ch01-03 stress & strain & properties

01 Solutions 46060 5/6/10 2:43 PM Page 35
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1–51. During the tension test, the wooden specimen is
subjected to an average normal stress of 2 ksi. Determine
the axial force P applied to the specimen. Also, find the
average shear stress developed along section a–a of
the specimen.
P
a
Internal Loading: The normal force developed on the cross section of the middle
portion of the specimen can be obtained by considering the free-body diagram
shown in Fig. a.
4 in.
2 in.
a
1 in.
+ c ©F y = 0; P 2 + P 2 - N = 0 N = P
4 in.
Referring to the free-body diagram shown in fig. b, the shear force developed in the
shear plane a–a is
P
+ c ©F y = 0; P 2 - V a - a = 0 V a - a = P 2
Average Normal Stress and Shear Stress: The cross-sectional area of the specimen is
A = 1(2) = 2 in 2 . We have
s avg = N A ; 2(103 ) = P 2
P = 4(10 3 )lb = 4 kip
Using the result of P, V a - a = P 2 = 4(103 )
2
A a - a = 2(4) = 8 in 2 . We obtain
At a - a B avg = V a - a
= 2(103 )
= 250 psi
A a - a 8
Ans.
= 2(10 3 ) lb. The area of the shear plane is
Ans.
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