CIV3221 Building Structures & Technology

CIV3221 – Building Structures & Technology

Table of Contents 1. Floor Framing System.................................................................................................................................................... 3

1.1 Introduction to Floor Framing Systems .................................................................................................................. 3

1.2 Types of Floor Systems............................................................................................................................................ 4

1.2.1 One-way Spanning Slabs .................................................................................................................................. 4

1.2.2 Two-way Spanning Slabs .................................................................................................................................. 5

1.2.3 Beams for one & two-way spanning slabs ....................................................................................................... 5

1.2.4 Flat Slabs .......................................................................................................................................................... 6

1.3 Prestressed Concrete .............................................................................................................................................. 6

2. Facade ........................................................................................................................................................................... 7

2.1 Introduction ...................................................................................................................................................... 7

2.1.1 Classifying Facades ........................................................................................................................................... 7

2.2 Common Issues ................................................................................................................................................. 8

3. Load Paths ................................................................................................................................................................... 10

3.1 Types of Design Problems ..................................................................................................................................... 10

3.2 Load Paths in Multi-Storey Structures .................................................................................................................. 10

3.3 Frames ................................................................................................................................................................... 10

3.3.1 Stability in Frames .......................................................................................................................................... 12

4. Loading (Wind & Earthquake) ..................................................................................................................................... 13

4.1 Limit State Design ................................................................................................................................................. 13

4.2 Load Combinations ............................................................................................................................................... 14

4.3 Dead Load (G) ........................................................................................................................................................ 16

4.4 Live Load (Q) ......................................................................................................................................................... 16

4.5 Wind Load (W) ...................................................................................................................................................... 17

4.5.1 Design Wind Action ........................................................................................................................................ 18

4.6 Earthquake Load (E) .............................................................................................................................................. 21

4.6.1 Static Earthquake Design ............................................................................................................................... 22

4.6.2 Static Analysis ................................................................................................................................................. 24

4.6.2 Earthquake Loading Summary ....................................................................................................................... 27

5. Limit State Design and Methods of Analysis ............................................................................................................... 28

5.1 Concept of Limit State Design ......................................................................................................................... 28

5.2 Methods of Analysis .............................................................................................................................................. 29

5.3 Second Order Effects............................................................................................................................................. 30

6. Moment Distribution Method (MDM) ........................................................................................................................ 33

6.1 Background ........................................................................................................................................................... 33

6.2 Main Concepts of MDM ........................................................................................................................................ 35

6.3 MDM iterative Procedure ..................................................................................................................................... 38

6.4 MDM Summary ..................................................................................................................................................... 39

7. Slab Design .................................................................................................................................................................. 40

7.1 General Slab Design .............................................................................................................................................. 40

7.2 RC Floor Slabs ........................................................................................................................................................ 41

7.3 Composite Floor Slabs ........................................................................................................................................... 44

7.3.1 Design Summary for composite floor slabs ................................................................................................... 46

8. Composite Beam Design ............................................................................................................................................. 47

8.1 Introduction .......................................................................................................................................................... 47

8.2 Shear (fvs) ............................................................................................................................................................... 48

8.3 Design Issues ......................................................................................................................................................... 49

CIV3221: Building Structures & Technology

8.3.1 Effective width of Composite Slab (bcf) .......................................................................................................... 49

8.3.2 Design of Shear Connection ........................................................................................................................... 50

8.3.3 Ultimate Strength of the Cross Section .......................................................................................................... 51

8.4 Design Summary for a Composite Beam .............................................................................................................. 52

9. Steel Beams ................................................................................................................................................................. 54

9.1 Potential Failure Modes ........................................................................................................................................ 54

9.2 Limit State Design (ULS) ........................................................................................................................................ 55

9.3 Section Capacity (Ms) ............................................................................................................................................ 56

9.4 Member Capacity (Mb) .......................................................................................................................................... 57

9.5 Steel Beam Design Summary ................................................................................................................................ 60

10. Steel Columns............................................................................................................................................................ 61

10.1 Potential Failure Modes ...................................................................................................................................... 61

10.2 Limit State Design ............................................................................................................................................... 61

10.3 Section Capacity (Ns) ........................................................................................................................................... 62

10.4 Member Capacity (φNc) ...................................................................................................................................... 63

11. Steel Beam-Columns ................................................................................................................................................. 64

11.1 Combined Actions ............................................................................................................................................... 64

11.2 Section Capacity .................................................................................................................................................. 65

11.3 Member Capacity ................................................................................................................................................ 66

11.4 Design of beam-column summary ...................................................................................................................... 68

11.5 Interaction diagram ............................................................................................................................................ 69

12. Steel Connections ..................................................................................................................................................... 70

12.1 Types of Connections ...................................................................................................................................... 70

12.2 Moment Connections (bolted end plate) ........................................................................................................... 70

12.2.1 Actions for design of each components ....................................................................................................... 71

12.2.2 Design Capacities .................................................................................................................................... 72

12.3 Steel connection summary ................................................................................................................................. 74

13. Footing Design .......................................................................................................................................................... 75

13.1 Introduction ........................................................................................................................................................ 75

13.2 Isolated Pad Footings .......................................................................................................................................... 76

13.3 Isolated Pad Footings Design Summary .............................................................................................................. 80

CIV3221: Building Structures & Technology Page 4

1.2 Types of Floor Systems

We can classify floor systems in different ways: 1) By material:

floor slab – concrete beams – concrete or steel

2) By structural action of the slab one way spanning slab two way spanning slab flat slab

3) By method of construction steel beams with cast-in-situ slab steel beams with precast slab cast-in-situ concrete beams with cast-in-situ slab precast beams with precast slab

The following sections provide ‘rules-of- thumb’ for preliminary sizing of slabs and beams (use ratios to make realistic/conceptual designs) The thickness of the slab, or the depth of the beam, is given as a span-to-depth ratio, L/d (Note: d = effective thickness or depth (does not include conc cover) D = overall depth (including cover) L = Span (consider if one or two-way spanning) say cover = 40 mm and L/d =30 and slab span = 6 metres, so thickness = 200+40 = 240 mm

1.2.1 One-way Spanning Slabs

The slab spans in one direction between beams or walls

- if slab simply-supported (ie one span only), L/d = 24 - if slab is continuous (ie 2 or more spans), L/d = 28 - if slab has a cantilever span, L/d = 10 - the slab might be cast on metal decking (usually on steel beams)

Note: if slab is supported by beams on 4 edges, but the aspect ratio i.e. 𝑙𝑜𝑛𝑔𝑒𝑟 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ

𝑠ℎ𝑜𝑟𝑡𝑛𝑒𝑟 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ > 2, treat as a one-way slab

Typical Slabs o Primary/Secondary Beams (Composite system)

- slab may span one-way onto secondary beams, which in turn span onto primary beams (load path = slab to secondary beams to primary beam to columns

o Ribbed Slab - If the beams are at very close centres, the floor

system becomes a ribbed slab (ribbed slabs require a lot of labour to build the formwork for the slab)

o Band Beams - Wide and shallow concrete beams support the slab, - Simple formwork, and are economical with labour

o Proprietary Systems - Precast floor systems used w/ one-way slabs - Precast systems are proprietary systems – ie they

are products which you buy from a manufacturer - Precast planks are one proprietary system

(Hollowcore brand) – rectangular planks of concrete laid on steel or precast concrete beams

- Precast T-beams is another proprietary system


1.2.4 Flat Slabs

Flat slabs you do not use beams or walls to support the slab, but instead sit it directly on top of the columns

- No beams ∴ formwork is simple & easy

- Punching Shear failure must be considered, ensure enough slab strength or thickness at the slab/column

junction

- No beams or walls so flat slabs tend to have ↑ deflections

- L/d = 33 (based on longer span)

Main types o Flat Plate

- Completely flat soffit (that is the underside) - Slab thickness is usually determined by need to

avoid punch through at slab/column junction, and then this thickness is used throughout

- Economical on formwork (labour), but expensive on material

o Flat Slab - Thickening at the slab/column junction - Thickening can be in the slab – called a drop panel - Thickening can be at the top of the column – called a

column capital

1.3 Prestressed Concrete

- Prestressing is the practice of placing high tensile wires in the concrete & stretching/tensioning them once the concrete has hardened.

- Prestressed concrete will not be dealt with in this subject, but it is commonly used in floor slabs and beams, and results in thinner slabs and beams and/or longer spans.


2.2 Common Issues

▪ Weatherproofing 1) Impermeable facades i.e glass, plastic, metal sheeting

- do not allow ventilation ∴ can cause condensation problem - require careful detailing at junctions - usually require an extensive framing system

➢ Glass wall systems

- use proprietary components - aluminium sections are complex extruded shapes - curtain walls are large assemblies of glass and infill panels supported by a grid of aluminium members

2) Low permeability facades i.e thick concrete or masonry, or tilt-up precast panels - when wet, water penetrates into the façade by capillary action (moisture in voids) - when dry, water evaporates from the faces as vapour

∴ wall must have sufficient thickness to ensure that the absorbed water can be stored w/ the façade until the wall dries, without reaching the inside face - Acceptable in tropical climates but not reliable in temperate climates - coatings ↓ permeability, or even cavity systems are used in critical applications - Sealings of joints between panels is critical

3) Cavity wall construction - The wall is constructed as two ‘leafs’ with a vertical gap between - Water penetrates through the outer leaf of the wall, and drains down the inside of the outer leaf - ‘Weep holes’ are provided at the base of the cavity to drain the water away - The inside leaf remains dry & the wall allows some ventilation


4.6 Earthquake Load (E)

▪ Introduction to Earthquakes

- Resources: AS 1170.4

- Earthquakes cause several major hazards including building collapse, landslides, fires, tsunamis & volcanoes

- Earthquakes don’t kill people, the buildings that collapse around them do

-

▪ General Design

- Design must consider Strength, Ductility and Cyclic Load Capacity

- Ductile failure is preferred over brittle as max force is reached for large

elongation in ductile behaviour (bar also has residual resistance)

- Want to replicate this behaviour in our structures to w/stand cyclic loading

▪ Strong-Column & Weak-Beam Design

1) Rigid frame structure during earthquake causes plastic hinge to develop at base & first floor

2) Soft floors at base and occurring in middle of building

3) Use plastic hinges in our design, but place them in certain locations (at base of columns)

so the structure is designed to behaviour like sway frame (Better to have plastic hinges in the beams

or in the top floor) ∴ the detailing of connections is important

- Hence to get proper sway behaviour need strong column & weak beam

For earthquake resistance in building design, which

design is better, strong column or strong beam?

Need strong column & weak beam to get proper sway

behaviour preventing Soft floors. Earthquake loads are

transferred to columns so they must remain elastic to

provide strength & stability to the floors above. & use

plastic hinges at column bases


5.2 Methods of Analysis

- This section just covers basic definitions & general concepts for methods of structural analysis

Method of Analysis o 1st Order Elastic Analysis

Assumptions: - Geometry of structure remains unchanged - Material properties remain unchanged - Principle of superposition applies

o 2nd Order Elastic Analysis Assumptions: - Geometry of structure keeps changing (P-∆ and P-δ effects) - Material properties remain unchanged - Principle of superposition doesn’t apply

o Elastic buckling analysis Assumption: - Only P-δ effect is considered - Only elastic buckling load (Nom) is obtained

o 1st Order Plastic Analysis Assumption: - Geometry of structure remains unchanged - Material properties keep changing (from elastic to plastic) (Stress level ↑ w/in section until reach fully plastic section)

- During loading: Plastic hinges (Plastic mechanism)

o Advanced Assumption: - Geometry of structure keeps changing - Material properties keep changing

(Includes residual stresses, geometrical imperfections, erection procedures, interaction w/ foundations etc.)

Method of Analysis Assumptions

Structure Geometry Material Properties Other

1st order Elastic Unchanged Unchanged Superposition principle applies

2nd order Elastic Changes (P-∆ & P-δ effects) Unchanged Superposition doesn’t apply

Elastic Buckling - - Elastic buckling load (Nom) obtained P-δ effect considered

1st order Plastic Unchanged Changes Stress ↑ until Plastic hinges forms & reach fully plastic section

Advanced Analysis Changes Changes Residual stresses, geometrical imperfections, erection procedures, interaction w/ foundations etc.


6.4 MDM Summary

If cantilever; K = 0 & DF =0

If external moment acting; must consider its carry over

General Notes:

- Must use superposition principle for non-typical cases (i.e split up into typical load cases then Σ result)

- For FEM w/ external moments applied; must distribute external moment across joint

- Always finish iterations on a ‘dist’


7. Slab Design

7.1 General Slab Design

Rules of Thumb Review o One-way Slab

- If slab simply-supported (ie one span only), L/d = 24

- If slab is continuous (ie 2 or more spans), L/d = 28

o Two-way Slab

- If the slab is simply-supported (ie one span only), L/d = 28

- If the slab is continuous (ie 2 or more spans), L/d = 39

where L is the shorter span

Notes:

1) If aspect ratio i.e. 𝑙𝑜𝑛𝑔𝑒𝑟 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ

𝑠ℎ𝑜𝑟𝑡𝑒𝑟 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ > 2, treat as a one-way slab

▪ Action

▪ Types (in terms of materials):

- Reinforced Concrete floor slabs i.e one way spanning slab, two way spanning slab in terms of action, recall Week 2

where, top reinf. carries tension introduced by negative BM, bottom reinf. carries compression introduced by positive BM - Composite floor slabs i.e one way slab w/ metal sheeting where, top reinf. carries tension introduced by negative BM, metal sheeting carries compression introduced by positive BM

▪ Capacity

- Think of the slab as a beam w/ width of one meter! (Beam capacity formulations are applicable from CIV2226) - Important considerations for slab design are: Ensure actions > capacity

1) Ultimate limit state – bending (strong enough?)

2) Serviceability limit state – deflection (stiff enough?)

Note: Shear is not usually a problem (ligatures not required)

For slab design we need BMD

- For continuous one-way spanning slab, need to find

BMD from MDM (hand or excel) or use SpaceGass

- Then check range of BM using approximation method

using BM coefficients, for multiple spans w/ simply

supported or fixed support i.e Moment = Coeff *

Fd*Ln2, use 1.2DL+1.5LL (see CIV2226 p.g 5)


7.3.1 Design Summary for composite floor slabs

1) Estimate slab thickness (Dc) - Use rules of thumb, then compare to minimum thickness

Rules of Thumb Review o One-way Slab

- If slab simply-supported (ie one span only), L/d = 24

- If slab is continuous (ie 2 or more spans), L/d = 28

o Two-way Slab

- If the slab is simply-supported (ie one span only), L/d = 28

- If the slab is continuous (ie 2 or more spans), L/d = 39

where L is the shorter span

2) Load calculation (G, Q) G = DL + SIDL = slab thickness * conc. density (25kN/m3)*1m width [kN/m per m width]

Q = LL = x kPa * 1m width [kN/m per m width]

Then factored load for ULS, w = 1.2DL + 1.5LL [kN/m per m width]

3) Design bending moment (structural action) matrix M* = design bending moment [kNm per m width]

Use BM coefficients i.e M* = Fd*Ln2

*coeff. (use appropriate coeff. for simply-supported or continuous)

where Fd = factor load 1.2DL+1.5LL [kNm] & Ln = span length [m]

Or, take critical moment from BMD (must consider 1.2DL+1.5LL)

4) Calculation of Tsh, min of: Must remember these eqns. & also must look up sheeting properties (see page 54)

- For sheeting yield

- For concrete crushing

- For initiation of concrete-sheeting slip

5) Calculate capacity for positive (ultimate) moment (ULS) on the basis of failure condition above: Must remember this eqn.

φMu = Design capacity (φ=0.8 for bending) [kNm] (Note: must be able to derive this eqn. by assuming C=T)

Tsh = tensile force in sheeting [kN]

Dc = overall depth of composite slab (including sheeting thickness) [mm]

ysh = height at which the sheeting tensile force acts above slab bottom [mm]

f’c = characteristic compressive strength of conc at 28 days [MPa]

b = breadth of slab [mm]

6) Calculate capacity for negative moment (ULS, treat as a normal reinforced concrete slab): - Calc the Ast needed on top to resist negative M*

7) Check the Span-to-Depth ratio (SLS, treat as a normal one-way RC slab): - Check Lef/d > assumed L/d to comply (else will have to↑depth or↓span to↑stiffness)

See page 51 for details, assume kcs = 2 for composite slabs (conservative assumption)

Fdef = [kPa] (don’t use kN/m as units are inconsistent for L/d eqn.)


8.4 Design Summary for a Composite Beam

4) Calculate loads & design actions - G = DL = slab thickness (Dc) * conc. density (25kN/m3) + SIDL [kPa]

DL * beam spacing to get kN/m

- Q = LL = Typically given [kPa]

LL * beam spacing to get kN/m

- Then factored load for ULS, w = 1.2DL + 1.5LL

- Calculate design actions (maximum shear & bending)

For s-s: M* = 𝑤𝐿2

8 & V* =

𝑤𝐿

2

5) Estimate steel beam cross section - Composite beams are very efficient bcas of the wide concrete flange, so guess beam depth = span/15 - Dc

(Compared to normal simply supported beam depth as span/12)

> So guess span/15 = x, then estimate depth of steel beam = x – slab thickness (so try a beam w/ a resulting depth greater)

6) Effective width of the slab (bcf) - bcf = min[

𝑠𝑝𝑎𝑛

4, beam spacing, bf + 8*Dc]

where, Dc = depth of slab & bf = breadth of beam flange

7) Design for complete shear connection at mid-span - Assume NA in concrete slab

- Then let Fst = Fcc for force equilibrium & solve for dc

- Check dc (i.e NA must be in slab i.e above ribs)

> For composite slab dc = min(dc , Dc-hr)

i.e take smaller value as actual conc in compression

Note: If calculation shows that dc is not in the slab (above the ribs), ↑ the slab thickness accordingly

8) Check Moment Capacity - Calc φMbc (must remember this eqn.)

- Check capacity > action (φMbc > M*)

9) Design the shear connectors The strength of one stud is the least of:

1) If failure occurs in the steel stud 2) Failure occurs in surrounding conc.

Where, fvs = strength of one stud [N]

dbs = stud diameter [mm]

fuc = characteristic tensile strength of the shear connector material ≈ 500 MPa

f’c = characteristic compressive strength of concrete [MPa]

Ec = elastic modulus of concrete = 𝜌1.5 ∗ 0.043 ∗ √𝑓′𝑐 [MPa] (ρ = density of concrete ≈ 25kN/m3)

Then studs between end & mid-span must carry interface horizontal shear force, F = Fst = Fcc

So no. of studs between cross section & support, the F transferred at that cross section is:

F = horizontal force that can be transferred at that cross section (this must be resisted by the shear studs) [N or kN]

n = no. of studs in range of free end to mid-span

φ = 0.85

fvs = Shear strength of one welded stud shear connector [N]

kn = factor to allow for the reliability of the connection ↑ w/ ↑ no. of studs

➢ To calculate F, firstly assume kn=1,

then calculate n by Eq. (1);

substitute the resulting n into Eq. (2) for kn;

repeat until there is no changes of n or kn


12. Steel Connections

12.1 Types of Connections

1. Flexible Connections = High rotation but low moment capacity

Flexible or pin connection are designed to resist vertical loads like shear

i.e Angle cleat (CIV2225)

2. Rigid Connections = High moment by low rotation capacity

Rigid connections are designed to resist moments & rotation

i.e Bolted moment end plate connection

3. Semi-rigid Connections

12.2 Moment Connections (bolted end plate)

▪ Components & Dimensions

Profile of primary beam is welded to end plate & end plate is bolted to column

▪ Possible failure modes & components (for rigid bolted end plate connections): 1) Flange weld failure – weld size (or called leg length or throat thickness), weld length (i.e. flange width) 2) Web weld failure - weld size (or called leg length or throat thickness), weld length (i.e. web depth) 3) Bolt failure – bolt size, number of bolts (i.e single bolt failure or bolt group) 4) Plate failure in shear – plate thickness, width of plate, depth of plate, bolt hole size, plate yield stress 5) Plate failure in bending – plate thickness, distance between the centre of bolt hole to the top of flange For steel connections we have the following actions:

a) Moment (M*)

b) Shear Force (V*)

c) Axial Force (N*)

▪ Minimum design actions For a guaranteed minimum design capacity w/ some inherent robustness:

1) Bending moment = 0.5 x member (beam) moment capacity

2) Shear force = 40 kN

3) Axial force = 0


12.2.1 Actions for design of each components

▪ Assumptions - Flanges & web transmit a share of the axial force (N*)

- Moment (M*) is transmitted through the flange area (i.e flange carries majority of the moment force)

- Shear force (V*) is transmitted through the web (i.e web carries majority of the shear force)

Actions for design of each component

a) For the flange welds connecting the beam to the end plate:

N*fw = Design axial force on the flange welds [kN] M* & N* = Design moment & axial forces [kNm & kN] kmw = proportion of the bending moment transmitted by the web (see tables below) At = area of tension flange [mm2] A = total area of the section [mm2] db = overall depth of beam [mm] tfb = thickness of beam flange [mm]

b) For the web welds connecting the beam to the end plate: Nw* = Axial force component = kw N* Mw* = Moment component = kmw M* Vw* = Shear force component = V* (this assumes entire shear force is transferred to the web welds) kw = (area of the web) / (total cross-sectional area) kmw = proportion of the bending moment transmitted by the web (see tables above)

c) For the bolts, end plate and stiffeners: i) Total design axial force in tension flange (N*ft): ii) Total design axial force in compression flange (N*fc): iii) Total design shear force at end plate/column interface (V*vc):

Notes:

1) You must remember these Beam-Column Moment Connections Actions for the exam (but not the capacity eqns.)


13.2 Isolated Pad Footings

Isolated column or pad footings can fail in (1) bending, (2) shear, or (3) punching shear

Note: You must remember all action equations for bending, shear & punching shear

1. Flexural Reinforcement

Footings can fail in bending as a wide beam Wide beam acts as cantilever: M* = Design BM at critical cross-section = max BM at end of cantilever = force * lever arm

a) Design BM at critical cross-section (M*):

q = uniformly distribution soil pressure = 1.2𝐷𝐿 + 1.5𝐿𝐿

𝑓𝑜𝑜𝑡𝑖𝑛𝑔 𝑎𝑟𝑒𝑎 =

𝑁∗

𝑋𝑓∗𝑌𝑓 [kPa]

Yf = distance for footing in y direction Xf = distance for footing in x direction Xc = column width in x direction Yc = column width in y direction ∴ (Xf – Xc)/2 = span direction

➢ Note: Must also consider bending in perpendicular direction (i.e consider bending in both directions)

i.e For rectangular beams M*x != M*y

So check wide beam bending of red part & check wide beam bending on blue part, see figure above) Where, red width = Yf & blue width = Xf If footing is square, results are the same (but must check both if rectangular)

b) Ultimate moment capacity (φMu):

φ = capacity reduction factor = 0.8 b*d = area of cross-section [mm2] (not to be confused w/ area the soil pressure acts) Ast = area of steel in the cross-section (in tension??) [mm2]

ρ = Reinf. ratio = 𝐴𝑠𝑡

𝑏∗𝑑

d = depth of steel from top fibre [mm] fsy = cylindrical strength of concrete ≈ 32 MPA

➢ To derive the eqn. for φMu:

To derive, use equivalent stress block theory:

a) Assume C = T to derive eqn.1

b) Take moments about C

i.e Mu = ΣM about C

c) Solve eqn.1 in terms of ku

d) Substitute ku into eqn.1

CIV3221 Building Structures & Technology

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