sm7 5

________________________________________________________________________
PROBLEM (7.5) A steel rod of moludulus of elasticity E and semicircular cross section with radius
r is acted upon by a bending moment Mz (Fig. P7.5). Calculate:
(a) The maximum tensile and compressive strains in the rod.
(b) The radius of curvature of the rod.
Given: Mz = - 1.5 kip⋅in. , E = 30 x 106 psi, r = 1 in.
SOLUTION
x
y
2in.
r
0.576 in.
4r=0.424 in.
C
M
M
z=M
r = in.1
(a) 44
0.11 0.11(1) 0.11 .
z4
I
ri== =n
1500(0.576) 7.855
0.11
tMc ksi
I
σ == =
1500(0.424) 5.782
0.11
cMc ksi
I
σ =− =− =−
Then
6
7855 262
30 10
t
tE
σ
ε
μ == =
×
6
5782 193
30 10
c
cE
σ
ε
μ ==− =−
×
(b) 6
1 1500
30 10 (0.11)
M
EI
ρ
==
×, 2200 . 183.3in ft
ρ
=
=
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.