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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( . .
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Design of Compression Members
)The concept of stress(
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)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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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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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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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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Compression members with moment design-continued
Member buckling resistance (4.8.3.3)
Flexural buckling: ( )
Lateral-torsional buckling: (
)
Compression members with moment design-continued
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