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.
_______________________________________________________________________
PROBLEM (*9.52) A typical cantilever steel beam with modulus of elasticity E = 200 GPa is
loaded as shown in Fig. P9.52. Compute the magnitude of load P and distance d.
Given: The normal strains A
ε
= 600
μ
and B
ε
= -200
μ
occur at the extreme fibers at points A
and B.
*SOLUTION
33 64
1(120 160 100 120 ) 26.56 10
12
I
mm=×−×=×
23
102.7)120(100)160(120 mmA ×=−=
PdM )9.08.0( −= (1)
0.8 (0.08)
AA PM
EAI
σε
== + (2)
0.8 (0.08)
BB PM
EAI
σε
== − (3)
Add Eqs. (2) and (3):
66 3
1.6 1.6
( ) ; 200 10 (400 10 ) 7.2 10
AB PP
EA
εε
−
−
+= × × =×
kNP 360=
Subtract Eq.(3) from Eq.(2):
66 6
0.16 0.16
( ) ; 200 10 (400 10 ) 26.56 10
AB MM
EI
εε
−
−
+= × × = ×
mkNM ⋅= 56.26
Thus, Eq.(1) yields
)10360)(9.08.0(1056.26 33 ×−=× d
or
md 217.1=
0.8P
0.8 P
0.6P
y
1.5
m
M
z
d
120
20
20
20
120
C
1
/
1
100%