sm9 90

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PROBLEM (9.90) At a critical point in a loaded ASTM-A36 structural steel bracket, the plane
stresses have the magnitudes and directions shown on element A in Fig. P9.90. Determine whether the
loading will cause bracket to fail, on the basis of a safety factor of
s
n= 1.2, according to:
(a) The maximum shear stress theory.
(b) The maximum energy of distortion theory.
SOLUTION
120 100 0
yxy x
MPa MPa
σ
τσ ==−=
250
y
M
Pa
σ
= (Table B.4)
Hence
22
1,2 ()
22
yy
x
y
σσ
σ
τ
−
=± +
22
60 ( 60) ( 100) 60 116.6=±− +− =±
or
12
176.6 56.6
M
Pa MPa
σ
σ ==−
(a) Maximum shear stress memory:
12 y
s
n
σ
σσ −≤
250
176.6 ( 56.6) 1.2 −− ≤
233.2 208.3>
Failure will occur.
(b) Maximum energy of distortion theory:
22
1122
()
y
s
n
σ
σσσσ −+≤
12
22
(176.6) (176.6)( 56.6) ( 56.6) 208.3−−−− ≤
194.9 208.3<
Failure will not occur.