3EQYA SEISMIC 13. DL + 0.3LL - EQXA – 0.3EQYA SEISMIC 14. DL + 0.3LL + EQYA + 0.3EQXA SEISMIC 15. DL + 0.3LL + EQYA – 0.3EQXA SEISMIC 16. DL + 0.3LL - EQYA + 0.3EQXA SEISMIC 17. DL + 0.3LL - EQYA – 0.3EQXA

SEISMIC 18. DL + 0.3LL + EQXB + 0.3EQYB SEISMIC 19. DL + 0.3LL + EQXB – 0.3EQYB SEISMIC 20. DL + 0.3LL - EQXB + 0.3EQYB SEISMIC 21. DL + 0.3LL - EQXB – 0.3EQYB SEISMIC 22. DL + 0.3LL + EQYB + 0.3EQXB SEISMIC 23. DL + 0.3LL + EQYB – 0.3EQXB SEISMIC 24. DL + 0.3LL - EQYB + 0.3EQXB SEISMIC 25. DL + 0.3LL - EQYB – 0.3EQXB

Serviceability limit state (SLS)

STATIC 1. DL + LL

7.0 Design preferences

ETABS: Options > Preferences > Steel frame design

Figure 7.1: Steel frame design preferences

2

3

4

1

5

6

Table 7.1: Steel frame design parameters

Note 1: Reliability class

Class section classification according to EN1998-1-1,cl.6.5.3(2)

1. Depending on the ductility class and the behavior factor q used in the design, the

requirements regarding the cross-sectional classes of the steel elements which

dissipate energy are indicated in table below (EN1998-1-1,cl.6.5.3(2).

Ductility class Reference q factor Cross-Section Class

Lower

limit

q factor Upper

limit

DCM 1.5< q ≤ 2 Class 1, 2 or 3

2.0< q ≤ 4 Class 1 or 2

DCH 4.0< q Class 1

Note 2: Frame type

See section 2.0 of this manual

Note 3: Gamma factors

Partial factors Values Reference

Resistance of cross-sections whatever the

class

γΜ0=1.00 EN1993-1-1,cl.6.1(1)

Resistance of members to instability assessed

by member checks

γΜ1=1.00 EN1993-1-1,cl.6.1(1)

Resistance of cross-sections in tension to

fracture

γΜ1=1.25 EN1993-1-1,cl.6.1(1)

Note 4: Behavior factor

See section 2.0 of this manual

Note 5: System Omega

Omega Factor (System Overstrength Factor) axial load member: (𝛀 = 𝑵𝒑𝒍,𝑹𝒅/𝑵𝑬𝒅)

Omega factor may different for each diagonal member.

1. Run the design analysis with the Ω=1

2. Find the Npl,Rd and NEd of the bracing member and then overwrite the omega factor for

each diagonal member separately and then re-run the analysis.(Ω=1).

Note: Omega factor should be limited to the following for all diagonal members

Note 6: Vertical deflection limits

STEEL MEMBERS (CYS NA EN1993-1-1,table NA.1)

Vertical deflection Limits

wmax Cantilevers L/180

Beams carrying plaster or other brittle finish L/360

Other beams (except purlin and sheeting rails)

L/250

Purlins and sheeting rails To suit cladding

General use L/300

ETABS deflection limits

DL limit, L/ 360

Super DL+LL Limit, L/ 360

Live load Limit, L/ 360

Total Limit, L/ 360

Total Camper Limit, L/ 360

Check_16 if Ωmax 1.25Ωmin≤ "OK", "NOT OK", ( ):=

8.0 Analysis and design requirements for Concentrically braced frames according to

EN1998-1-1,cl.6.7.2

Analysis requirements according to EN1998-1-1,cl.6.7.2 Beams & Columns

1. Under gravity load conditions, only beams and columns shall be considered to resist such loads, without taking into account the bracing members (EN1998-1-1,cl6.7.2(1)P).

Diagonal members

2. The diagonals shall be taken into account as follows in an elastic analysis of the structure for the seismic action: a) in frames with diagonal bracings, only the tension diagonals shall be taken into

account, b) in frames with V bracings, both the tension and compression diagonals shall be

taken into account (EN1998-1-1,cl6.7.2(2).

3. Taking into account of both tension and compression diagonals in the analysis of any type of concentric bracing is allowed provided that all of the following conditions are satisfied: a) a non-linear static (pushover) global analysis or non-linear time history analysis is

used,

b) both pre-buckling and post-buckling situations are taken into account in the modeling of the behavior of diagonals and,

c) background information justifying the model used to represent the behavior of diagonals is provided (EN1998-1-1,cl6.7.2(3).

8.1 Steps of the design detail of Concentric steel frames

Table 8.1: Detail steel frame design

Design step

number

Description

Step 1 Design of slab under gravity loads (without CBF bracings) considering columns

as fixed supports

Step 2 Design columns under gravity loads (without CBF bracings)

Step 3 Design beams under gravity loads (without CBF bracings)

Step 4 Check concentric bracings under gravity loads combination

Step 5 Accidental torsional effects

Step 6 Second order effects (P-Δ) (P loads are those taken in the definition of the

seismic mass “m”)

Step 7 Check of beams and of concentric bracings under gravity loads combination

Step 8 Design of concentric bracing under seismic combination of loads with the

accidental torsional effects and P-Δ effects taken into account

Step 9 Check of beams and columns under seismic combination of loads with bracings

overstrength factors Ω and with second order effects taken into account

Step 10 Re-run the analysis with the modified overstrength factors Ω

8.2 Classification of steel sections

Table 8.2: Section classification (EN1993-1-1,cl.5.5) Classes Analysis type Description

Class 1 Plastic analysis Section can form a plastic hinge with the rotation capacity

required from plastic analysis, without reduction of the resistance

Class 2 Plastic/ Elastic analysis Section can develop its plastic moment capacity, but has limited

rotation capacity.

Class 3 Elastic analysis Section in which the stress in the extreme compression fiber of the

section, assuming an elastic distribution of stresses, can reach the

yield strength, but local buckling is likely to prevent the

development of the plastic moment capacity.

Description of detail

requirements

Equations References

Reduction of yield and

ultimate strength of sections

EN10025-2

ε - Factor EN1993-1-1,Table 5.2

Depth of a part of section for

internal compression

(I-sections)

EN1993-1-1,Table 5.2

Section classification for web

element

EN1993-1-1,Table 5.2

fy. fy t 16mm<if

fy 10N mm 2−⋅− 16mm t< 40mm<if

fy 20N mm 2−⋅− 40mm t< 80mm<if

:=

fu. fu t 16mm≤if

fu 10N mm 2−⋅− 16mm t< 40mm≤if


:=

ε235fy

:=

cw h 2 tf⋅− 2 r⋅−:=

Class_type web "CLASS 1"cwtw

72 ε⋅≤if

"CLASS 2" 84 ε⋅cwtw

< 83 ε⋅≤if


< 124 ε⋅≤if

:=

Depth of a part of section for

oustand flange

(I-sections)

EN1993-1-1,Table 5.2

Section classification for

flange element

EN1993-1-1,Table 5.2

cfb tw− 2.r−( )

2:=

Class_type flange "CLASS 1"cftf

9 ε⋅≤if

"CLASS 2" 9 ε⋅cftf

< 10 ε⋅≤if


< 14 ε⋅≤if

:=

8.3 Design of composite slab under gravity loads

Table 8.3: Detail design of composite slab (with steel sheeting) Partial factor Value References

Partial factor of longitudinal shear in composite slabs γvs = 1.25 CYS EN1994-1-

1cl.2.4.1.2(6)P

Partial factor for shear connector γv = 1.25 CYS EN1994-1-

1cl.2.4.1.2(5)P

Partial factor for steel reinforcement γs = 1.15 CYS EN1992-1-1,table 2.1

Partial factor of concrete γc = 1.5 CYS EN1992-1-1,table 2.1

Partial factor of structural steel γM0 = 1.0 CYS EN1993-1-1,cl 6.1(1)

Description of detail requirements Equations References

Minimum nominal thickness of profile steel sheets t ≥ 0.70mm CYS EN1994-1-1,cl.3.5(2)

Minimum depth of slab h ≥ 90mm EN1994-1-1,cl.9.2.1(2)

Depth of concrete slab above steel sheeting hc ≥ 50mm EN1994-1-1,cl.9.2.1(2)

Minimum steel reinforcement in both direction As.prov ≥80mm2/m EN1994-1-1,cl.9.2.1(4)

Spacing of the reinforcement bars s = min{2h,350mm} EN1994-1-1,cl.9.2.1(5)

Maximum height of steel decking hp ≤ 85mm EN1994-1-1,cl.6.6.4.2(3)

Minimum width per ribs b0 ≥ hp EN1994-1-1,cl.6.6.4.2(3)

Diameter of stud that welded in the sheeting d ≤ 20mm EN1994-1-1,cl.6.6.4.2(3)

For holes provided in the sheeting, the diameter of the stud d ≤ 22mm EN1994-1-1,cl.6.6.4.2(3)

Maximum overall height of stud hsc ≤ hp +75mm EN1994-1-1,cl.6.6.4.1(2)

Design

stage Description of checks Equations References

Resistance verifications of metal decking at the construction stage

Construction Stage

Moment resistance of steel sheeting From manufacture data -

Concrete compressive strength fcd = fck / γc EN1994-1-1,cl.2.4.1.2(2)P

Design yield strength fyo,d = fyp / γM0 -

Bending resistance of metal decking MEd / MRd <1.0 EN1993-1-3,cl.6.1.1

Shear resistance of metal decking 𝑉!,!" =

!!!"#$

𝑡 𝑓!"𝛾!!

EN1993-1-3,cl.6.1.5(1)

Deflection of metal decking 𝛿!"# =

!"!

!"#!" (W in kN/m2) -

δmax ≤ min {L / 180,20mm) EN1994-1-1,cl.9.6(2)

Resistance verifications of composite slab at the composite stage

Composite Stage

Area of concrete Ac = b hc (b=1m) -

Compression design force of concrete Nc = 0.85 fcd Ac EN1994-1-1,cl.6.2.1.2

Tensile resistance of profiles steel sheeting Np = fyp,d Ap EN1994-1-1,cl.6.2.1.2

Location of neutral axis Neutral axis=if{Np < Nc “Lie above steel sheeting”, “Lie

below steel sheeting”} EN1994-1-1,9.7.2(5) & (6)

Depth of concrete in compression xpl = Ape fyp,d / 0.85 b fcd EN1994-1-1,fig.9.6

Moment resistance (full shear connection) Mpl, Rd = Ap fyd (dp – 0.5 xpl) -

Bending resistance of slab MEd / Mpl,Rd <1.0 -

The design values of m and k Should be obtain from the manufacture -

Shear span (for UDL load) Ls = L / 4 EN1994-1-1,cl.9.7.3(5)

Shear span (for UDL & point load) Ls = 3L/8 EN1994-1-1,cl.9.7.3(5)

Shear resistance (in longitudinal direction) Vl,Rd = bdp /γvs [(mAp / bLs ) + k] EN1994-1-1,Eq. 9.7

Longitudinal shear resistance of slab VEd / Vl,Rd -

Coefficient factor k k = 1+(200 / dp)1/2 EN1992-1-1,cl.6.2.2(1)

Value of vmin vmin = 0.035k3/2 fck1/2 CYS EN1992-1-1,Eq.6.3

Design vertical shear resistance Vv,Rd = vmin bs dp 1 EN1992-1-1,Eq.6.2b

Vertical shear resistance check VEd / Vv,Rd < 1.0 -

Serviceability limit state (SLS) - Deflection

Calculation of deflection (simply supported slab) 𝛿!"# =!"!

!"#!" (W in kN/m2) -

Deflection limits (imposed load) L / 350 (not greater than 20mm)

Deflection limits (total load) L / 250 (not greater than 30mm) EN1992-1-1,cl.7.4.1(4)

Serviceability limit state (SLS) - Cracking

Minimum amount of steel ratio (un-propped) As = 0.2% Ac EN1994-1-1,cl.9.8.1(2)

Minimum amount of steel ratio (propped) As = 0.4% Ac EN1994-1-1,cl.9.8.1(2)

Serviceability limit state (SLS) – Floor vibration

Floor vibration limits f = 18 / √δa SCI-P-076 : Design guide

on the vibration of floors

Note 1: Although in reality the slab is continuous, it is normally convenient to design it as simply supported. As a consequence of this, the beneficial effect of

compression from the hogging moment at the support is neglected, such that σcp = 0.

8.4 Design of composite beam (with steel sheeting) under gravity loads

Table 8.4: Detail design of composite beam

Minimum height of stud EN1994-1-1,cl.6.6.1.2(1)

Nominal diameter of stud EN1994-1-1,cl.6.6.1.2(1)

Ultimate strength of shear connector EN1994-1-1,cl.6.6.4.2(1)

Check the minimum spacing of studs EN1994-1-1,cl.6.6.5.5(3)

Preliminary depth of beams

EN1994-1-1,cl.6.4.3(1)

Ultimate limit state

Bending Resistance of the steel section (EN1993-1-1,cl.6.2.5)

Moment resistance of steel

section Y-Y axis

Mc,Rd,y =Mpl,Rd,y = Wpl,y fy / γM0 EN1993-1-1,cl.6.2.5(2)

Vertical Shear resistance of the steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)

Factor for shear area η = 1.0 (conservative value) EN1993-1-1,cl.6.2.6(3g)

Shear area 1 Av = A -2 b tf + (tw + 2r) tf ≥ η hw tw EN1993-1-1,cl.6.2.6(3a)

Shear resistance of steel Vpl,Rd y = Av (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)

hmin if hsc 4d≥ "OK", "NOT OK", ( ):=

dlim if 16mm d< 25mm< "OK", "NOT OK", ( ):=

fus 450N mm 2−⋅:=

slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK", ( ):=

hmax 600mm fy 235N mm 2−⋅≤if

550mm 235N mm 2−⋅ fy< 275N mm 2−

⋅≤if

400mm 275 N⋅ mm 2−⋅ fy< 355N mm 2−

⋅≤if

270mm 355 N⋅ mm 2−⋅ fy< 460N mm 2−

⋅≤if

:=

Construction

Stage

section Y-Y axis

Check if the verification of

shear buckling resistance

required or not

(EN1993-1-1,cl.6.2.6(6))

Bending and shear interaction check (cl.6.2.2.4)

Area of web Aw = hw tw EN1993-1-1,cl.6.2.8(5)

Coefficient of interaction vy=VEd / Vpl.Rd,y EN1993-1-1,cl.6.2.8(5)

Reduced yield strength ρ = [(2VEd / Vpl.Rd,y) – 1] 2 EN1993-1-1,cl.6.2.8(3)

Reduced design plastic

resistance moment Y-Y axis EN1993-1-1,cl.6.2.8(5)

Lateral torsional buckling of the steel beam

It is assumed that the steel beam is laterally restrained by the steel sheeting during construction. In order to provide restraint, the sheeting is

fixed to the beam either by the action of through-deck welding or by short-fired pins

Effective width of composite beam (cl.5.4.1.2(5))

Effective width of composite

beam

(EN1994-1-1cl. 5.4.1.2(5))

Plastic resistance moment of composite section with full shear connection (cl.6.2)

hwtw

72ε

η⋅<

Ma.pl.Rd.

Wpl.yρ Aw

2⋅

4tw−

⎛⎜⎜⎝

⎞⎟⎟⎠fy⋅

γM0vy 0.5>if

Ma.pl.Rd vy 0.5<if

:=

beff bo 2 minL12

L22

+Le8

, ⎛⎜⎝

⎞⎟⎠

⎛⎜⎝

⎞⎟⎠

+:=

Composite

Stage

Tensile resistance of steel

section (EN1993-1-1,cl.6.2.3(2))

Compression resistance of

concrete slab

(EN1994-1-1,cl.6.2.1.2(1d)

Tensile resistance in web of

steel section -

Location of neutral axis (EN1994-1-1,cl.6.2.1.2(1))

Bending resistance with full

shear connection

(EN1994-1-1,cl.6.1.2)

Bending resistance

check checks (EN1993-1-1,cl.6.2.5(1))

Vertical Shear resistance of the composite steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)

Design of shear

resistance check (EN1993-1-1,cl.6.2.6(1)P)

Check if the verification of

shear buckling resistance (EN1993-1-1,cl.6.2.6(6))

Npl.afy A⋅

γM0:=

Nc.f 0.85 fcd⋅ beff⋅ hc⋅:=

Npl.w fy tw⋅ ha 2 tf⋅−( )⋅:=

Location_neutral axis "Lies in the concrete slab" Nc.f Npl.a>if

"Lies in the top flange of the beam" Nc.f Npl.a≤if

"Lies in the web of the beam" Nc.f Npl.w<if

:=

Mpl.Rd Npl.aha2

h+Npl.aNc.f

hc2

⋅−⎛⎜⎝

⎞⎟⎠

⋅ Location_neutral axis "Lies in the concrete slab"if

Npl.aha2

⋅ Nc.fhc2

hp+⎛⎜⎝

⎞⎟⎠

⋅+ Location_neutral axis "Lies in the top flange of the beam"if

Ma.pl.Rd Nc.fhc ha+ 2hp+

2

⎛⎜⎝

⎞⎟⎠

⋅+Nc.f

2

Npl.w

ha4

⋅− Location_neutral axis "Lies in the top flange of the beam"if

:=

Check_7 if MEd Mpl.Rd≤ "OK", "NOT OK", ( ):=

Check_8 if VEd Vpl.Rd≤ "OK", "NOT OK", ( ):=

Check_9 ifhwtw

72ε

η⋅< "Not required shear buckling resistance", "Required shear buckling resistance",

⎛⎜⎝

⎞⎟⎠

:=

Composite

Stage

required or not

Design resistance of shear stud connector (cl.6.6.3.1(1))

Upper limit of reduction

factor kt

(EN1994-1-1,Table:6.2)

Reduction factor kt

Ribs transverse to the supporting beams

(EN1994-1-1,cl.6.6.4.2)

Limitation of kt (EN1994-1-1,cl.6.6.4.2(2))

Reduction factor kt

Ribs parallel to the supporting beams

(EN1994-1-1,cl.6.6.4.1)

Minimum height of shear stud (EN1994-1-1,cl.6.6.1.2(1))

Limitation of stud diameter (EN1994-1-1,cl.6.6.1.2(1))

Factor α

(EN1994-1-1,cl.6.6.3.1(1))

kt.max 0.85 nr 1 1mm ts≥∧ d 20mm<∧if

1.0 nr 1 1mm ts<∧ d 20mm<∧if

0.75 nr 1 1mm ts≥∧ 19mm d≤ 22mm<∧if

0.75 nr 1 1mm ts<∧ 19mm d≤ 22mm<∧if

0.70 nr 2 1mm ts≥∧ d 20mm<∧if

0.80 nr 2 1mm ts<∧ d 20mm<∧if

0.60 nr 2 1mm ts≥∧ 19mm d≤ 22mm<∧if

0.60 nr 2 1mm ts<∧ 19mm d≤ 22mm<∧if

:=

kt0.7

nr

bohp⋅

hschp

1−⎛⎜⎝

⎞⎟⎠

⋅:=

Check_10 if kt kt.max< "OK", "NOT OK", ( ):=

kt 0.6bohp⋅

hschp

1−⎛⎜⎝

⎞⎟⎠

⋅ 1.0≤:=

hmin if hsc 4d≥ "Ductile", "Not Ductile", ( ):=

dlim if 16mm d< 25mm< "Ductile", "Not ductile", ( ):=

α 0.2hscd

1+⎛⎜⎝

⎞⎟⎠

⋅ 3hscd

≤ 4≤if

1hscd

4>if

1=:=

Composite

Stage

Design shear resistance of a

headed stud

(EN1994-1-1,cl.6.6.3.1(1))

Degree of shear connection (cl.6.6.1.2(1))

Ratio of the degree shear

connection (EN1994-1-1,cl.6.2.1.3(3))

Minimum degree of shear

connection for equal flange

(EN1994-1-1,cl.6.6.1.2(1))

Check the degree of shear

interaction within the limits (EN1994-1-1,cl.6.6.1.2(1))

Number of shear connector

required -

Stud spacing -

Check the minimum

spacing of studs (EN1994-1-1,cl.6.6.5.7(4))

Adequacy of the shear connection

(EN1994-1-1,cl.6.6.1.3(3))

Design of transverse reinforcement (cl.6.6.6.2) & (EN1992-1-1,cl.6.2.4)

Length under consideration -

PRd kt min0.8 fus⋅ π⋅

d2

4⋅

γ v

0.29α⋅ d2⋅ fck Ecm⋅⋅

γ v,

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

⋅:=

ηNc.fNpl.a

:=

ηmin 1355fy

N mm 2−⋅

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

0.75 0.03Lem

⋅−⎛⎜⎝

⎞⎟⎠

⋅− Le 25m<if

1.0 Le 25m>if

:=

Check_11 if η ηmin> η 0.4≥∧ "OK", "NOT OK", ( ):=

n2 Npl.a⋅

PRd:=

sprovLe

Nstud:=


Check_12 if Mpl.Rd 2.5 Ma.pl.Rd⋅< "Uniform spacing", "Not uniform spacing", ( ):=

Δ xLe2

:=

Longitudinal shear stress (EN1992-1-1,cl.6.2.4(3))

Strength reduction factor (EN1992-1-1,Eq.6.6N)

Area of transverse

reinforcement required

(EN1992-1-1,cl.6.2.4(4))

Check the crushing

compression in the flange (EN1992-1-1cl.6.2.4(4))

Serviceability limit state

Vertical deflection

Construction

Stage

Maximum deflection at

construction stage -

Vertical deflection limit (CYS NA EN1993-1-1,table

NA.1)

Composite

Stage

Short term elastic modular

ration

(EN1994-1-1,cl.7.2.1)

Second moment of area of the

composite section -

Deflection with full shear

connection -

Vibration of floor (Simplified analysis) (EN1990 A1.4.4)

vEdNpl.a2 hc⋅ Δ x⋅

:=

v 0.6 1fck

250 N⋅ mm 2−⋅

−⎛⎜⎜⎝

⎞⎟⎟⎠

⋅:=

As.reqvEd hc⋅ sf⋅

fydsin θf( )cos θf( )⋅

:=

Check_14 if vEd v fcd⋅ sin θf( )⋅ cos cos θf( )( )⋅≤ "OK", "NOT OK", ( ):=

δc5 Gk.c Qk.c+( )⋅ Le

4⋅

384 Es⋅ Iyy⋅:=

Check_15 if δcLe250

< "OK", "NOT OK", ⎛⎜⎝

⎞⎟⎠

:=

noEsEcm

:=

rA

beff hc⋅:=

IcA h 2 hp⋅+ hc+( )2⋅

4 1 no r⋅+( )⋅

beff hc3

⋅

12 no⋅+ Iyy+:=

δcom5 Gk Qk+( )⋅ Le( )4⋅

384 Es⋅ Ic⋅:=

Total load on beam is EN1990,A1.4.4

Increase the inertia, Ic by 10% to allow for the

increased dynamic stiffness of the composite beam -

Instantaneous deflection caused by re-application of

the self weigth of the floor and the beam to the

composite beam -

Natural frequency

SCI P354

Check natural frequency limitation -

Fv Gk ψ1 Qk⋅+:=

Icl Iy Iy 0.1⋅( )+:=

δα

5 Fv Le⋅( )⋅ Le3

⋅

384 Es⋅ Icl⋅:=

f18 Hz⋅

δα

mm

:=

Check_17 if f 4Hz< "OK", "NOT OK", ( ):=

8.5 Detail design of steel columns under gravity loads

Table 8.5: Detail design of composite beam

Partial factor Value References

Partial factor of cross-sections whatever the class

is γM0 = 1.0

CYS EN1993-1-1,cl 6.1(1)

Partial factor of member to instability assessed by

member checks γM1 = 1.0

CYS EN1993-1-1,cl 6.1(1)

Description of detail requirements Equations References

Design plastic resistance of the gross cross-section Npl,Rd = A fy / γM0 EN1993-1-1,cl.6.2.3(2)

Compression resistance of steel section Nc,Rd =A fy / γM0 EN1993-1-1,cl.6.2.4(1)

Bending interaction check

Moment resistance of steel section Y-Y axis Mc,Rd,y =Mpl,Rd,y = Wpl,y fy / γM0 EN1993-1-1,cl.6.2.5(2)

Moment resistance of steel section Z-Z axis Mc,Rd,z= Mpl,Rd,z = Wpl,z fy / γM0 EN1993-1-1,cl.6.2.5(2)

Shear interaction check

Factor for shear area η = 1.0 (conservative value) EN1993-1-1,cl.6.2.6(3g)

Shear area 1 Av = A -2 b tf + (tw + 2r) tf ≥ η hw tw EN1993-1-1,cl.6.2.6(3a)

Shear resistance of steel section Y-Y axis Vpl,Rd y = Av (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)

Shear resistance of steel section Z-Z axis Vpl,Rd,z = 2b tf (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)

Bending and shear interaction check

Area of web Aw = hw tw EN1993-1-1,cl.6.2.8(5)

Coefficient of interaction vy=VEd / Vpl.Rd,y EN1993-1-1,cl.6.2.8(5)

Reduced yield strength ρ = [(2VEd / Vpl.Rd,y) – 1] 2 EN1993-1-1,cl.6.2.8(3)

Reduced design plastic resistance moment Y-Y axis EN1993-1-1,cl.6.2.8(5)

Coefficient of interaction vz=VEd / VRd,y EN1993-1-1,cl.6.2.8(5)

Reduced yield strength ρ = [(2VEd / Vpl.Rd,z) – 1] 2 EN1993-1-1,cl.6.2.8(3)

Reduced design plastic resistance moment Z-Z axis EN1993-1-1,cl.6.2.8(5)

Check combination of axial and bending EN1993-1-1,cl.6.2.1(7)

Bending and axial interaction check

Criteria 1 – Y-Y axis c1=NEd ≤ Npl,Rd EN1993-1-1,cl.6.2.9.1(4)

Criteria 2 – Y-Y axis c2=NEd ≤ (0.5 hw tw fy )/ γM0 EN1993-1-1,cl.6.2.9.1(4)

Check criteria c= max(cy1, cy2)

Factor a a = min {(A-2 b tf) / A) ,0.5} EN1993-1-1,cl.6.2.9.1(5)

Factor n n = NEd / Npl,Rd EN1993-1-1,cl.6.2.9.1(5)

Factor β EN1993-1-1,cl.6.2.9.1(6)

Reduced design value of the resistance to bending MN,y,Rd = Mpl,y,Rd (1-n)/(1-0,5a) if c>1.0 and

EN1993-1-1,cl.6.2.9.1(5)

Mc.Rd.y

Wpl.yρ Aw

2⋅

4tw−

⎛⎜⎜⎝

⎞⎟⎟⎠fy⋅

γM0vy 0.5>if

Mc.Rd.y vy 0.5<if

:=

Mc.Rd.z

Wpl.zρ Aw

2⋅

4tw−

⎛⎜⎜⎝

⎞⎟⎟⎠fy⋅

γM0vz 0.5>if

Mc.Rd.z vz 0.5<if

:=

Check_1 ifNEd

Npl.Rd

MEd.yMc.Rd.y

+MEd.z

Mc.Rd.z+ 1.0≤ "OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

β 5n 5n 1≥if

1 otherwise

1=:=

moments making allowance for the presence of

axial forces (Y-Y axis)

MN,y,Rd = Mpl,y,Rd if 0 ≤ c ≤ 1.0

Reduced design value of the resistance to bending

moments making allowance for the presence of

axial forces (Z-Z axis)

MN,z,Rd = Mpl,z,Rd for n<a and

MN,z,Rd = Mpl,z,Rd [1-(n-a/1-a)2] for n>a EN1993-1-1,cl.6.2.9.1(5)

Check combination of bi-axial bending EN1993-1-1,cl.6.2.9.1(6)

Buckling interaction check

Buckling length See: Figure 1: Effective length columns Design Guidance of EC3)

Elastic critical force for the relevant buckling mode based on the

gross cross sectional properties 𝑁!".! =

𝐸!𝐼!𝜋!

𝐿!".!! -

Non dimensional slenderness λ! =𝐴𝑓!𝑁!".!

EN1993-1-1,cl.6.3.1.2(1)

Buckling curve

EN1993-1-1,table 6.2

Imperfection factor a

EN1993-1-1,table 6.1

Check_1 ifMEd.y

MN.y.Rd

⎛⎜⎝

⎞⎟⎠

a MEd.zMN.z.Rd

⎛⎜⎝

⎞⎟⎠

β

+

⎡⎢⎢⎣

⎤⎥⎥⎦

1.0≤ "OK", "NOT OK",

⎡⎢⎢⎣

⎤⎥⎥⎦

:=

Buckling_class_Y

"a" tf 40mm<if

"b" 40mm tf< 100mm<if

hb

1.2>if

"b" tf 100mm≤if

"d" tf 100mm>if

hb

1.2≤if

:=

Value to determine the reduction factor χ Φ = 0.5 [1 + α (λ – 0.2) + λ2 EN1993-1-1,cl.6.3.1.2(1)

Reduction factor χ χ =1

Φ + Φ! − λ!≤ 1,0 EN1993-1-1,cl.6.3.1.2(1)

Design buckling resistance of a compression member 𝑁!,!" =𝜒𝐴𝑓!𝛾!!)

EN1993-1-1,cl.6.3.1.1(3)

Buckling length See: Figure 1: Effective length columns Design Guidance of EC3)

Elastic critical force for the relevant buckling mode based on the

gross cross sectional properties 𝑁!".! =

𝐸!𝐼!𝜋!

𝐿!".!! -

Non dimensional slenderness λ! =𝐴𝑓!𝑁!".!

EN1993-1-1,cl.6.3.1.2(1)

Buckling curve

EN1993-1-1,table 6.2

Imperfection factor a

EN1993-1-1,table 6.1

αy 0.1 Buckling_class_Y "ao"if

0.21 Buckling_class_Y "a"if

0.34 Buckling_class_Y "b"if

0.49 Buckling_class_Y "c"if

0.76 Buckling_class_Y "d"if

:=

Buckling_class_Y

"a" tf 40mm<if


hb

1.2>if

"b" tf 100mm≤if

"d" tf 100mm>if

hb

1.2≤if

:=

Value to determine the reduction factor χ Φ = 0.5 [1 + α (λ – 0.2) + λ2 EN1993-1-1,cl.6.3.1.2(1)

Reduction factor χ χ =1

Φ + Φ! − λ!≤ 𝜒 ≤ 1,0 EN1993-1-1,cl.6.3.1.2(1)

Design buckling resistance of a compression member 𝑁!,!",! =𝜒𝐴𝑓!𝛾!!)

EN1993-1-1,cl.6.3.1.1(3)

Non dimensional slenderness EN1993-1-1,cl.6.3.1.2(1)

Check the bukling effects if can be ignored and only cross

section check is adequate

EN1993-1-1,cl.6.3.1.2(4)

Lateral torsional buckling interaction check

Elastic critical moment for lateral torsional buckling NCCI: SN003a-EN-EU

Effective length factor (Pinned End) k = 1.0 NCCI: SN003a

Factor for end warping kw = 1.0 NCCI: SN003a

Coefficient factor C1 (Load condition: UDL)

NCCI: SN003a

Coefficient factor C2 C2 = 1.554 NCCI: SN003a

Distance between the point of load application and the

shear centre (load applied on centre) zg = 0m NCCI: SN003a

αz 0.1 Buckling_class_Z "ao"if

0.21 Buckling_class_Z "a"if

0.34 Buckling_class_Z "b"if

0.49 Buckling_class_Z "c"if

0.76 Buckling_class_Z "d"if

:=

λ max λy λz, ( ):=

Check if λ 0.2< "Ignored buckling effects", "Consider buckling effects", ( ):=

Mcr C1π2 Es⋅ Izz⋅

k Lcr⋅( )2⋅

kkw

⎛⎜⎝

⎞⎟⎠

2 IwIzz⋅

k Lcr⋅( )2G It⋅

π2Es Izz⋅

+ C2 zg⋅( )2+⋅ C2 zg⋅−:=

C1 1.88 1.40ψ− 0.52ψ 2+:=

Check_5 if C1 2.7≤ "OK", "NOT OK", ( ):=

Lateral torsional buckling curves

EN1993-1-1,table 6.4

Imperfection factors for lateral torsional buckling curves

EN1993-1-1,table 6.3

Non dimensional slenderness for lateral torsional buckling

EN1993-1-1,cl.6.3.2.2(1)

Value to determine the reduction factor χLT EN1993-1-1,cl.6.3.2.2(1)

Reduction factor for lateral-torsional buckling EN1993-1-1,cl.6.3.2.2(1)

Check if the lateral torsional buckling

can be ignored

EN1993-1-1,cl.6.3.2.2(4)

Moments due to the shift of the centroidal axis for

class sections 1,2 & 3

EN1993-1-

1,cl.6.3.3(4)/table 6.7

Characteristic resistance to normal force of the

critical cross-section

EN1993-1-

1,cl.6.3.3(4)/table 6.7

Characteristic moment resistance of the critical

cross-section

E1993-1-1,cl.6.3.3(4)/table

6.7)

Buckling_curve_Z "a"hb

2≤if

"b"hb

2>if

:=

αLT 0.21 Buckling_curve_Z "a"if

0.34 Buckling_curve_Z "b"if

0.49 Buckling_curve_Z "c"if

0.76 Buckling_curve_Z "d"if

:=

λLTWpl.y fy⋅

Mcr:=

φLT 0.5 1 αLT λLT 0.2−( )⋅+ λLT2

+⎡⎣

⎤⎦⋅:=

χLT1

φLT φLT2

λLT2

−+

:=

Check_6 if λLT λLTO< "Ignored torsional buckling effects", "Consider torsional buckling effects", ( ):=

Check_7 ifMEd.yMcr

λLTO2

< "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛⎜⎝

⎞⎟⎠

:=

ΔMEd.z 0:=

ΔMEd.y 0:=

NRk fy A⋅:=

My.Rk fy Wpl.y⋅:=

Mz.Rk fy Wpl.z⋅:=

Ratio of end moments

EN193-1-1,Table B2)

Equivalent uniform moment factor

EN1993-1-1,table B.1&B.2

Interaction factors

EN1993-1-1,table B.1&B.2

Combined bending and axial compression

EN1993-1-1,Eq.6.61

ψyMEd.y1MEd.y2

1−MEd.y1MEd.y2

≤ 1≤if

MEd.y2MEd.y1

1−MEd.y2MEd.y1

≤ 1≤if

:=

ψzMEd.z1MEd.z2

1−MEd.z1MEd.z2

≤ 1≤if

MEd.z2MEd.z1

1−MEd.z2MEd.z1

≤ 1≤if

:=

Cmy 0.6 0.4ψy⋅+:=

Cmz 0.6 0.4ψz⋅+:=

kyy min Cmy 1 λy 0.2−( )NEd

χyNRkγM1⋅

⋅+⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

Cmy 1 0.8NEd

χyNRkγM1⋅

⋅+⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

⋅, ⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

:=

kzz min Cmz 1 2λz 0.6−( )NEd

χzNRkγM1⋅

⋅+⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

Cmz 1 1.4NEd

χzNRkγM1⋅

⋅+⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

⋅, ⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

:=

kyz 0.6kzz:=

kzy 0.6kyy:=

NEdxy NRk⋅

γM1

kyyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅

⋅+ kyzMz.Ed ΔM Ed.z+

Mz.Rk

γM1

⋅+

Combined bending and axial compression

EN1993-1-1,Eq.6.62

Note: This equations is applicable only for I and H sections with section class 1 and 2

Note 1: The shear area is for rolled I and H sections, load parallel to web

NEdχz NRk⋅

γM1

kzyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅

⋅+ kzzMEd.z ΔM Ed.z+

Mz.Rk

γM1

⋅+

8.6 Detail design rules of steel Concentric Braced Frames (CBF) according to Eurocode 8

8.6.1 Detail design rules of steel bracing according to Eurocode 8

Description Value References

Overstrength factor used in design γov = 1.25 CYS EN1998-1-1cl.6.2(3)P

Non-dimensional slenderness (X bracing) EN1998-1-1,cl.6.7.3(1)

Non-dimensional slenderness (one diagonal) λ ≤ 2.0 EN1998-1-1,cl.6.7.3(2)

Non-dimensional slenderness (V bracing) λ ≤ 2.0 EN1998-1-1,cl.6.7.3(3)

Non-dimensional slenderness (V,X & one bracing) EN1998-1-1,cl.6.7.3(4)

Yield resistance check EN1998-1-1,cl.6.7.3(5)

Check Ω factor EN1998-1-1,cl.6.7.3(8)

Check Ω factor EN1998-1-1,cl.6.7.3(8)

Ductility class require for seismic design

EN1998-1-1,cl.6.5.3(2)

Check_6 if 1.3 λy< 2< "OK", "NOT OK", ( ):=

Check_5 if Ns 3≥ "Consider limitation (As EC8)", "Ignore limitation (As EC3)", ( ):=

Check_15 if NEd Npl.Rd≤ "OK", "NOT OK", ( ):=

Ω.Npl.RdNEd

:=


Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if

"CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if

"CLASS 1" q 4> Ductility_class "DCH"∧if

:=

8.7 Detail design rules of steel columns and beams according to Eurocode 8



Yield resistance check EN1998-1-1,cl.6.7.3(5)

Check Ω factor

EN1998-1-1,cl.6.7.3(8)

Minimum resistance requirement, NEd

EN1998-1-1,cl.6.7.4(1)


EN1998-1-1,cl.6.5.3(2)


Ω.Npl.RdNEd

:=

NEd. NEd.G 1.1 γ ov⋅ Ω⋅ NEd.E⋅+:=




:=

8.8 Detail design rules of steel composite members according to Eurocode 8


Minimum concrete strength C20/25 – C40/50 CYS EN1998-1-1cl.7.2.1(1)

Steel reinforcement class B or C

EN1998-1-1,cl.7.2.2(2)

Minimum degree of connection η ≤ 0.8 EN1998-1-1,cl.7.6.2(3)

Reduction factor kt = 0.75

EN1998-1-1,cl.7.6.2(4)

Profiled steel sheeting with ribs transverse to the

supporting beams is used, the reduction factor

kt = kt * kr

EN1998-1-1,cl.7.6.2(6)

Yield strength of steel

EN1998-1-1,cl.7.6.2(8)


EN1998-1-1,cl.6.5.3(2)

fy "fy=355" 1.5 q< 4≤ Ductility_class "DCM"∧xd

0.27≤∧if

"fy=235" 1.5 q< 4≤ Ductility_class "DCM"∧ 0.27xd

< 0.36≤∧if

"fy=355" q 4> Ductility_class "DCH"∧xd

0.20≤∧if

"fy=235" q 4> Ductility_class "DCH"∧ 0.20xd

< 0.27≤∧if

:=

xx




:=

8.9 Detail design rules of steel moment resistance frames (MRF) according to Eurocode 8

8.9.1 Detail design rules for MRF - Design criteria


Below design criteria apply to (Bottom – Top) Single/Multi-story buildings EN1998-1-1cl.6.6.1(1)

Moment capacity (where fixed support is provided) ∑MRc ≥ 1.3MRb EN1998-1-1,cl.4.4.2.3(4)

8.9.2 Detail design rules of steel beam for MRF


Moment capacity verification 𝑀!"

𝑀!".!" ≤ 1.0 EN1998-1-1,cl.6.6.2.(2)

Design shear force

VEd = VEd.G + VEd.M

Where

VEd.M = (Mpl.Rd.A + Mpl.Rd.B)/L

EN1998-1-1,cl.6.6.2.(2)

Shear capacity verification 𝑉!"𝑉!".!"

≤ 0.5 EN1998-1-1,cl.6.6.2.(2)

Axial capacity verification 𝑁!"𝑁!".!"

≤ 0.15 EN1998-1-1,cl.6.6.2.(2)

8.9.3 Detail design rules of steel column for MRF



Check Ω factor (derivate from all beam with

moment connection) Ω!"# =

!!".!"

!!".! MEd.E : Lateral force

EN1998-1-1cl.6.6.3(1P)

Design axial compression force NEd = NEd.G +1.1γvoΩ NEd.E NEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)

Design bending moment MEd = MEd.G +1.1γvoΩ MEd.E MEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)

Design shear force VEd = VEd.G +1.1γvoΩ VEd. VEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)

Design shear force verification 𝑉!"𝑉!".!"

≤ 0.5 EN1998-1-1cl.6.6.3(4)

9.0 Design of steel frames

9.1 Design of steel member overwrites data

Figure 9.1: Steel design result of the member

Overwrites

Figure 9.2: Steel frame design overwrites for Eurocode 3

3

2

1

4

7

8

9

10

11

12

5

6

Table 9.1: Steel frame design overwrites for Eurocode 3

Explanation of Steel frame design overwrites for Eurocode 3

Note No. Parameter Values

1 Effective length factor

2 Moment coefficient

kyy

kzz

3 Bending Coefficient (C1)

4 Moment coefficient

5 Overstrength factor

used in design1

6 Omega gamma

factor γov = 1.25

7 Compressive/Tensile

capacity

8 Major bending

capacity, Mc3Rd

9 Minor bending

capacity, Mc2Rd

10 Buckling resistance

moment

Ω.Npl.RdNEd

:=

11 Major shear capacity, Vc3Rd

12 Minor shear

capacity, Vc2Rd

Notes: 1Ω is not calculated automatically by the program. Rather, its value can be overwritten by the user through design Preference and Overwrites.

9.2 Design of columns / beams using ETABS – Gravity load analysis only

STEP 1: Analyze > Run Analysis STEP 2: Design > Steel frame design > Select design combo… Note: Under gravity load conditions, only beams and columns shall be considered to resist such loads, without taking into account the bracing members (EN1998-1-1,cl6.7.2(1)P). Design combination at ULS

STATIC 1. 1.35DL + 1.5LL STATIC 10. 1.00DL + 0.3LL

Figure 9.3: Gravity load combination at ULS

Design combination at SLS

DSTLD 1. DL + LL DSTLD 2. DL

Figure 9.4: Gravity load combination at SLS

Figure 9.5: Steel design under gravity load ONLY

Write click on each member in order to check it individually Column name: C2 Storey level: Storey 1

Figure 9.6: Steel design result of the member

Figure 9.7: Ultimate moment results under worst case combination

ETABS: Display > Show tables

Worst case combination

Take the ultimate moment and shear force from the above table and place them into the Excel

spreadsheet or Mathcad file in order to verify the steel design results of ETABS.

Table 9.2: Summarize of design values required to carry out the design of steel member

Design value Symbol Results

(kN)

Design axial force for gravity load combination (G+0.3Q) NEd.GV 344.75

Design moment at y-y at end 1 (seismic load combination) MEd.GV.y1 -1.293

Design moment at y-y at end 2 (seismic load combination) MEd.GV.y2 3.195

Design moment at z-z at end 1 (seismic load combination) MEd.GV.z1 -0.173

Design moment at z-z at end 2 (seismic load combination) MEd.GV.z2 -0.142

Shear forces at y-y at end (seismic load combination) VEd.GV.y -0.01

Shear force at z-z at end 1 (seismic load combination) VEd.GV.z -1.63

Press the button summary

Design results of ETABS

ETABS/HAND Description of

comparison Results

ETABS Equation 6.62 in EC3

0.160

HAND (see section 9.3) 0.135

ETABS/HAND N.c.Rd N.t.Rd N.pl.Rd

ETABS 2675.75 2675.75 2675.75

HAND (see section 9.3) 2675.75 2675.75 2675.75

ETABS/HAND Curve Alpha LambarBar Phi Chi Nb.Rd

y-y z-z y-y z-z y-y z-z y-y z-z y-y z-z y-y z-z

ETABS “b” “c” 0.340 0.490 0.268 0.454 0.548 0.66 0.976 0.868 2610 2322

HAND (see section 9.3) “b” “b” 0.340 0.340 0.248 0.42 0.539 0.625 0.983 0.918 2630 2534

ETABS/HAND M.c.Rd M.v.Rd

M.b.rd y-y z-z y-y z-z

ETABS 305.8 142.45 305.8 142.45 302.05

HAND (see section 9.3) 305.8 142.45 305.8 142.45 305.80

ETABS/HAND Curve AlphaLT LambdaBarLT PhiLT ChiLT C1 Mcr

ETABS a 0.21 0.255 0.538 0.988 2.532 4694

HAND (see section 9.3) b 0.34 0.24 0.535 0.986 2.532 4679

ETABS/HAND kyy kyz kzy kzz

ETABS 0.442 0.582 0.964 0.970

HAND (see section 9.3) 0.441 0.576 0.265 0.96

ETABS/HAND V.c.Rd

V.pl.Rd η y-y z-z

ETABS 504 1234 504 1.2

HAND (see section 9.3) 504 1156 504 1.0

9.3 Design of steel column (Gravity design situation) – Hand calculations

1. Rolled I - section 2. Limit to class 1 and 2 section 3. Column not susceptible to torsional deformations

Length of column

Total axial load on column, NEd

Shear force y-y axis

Shear force z-z axis

Design moment y-y axis


Maximum moment

Design moment z-z axis


Maximum moment

Section properties:

Depth of section,h: Width of section,b:

Thickness of web, tw:

Thickness of flange, tf :

Thickness of element

Second moment of area z-z:

Second moment of area y-y:

Cross section area, A:

Radius of section:

Heigth of web, hw

hc 3m:=

NEd 344.798kN:=

VEd.y 0.011kN:=

VEd.z 1.626kN:=

MEd.y1 3.195kNm⋅:=

MEd.y2 1.293− kNm⋅:=

MEd.y maxMEd.y1 MEd.y2, ( ) 3.195kNm⋅⋅=:=

MEd.z1 0.142− kNm⋅:=

MEd.z2 0.173− kNm⋅:=

MEd.z maxMEd.z1 MEd.z2, ( ) 0.142− kNm⋅⋅=:=

h 270mm:=

b 280mm:=

tw 8mm:=

tf 13mm:=

t max tw tf, ( ) 13mm⋅=:=

Izz 47630000mm4:=

Iyy 1.367 108⋅ mm4:=

A 9730mm2:=

r 24mm:=

hw h 2tf− 2r− 196mm⋅=:=

Area of the web

Warping Constant, Iw:

Torsional Constant, IT:

Plastic Modulus, Wply

Plastic Modulus, Wplz

Elastic modulus, E:

Yield strength of steel , fy:

Ultimate strength, fu:

Shear modulus

Reduction of yield and ultimate strength of sections EN10025-2

Partial safety factor

Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1))

Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1))

Resistance of cross-section in tension (CYS EN1993-1-1,cl.6.1(1))

Section classification

For section classification the coefficient ε is:

For a flange element:

Aw hw tw⋅ 1.568 103× mm2⋅=:=

Iw 753.7 109⋅ mm6⋅:=

It 635000mm4:=

Wpl.y 1112000mm3:=

Wpl.z 518000mm3:=

Es 210kNmm 2−⋅:=

fy 275N mm 2−⋅:=

fu 430N mm 2−⋅:=

G 81kNmm 2−⋅:=

fy fy t 16mm≤if

fy 10N mm 2−⋅− 16mm t< 40mm≤if


:=

fy 275 N mm 2−⋅⋅=

fu fu t 16mm≤if



:=

fu 430 N mm 2−⋅⋅=

γM0 1:=

γM1 1:=

γM2 1.25:=

ε235fy

N mm 2−⋅

0.924=:=

For a web element:

Tension resistance (cl.6.2.3)

Design plastic resistance of the cross section (EN1993-1-1,cl.6.2.3(2)

Design ultimate resistance (EN1993-1-1,cl.6.2.3(2b))

Design tension resistance (EN1993-1-1,cl.6.2.3(2))

Check tension capacity

cfb tw− 2.r−( )

2112mm⋅=:=Class_type flange "CLASS 1"

cftf

9 ε⋅≤if


< 10 ε⋅≤if


< 14 ε⋅≤if

:=

Class_type flange "CLASS 2"=

cw h 2 tf⋅− 2 r⋅− 196mm⋅=:=


72 ε⋅≤if


< 83 ε⋅≤if


< 124 ε⋅≤if

:= Class_type web "CLASS 1"=

Class_type if Class_type flange Class_type web Class_type flange, "ADD MANUALY", ( ):=

Class_type "ADD MANUALY"=

Npl.RdA fy⋅

γM02.676 103× kN⋅=:=

Nu.Rd0.9A fy⋅

γM21.927 103× kN⋅=:=

Nt.Rd min Nu.Rd Npl.Rd, ( ) 1.927 103× kN⋅=:=

Check1 ifNEd

Nt.Rd1.0≤ "OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

Check1 "OK"=

Compression resistance (cl.6.2.4)

Compression resistance of steel section (EN1993-1-1,cl.6.2.4(1))

Check compression capacity (EN1993-1-1,cl.6.2.4(1)P)

Bending resistance (cl.6.2.5) Moment resistance of steel section at Y-Y (EN1993-1-1,cl.6.2.5(2)

Moment resistance of steel section at Z-Z (EN1993-1-1,cl.6.2.5(2)

Shear resistance (cl.6.2.6)

Factor for shear area (EN1993-1-1,cl.6.2.6(g))

Shear area of steel section (EN1993-1-1,cl.6.2.6(3))

Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2))


Shear resistance of steel section Z-Z (EN1993-1-1,cl.6.2.6(2))

Nc.Rd Npl.Rd 2.676 103× kN⋅=:=

Check2 ifNEd

Nc.Rd1.0≤ "OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

Check2 "OK"=

Mc.Rd.yWpl.y fy⋅

γM0305.8kNm⋅⋅=:=

Mc.Rd.zWpl.z fy⋅

γM0142.45kNm⋅⋅=:=

η 1:=

Avy A 2 b⋅ tf⋅− tw 2r+( ) tf⋅+:=

Av Avy Avy η tw⋅ hw⋅>if

η tw⋅ hw⋅ Avy η tw⋅ hw⋅<if

:= Av 3.178 103× mm2⋅=

Vpl.Rd.y Avfy 3( ) 1−⋅

γM0⋅ 504.575kN⋅=:=

Avz 2 b⋅ tf⋅ 7.28 103× mm2⋅=:=

Vpl.Rd.z 2 b⋅ tf⋅fy 3( ) 1−⋅

γM0⋅ 1.156 103× kN⋅=:=

Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6))

Bending and shear interaction check (cl.6.2.8)

Strong axis Y-Y

Interaction check 1

Reduced yield strength

Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5))

Weak axis Z-Z

Interaction check 1



Check ifhwtw

72ε


⎛⎜⎝

⎞⎟⎠

:=

Check "Not required shear buckling resistance"=

vyVEd.yVpl.Rd.y

2.18 10 5−×=:=

ρ2VEd.yVpl.Rd.y

1−⎛⎜⎝

⎞⎟⎠

2

1=:=

Mc.Rd.y

Wpl.yρ Aw

2⋅

4tw−

⎛⎜⎜⎝

⎞⎟⎟⎠fy⋅

γM0vy 0.5>if

Mc.Rd.y vy 0.5<if

:=

Mc.Rd.y 305.8kNm⋅⋅=

vzVEd.zVpl.Rd.z

1.407 10 3−×=:=

ρ2VEd.zVpl.Rd.z

1−⎛⎜⎝

⎞⎟⎠

2

0.994=:=

Mc.Rd.z

Wpl.zρ Aw

2⋅

4tw−

⎛⎜⎜⎝

⎞⎟⎟⎠fy⋅

γM0vz 0.5>if

Mc.Rd.z vz 0.5<if

:=

Mc.Rd.z 142.45kNm⋅⋅=

Check combination of axial and bending (EN1993-1-1,cl.6.2.1(7))

Unity factor

Bending and axial force interaction check (cl.6.2.9)

Factor a

Factor n

Factor β

Coefficient 1

Coefficient 2

Coefficient check

Strong axis Y-Y Reduced design value of the resistance to

bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5))

Check_1 ifNEd

Npl.Rd

MEd.yMc.Rd.y

+MEd.z


⎛⎜⎝

⎞⎟⎠

:=

NEdNpl.Rd

MEd.yMc.Rd.y

+MEd.zMc.Rd.z

+ 0.138=

Check_1 "OK"=

a minA 2b tf⋅−( )

A0.5,

⎡⎢⎣

⎤⎥⎦

0.252=:=

nNEdNpl.Rd

0.129=:=

β 5n 5n 1≥if

1 otherwise

1=:=

c1NEd

0.25Npl.Rd0.515=:=

c2NEd

0.5hw tw⋅ fy⋅1.599=:=

c max c1 c2, ( ) 1.599=:=

MN.y.RdMc.Rd.y 1 n−( )⋅

1 0.5a−c 1>if

Mc.Rd.y 0 c≤ 1≤if

:=

MN.y.Rd 304.764kNm⋅⋅=

Weak axis Z-Z Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5))

Check combination of bi-axial bending (EN1993-1-1,cl.6.2.9.1(6))

Unity factor

Bucking interaction check (cl.6.3)

Strong axis Y-Y

Status of effective length

Effective length factor (Guidance of EC3)

Buckling length of column (fixed end)

Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1)

MN.z.Rd Mc.Rd.z n a≤if

Mc.Rd.z 1n a−1 a−⎛⎜⎝

⎞⎟⎠

2−

⎡⎢⎣

⎤⎥⎦

⋅ n a≥if

:=

MN.z.Rd 142.45kNm⋅⋅=

Check_1 ifMEd.y

MN.y.Rd

⎛⎜⎝

⎞⎟⎠

a MEd.zMN.z.Rd

⎛⎜⎝

⎞⎟⎠

β

+

⎡⎢⎢⎣

⎤⎥⎥⎦

1.0≤ "OK", "NOT OK",

⎡⎢⎢⎣

⎤⎥⎥⎦

:=

MEd.yMN.y.Rd

⎛⎜⎝

⎞⎟⎠

a MEd.zMN.z.Rd

⎛⎜⎝

⎞⎟⎠

β

+ 0.316=

Check_1 "OK"=

Effective_Length " Pinned Fixed":=

k 0.7 Effective_Length "Fixed Fixed"if

0.85 Effective_Length "Partial restraint"if

0.85 Effective_Length " Pinned Fixed"if

1 Effective_Length "Pinned Pinned"if

0.85=:=

Lcr k hc 2.55m=:=

NcryEs Iyy⋅ π

2⋅

Lcr2

4.357 104× kN⋅=:=

Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.2(1)

Buckling curve (EN1993-1-1,table 6.2)

Imperfection factor (EN1993-1-1,table 6.1)

Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))

Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))

Reduction factor χ check

Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3))

Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1))

λyA fy⋅

Ncry0.248=:=

Buckling_class_Y

"a" tf 40mm<if


hb

1.2>if

"b" tf 100mm≤if

"d" tf 100mm>if

hb

1.2≤if

:=

Buckling_class_Y "b"=

αy 0.1 Buckling_class_Y "ao"if

0.21 Buckling_class_Y "a"if

0.34 Buckling_class_Y "b"if

0.49 Buckling_class_Y "c"if

0.76 Buckling_class_Y "d"if

:=

αy 0.34:=

φ y 0.5 1 αy λy 0.2−( )⋅+ λy2

+⎡⎣

⎤⎦⋅ 0.539=:=

χy1

φ y φ y2

λy2

−+

0.983=:=

Check1 if χy 1.0≤ "OK", "NOT OK", ( ):=

Check1 "OK"=

Nb.Rd.yχy A⋅ fy⋅

γM12.63 103× kN⋅=:=

Check2 ifNEd

Nb.Rd.y"OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

Check2 "OK"=

Weak axis Z-Z




Check if the buckling may be ignored (EN1993-1-1,cl.6.3.1.2(4))

Slenderness parameter

MinimumEuler Buckling



Lcr k hc⋅ 2.55m=:=

NcrzEs Izz⋅ π

2⋅

Lcr2

1.518 104× kN⋅=:=

λzA fy⋅

Ncrz0.42=:=

λ max λy λz, ( ):=

Ncr min Ncry Ncrz, ( ):=

Check_2 if λ 0.2<NEdNcr

0.04<∧ "Ignored buckling effects", "Consider buckling effects", ⎛⎜⎝

⎞⎟⎠

:=

Check_2 "Consider buckling effects"=

Buckling_class_Z

"a" tf 40mm<if


hb

1.2>if

"b" tf 100mm≤if

"d" tf 100mm>if

hb

1.2≤if

:=

Buckling_class_Z "b"=

αz 0.1 Buckling_class_Z "ao"if

0.21 Buckling_class_Z "a"if

0.34 Buckling_class_Z "b"if

0.49 Buckling_class_Z "c"if

0.76 Buckling_class_Z "d"if

:=

αz 0.34:=






Lateral torsional buckling check (cl.6.3.2)

Effective length factor, k (SN003a-EN-EU)

Factor for end warping, kw (SN003a-EN-EU)

Ratio of the smaller and larger moment

Coefficient factor C1 (SN003a-EN-EU)

Coefficient factor C1 check (SN003a-EN-EU)


Distance between the point of load application and the shear centre

φ z 0.5 1 αz λz 0.2−( )⋅+ λz2

+⎡⎣

⎤⎦⋅ 0.625=:=

χz1

φ z φ z2

λz2

−+

0.918=:=

Check_3 if χz 1.0≤ "OK", "NOT OK", ( ):=

Check_3 "OK"=

Nb.Rd.zχz A⋅ fy⋅

γM12.457 103× kN⋅=:=

Check_4 ifNEd

Nb.Rd.z"OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

Check_4 "OK"=

k 0.85=

kw 1.0:=

ψMEd.y2MEd.y1

0.405−=:=

C1 1.88 1.40ψ− 0.52ψ 2+ 2.532=:=


Check_5 "OK"=

C2 1.554:=

zg 0m:=

Elastic critical moment for lateral torsional buckling (SN003a-EN-EU)

Lateral torsional buckling curve (EN1993-1-1,table 6.4)

Imperfection factor for lateral torsional (EN1993-1-1,table 6.3)

Non dimensional slenderness (EN1993-1-1,cl.6.3.2.2(1))

Value to determine the reduction factor (EN1993-1-1,cl.6.3.2.2(1))

Reduction factor for lateral-torsional buckling (EN1993-1-1,cl.6.3.2.2(1))

Parameter λ LTO (EN1993-1-1,cl.6.3.2.3(1))

Design buckling resistance moment (EN1993-1-1,cl.6.3.2.1(3))


Lcr( )2⋅

kkw

⎛⎜⎝

⎞⎟⎠

2 IwIzz⋅

Lcr( )2G It⋅

π2Es Izz⋅

+ C2 zg⋅( )2+⋅ C2 zg⋅− 4.679 103× kNm⋅⋅=:=

Buckling_curve_Z "b"hb

2≤if

"c"hb

2>if

:=

Buckling_curve_Z "b"=





:=

αLT 0.34=

λLTWpl.y fy⋅

Mcr0.256=:=

φLT 0.5 1 αLT λLT 0.2−( )⋅+ λLT2

+⎡⎣

⎤⎦⋅ 0.542=:=

χLT1

φLT φLT2

λLT2

−+

0.98=:=

Check_6 if χLT 1≤ χLT1

λLT2

≤∧ "OK", "NOT OK", ⎛⎜⎜⎝

⎞⎟⎟⎠

:=

Check_6 "OK"=

λLTO 0.4:=

Mb.Rd χLTWpl.y⋅fyγM1⋅ 299.741kNm⋅⋅=:=

Check_7 ifMEd.yMb.Rd

1≤ "OK", "NOT OK", ⎛⎜⎝

⎞⎟⎠

:=

Check if the lateral torsional buckling be ignored (EN1993-1-1,cl.6.3.2.2(4))

Combine bending and axial compression cl.6.3.3

Moments due to the shift of the centroidal axis for class sections 1,2 & 3 (EN1993-1-1,cl.6.3.3(4)/table 6.7)

Characteristic resistance to normal force of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7)

Characteristic moment resistance of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7)

Ratio of end moments (EN1993-1-1,Table B2)



Check_7 "OK"=

Check_8 if λLT λLTO<MEd.yMcr

λLTO2

<∧ "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛⎜⎝

⎞⎟⎠

:=

Check_8 "Ignored torsional buckling effects"=

ΔMEd.z 0:=

ΔMEd.y 0:=

NRk fy A⋅ 2.676 103× kN⋅=:=

My.Rk Mc.Rd.y 305.8kNm⋅⋅=:=

Mz.Rk Mc.Rd.z 142.45kNm⋅⋅=:=

ψyMEd.y1MEd.y2

1−MEd.y1MEd.y2

≤ 1≤if

MEd.y2MEd.y1

1−MEd.y2MEd.y1

≤ 1≤if

:=

ψzMEd.z1MEd.z2

1−MEd.z1MEd.z2

≤ 1≤if

MEd.z2MEd.z1

1−MEd.z2MEd.z1

≤ 1≤if

:=

Cmy 0.6 0.4ψy⋅+ 0.438=:=

Cmz 0.6 0.4ψz⋅+ 0.928=:=

Interaction factors (EN1993-1-1,table B.1&B.2)

EN1993-1-1,Equation 6.61

Unity factor


Unity factor


χyNRkγM1⋅

⋅+⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

Cmy 1 0.8NEd

χyNRkγM1⋅

⋅+⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

⋅, ⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

0.441=:=


χzNRkγM1⋅

⋅+⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

Cmz 1 1.4NEd

χzNRkγM1⋅

⋅+⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

⋅, ⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

0.96=:=

kyz 0.6kzz 0.576=:=

kzy 0.6kyy 0.265=:=

Check_9 ifNEd

χy NRk⋅

γM1

kyyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅

⋅+ kyzMEd.z ΔM Ed.z+

Mz.Rk

γM1

⋅+ 1.0≤ "OK", "NOT OK", ⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

:=

NEdχy NRk⋅

γM1

kyyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅


Mz.Rk

γM1

⋅+ 0.135=

Check_9 "OK"=

Check_10 ifNEd

χz NRk⋅

γM1

kzyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅


Mz.Rk

γM1

⋅+ 1.0≤ "OK", "NOT OK", ⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

:=

NEdχz NRk⋅

γM1

kzyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅


Mz.Rk

γM1

⋅+ 0.142=

Check_10 "OK"=

9.4 Design of steel column (Seismic design situationn)

Column name: C2 Storey level: Storey 1

Step 1: Option > Preferences > Steel frame design

Step 2: Design > Steel frame design > Select design combo…

Figure 9.7: Lateral/gravity load combination at ULS

Modify the existing “System Omega”. The omega factor is equal to the minimum section overstrength factor of concentric bracing. See below:

Note: the minimum value of Ω is calculate over all the diagonals of the braced frame system




STATIC 1. 1.35DL + 1.5LL STATIC 2. 1.35DL + 1.5LL + 0.75WINDX STATIC 3. 1.35DL + 1.5LL - 0.75WINDX STATIC 4. 1.35DL + 1.5LL + 0.75WINDY STATIC 5. 1.35DL + 1.5LL - 0.75WINDY STATIC 6. 1.35DL + 1.5WINDX + 1.05LL STATIC 7. 1.35DL - 1.5WINDX – 1.05LL STATIC 8. 1.35DL + 1.5WINDY + 1.05LL

STATIC 9. 1.35DL - 1.5WINDY – 1.05LL STATIC 10. DL + 0.3LL




DSTLD 1. DL + LL DSTLD 2. LL

ETABS: Display > Show Tables

Table 9.3a: Analysis results of gravity load combination (STATIC 10: G + 0.3Q)

Story Column Load Loc P V2 V3 T M2 M3

STORY1 C2 STATIC10 0 -‐245.17 -‐0.28 -‐0.27 0 -‐0.43 0.001 STORY1 C2 STATIC10 1.38 -‐244.13 -‐0.28 -‐0.27 0 -‐0.055 0.389

Select all combinations

STORY1 C2 STATIC10 2.76 -‐243.1 -‐0.28 -‐0.27 0 0.321 0.776 Note: P = NEd.G

Table 9.3b: Analysis results of seismic action (MODAL EQX / EQY)


STORY1 C2 EQX 0 38.99 29.66 0.49 -‐0.001 0.884 58.02 STORY1 C2 EQX 1.38 38.99 29.66 0.49 -‐0.001 0.202 17.094 STORY1 C2 EQX 2.76 38.99 29.66 0.49 -‐0.001 -‐0.48 -‐23.833 STORY1 C2 EQX 0 33.61 26.3 1.15 0.001 1.917 51.189 STORY1 C2 EQX 1.38 33.61 26.3 1.15 0.001 0.332 14.928 STORY1 C2 EQX 2.76 33.61 26.3 1.15 0.001 1.256 21.431 STORY1 C2 EQY 0 3.55 2.72 8.97 0.003 14.692 5.227 STORY1 C2 EQY 1.38 3.55 2.72 8.97 0.003 2.313 1.468 STORY1 C2 EQY 2.76 3.55 2.72 8.97 0.003 10.076 2.297 STORY1 C2 EQY 0 2.6 1.89 10.93 0.002 17.899 3.709 STORY1 C2 EQY 1.38 2.6 1.89 10.93 0.002 2.813 1.097 STORY1 C2 EQY 2.76 2.6 1.89 10.93 0.002 -‐12.273 -‐1.516 Note: P = NEd.E

Results of Seismic load combination (SEISMIC 1-8)

Select all the seismic load combinations Sort out the highest values of P, V and M

Table 9.4: Analysis result of design values of V and M based on worst case seismic design

combination


STORY1 C2 SEISMIC1 MIN 0 -‐279.84 -‐27.4 -‐4.11 -‐0.002 -‐6.755 -‐52.756 STORY1 C2 SEISMIC1 MIN 1.38 -‐278.8 -‐27.4 -‐4.11 -‐0.002 -‐1.081 -‐14.979 STORY1 C2 SEISMIC1 MIN 2.76 -‐277.77 -‐27.4 -‐4.11 -‐0.002 -‐3.958 -‐21.344



(kN/kNm)

Design axial force for gravity load combination (G+0.3Q) NEd.G 245

Design axial force for the design seismic action alone NEd.E 39

Design moment at y-y at end 1 (seismic load combination) MEd.SC.y1 52.8

Design moment at y-y at end 2 (seismic load combination) MEd.SC.y2 21.3

Design moment at z-z at end 1 (seismic load combination) MEd.SC.z1 6.8

Design moment at z-z at end 2 (seismic load combination) MEd.SC.z2 4.0

Shear forces at y-y at end (seismic load combination) VEd.SC.y 27.4

Shear force at z-z at end 1 (seismic load combination) VEd.SC.z 4.1

9.4.1 Design of steel column (Seismic design situation – Hand calculation)

Detail design of steel column using Eurocode 3 and Eurocode 8

1. Rolled I - section 2. Limit to class 1 and 2 section 3. Column not susceptible to torsional deformations Design data

Length of column Overstrength factor (EN1998-1-1,cl.6.1.3(2))

Omega factor of bracing members at storey 1

Behavior factor q

Ductlity class

Total axial force due to the non-seismic actions (G+ψ EiQ)

Total axial force due to the non-seismic actions (seismic)

Design shear force due to Eurocode requirement (EN1998-1-1,cl.6.7.4(1))


Design moment y-y axis (seismic combination)




Maximum moment

Maximum moment

hc 3m:=

γ ov 1.25:=

Ω 2.5:=

q 4:=

Ductility_class "DCM":=

NEd.G 245.17kN:=

NEd.E 39kN:=

VEd.y 4.11kN:=

VEd.z 27.4kN:=

MEd.y1 52.76kNm⋅:=

MEd.y2 21.34kNm⋅:=

MEd.z1 6.75kNm⋅:=

MEd.z2 3.96kNm⋅:=


MEd.z maxMEd.z1 MEd.z2, ( ) 6.75 kNm⋅⋅=:=


Section properties:

Depth of section,h: Width of section,b:

Thickness of web, tw: Thickness of flange, tf :

Thickness of element Second moment of area z-z: Second moment of area y-y:


Radius of section,r:

Heigth of web, hw

Area of the web





Elastic modulus, E:



Shear modulus

NEd NEd.G 1.1 γ ov⋅ Ω⋅ NEd.E⋅+ 379.233kN⋅=:=

h 270mm:=

b 280mm:=

tw 8mm:=

tf 13mm:=


Izz 47630000mm4:=

Iyy 1.367 108⋅ mm4:=

A 9730mm2:=

r 24mm:=

hw h 2tf− 2r− 196mm⋅=:=

Aw hw tw⋅ 1.568 103× mm2⋅=:=

Iw 753.7 109⋅ mm6⋅:=

It 635000mm4:=

Wpl.y 1112000mm3:=

Wpl.z 518000mm3:=

Es 210kNmm 2−⋅:=

fy 275N mm 2−⋅:=

fu 430N mm 2−⋅:=

G 81kNmm 2−⋅:=

Reduction of yield and ultimate strenght of sections EN10025-2








fy fy t 16mm≤if



:=

fy 275 N mm 2−⋅⋅=

fu fu t 16mm≤if



:=

fu 430 N mm 2−⋅⋅=

γM0 1:=

γM1 1:=

γM2 1.25:=

ε235fy

N mm 2−⋅

0.924=:=

cfb tw− 2.r−( )

2112mm⋅=:=


9 ε⋅≤if


< 10 ε⋅≤if


< 14 ε⋅≤if

:=


Note: The column now has to be check using the resistance verification checks of Eurocode

3 as shown in section 9.3 of this document.

For a web element:

Requirements on cross-sectional class of dissipative elements depending on Ductility class (EN1998-1-1,cl.6.5.3(2))

Section classification rule for EC8 (EN1998-1-1,cl.6.5.3(2))

cw h 2 tf⋅− 2 r⋅− 196mm⋅=:=


72 ε⋅≤if


< 83 ε⋅≤if


< 124 ε⋅≤if

:=Class_type web "CLASS 1"=


Class_type "ADD MANUALY"=




:=

Class_type_req "CLASS 1 or 2"=

9.5 Design of composite beams - Hand calculations

ETABS: Define > Wall/Slab/Deck sections

Figure 9.9: Define deck section Comflor60 -Corus

Figure 9.10: Modified “Stiffness Modifiers” (crack-sections)

ETABS: Analyze > Run analysis

ETABS: Display > Show Tables >

Select all combinations

Assumptions - Design and analysis

This design process is envisaging a analyzed to determine the forces and moments in the individual structural members. Simple design approach: This method applies to structures in which the connections between members will not develop any significant restraint moments. Members forces and moments are calculated on the basic of the following assumptions: 1. Simply supported beam. 2. The steel sheeting with ribs is placed transverse to the beam. 3. Limited only to I abd H rolled sections with equal flanges 4. Ignored any contribution of steel sheeting to the transverse reinforcements

Length of beam

Spacing of the secondary beams (LHS)

Spacing of the secondary beams (RHS)

Loading length

Slab design data

Comfloor 60

Overall depth of slab

Steel sheeting deck profile (Comflor 60)

Depth of concrete slab above steel sheeting

Rib width at top

Rib width at bottom

Le 5m:=

L1 5m:=

L2 5m:=

LL12

L22

+ 5m=:=

h 150mm:=

hp 60mm:=

hc h hp− 90mm⋅=:=

b1 131mm:=

b2 180mm:=

Distance between shear connector (Assume single shear connector)

Space of each troughs

Thickness of steel sheeting

Structural steel properties

Depth of section, h:

Width of section,b:




Radius of section,r:

Heigth of web, hw

Area of the web

Radious of gyration








Yield strength

Ultimate strength

Modulus of Elasticity

Shear modulus

bob1 b2+

2155.5mm⋅=:=

e 300mm:=

ts 1mm:=

ha 240mm:=

b 120mm:=

tw 6.2mm:=

tf 9.8mm:=

t max tw tf, ( ) 9.8mm⋅=:=

r 15mm:=

hw ha 2tf− 2r− 190.4mm⋅=:=

Aw hw tw⋅ 1.18 103× mm2⋅=:=

iz 26.9507mm:=

Izz 2840000mm4:=

Iyy 38920000mm4:=

A 3910mm2:=

It 130000mm4:=

Iw 753.7 109⋅ mm6⋅:=

Wpl.y 367000mm3:=

Wpl.z 73900mm3:=

fy 275N mm 2−⋅:=

fu 430N mm 2−⋅:=

Es 210kNmm 2−⋅:=

G 81kNmm 2−⋅:=

Concrete properties

Yield strength of reinforcement

Cylinder strength

Modulus of Elasticity

Shear connector properties

Diameter Overall height before welding

Ultimate strength of shear connector

Number of stud per in one rib

Material partial factors for resistance



Partial factor for concrete (EN 1992 1-1 Table 2.1N)

Partial factor for reinforcing steel (EN 1992 1-1 Table 2.1N)

Partial factor for design shear resistance of a headed stud (CYS EN1994-1-1,cl.2.4.1.2(5)P)

Partial factor for design shear resistance of a composite slab (CYS EN1994-1-1,cl.2.4.1.2(6)P)

Partial factor for permanent action

Partial factor for variable action

Design value of the cylinder compressive strength of concrete (EN1992-1-1,cl.

fyk 500N mm 2−⋅:=

fck 25N mm 2−⋅:=

Ecm 31kNmm 2−⋅:=

d 19mm:=

hsc 95mm:=

fus 450N mm 2−⋅:=

nr 1:=

γM0 1.0:=

γM1 1.0:=

γ c 1.5:=

γ s 1.15:=

γ v 1.25:=

γ vs 1.25:=

γG 1.35:=

γQ 1.5:=

fcdfckγ c

16.667N mm 2−⋅⋅=:=

Design value of the yield strength of structural steel

Loading at construction stage

Dead load

Weight of steel deck (Comfloor 60)

Weight of wet concrete

Weight of steel beam (IPE240)

Live load

Construction live load

Total load at construction stage

Moment at construction stage

Shear force at construction stage

Design moments and shear forces

Shear force at composite stage

Design moment at composite stage

Shear force at composite stage

Design moment at composite stage

fydfykγ s

434.783N mm 2−⋅⋅=:=

gk.deck 0.114kNm 2−⋅:=

gk.c.wet 2.79kNm 2−⋅:=

gk.b 0.8kNm 1−⋅:=

qk 0.75kNm 2−⋅:=

FEd γG gk.deck L⋅ gk.c.wet L⋅+ gk.b+( )⋅ γQ qk⋅ L⋅+ 26.307kNm 1−⋅⋅=:=

MEd.cFEd L

2⋅

882.209kNm⋅⋅=:=

VEd.cFEd L⋅

265.767kN⋅=:=

VEd.c 65.767kN⋅=

MEd.c 82.209kNm⋅⋅=

VEd 55.5kN:=

MEd 132kNm⋅:=

Ultimate limit state verification

Construction stage

Section classification (EN19931-1,cl.5.6(6))

Reduction of yield and ultimate strength of sections EN10025-2



fy fy t 16mm≤if



:=

fy 275 N mm 2−⋅⋅=

fu fu t 16mm≤if



:=

fu 430 N mm 2−⋅⋅=

ε235fy

N mm 2−⋅

0.924=:=

cfb tw− 2.r−( )

241.9mm⋅=:=


9 ε⋅≤if


< 10 ε⋅≤if


< 14 ε⋅≤if

:=


For a web element:

Bending Resistance of the steel section (EN1993-1-1,cl.6.2.5)

Design resistance for bending (EN1993-1-1,cl.6.2.5(2))

Bending resistance check checks (EN1993-1-1,cl.6.2.5(1))

Vertical Shear resistance of the steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)




cw ha 2 tf⋅− 2 r⋅− 190.4mm⋅=:=


72 ε⋅≤if


< 83 ε⋅≤if


< 124 ε⋅≤if

:= Class_type web "CLASS 1"=


Class_type "CLASS 1"=

Ma.pl.RdWpl.y fy⋅

γM0100.925kNm⋅⋅=:=

Check_1 if MEd.c Ma.pl.Rd≤ "OK", "NOT OK", ( ):=

Check_1 "OK"=

η 1:=

Av1 A 2 b⋅ tf⋅− tw 2r+( ) tf⋅+:=

Av Av1 Av1 η tw⋅ hw⋅>if

η tw⋅ hw⋅ Av1 η tw⋅ hw⋅<if

:= Av 1.913 103× mm2⋅=

Vpl.Rd Avfy 3( ) 1−⋅

γM0⋅ 303.691kN⋅=:=

Design of shear resistance check (EN1993-1-1,cl.6.2.6(1)P)


Bending and shear interaction check (cl.6.2.2.4)

Strong axis Y-Y

Interaction check 1



Lateral torsional buckling resistance of steel beam (EN1993-1-1,cl.6.3.2)




Check_2 "OK"=

Check_3 ifhwtw

72ε


⎛⎜⎝

⎞⎟⎠

:=

Check_3 "Not required shear buckling resistance"=

vyVEdVpl.Rd

0.183=:=

ρ2VEdVpl.Rd

1−⎛⎜⎝

⎞⎟⎠

2

0.403=:=

Ma.pl.Rd.

Wpl.yρ Aw

2⋅

4tw−

⎛⎜⎜⎝

⎞⎟⎟⎠fy⋅

γM0vy 0.5>if

Ma.pl.Rd vy 0.5<if

:=

Ma.pl.Rd 100.925kNm⋅⋅=

Effective_Length "Pinned Pinned":=

k 0.7 Effective_Length "Fixed Fixed"if




1=:=

Effective length (pinned)






Lateral torsional buckling curve (EN1993-1-1,table 6.4)

Imperfection factor for lateral torsional (EN1993-1-1,table 6.3)


Parameter introducing the effect of biaxial bending (EN1994-1-1,cl.6.3.2.3(1))


Lcr k Le⋅ 5m=:=

kw 1.0:=

C1 1.348:=

C2 0.454:=

zg 0m:=


Lcr( )2⋅

kkw

⎛⎜⎝

⎞⎟⎠

2 IwIzz⋅

Lcr( )2G It⋅

π2Es Izz⋅

+ C2 zg⋅( )2+⋅ C2 zg⋅− 176.744kNm⋅⋅=:=

Buckling_curve_Z "b"hb

2≤if

"c"hb

2>if

:=

Buckling_curve_Z "b"=





:=

αLT 0.34=

λLTWpl.y fy⋅

Mcr0.756=:=

β 0.75:=

λLTO 0.4:=



Design plastic resistance (EN1993-1-1,cl.6.3.2.1)

Section verification for lateral torsional buckling (EN1993-1-1,cl.6.3.2.1(1))

Composite stage

Effective width of composite beam (cl.5.4.1.2(5))

Total effective width at mid-span (EN1994-1-1cl. 5.4.1.2(5))

Plastic resistance moment of composite section with full shear connection (cl.6.2)

Tensile resistance of steel section (EN1993-1-1,cl.6.2.3(2))

Compression resistance of concrete slab (EN1994-1-1,cl.6.2.1.2(1d)

Tensile resistance in web of steel section

φLT 0.5 1 αLT λLT λLTO−( )⋅+ β λLT2

⋅⎛⎝

⎞⎠+⎡

⎣⎤⎦⋅ 0.775=:=

χLT1

φLT φLT2

β λLT2

−+

0.841=:=


λLT2

≤∧ "OK", "NOT OK", ⎛⎜⎜⎝

⎞⎟⎟⎠

:=

Check_5 "OK"=

Mb.Rd χLTWpl.y fy⋅

γM1⋅ 84.882kNm⋅⋅=:=

Check_6 ifMEd.cMb.Rd

1< "OK", "NOT OK", ⎛⎜⎝

⎞⎟⎠

:=

Check_6 "OK"=

beff bo 2 minL12

L22

+Le8

, ⎛⎜⎝

⎞⎟⎠

⎛⎜⎝

⎞⎟⎠

+:=

Npl.afy A⋅

γM01.075 103× kN⋅=:=

Nc.f 0.85 fcd⋅ beff⋅ hc⋅ 1.792 103× kN⋅=:=

Npl.w fy tw⋅ ha 2 tf⋅−( )⋅:=

Location of neutral axis (EN1994-1-1,cl.6.2.1.2(1))

Bending resistance with full shear connection (EN1994-1-1,cl.6.1.2)

Bending resistance check checks (EN1993-1-1,cl.6.2.5(1))

Vertical Sheat resistance of the composite steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)


Design of shear resistance check (EN1993-1-1,cl.6.2.6(1)P)

Location_neutral axis "Lies in the concrete slab" Nc.f Npl.a>if

"Lies in the top flange of the beam" Nc.f Npl.a≤if

"Lies in the web of the beam" Nc.f Npl.w<if

:=

Location_neutral axis "Lies in the concrete slab"=

Mpl.Rd Npl.aha2

h+Npl.aNc.f

hc2

⋅−⎛⎜⎝

⎞⎟⎠

⋅ Location_neutral axis "Lies in the concrete slab"if

Npl.aha2

⋅ Nc.fhc2

hp+⎛⎜⎝

⎞⎟⎠

⋅+ Location_neutral axis "Lies in the top flange of the beam"if

Ma.pl.Rd Nc.fhc ha+ 2hp+

2

⎛⎜⎝

⎞⎟⎠

⋅+Nc.f

2

Npl.w

ha4

⋅− Location_neutral axis "Lies in the top flange of the beam"if

:=

Mpl.Rd 261.285kNm⋅⋅=

Check_7 if MEd Mpl.Rd≤ "OK", "NOT OK", ( ):=

Check_7 "OK"=

Vpl.Rd 303.691kN⋅=


Check_8 "OK"=


Design resistance of shear stud connector (cl.6.6.3.1(1))

For sheeting with ribs transverse to the beam For sheeting parallel to the beam see Equation 6.22 of EC4

Upper limit of reduction factor kt (EN1994-1-1,Table:6.2)

Reduction factor kt (EN1994-1-1,cl.6.6.4.2)

Limitation of kt (EN1994-1-1,cl.6.6.4.2(2))

Minimum height of shear stud (EN1994-1-1,cl.6.6.1.2(1))

Check_9 ifhwtw

72ε


⎛⎜⎝

⎞⎟⎠

:=


kt.max 0.85 nr 1 1mm ts≥∧ d 20mm<∧if

1.0 nr 1 1mm ts<∧ d 20mm<∧if

0.75 nr 1 1mm ts≥∧ 19mm d≤ 22mm<∧if

0.75 nr 1 1mm ts<∧ 19mm d≤ 22mm<∧if

0.70 nr 2 1mm ts≥∧ d 20mm<∧if

0.80 nr 2 1mm ts<∧ d 20mm<∧if

0.60 nr 2 1mm ts≥∧ 19mm d≤ 22mm<∧if

0.60 nr 2 1mm ts<∧ 19mm d≤ 22mm<∧if

:=

kt.max 0.75=

kt 0.6bohp⋅

hschp

1−⎛⎜⎝

⎞⎟⎠

⋅:=

kt kt kt kt.max<if

kt.max otherwise

0.75=:=

hmin if hsc 4d≥ "Ductile", "Not Ductile", ( ):=

hmin "Ductile"=

Limitation of stud diameter (EN1994-1-1,cl.6.6.1.2(1))

Factor α (EN1994-1-1,cl.6.6.3.1(1))

Design shear resistance of a headed stud (EN1994-1-1,cl.6.6.3.1(1))

Degree of shear connection (cl.6.6.1.2(1))

Ratio of the degree shear connection (EN1994-1-1,cl.6.2.1.3(3))

Minimum degree of shear connection for equal flange (EN1994-1-1,cl.6.6.1.2(1))

Check the degree of shear interaction within the limits (EN1994-1-1,cl.6.6.1.2(1))

Number of shear connector required

Numper of stud provided

Stud spacing

dlim if 16mm d< 25mm< "Ductile", "Not ductile", ( ):=

dlim "Ductile"=

α 0.2hscd

1+⎛⎜⎝

⎞⎟⎠

⋅ 3hscd

≤ 4≤if

1hscd

4>if

1=:=

PRd kt min0.8 fus⋅ π⋅

d2

4⋅

γ v

0.29α⋅ d2⋅ fck Ecm⋅⋅

γ v,

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

⋅ 55.298kN⋅=:=

ηNc.fNpl.a

1.667=:=

ηmin 1355fy

N mm 2−⋅

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

0.75 0.03Lem

⋅−⎛⎜⎝

⎞⎟⎠

⋅− Le 25m<if

1.0 Le 25m>if

:=

ηmin 0.225=

Check_11 if η ηmin> η 0.4≥∧ "OK", "NOT OK", ( ):=

Check_11 "OK"=

n2 Npl.a⋅

PRd38.889=:=

Nstud 40:=

sprovLe

Nstud0.125m=:=

Check the minimum spacing of studs (EN1994-1-1,cl.6.6.5.7(4))

Adequacy of the shear connection (EN1994-1-1,cl.6.6.1.3(3))

Design of transverse reinforcement (cl.6.6.6.2) & (EN1992-1-1,cl.6.2.4)

Length under consideration

Longitudinal shear stress (EN1992-1-1,cl.6.2.4(3))

Strength reduction factor (EN1992-1-1,Eq.6.6N)

Angle between the diagonal strut (EN1992-1-1,cl.6.2.4(4))

Assume spacing of the bars

Area of transverse reinforcement required (EN1992-1-1,cl.6.2.4(4))

Area of transverse reinforcement provided

Check the crushing compression in the flange (EN1992-1-1cl.6.2.4(4))


slim "OK"=

Check_12 if Mpl.Rd 2.5 Ma.pl.Rd⋅< "Uniform spacing", "Not uniform spacing", ( ):=

Check_12 "Not uniform spacing"=

Δ xLe2

2.5m=:=

vEdNpl.a2 hc⋅ Δ x⋅

:=

v 0.6 1fck

250 N⋅ mm 2−⋅

−⎛⎜⎜⎝

⎞⎟⎟⎠

⋅:=

θf 45deg:=

sf 200mm:=

As.reqvEd hc⋅ sf⋅

fydsin θf( )cos θf( )⋅

:=

As.prov 193mm2:=

Check_13 if As.req As.prov≤ "OK", "NOT OK", ( ):=

Check_13 "OK"=

Check_14 if vEd v fcd⋅ sin θf( )⋅ cos cos θf( )( )⋅≤ "OK", "NOT OK", ( ):=

Check_14 "OK"=

Serviceability limit state verification

Construction stage

Dead load at composite stage

Live load at composite stage

Maximum deflection at construction stage

Vertical deflection limit (CYS NA EN1993-1-1,table NA.1)

Short term elastic modular ration (EN1994-1-1,cl.7.2.1)

Second moment of area of the composite section, Ic

Deflection with full shear connection

Vertical deflection limit (CYS NA EN1993-1-1,table NA.1)

Gk 10.88kNm 1−⋅:=

Qk 5.0kNm 1−⋅:=

δcon5 Gk Qk+( )⋅ Le

4⋅

384 Es⋅ Iyy⋅15.812mm⋅=:=

Check_15 if δconLe250

< "OK", "NOT OK", ⎛⎜⎝

⎞⎟⎠

:=

Check_15 "OK"=

noEsEcm

:=

rA

beff hc⋅:=

IyA h 2 hp⋅+ hc+( )2⋅

4 1 no r⋅+( )⋅

beff hc3

⋅

12 no⋅+ Iyy+ 1.563 10 4−

× m4=:=

δcom5 Gk Qk+( )⋅ Le( )4⋅

384 Es⋅ Iy⋅3.938mm⋅=:=

Check_16 if δcomLe200

< "OK", "NOT OK", ⎛⎜⎝

⎞⎟⎠

:=

Check_16 "OK"=

Vibration (Simplified analysis):

Loading:

Permanent load

Imposed load

For category B building

Total weigth floor, Fv

Increase the inertia, Ic by 10% to allow for the increased dynamic stiffness of the composite beam, Icl

Instantaneous deflection caused by re-application of the self weight of the floor and the beam to the composite beam, δ α

Natural frequncy, f

Check beam vibration (SCI-P-076)

Gk 10.88 kNm 1−⋅⋅=

Qk 5 kNm 1−⋅⋅=

ψ1 0.5:=

Fv Gk ψ1 Qk⋅+:=

Icl Iy Iy 0.1⋅( )+:=

δα

5 Fv Le⋅( )⋅ Le3

⋅

384 Es⋅ Icl⋅3.016mm⋅=:=

f18

δα

mm

⎛⎜⎜⎝

⎞⎟⎟⎠

Hz 10.364Hz⋅=:=

Check_17 if f 4 Hz⋅> "OK", "NOT OK", ( ):=

Check_17 "OK"=

9.5 Design of steel bracing

9.5.1 Main configuration of design of steel bracing

Basic theory: Tension only, utilises two members at each storey but only the tension element is assumed to resist wind load and seismic load, the compression element is assumed to buckle and offer no resistance to lateral movement. Eurocode 8 requirement: The diagonals shall be taken into account as follows in an elastic analysis of the structure for the seismic action:

a) in frames with diagonal bracings, only the tension diagonals shall be taken into

account, b) in frames with V bracings, both the tension and compression diagonals shall be taken

into account (EN1998-1-1,cl6.7.2(2).

Taking into account of both tension and compression diagonals in the analysis of any type of concentric bracing is allowed provided that all of the following conditions are satisfied:

a) a non-linear static (pushover) global analysis or non-linear time history analysis is used,

b) both pre-buckling and post-buckling situations are taken into account in the modeling of the behavior of diagonals and,

c) background information justifying the model used to represent the behavior of diagonals is provided (EN1998-1-1,cl6.7.2(3).

Figure 9.11: Method of design bracing in this manual

Steps for designing steel bracing member:

1. Delete the compression member.

2. Leave the tension members only.

3. Run the design of steel frame.

4. Find the suitable section and ensure that the section pass all the checks.

5. Ensure that the compression member has been placed at the construction drawings.

Ignore compression members

Compression members Tension members

Direction of shear

9.5.2 Simplified design of frames with X bracing (Extract from Design guidance to EC8)

In a standard design, the following simplified approach may be used:

• The analysis of the structure is realized considering that only one diagonal in each X

bracing is present, the other diagonal being considered as already buckled and unable to

provide strength. This corresponds to an underestimation of both the stiffness and the

strength of the structural system at the initial (pre-buckling) stage, but to a safe-side

estimate at the post-buckling stage.

• The beams and columns are capacity designed according to the real yield strength of the

diagonals, for bending with increased axial force and bending moment from the analysis

for the combination of the design seismic action with gravity loads.

However, this simplified approach could be dangerous for the stability of the structure, if it does

not take into account that action effects of compression in columns and beams at the pre-buckling

stage are higher than in the post-buckling stage envisaged in the analysis. Indeed, if the buckling

loads of the diagonal are closed to their yield load in tension, the initial shear resistance Vinit of

the X bracing is underestimated by a model where only one diagonal is considered present. If

low-slenderness diagonals are used, Vinit can be close to double the value of Vpl.Rd computed with

the hypothesis of one active yielded diagonal. The only way to prevent this unsafe situation is to

design slender diagonal having their buckling load at most around 0.5Npl.Rd. This condition is

behind the prescribed lower bound limit value of 1.3 for the slenderness λ. The prescribed upper

bound limit max λ=2, is justified by the aim to avoid shock effects during the load reversal in

diagonals.

9.5.3 Model in ETABS

Figure 9.12: Amendment model

Assume that the steel bracing resist the lateral force at the +X direction

Assume that the steel bracing resist the lateral force at the -X direction

Assume that the steel bracing resist the lateral force at the -Y direction

Assume that the steel bracing resist the lateral force at the +Y direction

STEP 2: Design > Steel frame design > Select design combo…

Figure 9.13: Lateral/gravity load combination at ULS




STATIC 11. 1.35DL + 1.5LL + 0.75WINDX STATIC 12. 1.35DL + 1.5LL - 0.75WINDX STATIC 13. 1.35DL + 1.5LL + 0.75WINDY STATIC 14. 1.35DL + 1.5LL - 0.75WINDY STATIC 15. 1.35DL + 1.5WINDX + 1.05LL STATIC 16. 1.35DL - 1.5WINDX – 1.05LL STATIC 17. 1.35DL + 1.5WINDY + 1.05LL STATIC 18. 1.35DL - 1.5WINDY – 1.05LL




DSTLD 3. DL + LL

Figure 9.15: Design steel bracing member

Write click on member Brace name: D3 Storey level: Storey 1

Table 9.6: Design value of brace D3

Story Brace Load Loc P V2 V3 T M2 M3

STORY1 D3 SEISMIC1 MIN 0 -‐361.83 -‐1.41 -‐0.05 -‐0.044 -‐0.173 -‐1.792 STORY1 D3 SEISMIC2 MIN 0 -‐361.83 -‐1.41 -‐0.05 -‐0.044 -‐0.173 -‐1.792 STORY1 D3 SEISMIC3 MIN 0 -‐361.83 -‐1.41 -‐0.05 -‐0.044 -‐0.173 -‐1.792 STORY1 D3 SEISMIC4 MIN 0 -‐361.83 -‐1.41 -‐0.05 -‐0.044 -‐0.173 -‐1.792 STORY1 D3 SEISMIC1 MIN 2.915 -‐361.06 -‐0.13 -‐0.05 -‐0.044 -‐0.054 0.443 STORY1 D3 SEISMIC2 MIN 2.915 -‐361.06 -‐0.13 -‐0.05 -‐0.044 -‐0.054 0.443 STORY1 D3 SEISMIC3 MIN 2.915 -‐361.06 -‐0.13 -‐0.05 -‐0.044 -‐0.054 0.443 STORY1 D3 SEISMIC4 MIN 2.915 -‐361.06 -‐0.13 -‐0.05 -‐0.044 -‐0.054 0.443

Worst case combination

Modify the default steel design data if needed



(kN/kNm)

Design axial force for the worse case design load combination NEd 361.83

Design moment at y-y at end 1 (worse case combination) MEd.y1 -1.792

Design moment at y-y at end 2 (worse case combination) MEd.y2 0.443

Design moment at z-z at end 1 (worse case combination) MEd.z1 -0.173

Design moment at z-z at end 2 (worse case combination) MEd.z2 -0.054

Shear forces at y-y at end (worse case combination) VEd.y -0.05

Shear force at z-z at end 1 (worse case combination) VEd.z -1.41

Modify the omega factors if needed

Modify the effective length factor if needed

9.5.4 Design of steel bracing (Gravity/Seismic design situation) – Hand calculation

1. Rolled I - section 2. Limit to class 1 and 2 section

Design data

Overstrength factor (EN1998-1-1,cl.6.1.3(2))

Behavior factor q

Ductlity class

Number of storeys

Length of bracing

Total axial load on column, NEd

Shear force y-y axis

Shear force z-z axis



Maximum moment



Maximum moment

Section properties:

Depth of section,d: Width of section,b:




γ ov 1.25:=

q 4:=

Ductility_class "DCM":=

Ns 3:=

hc 5.831m:=

NEd 361.83kN:=

VEd.y 0.05kN:=

VEd.z 1.41kN:=

MEd.y1 1.792kNm⋅:=

MEd.y2 0.443kNm⋅:=


MEd.z1 0.173− kNm⋅:=

MEd.z2 0.054− kNm⋅:=

MEd.z maxMEd.z1 MEd.z2, ( ) 0.054− kNm⋅⋅=:=

d 120mm:=

b 120mm:=

tw 16mm:=

tf 16mm:=









Elastic modulus, E:



Shear modulus

Reduction of yield and ultimate strenght of sections EN10025-2





Izz 12280000mm4:=

Iyy 12280000mm4:=

A 6656mm2:=

Iw 0 mm6⋅:=

It 18000000mm4:=

Wpl.y 261600mm3:=

Wpl.z 261600mm3:=

Es 210kNmm 2−⋅:=

fy 275N mm 2−⋅:=

fu 430N mm 2−⋅:=

G 81kNmm 2−⋅:=

fy fy t 16mm≤if



:=

fy 275 N mm 2−⋅⋅=

fu fu t 16mm≤if



:=

fu 430 N mm 2−⋅⋅=

γM0 1:=

γM1 1:=

γM2 1.25:=



Requirements on cross-sectional class of dissipative elements depending on Ductility class (EN1998-1-1,cl.6.5.3(2))

Section classification rule for EC8 (EN1998-1-1,cl.6.5.3(2))

ε235fy

N mm 2−⋅

0.924=:=

cf d 2tf− 88mm⋅=:=

Class_type_flange "CLASS 1"cft

33 ε⋅≤if

"CLASS 2" 33 ε⋅cft

< 38 ε⋅≤if

"CLASS 3" 38 ε⋅cft

< 42 ε⋅≤if

:=

Class_type_flange "CLASS 1"=

cw d 2tw− 88mm⋅=:=

Class_type_web "CLASS 1"cwt

72 ε⋅≤if

"CLASS 2" 72 ε⋅cwt

< 83 ε⋅≤if

"CLASS 3" 83 ε⋅cwt

< 124 ε⋅≤if

:=

Class_type_web "CLASS 1"=

Class_type if Class_type_flange Class_type_web Class_type_flange, "ADD MANUALY", ( ):=

Class_type "CLASS 1"=




"CLASS 1 or 2"=:=

Class_type_req "CLASS 1 or 2"=

Tension resistance (cl.6.2.2)

Design plastic resistance of the cross section (EN1993-1-1,cl.6.2.3(2a))

Modified plastic resistance of cross section as described in "Design Guidance to EC8" (cl.6.10.2)

Design ultimate resistance (EN1993-1-1,cl.6.2.3(2b))

Design tension resistance (EN1993-1-1,cl.6.2.3(2))

Check tension capacity (EN1993-1-1,cl.6.2.3(1)P)

Compression resistance (cl.6.2.3)

Compression resistance of steel section (EN1993-1-1,cl.6.2.4(1))

Check compression capacity (EN1993-1-1,cl.6.2.4(1)P)

Bending resistance (cl.6.2.5) Moment resistance of steel section at Y-Y (EN1993-1-1,cl.6.2.5(2)

Moment resistance of steel section at Z-Z (EN1993-1-1,cl.6.2.5(2)

Sheat resistance (cl.6.2.6)





Npl.RdA fy⋅

γM01.83 103× kN⋅=:=

Npl.Rd 0.5Npl.Rd⋅ 915.2kN⋅=:=

Nu.Rd0.9A fy⋅

γM21.318 103× kN⋅=:=

Nt.Rd min Nu.Rd Npl.Rd, ( ) 915.2kN⋅=:=

Check_1 ifNEd

Nt.Rd1.0≤ "OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

Check_1 "OK"=

Nc.Rd Npl.Rd 915.2kN⋅=:=

Check_2 ifNEd

Nc.Rd1.0≤ "OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

Check_2 "OK"=

Mc.Rd.yWpl.y fy⋅

γM071.94kNm⋅⋅=:=

Mc.Rd.zWpl.z fy⋅

γM071.94kNm⋅⋅=:=

η 1:=

AvyA b⋅b d+

3.328 103× mm2⋅=:=

AvzA d⋅b d+

3.328 103× mm2⋅=:=

Vpl.Rd.y Avyfy 3( ) 1−⋅

γM0⋅ 528.391kN⋅=:=

Shear resistance of steel section Z-Z (EN1993-1-1,cl.6.2.6(2))


Bending and shear interaction check (cl.6.2.8)

Strong axis Y-Y

Interaction check 1



Weak axis Z-Z

Interaction check 1


Vpl.Rd.z Avzfy 3( ) 1−⋅

γM0⋅ 528.391kN⋅=:=

Check_3 ifdt

72ε

η⋅< "Not required shear buckling resistance", "Required shear buckling resistance", ⎛⎜

⎝⎞⎟⎠

:=


vyVEd.yVpl.Rd.y

9.463 10 5−×=:=

ρ2VEd.yVpl.Rd.y

1−⎛⎜⎝

⎞⎟⎠

2

1=:=

Mc.Rd.y

Wpl.yρ A2⋅

4t−

⎛⎜⎝

⎞⎟⎠fy⋅

γM0vy 0.5>if

Mc.Rd.y vy 0.5<if

:=

Mc.Rd.y 71.94kNm⋅⋅=

vzVEd.zVpl.Rd.z

2.668 10 3−×=:=

ρ2VEd.zVpl.Rd.z

1−⎛⎜⎝

⎞⎟⎠

2

0.989=:=



Unity factor

Bending and axial force interaction check (cl.6.2.9)

Factor a

Factor a

Factor n

Factor β

Factor α

Mc.Rd.z

Wpl.zρ A2⋅

4t−

⎛⎜⎝

⎞⎟⎠fy⋅

γM0vz 0.5>if

Mc.Rd.z vz 0.5<if

:=

Mc.Rd.z 71.94kNm⋅⋅=

Check_4 ifNEd

Npl.Rd

MEd.yMc.Rd.y

+MEd.z


⎛⎜⎝

⎞⎟⎠

:=

NEdNpl.Rd

MEd.yMc.Rd.y

+MEd.zMc.Rd.z

+ 0.42=

Check_4 "OK"=

aw minA 2b tw⋅−( )

A0.5,

⎡⎢⎣

⎤⎥⎦

0.423=:=

af minA 2d tf⋅−( )

A0.5,

⎡⎢⎣

⎤⎥⎦

0.423=:=

nNEdNpl.Rd

0.395=:=

β1.66

1 1.13n2−

1.66

1 1.13n2−

6≤if

6 otherwise

2.016=:=

a β 2.016=:=

Strong axis Y-Y Reduced design value of the resistance to

bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5))

Weak axis Z-Z Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5))


Unity factor

Bucking interaction check (cl.6.3)

Strong axis Y-Y



MN.y.RdMc.Rd.y 1 n−( )⋅

1 0.5aw−:=

MN.y.Rd MN.y.Rd MN.y.Rd Mc.Rd.y≤if

Mc.Rd.y MN.y.Rd Mc.Rd.y>if

:=

MN.y.Rd 55.168kNm⋅⋅=

MN.z.RdMc.Rd.z 1 n−( )⋅

1 0.5af−:=

MN.z.Rd MN.z.Rd MN.z.Rd Mc.Rd.z≤if

Mc.Rd.z MN.z.Rd Mc.Rd.z>if

:=

MN.z.Rd 55.168kNm⋅⋅=

Check_5 ifNEd

Npl.Rd

MEd.yMc.Rd.y

+MEd.z


⎛⎜⎝

⎞⎟⎠

:=

NEdNpl.Rd

MEd.yMc.Rd.y

+MEd.zMc.Rd.z

+ 0.42=

Check_5 "OK"=


ky 0.7 Effective_Length "Fixed Fixed"if




1=:=




Check for X bracing (EN1998-1-1,cl.6.7.3(4))


Type of the section






Lcry ky hc 5.831m=:=

NcryEs Iyy⋅ π

2⋅

Lcry2

748.568kN⋅=:=

λyA fy⋅

Ncry1.564=:=


Check_6 "Consider limitation (As EC8)"=

Check_7 if 1.3 λy< 2< "OK", "NOT OK", ( ):=

Check_7 "OK"=

Section "Hot finished":=

Buckling_curve "a" Section "Hot finished"if

"c" Section "Cold formed"if

:=

Buckling_curve "a"=

αy 0.21 Buckling_curve "a"if

0.49 Buckling_curve "c"if

:=

αy 0.21=

φ y 0.5 1 αy λy 0.2−( )⋅+ λy2

+⎡⎣

⎤⎦⋅ 1.866=:=

χy1

φ y φ y2

λy2

−+

0.347=:=

Check_8 if χy 1.0≤ "OK", "NOT OK", ( ):=

Check_8 "OK"=



Weak axis Z-Z








Type of the section

Nb.Rd.yχy A⋅ fy⋅

γM1634.758kN⋅=:=

Check_9 ifNEd

Nb.Rd.y"OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

Check_9 "OK"=


kz 0.7 Effective_Length "Fixed Fixed"if




1=:=

Lcrz kzhc 5.831m=:=

NcrzEs Izz⋅ π

2⋅

Lcrz2

748.568kN⋅=:=

λzA fy⋅

Ncrz1.564=:=


Check_10 "Consider limitation (As EC8)"=

Check_11 if 1.3 λz< 2< "OK", "NOT OK", ( ):=

Check_11 "OK"=

Section "Hot finished":=







Lateral torsional buckling check (cl.6.3.2)

Effective length factor, k (SN003a-EN-EU)


Ratio of the smaller and larger moment


Buckling_curve "a" Section "Hot finished"if

"c" Section "Cold formed"if

:=

Buckling_curve "a"=

αz 0.21 Buckling_curve "a"if

0.49 Buckling_curve "c"if

:=

αz 0.21=

φ z 0.5 1 αz λz 0.2−( )⋅+ λz2

+⎡⎣

⎤⎦⋅ 1.866=:=

χz1

φ z φ z2

λz2

−+

0.347=:=

Check_12 if χz 1.0≤ "OK", "NOT OK", ( ):=

Check_12 "OK"=

Nb.Rd.zχz A⋅ fy⋅

γM1634.758kN⋅=:=

Check_13 ifNEd

Nb.Rd.z"OK", "NOT OK",

⎛⎜⎝

⎞⎟⎠

:=

Check_13 "OK"=

kz 1=

kw 1.0:=

ψMEd.y2MEd.y1

0.247=:=

C1 1.88 1.40ψ− 0.52ψ 2+ 1.566=:=

Coefficient factor C1 check (SN003a-EN-EU)




Imperfection factor for lateral torsional CHS sections (EN1993-1-1,table 6.3)





Design buckling resistance moment (EN1993-1-1,cl.6.3.2.1(3))


Check_14 "OK"=

C2 1.554:=

zg 0m:=


Lcrz( )2⋅

kzkw

⎛⎜⎝

⎞⎟⎠

2 IwIzz⋅

Lcrz( )2G It⋅

π2Es Izz⋅

+ C2 zg⋅( )2+⋅ C2 zg⋅− 1.636 103× kNm⋅⋅=:=

αLT 0.76:=

λLTWpl.y fy⋅

Mcr0.21=:=

φLT 0.5 1 αLT λLT 0.2−( )⋅+ λLT2

+⎡⎣

⎤⎦⋅ 0.526=:=

χLT1

φLT φLT2

λLT2

−+

0.992=:=


λLT2

≤∧ "OK", "NOT OK", ⎛⎜⎜⎝

⎞⎟⎟⎠

:=

Check_15 "OK"=

λLTO 0.4:=

Mb.Rd χLTWpl.y⋅fyγM1⋅ 71.389kNm⋅⋅=:=

Check_16 ifMEd.yMb.Rd

1≤ "OK", "NOT OK", ⎛⎜⎝

⎞⎟⎠

:=

Check if the lateral torsional buckling be ignored (EN1993-1-1,cl.6.3.2.2(4))

Combine bending and axial compression cl.6.3.3

Moments due to the shift of the centroidal axis for class sections 1,2 & 3 (EN1993-1-1,cl.6.3.3(4)/table 6.7)

Characteristic resistance to normal force of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7)

Characteristic moment resistance of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7)

Ratio of end moments (EN1993-1-1,Table B2)



Check_16 "OK"=

Check_17 if λLT λLTO<MEd.yMcr

λLTO2

<∧ "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛⎜⎝

⎞⎟⎠

:=

Check_17 "Ignored torsional buckling effects"=

ΔMEd.z 0:=

ΔMEd.y 0:=

NRk fy A⋅ 1.83 103× kN⋅=:=

My.Rk fy Wpl.y⋅ 71.94kNm⋅⋅=:=

Mz.Rk fy Wpl.z⋅ 71.94kNm⋅⋅=:=

ψyMEd.y1MEd.y2

1−MEd.y1MEd.y2

≤ 1≤if

MEd.y2MEd.y1

1−MEd.y2MEd.y1

≤ 1≤if

:=

ψzMEd.z1MEd.z2

1−MEd.z1MEd.z2

≤ 1≤if

MEd.z2MEd.z1

1−MEd.z2MEd.z1

≤ 1≤if

:=

Cmy 0.6 0.4ψy⋅+ 0.699=:=

Cmz 0.6 0.4ψz⋅+ 0.725=:=


χyNRkγM1⋅

⋅+⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

Cmy 1 0.8NEd

χyNRkγM1⋅

⋅+⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

⋅, ⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

1.018=:=

Interaction factors (EN1993-1-1,table B.1&B.2)


Unity factor


Unity factor


χzNRkγM1⋅

⋅+⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

Cmz 1 1.4NEd

χzNRkγM1⋅

⋅+⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

⋅, ⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

1.303=:=

kyz 0.6kzz 0.782=:=

kzy 0.6kyy 0.611=:=

Check_18 ifNEd

χy NRk⋅

γM1

kyyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅


Mz.Rk

γM1

⋅+ 1.0≤ "OK", "NOT OK", ⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

:=

NEdχy NRk⋅

γM1

kyyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅


Mz.Rk

γM1

⋅+ 0.595=

Check_18 "OK"=

Check_19 ifNEd

χz NRk⋅

γM1

kzyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅


Mz.Rk

γM1

⋅+ 1.0≤ "OK", "NOT OK", ⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

:=

NEdχz NRk⋅

γM1

kzyMEd.y ΔM Ed.y+

χLTMy.RkγM1

⋅


Mz.Rk

γM1

⋅+ 0.584=

Check_19 "OK"=

Eurocode 8 requirements

Yield resistance (EN1998-1-1,cl.6.7.3(5))

Yield resistance check (EN1998-1-1,cl.6.7.3(5))

Check omega factor (EN1998-1-1,cl.6.7.3(8))

Axial force at storey 3

Axial force at storey 2

Area of steel section (RHS 100X100X10)

Design plastic resistance of the cross section Storey 3: RHS 100X100X10 (EN1993-1-1,cl.6.2.3(2a))

Omega factor

Omega factor

Omega factor

Minimum omega

Minimum omega

Check Ω factor (EN1998-1-1,cl.6.7.3(8))


Check_20 "OK"=

NEd.3 162.34kN:=

NEd.2 317.56kN:=

A 3600mm2:=

Npl.Rd.30.5A fy⋅

γM0495 kN⋅=:=

Ωstorey1Npl.RdNEd

2.529=:=

Ωstorey2Npl.RdNEd.2

2.882=:=

Ωstorey3Npl.Rd.3NEd.3

3.049=:=

Ωmin min Ωstorey1 Ωstorey2, Ωstorey3, ( ):=

Ωmin 2.529=

Ωmax maxΩstorey1 Ωstorey2, Ωstorey3, ( ):=

Ωmax 3.049=


Check_21 "OK"=

10.0 Modal response spectrum analysis

10.1 Set the analysis options

1. ETABS: Analyze > Set analysis Options

Calculate the number of modes:

Figure 10.1: Set the modal analysis parameters

10.2 Evaluate the analysis results of the structure according to the modal analysis

requirements

2. ETABS: Display > Show Tables

Figure 10.2: Modal response spectrum results

10.2.1 Assess the modal analysis results based on the EN1998

The requirements of the sum of effective modal masses for the modes taken into account

amounts to at least 90% of the total mass of the structure is satisfied (EN1998-1-

1,cl.4.3.3.3.1(3)).

Effective mass of mode 6 = 97% > 90% “OK”

11.0 Second order effects (P – Δ effects) according to EN1998-1-1,cl.4.4.2.2

The criterion for taking into account the second order effect is based on the interstorey drift

sensitivity coefficient θ, which is define with equation (EN 1998-1-1,cl.4.4.2.2(2)).

Θ =P!"! ∙ d!V!"! ∙ h

dr: is the interstorey drift

h: is the storey height.

Vtot: is the total seismic storey shear.

Ptot: is the total gravity load at and above storey considered in the seismic design situation

(G+0.3Q).

Table 11.1: Consequences of value of P-Δ coefficient θ on the analysis

θ≤0,1 No need to consider P-Δ effects

0,1≤θ≤0,2 P-Δ effects may be taken into account approximately by

amplifying the effects of the seismic actions by !!!!

0,2≤θ≤0,3 P-Δ effects must be accounted for by an analysis including

second order effects explicity

θ≥0,3 Not permitted

Important note: If the above expression is not satisfied, second order effects, should be

enable in ETABS.

ETABS: Analyze > Set analysis option > > Set the parameters

11.1 Displacement calculation according to EN1998-1-1,cl.4.4.2.2

d! = q ∗ d!

ds : is the displacement of a point of the structural system induced by the design seismic action.

qd : is the displacement behaviour factor, assumed equal to q unless otherwise specified. de : is the displacement of the same point of the structural system, as determined by a linear

analysis based on the design response spectrum.

11.2 Interstorey drift

Interstorey drift is the design interstorey drift, evaluated as the difference of the average lateral

displacements ds at the top and bottom of the storey under consideration and calculated in

accordance with EN1993-1-1,cl.4.3.4.

d! =d!.!"# − d!.!"#

2

11.3 Calculation of second order effect using ETABS

3. ETABS: Run the model

4. ETABS: Display > Show tables

Select the design combinations

Static load case combination (include wind load)

STATIC 2. 1.35DL + 1.5LL + 0.75WINDX STATIC 3. 1.35DL + 1.5LL - 0.75WINDX STATIC 4. 1.35DL + 1.5LL + 0.75WINDY STATIC 5. 1.35DL + 1.5LL - 0.75WINDY STATIC 6. 1.35DL + 1.5WINDX + 1.05LL STATIC 7. 1.35DL - 1.5WINDX – 1.05LL STATIC 8. 1.35DL + 1.5WINDY + 1.05LL STATIC 9. 1.35DL - 1.5WINDY – 1.05LL

Seismic load case combination


Figure 11.1: Displacement due to lateral load

11.3.1 Interstorey drift displacement

For floor with the non use of diaphragm, the maximum displacement can be found in this table

For floor with the use of diaphragm, the maximum displacement can be found in this table

Table 11.2: Displacement due to lateral load

Storey no. Max Displacement at X Max Displacement at Y

Storey 3

Storey 2

Storey 1

Sort smallest to largest in order to find the maximum displacement

or Sort largest to smallest in order to find the maximum displacement

Consider the maximum value

Do this process for all storeys separately as

showing below

Table 11.3: Drift displacement

Storey

Displacement Direction x

dx.e (mm)

Displacement Direction y

dy.e (mm)

Behaviour factor q

Displacement dsx (mm)

cl.4.4.2.2

Displacement dsy (mm)

cl.4.4.2.2

Interstorey drift drx (mm)

Interstorey drift dry (mm)

Storey 3 11.742 11.7452 4 46.968 46.9808 6.7754 6.7776

Storey 2 8.3543 8.3564 4 33.4172 33.4256 9.0274 9.0296

Storey 1 3.8406 3.8416 4 15.3624 15.3664 7.6812 7.6832

d!" = q ∗ d!"

d!" = q ∗ d!" d!" =

d!".!"# − d!".!"#2

d!" =d!".!"# − d!".!"#

2

11.3.2 Total gravity load Ptot



Static load case combination

STATIC 10. DL + 0.3LL

Export the results in Excel sheet

Filter the value of the bottom storey

Story Load Loc P

STORY3 STATIC10 Bottom 1402.76 STORY2 STATIC10 Bottom 2804.93 STORY1 STATIC10 Bottom 4207.11

11.3.2 Total seismic storey shear Vtot


Record the total gravity load (G+ψEiQ) of each storey


Seismic load case combination


Export the results in Excel sheet

Sort smallest to largest in order to find the maximum shear force

or Sort largest to smallest in order to find the maximum shear force Consider the worst load

combination

Do this process for all storeys separately as

showing below

Story Load Loc P VX

STORY1 SEISMIC1 MAX Bottom 4207.11 663.91 STORY2 SEISMIC1 MAX Bottom 2804.93 550.8 STORY3 SEISMIC1 MAX Bottom 1402.76 330

Repeat the above procedure in order to obtain the Vtot at Y-direction

Story Load Loc P VY

STORY1 SEISMIC5 MAX Bottom 4207.11 663.91 STORY2 SEISMIC5 MAX Bottom 2804.93 550.8 STORY3 SEISMIC5 MAX Bottom 1402.76 330

Filter the value of the bottom storey

Filter the values using the worst case combination

Record the total seismic shear of each storey for Vtot at X-direction

Table 11.4: Second order effects check (EN1993-1-1,cl.4.4.2.2(2))

Storey


dx.e (mm)


dy.e (mm)

Behaviour factor q


cl.4.4.2.2


cl.4.4.2.2



Storey 3 11.742 11.7452 4 46.968 46.9808 6.7754 6.7776

Storey 2 8.3543 8.3564 4 33.4172 33.4256 9.0274 9.0296

Storey 1 3.8406 3.8416 4 15.3624 15.3664 7.6812 7.6832

Total gravity load

Ptot (kN)

Total seismic

storey shear Vtotx (kN)

Total seismic

storey shear Vtoty (kN)

Height of each storey (mm)

Interstorey drift sensitivity coefficient θ

at X direction

Interstorey drift sensitivity coefficient θ

at Y direction

663.91 663.91 663.91 3000 OK OK

550.8 550.8 550.8 3000 OK OK

330 330 330 3000 OK OK

Θ =P!"! ∙ d!"V!"!# ∙ h

≤ 0.10 Θ =P!"! ∙ d!"V!"!# ∙ h

≤ 0.10

12.0 Damage limitation according to EN1998-1-1,cl.4.4.3

The “damage limitation requirement” is considered to have been satisfied, if, under a seismic

action having a larger probability of occurrence than the design seismic action corresponding

to the “no-collapse requirement” in accordance with 2.1(1)P and 3.2.1(3), the interstorey

drifts are limited in accordance with 4.4.3.2.

The damage limitation requirements should be verified in terms of the interstorey drift (dr)

(EN 1998-1-1,cl.4.4.3.2) using the equation below:

d! ∙ v ≤ 0.005 ∙ h

dr: is the difference of the average lateral displacement ds in CM at the top and bottom of storey.

v: is the reduction factor which takes into account the lower return period of the seismic action.

h: is the storey height

Table 12.1: Damage limitation (EN1998-1-1,cl.4.4.3)

For non-structural elements of brittle material attached to the structure drv≤0.005h

For building having ductile non structural elements drv≤0.0075h

For building having non-structural elements fixed in a way so as not to

interfere with structural deformation drv≤0.010h

Table 12.2: Reduction factor of limitation to interstorey drift (CYA NA EN1998-1-

1,cl.NA.2.15)

Importance class Reduction factor v

I 0.5

II 0.5

III 0.4

IV 0.4

12.1 Calculation of damage limitation

Table 12.3: Interstorey drift (see table 11.3)

Storey


dx.e (mm)


dy.e (mm)

Behaviour factor q


cl.4.4.2.2


cl.4.4.2.2



Storey 3 11.742 11.7452 4 46.968 46.9808 6.7754 6.7776

Storey 2 8.3543 8.3564 4 33.4172 33.4256 9.0274 9.0296

Storey 1 3.8406 3.8416 4 15.3624 15.3664 7.6812 7.6832

Reduction factor

v cl.4.4.3.2(2)

Heigh of each storey (mm)

Damage limitation check

X-‐direction

Damage limitation check

Y-‐direction

0.4 3000 OK OK

0.4 3000 OK OK

0.4 3000 OK OK

d! ∙ v ≤ 0.005 ∙ h d! ∙ v ≤ 0.005 ∙ h

ANNEX - A

ANNEX A.1 - Assumptions made in the design algorithm (Manual of ETABS – EC3 &

EC8)

1. Load combination

• The automated load combinations are based on the STR ultimate limit states and the

characteristic serviceability limit states.

2. Axial force check

• Tubular sections are assumed to be hot finished for selecting the appropriate buckling

curve from EC3 Table 6.2. This is non conservative if cold formed sections are used.

3. Bending moment check

• The load is assumed to be applied at the shear center for the calculation of the elastic

critical moment.

• Any eccentric moment due to load applied at other locations is not automatically

accounted for.

4. Shear Force Check

• Plastic design is assumed such that Vc,Rd is calculated in accordance with EC3

6.2.6(2).

• The shear area, Av is taken from the input frame section property, rather than using

the equations defined in EC3 6.2.6(3).

• Transverse stiffeners exist only at the supports and create a non-rigid end post for the

shear buckling check. No intermediate stiffeners are considered.

• The contribution from the flanges is conservatively ignored for the shear buckling

capacity.

5. Combined Forces Check

• The interaction of bending and axial force is checked in accordance with EC3

6.2.1(7), which may be conservative compared to EC3 6.2.9.

• The calculation of the equivalent uniform moment factors, Cm, assumes uniform

loading, which is conservative.

A1.1:Limitation made in the design algorithm (Manual of ETABS – EC3&EC8)

6. General

• Class 4 sections are not designed (EC3 5.5) and should be considered using other

methods.

• The effects of torsion are not considered in the design (EC3 6.2.7) and should be

considered using other methods.

7. Axial Force Check

• The net area is not determined automatically. This can be specified on a member-by-

member basis using the Net Area to Total Area Ratio overwrite.

• The axial buckling check does not consider torsional or torsional-flexural buckling.

8. Combined Forces Check

• The effect of high shear is checked only for Class 1 or 2 I-sections when combined

with bending. Other section shapes and classes require independent checks to be

carried out.

ANNEX –B: Steel design flowcharts

w1 = Initial part of the deflection under permanent loads wc = Precamber in the unloaded structural member w2 = due to Permanent load w3 = due to Variable load

STEEL MEMBERS

(CYS NA EN1993-1-1,table NA.1) Vertical deflection Limits

wmax Cantilevers L/180

Beams carrying plaster or other brittle finish L/360 Other beams (except purlin and sheeting rails) L/250 Purlins and sheeting rails To suit

cladding General use L/300

Vertical deflection (EN1993-1-1,cl.7.2.1)

BASIS OF STRUCTURAL DESIGN (EN1990:2002)

u = Overall horizontal displacement over the building height H

ui = Horizontal displacement over height Hi


Horizontal deflection Limits wmax

Top of columns in single storey buildings, exept portal frames H/300

Columns in portal frame buildings, not supporting crane runways To suit cladding

In each storey of the building with more than one storey Storey height/300

On the multi-storey building as a whole Building height/500

Horizontal deflection (EN1993-1-1,cl.7.2.2)


Design situation Limits natural frequency

Floors over which people walk regularly 5Hz

Floor which is jumped or danced on in a rhythmical manner 9Hz

Dynamic effects (vibration of floors) (EN1993-1-1,cl.7.2.3)

Effective length (Design Guidance of EC3)

Figure 1: Effective length columns (Design Guidance of EC3)

End restraints Fixed/Fixed Partial restrain

in direction Pined/Fixed Pinned/Pined

Free in

position/Fixed Free/Fixed

Effective length

factor, ky,z 0.7L 0.85L 0.85L 1.0L 1.2L 2.0L

𝑀!.!" =𝑊!",!𝑓!𝛾!!

𝑀!.!" =𝑊!",!"#𝑓!𝛾!!

Bending resistance (EN1993-1-1,cl. 6.2.5)

Class 1 or 2 Class 3

𝑴𝑬𝒅 ≤ 𝑴𝒄.𝑹𝒅

Compression resistance (EN1993-1-1,cl. 6.2.4)

Class 1 or 2and3

𝛮!.!" =𝛢𝑓!𝛾!!

𝑵𝑬𝒅 ≤ 𝑵𝒄,𝑹𝒅

Fastener holes in tension flange may be ignored if:

𝑨𝒇,𝒏𝒆𝒕𝟎.𝟗𝒇𝒖/𝜸𝑴𝟐 ≥ 𝑨𝒇𝒇𝒚/𝜸𝑴𝟎

Shear resistance (EN1993-1-1,cl. 6.2.6)

Rolled I and H sections

(load parallel to web)

CHS

𝐴! = 𝐴 − 2𝑏𝑡! + 𝑡! + 2𝑟 𝑡!

𝐴! = 2𝐴/𝜋

RHS

𝐴! = 𝐴ℎ/(𝑏 +ℎ)Load parallel to

depth

𝐴! = 𝐴𝑏/(𝑏 +ℎ)Load parallel to

width

𝑽𝑬𝒅 ≤ 𝑽𝒄,𝑹𝒅

𝐴! = ℎ! ∙ 𝑡!

𝐴!/𝐴! ≥ 0.6

𝜏!" =𝑉!"𝐴!

𝑉!,!" =𝜏!"

𝑓!/( 3𝛾!!)

Elastic design

𝑽𝑬𝒅𝑽𝒄.𝑹𝒅

≤ 𝟏.𝟎

Plastic design

𝑉!".!" =𝐴!(𝑓!/ 3)

𝛾!!

Rolled C channel sections

(load parallel to web)

but ≥𝜂ℎ!𝑡!

𝜂= 1.0 (conservative

value)

Ignore Shear buckling resistance for webs without intermediate stiffeners

𝒉𝒘𝒕𝒘

> 72𝜺𝜼

Combine Bending and shear (EN1993-1-1,cl. 6.2.8)

Shear design resistance NO

Reduction of resistances

(effect on Mc,Rd)

YES NO Reduction of

resistances (no effect on Mc,Rd)

𝑉!" ≤ 0.5 ∙ 𝑉!".!"

𝜌 = 1 −2𝑉!"𝑉!",!"

− 1!

𝑉!".!" =𝐴!(𝑓!/ 3)

𝛾!!

𝑓!" = 1 − 𝜌 𝑓!

Reduced design plastic resistance moment

𝐴! = ℎ!𝑡!

𝑴𝒚.𝑽,𝑹𝒅 =(𝑾𝒑𝒍,𝒚 −

𝝆𝑨𝒘𝟐

𝟒𝒕𝒘)𝒇𝒚

𝜸𝑴𝟎 ≤ 𝑴𝒚,𝒄,𝑹𝒅

If torsion present:

𝜌 = 1 −2𝑉!"𝑉!",!,!"

− 1!

For an I and H sections

𝑉!",!,!" = 1 −𝜏!,!"

1.25 𝑓!/ 3 /𝛾!!𝑉!",!"

Bending & Axial force (EN1993-1-1,cl. 6.2.9)

Doubly symmetrical I and H sections

Z-Z axis

Doubly symmetrical I and H sections

Y-Y axis

𝑁!" ≤0.5 ∙ ℎ! ∙ 𝑡! ∙ 𝑓!

𝛾!!

𝑁!" ≤ 0.25𝑁!".!"

𝑀!,!,!" = 𝑀!",!,!"(1 − 𝑛)/(1 − 0,5𝑎)

MN,y,Rd≤ Mpl,y,Rd

𝑛 =𝑁!"𝑁!",!"

𝑎 =𝐴 − 2𝑏𝑡!

𝐴≤ 0,5

𝑁!" ≤ℎ! ∙ 𝑡! ∙ 𝑓!

𝛾!!

𝑛 =𝑁!"𝑁!",!"

𝑎 =𝐴 − 2𝑏𝑡!

𝐴≤ 0,5

𝑀!,!,!" = 𝑀!",!,!" 1 −𝑛 − 𝑎1 − 𝑎

!

𝑛 > 𝑎

𝑀!,!,!" = 𝑀!",!,!"

𝑛 < 𝑎

NO YES

Ignored axial force

Consider axial force

NO YES

Ignored axial force


Class 1 or 2

𝑵𝑬𝒅

𝑵𝑹𝒅+𝑴𝒚,𝑬𝒅

𝑴𝒚,𝑹𝒅+𝑴𝒛,𝑬𝒅

𝑴𝒛,𝑹𝒅≤ 𝟏.𝟎

For RHS Y-Y axis Z-Z axis

𝑁!" ≤ℎ! ∙ 𝑡! ∙ 𝑓!

𝛾!!

NO YES

Ignored axial force


Hollow section Welded box section

𝑎! = (𝐴 − 2𝑏𝑡)/𝐴) ≤ 0.5

𝑎! = (𝐴 − 2ℎ𝑡)/𝐴) ≤ 0.5

𝑎! = (𝐴 − 2𝑏𝑡!)/𝐴) ≤ 0.5

𝑎! = (𝐴 − 2ℎ𝑡!)/𝐴) ≤ 0.5

𝑀!,!,!" =𝑀!",!,!" 1 − 𝑛1 − 0.5𝑎!

≤ 𝑀!",!,!"

𝑀!,!,!" =𝑀!",!,!" 1 − 𝑛1 − 0.5𝑎!

≤ 𝑀!",!,!"

Bending & Axial force (EN1993-1-1,cl. 6.2.9)

Class 1 or 2

𝑴𝒚,𝑬𝒅

𝑴𝑵,𝒚,𝑹𝒅

𝒂

+𝑴𝒛,𝑬𝒅

𝑴𝑵,𝒛,𝑹𝒅

𝜷

≤ 𝟏.𝟎

I and H section CHS RHS

𝑎 = 2 𝛽 = 5𝑛 ≥ 1

𝑛 = 𝑁!"/𝑁!",!"

𝑎 = 2 𝛽 = 5𝑛 ≥ 1

𝑛 = 𝑁!"/𝑁!",!"

𝑎 = 𝛽 =1.66

1 − 1.13𝑛!

but𝑎 = 𝛽 ≤ 6

Buckling resistance in compression (EN1993-1-1,cl. 6.3.1.1)

𝑁!,!" =𝜒𝐴𝑓!𝛾!!)

Class 1 or 2and3

𝑵𝑬𝒅 ≤ 𝑵𝒃,𝑹𝒅

Φ = 0,5 1 + 𝑎 𝜆 − 0,2 + 𝜆!

λ =𝐴𝑓!𝑁!"

Buckling curve ao a b c d Imperfection factor a 0,13 0,21 0,34 0,49 0,76

χ =1

Φ + Φ! − λ!≤ 𝜒 ≤ 1,0

Slenderness for flexural buckling

𝑁!" =!!!"!!

for ideal strut

Cross-section Limits Buckling about axis

Buckling curve

Rolled I sections

h/b>1.2 tf≤40mm y-y a

z-z b

40mm<tf≤100mm y-y b z-z c

h/b≤1.2 tf≤ 100mm y-y b

z-z c

tf> 100mm y-y d z-z d

U-T and solid section any C L-sections any b

Hollow sections

Hot finished any a Cold formed any c

𝜆 ≤ 0.2 𝑁!"/𝑁!" ≤ 0.04

NO (consider buckling effects)

YES (ignored buckling effects)

Buckling resistance in bending (EN1993-1-1,cl. 6.3.2)

𝑀!,!" =𝜒!"𝑊!𝑓!𝛾!!

Class 1 or 2and3

𝑴𝑬𝒅

𝑴𝒃.𝑹𝒅≤ 𝟏.𝟎

λ!" =𝑊!𝑓!𝑀!"

Slenderness for flexural buckling

λ! = 𝜋𝐸𝑓!= 93,9𝜀 𝜀 =

235𝑓!

Class 1 or 2 Class 3

Wy=Wpl,y Wy=Wel,y

χ!" =1

Φ!" + Φ!"! − λ!"

!≤ 𝜒!" ≤ 1,0

Φ!" = 0,5 1 + 𝑎!" 𝜆!" − 0,2 + 𝜆!"!

Buckling curve a b c d Imperfection factor aLT 0,21 0,34 0,49 0,76

Cross-section Limits Buckling curve

Rolled I-sections h/b≤2 h/b>2

a b

Welded I-sections h/b≤2 h/b>2

c d

Other cross-sections - d

See following pages for calculation of Mcr and λL

Calculation process of Mcr (www.access-steel.com - Document SN003a&b)

𝛭!" = 𝐶!𝜋!𝐸𝐼!(𝑘𝐿!")!

𝑘𝑘!

! 𝐼!𝐼!+(𝑘𝐿!")!𝐺𝐼!𝜋!𝐸𝐼!

+ 𝐶!𝑧!!− 𝐶!𝑧!

Step 1: Define the properties of member Term Description Values

L Distance between point of lateral restraint

Lcr=kl

E Young’s modulus 210000 N/mm2

G Shear modulus 80770 N/mm2

Iz Second moment of area about the weak axis

From section table

It Torsion constant Iw Warping constant k Effective length factor 1.0 unless justified otherwise kw Factor for end warping 1.0 unless justified otherwise zg Distance between the point of

load application and the shear centre

+/-(h/2) or 0 if the load is applied through the shear

centre

Step 2: Calculate the coefficient C1 and C2

Loading and support conditions

C 2 Ψ=M1/M2 C1

Pinned UDL 0,454 1.00 1,00 Fixed UDL 1,554 0.75 1.14

Pinned central P 0,630 0.50 1,31 Fixed central P 1,645 0.25 1,62

0 1,77 -0.25 2,05 -0.50 2,33 -0.75 2,57 -1.00 2,55

Pinned UDL 1,127 Pinned, central P 1,348

𝛭!" =𝜋!𝐸𝐼!𝐿!"!

𝐼!𝐼!+𝐿!"!𝐺𝐼!𝜋!𝐸𝐼!

!.!

Point of application of the load is through the shear centre

YES zg=0

NO zg

Alternative method to calculate the Mcr and λLT

𝝀𝑳𝑻 =𝟏𝑪𝟏𝑼𝑽𝝀𝒛 𝜷𝒘

Non-dimensional slenderness

Simply supported rolled I, H and C section

!!!= 1.0(conservative value)

𝑈 = 0.9(conservative value)

𝑉 = 1.0 (conservative value)

𝜆! =𝑘𝐿𝑖!

K=1.0 for beams k=1.0 for free cantilever k=0.9 for lateral restraint to top flange k=0.8 for torsional restraint k=0.7 for lateral and torsional restraint

βw = 1.0 (conservative value)

Member combined bending and axial compression (EN1993-1-1,cl. 6.3.3)

𝑵𝑬𝒅𝝌𝒚𝑵𝑹𝒌𝜸𝑴𝟏

+ 𝒌𝒚𝒚𝑴𝒚,𝑬𝒅

𝝌𝑳𝑻𝑴𝒚,𝑹𝒌

𝜸𝑴𝟏

+ 𝒌𝒚𝒛𝑴𝒛,𝑬𝒅𝑴𝒛,𝑹𝒌𝜸𝑴𝟏

≤ 𝟏.𝟎

𝑵𝑬𝒅𝝌𝒛𝑵𝑹𝒌𝜸𝑴𝟏

+ 𝒌𝒛𝒚𝑴𝒚,𝑬𝒅

𝝌𝑳𝑻𝑴𝒚,𝑹𝒌

𝜸𝑴𝟏

+ 𝒌𝒛𝒛𝑴𝒛,𝑬𝒅𝑴𝒛,𝑹𝒌𝜸𝑴𝟏

≤ 𝟏.𝟎

Class 1 and 2 Class 3

Method 2:Interaction factor kij for members not susceptible to torsional deformations (Recommended by CYS NA EN 1993-1-1,cl.NA2.20 – Table B.1)

Interaction factors Type of sections Plastic cross-sectional properties

Class 1 and 2 Elastic cross-sectional properties

Class 3

kyy I-sections

RHS-sections

𝑪𝒎𝒚 𝟏 + 𝝀𝒚 − 𝟎.𝟐𝑵𝑬𝒅

𝝌𝒚𝑵𝑹𝒌/𝜸𝑴𝟏

≤ 𝑪𝒎𝒚 𝟏 + 𝟎.𝟖𝑵𝑬𝒅


𝑪𝒎𝒚 𝟏 + 𝟎.𝟔𝝀𝒚𝑵𝑬𝒅


≤ 𝑪𝒎𝒚 𝟏 + 𝟎.𝟔𝑵𝑬𝒅


kyz I-sections

RHS-sections 0.6kzz kzz

kzy I-sections

RHS-sections 0.6kyy 0.8kyy

kzz

I-sections

𝑪𝒎𝒛 𝟏 + 𝟐𝝀𝒛 − 𝟎.𝟔𝑵𝑬𝒅

𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏

≤ 𝑪𝒎𝒚 𝟏 + 𝟏.𝟏𝟒𝑵𝑬𝒅


𝑪𝒎𝒛 𝟏 + 𝟎.𝟔𝝀𝒛𝑵𝑬𝒅


≤ 𝑪𝒎𝒚 𝟏 + 𝟎.𝟔𝑵𝑬𝒅


RHS-sections

𝑪𝒎𝒛 𝟏 + 𝝀𝒛 − 𝟎.𝟐𝑵𝑬𝒅


≤ 𝑪𝒎𝒛 𝟏 + 𝟎.𝟖𝑵𝑬𝒅


Method 2:Interaction factor kij for members susceptible to torsional deformations (Recommended by CYS NA EN 1993-1-1,cl.NA2.20 – Table B.2)

Interaction factors

Plastic cross-sectional properties Class 1 and 2

Elastic cross-sectional properties Class 3

kyy Kyy from Table B.1 Kyy from Table B.1 kyz Kyz from Table B.1 Kyz from Table B.1

kzz

𝟏 −𝟎.𝟏𝝀𝒛

𝑪𝒎𝑳𝑻 − 𝟎.𝟐𝟓𝑵𝑬𝒅


≥ 𝟏 −𝟎.𝟏



for𝜆! < 0.4:

𝒌𝒛𝒚 = 𝟎.𝟔 + 𝝀𝒛

≤ 𝟏 −𝟎.𝟏𝝀𝒛



𝟏 −𝟎.𝟎𝟓𝝀𝒛



≥ 𝟏 −𝟎.𝟎𝟓



Summary design of steel member in bending

Choose yield strength of section, fy from table 3.1 in

EN 1993-1-1

Get starinε from table 5.2 in EN 1993-1-1

Substitute the value of εinto the class limits in table 5.2 to

work out the class of the flange and web

Take the latest favourable class from the flange outstand,

web in bending and web in compression results

Use the required value of W for the defined class to work

out Mc,Rd

Cross-section Resistance check

Design step Results

fy

ε

Flange Class

Web class

Overall Section Class

Mc,Rd

Steel grade

fy (N/mm2)

Nominal thickness of element t (mm) t≤16 16≤t≤40 40≤t≤63 63≤t≤80

S275 275 265 255 245 S355 355 345 335 325

𝜀 =235𝑓!

fy 235 275 355 420 ε 1.00 0.92 0.81 0.75

Flange under compression: c=(b-tw-2r)/2 c/tf

Web under pure bending: c=(h-2tf-2r) c/tw

Mc,Rd = Mpl,Rd = Wpl,yfy/γM0 Class 1 & 2 Mc,Rd = Mel,Rd = Wel,minfy/γM0 Class 3 Mc,Rd = Weff,minfy/γM0 Class 4

Class 1 or 2 Class 3 Class 4

Summary design of steel member in shear

Calculate the shear area of the section, Av

Calculate the design plastic shear resistance, Vpl,Rd

Shear resistance check

Design step Results

Av

Vpl,Rd

VEd≤Vc,Rd

Steel grade

fy (N/mm2)

Nominal thickness of element t (mm) t≤16 16≤t≤40 40≤t≤63 63≤t≤80

S275 275 265 255 245 S355 355 345 335 325

𝑉!".!" =𝐴!(𝑓!/ 3)

𝛾!!

Summary of buckling resistance in bending

Calculate the design bending moment and shear


Design step Results

MEd &VEd

Wy&fy

Calculate critical length Lcr

Calculate Critical moment Mcr

Calculate non-dimensional slenderness λLT

λLT

Calculate imperfection factor αLT

αLT

Calculate reduction factor φLT

φLT

Calculate modified/reduction factor for lateral-torsional

buckling χLTorχLT,mod

χLTχLT,mod

Buckling resistance check 𝑴𝑬𝒅

𝑴𝒃,𝑹𝒅≤ 𝟏.𝟎

Calculate buckling resistance Mb,Rd

Mb,Rd

ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8

Design

Transcript of ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8