sm7 7

________________________________________________________________________
PROBLEM (7.7) Moment M acts about the horizontal (x) axis of a square bar of sides b in
the two different positions shown in Fig. P7.7. Determine the maximum stress and the radius of
curvature of the bar, in terms of the modulus of elasticity E, b, and M, as required.
SOLUTION
Refer to Table B.6 and Appendix A.
43
(2) 6
12
M
bM
bb
σ ==
y
44
11
( 12)
z
2
M
MM
EI E b Eb
ρ
== =
b
C
For a triangle:
b
33
22
()
36 36 2 3 12
zbh bh bh h bh
IAd=+ =+ =
3
Hence, for square:
4
3
1
2[ ( 2)( ) ]
12 12
2
zbb
Ib
==
43
(2)62
12
z
M
cMb M
Ib b
σ == =
y
4
11
z
2
M
M
EI Eb
ρ
==
Therefore, 4
max 3
62 12
M
Eb
bM
σρ ==
z
2
b
b
2b
2
b
C
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