sm7 167

PROBLEM (7.167) A frame has an elliptical cross section as shown in Fig. P7.166. If the allowable
compressive and tensile stress is σall, determine the largest force P that can be applied to the member.
Given: r = 80 mm, r = 200 mm, a = 60 mm, b = 30 mm, σall = 80 MPa
SOLUTION
80 200
AB
rmmr m== m
1( ) 140
2oi
rrr m=−= m
2
(60)(30) 1800Aab mm ππ π == =
22
2[] dA b rra
ra
π
=−−
∫
P
22
2 (30)[140 140 60 ] 42.4394
60 mm
π
=−−=
1800 133.2456
42.4394
A
A
R
mm
dA
r
π
== =
∫
6.7544erR mm=−=
Using Eq.(7.70) with
M
PF
=
−:
()
[1 ]
B
BB
rR r
P
Aer
σ
−
=+
66(140)(133.2456 200)
80(10 ) 1
1800 (10 ) (6.7544)(200)
all
P
π
−
⎡
⎤
−
−= +
⎢
⎥
⎣
⎦
Solving
76.44
all
Pk=N
P
M
=-Pr B
A
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