sm7 18

________________________________________________________________________
PROBLEM (7.18) If a beam of the cross section shown in Fig. P7.18 is subjected to the
bending moment Mz=20 kN⋅m, what is the total force acting on the lower flange of the beam?
SOLUTION
Dimensions shown are in millimeters.
11 2 2 33
123
Ay Ay Ay
yAAA
++
=++
z
’
y
y
z
40
12.5
C
120
20
180
20
y
y
100
22.5
A
3
A2
B
A
1
120
A
z
z
120
120
120 20 170 120 20 100 120 40 20 77.5
120 20 120 20 120 40 mm
×× + ×× + ××
==
×+ ×+ ×
33
22
120(180) 100(120)
120 180(12.5) 100 120(22.5)
12 12
z
I=+×−−×
64
41.22 10 mm=×
A
M
c
I
σ =
y
33
6
20 10 (77.5 10 )
41.22 10
−
−
××
=×
37.6
M
Pa
=
B
x
37.5
37.6 18.19
77.5
B
M
Pa σ ==
77.5 m m
F
b
A
1( ) 27.9
2
avg A B
M
Pa σσσ =+=
Total force on the bottom flange:
6 27.9 10 (0.12 0.04)
bavg
FA σ ==× × 134 kN
=
0.04
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