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# sm8 79

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PROBLEM (8.79) A point in a structure is subjected to state of stress with
σx
= 15 ksi
σy
τ xz
= 10 ksi
acting as shown on a three-dimensional element in Fig. P8.79. Calculate two values of
σy
for which the
maximum shear stress equals 13 ksi.
SOLUTION
τ (ksi)
τ=13
σavg =7.5
R
O
1
2
1
= (15 + 0) = 7.5 ksi
2
σ −σ z 2 2
R= ( x
) + τ xz
2
σ avg = (σ x + σ z )
C
σ1
σ (ksi)
15 − 0 2
) + 10 2
= (
2
= 12.5 ksi
τ=−13
We have
σ 1,3 = σ avg &plusmn; R
σ 1 = 7.5 + 12.5 = 20 ksi
σ 3 = 7.5 − 12.5 = −5 ksi
Assume: σ max = σ 1 = 20 ksi
Then σ y = σ min = σ 1 − 2τ max
= 20 − 2(13) = −6 ksi
Assume : σ min = σ 3 = −5 ksi
Then σ y = σ max = σ min + 2τ max
= −5 + 2(13) = 21 ksi
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