Dr. Mahdi Damghani 1
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Dr. Mahdi Damghani 1
EC3 steel beam design
Laterally restrained
Class 1 Class 2
0, / MyplRdpl fWM
Class 3
0min,, / MyelRdel fWM
Class 4
0min,, / MyeffRdc fWM
0.1,
Rdc
Ed
M
M
Bending moment resistance
2Dr. Mahdi Damghani
Un-restrained (go to slide 6)
Shear resistance
wwfwfv
MyvRdpl
thtrtbtAA
fAV
)2(2
/)3/( 0,
0.1,
Rdc
Ed
V
V
Bending -Shear resistance
2
,
,,02
,,,
,
12
/)4/(
5.0
Rdpl
Ed
RdcyMwvyplyRdvy
RdplEd
V
V
MtAWfM
then
VV
if
Shear buckling resistance
y
w
w
f
where
t
h
275
72
Un-stiffened webs Stiffened webs
kt
h
w
w 31
1/ wha 1/ wha
2)/(34.54 ahk w2)/(434.5 ahk w
cshf
Etl
mmtll
mt
lmtll
swyw
wFe
fey
f
efey
2
2min
2
21
2
2
1
Laterally restrained steel beam continued
Resistance of the web to transverse forces
w
wFcr
cr
ywwyF
FF
yFeff
M
M
weffywRd
h
tEF
F
ftl
lL
tLfF
3
1
1
9.0
15.0
0.1
5.0F2
2 02.0
f
w
t
hm
5.0F
02 m
wyw
fyf
fsy
tf
bfm
ammtsl
1
21 )1(2
3Dr. Mahdi Damghani
Flange induced buckling
ffc
wfw
fc
w
yfw
w
btA
tthA
A
A
f
E
t
h
)2(
Class 1 Class 2 Class 4 Class 3
3.0 55.04.0
4
Laterally restrained steel beam continued
condition Deflection limit
Cantilevers Length/180
Beams carrying plaster or other brittle finish
Span/360
Other beams (except purlins and sheeting rails)
Span/200
Purlins and sheeting rails To suit the characteristics of particular cladding
Dr. Mahdi Damghani
Web under bending and shear
0.1
0.1
4.18.0
1
2
0
1
12
M
weffyw
Ed
M
ply
Ed
tLfF
WfM
Deflection check
Dr. Mahdi Damghani 5
6Dr. Mahdi Damghani
Un-restrained
0.1
0.1
1
1,
,
M
M
yyLTRdb
Rdb
Ed
fWM
M
M
Class 1 Class 2
yply WW ,
Class 3
yely WW ,
Class 4
yeffy WW ,
Buckling curve a b c d
Imperfection factor 0.21 0.34 0.49 0.76LT
Cross section Limits Buckling curve
Rolled I-sectionsh/b ≤ 2 a
h/b > 2 b
cr
yyLT
LTLTLTLT
LTLTLT
LT
M
fW
2
22
)2.0(15.0
11
General case Rolled sections only
75.0,4.0
)(15.0
1
11
0,
20,
2
22
LT
LTLTLTLTLT
LT
LT
LTLTLT
LT
and
Cross section Limits Buckling curve
Rolled I-sections
h/b ≤ 2 a
2 ≤ h/b< 3.1 c
h/b > 2 d
Bending moment curve between points of lateral restraint
1
2
mod,
1
0.1])8.0(0.21)[1(5.01
1
C
f
f
c
LTc
LTLT
2
2
2
2
2
81000)3.01(2
210000
)1(2
NmmE
G
EI
GIL
I
I
L
EIM
z
tcr
z
w
cr
zcr
Dr. Mahdi Damghani 7
Assumptions in obtaining Mcr
1- The beam is of uniform section with equal flanges.2- Beam ends are simply supported in the lateral
plane and prevented from lateral movement and twisting about the longitudinal axis but are free to rotate on plan.
3- The section is subjected to equal and opposite in plane end moments
4- The loads are not destabilising
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