sm9 81

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PROBLEM (9.81) A cantilever beam of width b, depth h, and length L is subjected to a
concentrated load of P at its free end. For y
σ
= 240 MPa. what is the factor of safety
s
n,
assuming failure occurs in accordance with the maximum energy of distortion theory?
Given: b = 60 mm, h = 80 mm, L = 1.2 m, P = 2 kN
SOLUTION
364
60(80) 12 2.56 10
I
mm==×
max max
22.4
AA
V V kN M M kN m== = = ⋅
Point A:
3
16
2.4 10 (0.04) 37.5
2.56 10
M
cI MPa σ
−
×
== =
×
222
1122 240
( ) ; 37.5 , 6.4
ys
ss
n
nn
σ
σσσσ −+= = =
Point B:
3
max
max 3
33210
0.625
224.810
V
M
Pa
A
τ
−
×
== =
×
max 1 2
τ
σσ ==−
Thus,
22222
1122 max
();3 ()
yy
ss
nn
σ
σ
σσσσ τ
−+= =
240
1.73(0.625) , 222
s
s
n
n
==
80 mm
A
M
A
1.2 m
B
P
=2 kN
VA
60 mm