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PROBLEM (9.80) A steel circular bar ( y
σ
= 10 MPa) of d = 50-mm diameter is acted upon
by combined moments M and axial compressive loads P at its ends. If M = 1.2 kN m, calculate,
on the basis of the maximum energy of distortion theory of failure, the largest permissible
value of P.
SOLUTION
3
223
4 32(1.2 10 )
(0.05) (0.05)
PMc P
AI
σππ
×
=− − =− −
6
509.3 97.79 10P=− − ×
We have
222
1122y
σ
σσ σ σ
−+= or 2y
σ
σ
=
So,
66
509.3 97.79 10 210 10 , 220
all
PPkN+×=× =
A
M
=1.2 kN
⋅
m
M
50 mm
P
P
A
P
10
σ
=
2
σ
1
/
1
100%