sm7 163

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PROBLEM (*7.163) A curved frame with a circular cross section of diameter d is fixed at one
end and carries a concentrated load P at the free end as shown in Fig. P7.163. Determine:
(a) The stress at point A.
(b) The stress at point B.
Given: a = 25 mm, b = 15 mm, d = 20 mm, P = 200 N
*SOLUTION
We have
110 25
2
cd mmrbc m
m== =+=
22
1[
2]
R
rrc=+− (by Table 7.1)
22
1[25 25 10 ] 23.9564
2mm=+−=
1.0436erR mm=−=
22
(10) 314.16Ac mm ππ == = 2
(a) From Eq.(7.70):
() ()()
[1 ]
AA
AAA
M
Rr arRr
PP
AAer A er
σ
−+
=− = + −
200 (50)(23.9564 15)
[1 ] 18.85
314.16 (1.0436)(15)
M
Pa
−
=+ =
(b) Using Eq.(7.70):
() ()()
[1
BB
BBB
M
Rr arRr
PP
AAer A er
σ
−+
=− = + −
200 50(29.1421 35)
[1 ] 8.55
314.16 1.0436(35)
M
Pa
−
=+ =−
A
O
b
P
P
a
M
=-P(a+r)
B
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