sm8 1

CHAPTER 8
PROBLEM (8.1) A 60-mm by 40-mm plate of 5-mm thickness is subjected to uniformly distributed
biaxial tensile forces (Fig. P8.1). What normal and shear stresses exist along diagonal AC? As was done
in the derivations given in Sec. 8.2, use an approach based upon the equilibrium equations applied to
the wedge-shaped half ABC of the plate.
SOLUTION
13
tan 56.3
2o
ACB − ∠= =
50 cos56.3
3
30(10 )
0.06(0.005)
x
σ =MPa100
=
3
10(10 )
0.04(0.005)
y
σ =MPa50
=
03.56sin1003.56cos50:0 22
'' =Δ−Δ−Δ=
∑oo
xx AAAF
σ
MPa
x6.8421.6939.15 '
=
+=
σ
'''
0: 50 sin56.3 cos56.3 100 sin56.3 cos56.3 0
oo oo
yxy
FAA A τ =Δ+Δ −Δ
∑=
MPa
yx 1.2316.4608.23 '' =+−=
τ
100 sin56.3AΔo
y
x
’
'xA
σ
Δ
x
''xy A
τ
Δ
56.3o
AΔ
C
B
A
o
y
’
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.