sm7 156

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PROBLEM (*7.156) A beam of the cross section shown in Fig. P7.150 is made of an elastoplastic
material for which E = 200 GPa and y
σ
= 250 MPa. Calculate the bending moment that produces a
bending strain of - 1250
μ
on the lower face of the flange.
*SOLUTION
Since 69
1250 10 (200 10 ) 250
M
Pa
−
××= , lower face of the flange yields.
100 mm
h
20 mm
20 mm
160 m
m
x
N
.A.
z
Strains
1250
μ
x
250 MPa
-250 MPa
Stresses
F
4
F
3
F
1
F2
160-2h
0:
x
F=
∑
6
6250 10
250 10 (0.02 0.1) 0.02
2h
×
−× × − ×
66
250 10 0.02 250 10 (0.16 2 )(0.02) 0
2hh
×
+×+×−
=
m
N
or
30hm=
1250(100 20) 500Fk=×=
23
250 (30 20) 75
2
FF k=− = × = N
N
4250(100 20) 500Fk=×=
zii
M
MF==
∑∑
y
or
22
500 40 75( 30) 75( 30) 500 80
33
M =×+ ⋅+ ⋅+×
63 kN m=⋅
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