sm8 53

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PROBLEM (8.53) Using Mohr's circle, solve Prob. 8.5.
SOLUTION
τ (MPa)
40 MPa
σ’=15
y’
R
10 MPa
o
22.5
70 MPa
x
O
(-40, -10)
55.3o
(σx’, σ y’)
(70, 10)
α
σ (MPa)
C
x’
10
= 10.3o
55
1
2
R = (10 + 552 ) 2 = 55.9
τ x ' y ' = 55.9 sin 55.3o = 46 MPa
α = tan −1
σ x ' = −55.9 cos 55.3o + 15
= −16.8 MPa
y’
16.8 MPa
46 MPa
70 MPa
o
22.5
x’
10 MPa
x
40 MPa
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