Cantilever Spring Bending Stress Problem Solution

________________________________________________________________________
PROBLEM (7.38) For the cantilever spring shown in Fig. P7.38, Calculate the largest bending
stress for two cases:
(a) The fillet radius is r = 3/16 in.
(b) The fillet radius is r = ¾ in.
Given: b = ½ in., P = 80 lb
SOLUTION
At a section through B
M
80(12) 960 .
Blb in==⋅
3
960(0.75) 5.12
1(0.5)(1.5)
12
B
nom Mc ksi
I
σ == =
(a) 0.1875 2.25
0.125 1.5
1.5 1.5
rD
dd
== ==
: 1.65K
=
(Fig. 7.13)
max 1.65(5.12) 8.45 ksi
σ
==
(b) 0.75 2.25
0.5 1.5
1.5 1.5
rD
dd
== ==
: 1.22K
=
(Fig. 7.13)
max 1.22(5.12) 6.25 ksi
σ
==
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