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PROBLEM (9.53) For the beam loaded as illustrated in Fig. P9.53, determine:
(a) The maximum bending stress.
(b) The location of the neutral axis.
Given: P = 20 kN, d = 0.2 m
SOLUTION
See solution Prob.9.52:
mkNPdM ⋅−=×−×=−= 8.141020)9.02.08.0()9.08.0( 3
(a) Maximum stress occurs at B:
0.8 (0.08)
BPM
AI
σ
=+
33
36
0.8(20 10 ) 14.8 10 (0.08)
7.2 10 26.56 10
−−
××
=+
××
2.22 44.59 46.8
B
M
Pa
σ
=+ =
MPa
A37.4259.4422.2 −=−=
σ
(b) Use Eq.(9.13):
3
3
36
14.8 10
0.8 0.8(20 10 )
0;0
7.2 10 26.56 10
nn
M
yy
P
AI −−
−×
×
=− = −
××
mmyn99.3−=
A
B
x
y
n
σ
B
N
.A
σA
1
/
1
100%