Lecture 4

STEEL INDUSTRIAL BUILDINGS

C.T

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dc

dd

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KK

KMM

KK

KMM

;

111 hMI N

i

M

iii IIII 0

DESIGN OF THE TRANSVERSAL FRAME

Local effects of the fixing between column and truss: moments in the members of the truss

Hinged connection

Rigid connection

1. STATIC SCHEMES

• Articulated (hinged) connection between the truss and the column

• Rigid (fully restraint) connection between the truss and the column

Left- Static scheme and rigidities (Ir, I -second moment area of the truss and of the column with constant cross section); Right- Transversal frames carrying crane girders ( Is, Ii - second moment areas of the top and bottom part of the columns)

Models of the frame geometry for rigid connection between the column and the truss

Effect of redundancy (rigid connection): a)- the column on the truss; b) the truss on the column; c) bending moment effects upon the chords of the truss

Type of structure Ii/Is Ii1/Ii Is1/Ii

Equal bays 7…10 10…30 1,5…3

Internal bays bigger than marginal bays 20…60 2.5…7

Ratio between the stiffness of the current columns of the transversal frames

Stiffness of the elements of the transversal frame

The static computation follows the stages: a)-preliminary design of the cross section of the girder considered simply supported for determining the moment of inertia Ir; b)-preliminary design of the top and bottom part of the stanchion on the basis of a simplified scheme for determining the moments of inertia Is and Ii; c)-static computation of the frame for certain loads in order to determine the maximum sectional efforts.

STIFFNESS OF THE STRUCTURAL ELEMENTS IN THE TRANSVERSAL FRAME

The static computation follows the stages: a)-preliminary design of the cross section of the girder considered simply supported for determining the moment of inertia Ir; b)-preliminary design of the top and bottom part of the stanchion on the basis of a simplified scheme for determining the moments of inertia Is and Ii; c)-static computation of the frame for certain loads in order to determine the maximum sectional efforts.

LOADING SCHEMES ON THE TRANSVERSAL FRAME WITHOUT CRANE GIRDERS

a)-the dead and live loads are always present; b)-only one alternative of each temporary loads presented on the schemes may taken once (for ex. snow on the left side or on the right side of the roof or on the whole roof, and so on); c)-the snow and the maximum temperature effects are not possible together; d)-the action of the force FT is always taken together with the action of the pair of forces R-r (or R-r); the action of the forces R-r may be taken without the action of the force FT; e)-if the seismic load is taken into account then neither the crab effects nor the wind are considered.

RULES FOR COMBINATIONS

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Fundamental group of actions:

ik

1ii0Fk1FminFmaxFFd QQGsauGS

iQ,11Q,1minG,1maxG,13

Accidental group of actions: ik1i

i2k11minmaxAd QQsauGGFS

Rare combinations in limit state of serviceability: ik1i

i2k11minmaxAd QQsauGGFS

Frequent combinations:

ik

1ii0Fk1FminFmaxFFd QQGsauGS

iQ,11Q,1minG,1maxG,13

Quasi-permanent combinations: ik1i

i2minmaxd QsauGGS

Permanent and quasi-permanent actions

a) dead loads transferred from the girder: 2

LqV Hpp

b) weight of the top (Gs) and bottom (Gi) of the column: ii

ss

h150G

h100G

Variable actions

a) snow, transferred from the girder:

ACTIONS, GROUPS OF ACTIONS AND COMBINATIONS

2

LqV Hzz

b) Reactions on the top of the column from wind on the roof, Vv, Hv and on the walls:

c) maximum vertical (R) and horizontal reactions (RF) transferred by the runway system to the columns (determined with the influence lines):

Timin

Timax

LqPr

LqPR icF FR

T'v

'v

Tvv

Lpq

Lpq

LOADING SCHEMES (INTERNAL FORCES AND MOMENTS) FOR DESIGN OF THE COLUMN FOR FRAMES WITH CRANE GIRDERS

M N T N M Tcoresp corespmax max, , ; , ,

Reactions from crane girder on the columns

Simplified schemes for the determinations of sectional efforts on columns

Combinations of the sectional efforts for the design of the columns

1654

321

;;

;;)(

eRMePMePM

ePMeGMeVVVM

sii

sssvzp

eb b

eb

et b

et bi s i

s

p s

i

p is

2 2 2 2; ; ;

11 1 1 0 X P

i

2

1

s

2

1

i

1P

s

1P

11

P11

dsmndsm

dsmMndsmM

X

11P XmMM

if XR

II Stage. Correction of internal forces and moments

3

3

1

33

1i

1

h

EI3

11n

n

h

EI3r

I Stage. Determine the unknown force or translation on the frame considering the joint is blocked:

0RR f

Area moment method applied

irR

i

f

r

R

f1

1111 RR

rXrXX

)dsmndsm(IE

1

dsmIE

1dsm

IE

1ds

IE

mds

IE

m

i

2

1

s

2

1

s

i

2

1

is

2

1

si i

2

1

s s

2

11

)dsmMdsmM(IE

1

dsmMIE

1dsmM

IE

1ds

IE

mMds

IE

mM

i

1P

s

1P

s

i

1P

is

1P

si i

1P

s s

1PP

Static computation of the frame with hinged joint between the column and the rafter

Reactions, bending moments and stiffness to horizontal displacements of columns with variable cross section and hinged connection to the rafter (fixed in foundations)

31

2s

2

1K;

I

In;

h

h

n

11n;

n

11n;

n

11n 4

4

3

3

2

2

2

23K1PX

1PXhM iA

2

20

ih

KM3X

0

iA MhXM

4i phK4

3X

2

phXhM iA

3

3

1ii

1

h

EI3RX

1;hRM iA

n= 0.2 for cranes with small lifting capacity and heavy roofs; n= 0.08 for cranes with heavy lifting capacity and light roofs.

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I. Sizing of the stiffness of the truss

k depends on the slope of the top chord of the girder (k = 0.9 for p = 0% and k = 0.7 for p = 10%).

I k I k A y A yx s s i i ( )2 2

Static computation of the frame with rigid joint between the column and the rafter

11

P11

P11ii

r

r

0rr

Σr11 - the sum of the reactions at the top of the column when 1=1; Σr1P - the sum of the horizontal reactions at the top of the stanchions due to the external loads applied to the column.

II. Area moment applied considering the rafter is infinitely rigid

DETERMINATION OF THE REDUNDANCY EFFECTS UPON TRUSS MEMBERS

N N N

N N N

ik ik ik

I

ik ik ik

I

0

0

( )

( )

max

min

minBikikik

maxBikikik

)T(qN

)T(qN

minmax/Bik

'

B'k'iBik

0

ikik )T(/MMNN

a. Hinged connection

b. Rigid connection

II Stage. Effect of the

redundancy

I Stage. Simply supported truss

1 ,1

1 ikik ik

ik

lN n

E A 2 ,2

1 ikik ik

ik

lN n

E A

,2ikn

ikN

Knowing the values in the restrained joints 1 and 2 and the rotations of the supports for the simple supported truss under external loading the equilibrium equations may be written.

2

1 ,1

1 ikik

ik

ln

E A 2

2 ,2

1 ikik

ik

ln

E A

,1 ,1

1 ikik ik

ik

ln n

E A

I. Rotations in the supports induced by unitary bending moments:

II. Rotations on the supports induced by external actions :

,1ikn internal forces in the members ik when at the extremities 1 and 2 unitary bending moments are acting

internal forces in the members ik undder external actions

The stiffness of the members k1 and k2 and the coefficients of transmission in the static computation, k12 and k21

21 2

1 2

k

12 2

1 2

k

12

2

k

21

1

k

c. Particular situation – uneven restraining conditions

Design of the connection between the column and the roof truss

b,c

2

v

2

h

1

v

1

2

i

maxih

11

NNNR

n

VN;

n

HT

y

yMN

eVeHTM

0

1

1

M

y2

shear

2

tech

angle

vp2

vt

2

ht2

0

ht

2

v

2

2

i

max2h

22

f3

td

N;

4

d

N

4

d

N;

4

d

N

n2

VN;

n2

HT

h2

hMN

eVeHTM

M1=(H+T)e +Ve2

M2=(H+T)e - Ve1 M1=(H+T)e