Steel Work Design 1 Dr Mustafa Batikha Lectures 2010 2011

8/13/2019 Steel Work Design 1 Dr Mustafa Batikha Lectures 2010 2011

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Steel Work design (1) toBS 5950- 1:2000

Dr Mustafa Batikha

The University of Damascus-Syria

References

BS 5950-1(2000). Structural use of steel work in building, Part 1,Code of practice for design rolled and welded section , BSI ,London.

Way, A. G. J. , Salter, P. R. (2003). Introduction to steelworkdesign to BS 5950-1:2000 , the steel construction institute, SCI , UK.

Case, J., Chilver, L., Ross, C.T.F. (1999). Strength of materials andstructures , John Willy & Sons Inc ., fourth edition, London.

McKenzie, W.M.C. (2006). Examples in structural analysis , Taylorand Francis , London.

).2003( .

).2006( . .

Dr Mustafa Batikha Damascus University


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2

Design of Compression Members

)The concept of stress(



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3

)Axial stresses(

topt

t toptop y

I Z

Z M

y I

M :

I M M

)Bending stresses(

bottomb

bbottombottom y Z I

Z : Elastic Section Modulus

I Z

y I

M

max



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F c =F T

= =

Plastic Section Modulus, S

c . c

M p =p y S

)(21

T c y y AS

S: Plastic Modulus

S

Z High Shape Factor

Early Yielding

Permanent Deformation

)The concept of plastic hinge(

M W

LW M p p

4

)1(4

)(

4

4

)(

p

y p

p

p

y p

p p y M

M L L

L

M

L L

M W

L LW M

Z S

f f

L L p :)1

1(

For rectangular section L L f p 31

5.1

For I section of f=1.13 L L f p 12.013.1



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5

Shear( stresses(

b I sV

r M T

S =First moment of area

J =Torsion constant.

Final stresses

Normal stress x I

M y

I M

A N

y

y

x

x

Shear stress

Principal stresses yy xx

xy

22tan



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Principal stresses and the failure

Mohrs circleand cracking

Crack is expected when the principal stresses have reached a critical strength

)The concept of Buckling(

Buckling of columns



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Lateral Torsional buckling of beams

Buckling of Frames

Local Buckling of yielding



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Buckling of plates and shells

Concept of Bifurcation Buckling



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9

Concept of Snap-Through Buckling

)Buckling of an Euler strut(P

yP M .

EI P

K yK y y EI P

y EI M

y 22""" :00

P

kx Bkx A y sincos General solution forthe deflected shape

Using the Boundary Conditions0sin0

sin000

kL B y L x

kx B y A y x

If KL 0 B=0 always y=0 No Buckling wrong assumption KL=0 or KL=n

2

22

2

222222000

L EI n

P EI P

Ln

n Lk nkL y Alwaysk kL E

2

2

1)( L EI

Pnload Criticalload smallest For E



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The concept of restraints

Column types

Horizontal Ties ) 2.4.5.2&2.4.5.3) Figure 1 & Figure 2

,75),(5.0max[ kN Tieonload vertical factored q N uut

4.7.1.2 Compressed N restraint =1% N compression member

4.7.3-a r yr r u S p M M M :%90

No directional restraint 5.0)/12.0( r r N k

N r =3 ](%1 columnedgeof forceecompressiv N uc

Critical buckling load of different deflection modes

2

22

L EI n

Pcr



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Columns under other boundary conditions and the

concept of the effective length

yP M .

PP M 22""" EI EI EI

kx Bkx A y sincos General solution forthe deflected shape

sin000 dy

kx B y A y x

dx

2

22

2

222222

)2(4420cos0,0

L EI n

P EI P

Ln

n Lk nkLkLk B cr

Note: The critical buckling load of a cantilever length L is as the critical loadof simply-supported ends of 2L

The Effective Length, L E

2

22

E

cr L

EI nP

LE=Ke .L



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Major and Minor axis of buckling

2

2

2

22

2

2

2

2

2

22

1

E L Er

A L EI

L

EI Pn

L

EI nP

E E cr

E cr

E cr

2

r sSlendernescr

:2 x y x y I I r r

y is the minor axis x is the major axis

Buckling about y-axis is more critical than buckling about x-axis for thesame length because the smallest radii of gyration is about y

Short ElementIntermediate Element Slender Element

)Buckling of a perfect column(

Intermediate

Slender

r sSlendernes E

2

2

,

E stress Euler E



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Empirical buckling of a perfect column

Rankine formula is the simplest safe empirical formula from test data

Y E F PPP111 P F = the real buckling failure strength

P E = the ideal Euler buckling loadP Y = the squash load Y E

Y E F



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31:111

nor n n

Y n

E

Y E F n

Y

n

E

n

F

For less conservative treatments

The effect of material non-linearity on buckling load

The non-linearity of material causesthe drop in results between Euler theoryand experiment data for intermediatecolumns

Tangent modulus theory is thesimple safe estimate of buckling

strength in Elastic-Plastic region

T cr T E

r L

x positionat sslendernes Modified E

2

2



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)Buckling of a imperfect column(

Perry Formula (1886)

Perr Formula BS 5950-1:2000 Annex C

2

0:))((r

zec E c yc E

2

2

2,

2

)1(:

E E

E y y E c

z: the distance of the extreme fiber from the neutral axis of buckling.r : Radii of gyration



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constant:01000/)(, 0 RobertsonisaaFactor Perry

0 is the limiting slenderness (short column)= 0.2( 2E/p y)0.5



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)Classification of sections(

)3.5.2(

Local Buckling

) / (

Stress distribution

Support conditions

Yield strength

Table 11&12

Element Geometry (b/T, d/t (Figure 5 & 6 :

Stress distribution r 1, r 2: (Section 3.5.5)

Yield strength :

Element Type Outstand element (External : ,(Internal element ( ( (3.5.1)



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Example 1:

S275, UB 45715252, Bending moment only about the major axis

( )

UB 45715252 t=7.6, T=10.9


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Effective section properties

Sections (3.5.6&3.6)

Semi-Compact Slender

S eff

3.5.6

CHS

3.6.6

Aeff , Z eff

Equal-legangle

3.6.4

Aeff , Z eff

section

3.6.2

Pure CompressionPure Bending

Fig. 8-a (A eff )Non-slender web slender web

Fig. 8-b (Z eff ) Fig. 9&Fig.8-b if flange is slender as well (Z eff )

Alternative method ( :(for slender section (3.6.5 ( y yr p p23 )(

Notice: Compression + Bending Compression only (A eff )+ Bending only (Z eff )

Example:

S275, Welded section pure Bending , ,Plastic flange ,slender web

f cw =f tw b eff =60 t=6018=480mm

0.4b eff =192, 0.6b eff =288

Try x=40mm First moment= a i y i 0

Try x=28mm First moment= a i y i 0

I x =95285cm 4 , y max =52cm

Z eff =95285/52=1832cm 3



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Effective length to BS 5950-1:2000

Angle, Channel orT sections

LE (4.7.3)

Simple structures GenerallyContinuousStructures

(4.7.10)

Single angles,Double angles,single channels

or single T-sections

Annex DTable 22

Single Storybuildings (D1)

Figures D1,

Supportinginternal platform

floors (D2)

Annex E

Table 25D2, D3, D4

and D5Table D.1

Notes: (4.7.10.1)Slenderness1.2

Conditions (4.7.13&4.7.9)

50vv

vvc r

L

yy

Eyymccmb r

L :4.122

L

4.7.9

max r

).e.4.7.13.1( .

. 16mm ). f.4.7.13.1(

).g.4.7.13.1( 300mm 32t t

4.7.13 . . . . ..

300mm 16t t )4.7.13.2.b.2(.

0.25Q c:Q=2.5%N cu



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Mohrs Circle

Anticlockwise rotation is positive

In Eqs, I xy is always to beused as positive. The

clockwise rotation is taken

Compressive strength, p c (4.7.5)Perry and Robertson formula (Annex C)

The formula was developed by an assumption that practical imperfections may exist

Note (4.7.5): For Welded section in compression only

Table 23, Figure 14

py= p y(table9)-20



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Compression Design Summary (4.2)

Rolled Section Welded Section

Section classification

py (Table 9)

py py=p y-20

LE

Slender section Non-Slender section

Aeff or p yr L E

g

eff E

A

A

r

L (4.7.4)P c=min(p cx, p cy) [table 23,24]

P c=min(p cx, p cy) [table 23,24]

P c =p c Aeff

P c =p c Ag

Design of Fully Restrained Beams



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Lateral Torsional Buckling of beam

Lateral Torsional Buckling of Beams

Lateral torsional buckling ( = (Lateral deflection ( ) Twisting + ( (



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For bending about x axis

2

2

0 dzvd

EI M x

For bending about y axis

20 dzu

EI M y

From Torsion

dzdu

M dzd

GJ GJ

dzdzdu

M d

GJ L M

d T 00

020

2

2

2

2

02

2

yGJEI M

dzd

dzud M

dzd GJ

yGJEI M

k kz Bkz A202:sincos

kL L z A z 0,000 ycr o GJEI L M

,

Other load cases

cr cr M m M ,0max, .

1

In BS 5950-1:2000 for steelwork design



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Lateral Torsional Buckling of an I beam

3

3iit bGGJ C

flange Euler flange y

y

cr P L

EI

L

I E

P ,2,

2

2

2 )2

(

Buckling of flange

The effect of load level

cr cr M m M ,0max, .

1 m is dependent on the ratio L 2 GJ/EI w

4

2 D I I yw

Example for

concentrated load atmid span



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Fully restrained beams

4.2.2 & 4.3.2.2

The restraint should resist a lateral force more than: 2.5% F fc

%2.5

Frictional force

Force in compression flange F fc

q1=2.5%(Load coefficient of friction)/LF fc=Mumax /D

q2=2.5% F fc/L q=q 1+q 2

5.0)/12.0( r r N k

N r =3



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Restrained beam Design Summary

y p275

70t d

Rolled section 70t d

Rolled section

62t d

Welded section

Plate girders (4.4.5)

62t d Welded section

Section Classifications

Av (Shear area, (4.2.3) (

(4.2.3)

vv PF

v yv A pP 6.0

Webs vary in thickness

yv p

b I

S F 7.0max

Shear verification

NoYes

Section is not ok on shear

To be continued

Restrained beam Design Summary-continued

Yes on shear

vv PF 6.0vv PF 6.0 S v=Dt2/4 for equalled-flange sections

. . . . . .

Plastic

or

Compact

Semi-compact

Z p M yc Or

eff yc S p M

Slender

eff yc Z p M

Z p M yr c Or

2]1)(2[ v

v

P

F S v =S-S f (or for A v )

PlasticSemi-compactSlender

S p M yc

Conservatively

Compact

)( v yc S S p M

)( veff yc S S p M

Or

)5.1

( v ycS

Z p M

)5.1

( veff ycS

Z p M Z p M yc 5.1

Z p M yc 2.1 4.2.5.1



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unrestrained beams (4.3)

Effective length L E ) (4.3.5) (

Destabilizing load ( ) increasing the twist =( (

Beams

Llt

a)b)Llt

Llt

=

Cantilevers

Table 14

c4 or d4 (Table 14)

Normal loada e

Normal load L E = 1.L lt

Destabilizing load L E = 1.2L lt

E

Note: Bending at tip

LE =max (1.3 Table14,Table14+0.3L)

LltL

LE=Llt

Destabilizing load

LE=1.2L lt Table 14 for L



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29Dr Mustafa Batikha Damascus University


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Compared between the design curve and research data

Mb

mLT (4.3.6.6)

Destabilizing loading

mLT=1

Cantilevers withoutintermediate lateral

restraint

mLT=1

Plates and flats

mLT=1

Others

Table 18

LT

b x m

M M



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Web subject to concentrated load

Web Bearing (4.5.2.1) Figure 13

n At the end 56.02 k b

n e

Away from the end 5n

kRolledK=T+r

WeldedK=T

load ed Concentrat tpnk bP ywbw )( 1

Web subject to concentrated load

Web Buckling (4.5.3.1)

Rotationanges

Movement

No rotation and no movementLE=0.7d

bw x Pd nk b

t P

)(

25

1

yw p275

ae 0.7d

P x =P x

a e


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Deflection (2.5)

Serviceability loads a) LL

b) 0.8LL+0.8WL

c) WL

. .

e) CV

f) CH

Deflection limits (Table 8)

82

Table EI

ML

Members with Combined Momentand Axial force



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Tension members with moment (4.8.2)

a d neglected moment

pure tension design

a 10%d neglected tensionload

Pure bending design

Tension members with moment design

y p275

Section classification

General Case For plastic& compact sections

Simplified method (4.8.2.2)

1cy

y

cx x

t t

M

M

M

M

P

F

More exact method (4.8.2.3)

Tension with major

axis moment only

Tension with minor

axis moment only

Tension with

biaxialmoments

rx yrx

rx x M M

ry yry

ry y M M Continued



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Tension members with moment design-continued

Tension with biaxial moments

I and H sectionswith equal flanges All others

Z1=2

Z2=1

Z1=Z 2=2Z1=Z 2=5/3Z1=Z2=1

21 Z Z M M

1 ryrx M M

Note : In all cases of tension members withmoment, lateral-torsional buckling should bechecked (4.8.2.1) LT

b

m

M M

Compression members with moment (4.8.3)

a d neglected moment

pure compression design

a 10%d neglected compression load

Pure bending design



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Compression members with moment design

y p275 Section classification

General Case For plastic& compact sections

Simplified method (4.8.3.2)

1cy

y

cx

x

yg

c

M

M

M

M

p A

F

More exact method (4.8.3.2)

Compression withmajor axis momentonly

Compression withminor axis momentonly

Compressionwith biaxial

moments

Slender section: A g=Aeff rx yrx

rx x M M ry yry

ry y M M Continued

Compression members with moment design-continued

Compression with biaxial moments

I and H sectionswith equal flanges All others

Z1=2

Z2=1

Z1=Z 2=2Z1=Z 2=5/3Z1=Z2=1

21 Z Z M M

1 ryrx

x

M M

Note : In all cases of compression members with moment, member bucklingresistance should be checked (4.8.3.3)



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Member buckling resistance (4.8.3.3)

Flexural buckling: ( )

Lateral-torsional buckling: (

)


Member buckling resistance (4.8.3.3)

: m x )Mx( )Lx( x)p cx) .(Table 26( Mxmax =Mx

: m y )My( )Ly( y)p cy) .(Table 26( Mymax =My

: m yx )My( )Lx( x)p cx) .(Table 26) (m yx :To be used with out-of-plane buckling.(

m LT(unrestrained beam), P c =Min(p cx ,p cy ), MLT=Mxmax in the segment where Mb occurs

Simplified method (4.8.3.3.1)

General buckling

1 y y

y y

x y

x x

c

c

Z P

M m

Z p M m

PF

Minor axis buckling

1 y y

y y

b

LT LT

cy

c

Z p

M m

M M m

PF

For plastic& compact sections

More exact method (4.8.3.3.2-4)



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Notes

Slender Section: Z=Z eff

= =t c , x .is according to compression with moments case with F c =0

In sway mode : m x,m y and m yx 0.85

Columns in simple structures (4.7.7)

Simple structures= pinned columns + bracing or shear wall for horizontal resistance



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Columns in simple structures

100mm

Nominal moment=M

ii

iii

L I

L I

/

/

2/5.1: 21max M M M Note

min

1 y y

y

bs

x

c

c

Z P

M

M

M

P

F LE (Table 22), Typically=(0.85L or L)

P c=min(P cx, P cy)

Mbs as unrestrained beam, LT=0.5L/r y for simplicity

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Steel Work Design 1 Dr Mustafa Batikha Lectures 2010 2011

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