sm12 101

________________________________________________________________________
PROBLEM (12.101) A diver of weight W jumps from the position shown in Fig. P12.99 onto
the end C of a wooden diving board. What is the permissible height h, if the allowable bending
stress in the wood is limited to all
σ
?
Given: W = 130 lb, d = 2.4 in., b = 1.6 in., a = 3.5 ft, L = 9.5 ft
E = 1.8 x 106 psi , all
σ
= 5 ksi
SOLUTION
We have
33
11
( ) (16)(2.4) 18.432 .
12 12 4
I
bt in== =
Static Deflection. Using Eq. (12.64):
2()
3
st WL
vLa
EI
=+
2
6
130(9.5 12) (9.5 3.5)12 2.648 .
3(1.8 10 )(18.432) in
×
=+
×=
Maximum Stress. The maximum force is . The largest stress occurs at
max
P
support B.
max max max max
( ) (9.5 12) 114
M
PLP P==×=
Hence
3
max max
max 114 (1.2)
;5(10) 18.432
Mc P
I
σ ==, max 673.7Plb
=
Maximum Height.
130 49.09 .
2.648
t
W
klbin
δ
== =
Then
max
max 673.7 13.72 .
49.09
CP
vv in
k
== = =
Hence
2
max max
1
()
2
Wh ; v kv+= 2
1
130( 13.73) (49.09)(13.72)
2
h+=
n
Solving,
21.8 .
hi=
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