sm12 99

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PROBLEM (12.99) A 40-kg diver jumps from the position shown in Fig. P12.99 onto the end C of a
diving board. Determine:
(a) The maximum deflection at C.
(b) The factor of safety ns , if maximum stress in the board is limited to max
σ
= 60 MPa.
Given: L = 5a = 2.5 m h = 100 mm E = 14 GPa
SOLUTION
From Eq. (12.64):
2()
3
CWL
va
EI
=+
L
For L= 5a: 3
25
C
vWLE=I
=× =
Where,
WN 40 9.81 392.4 36
1(0.25)(0.06) 4.5 10
12 4
I
m
−
==×
Thus,
3
96
2 392.4(2.5) 38.93
514 10(4.5 10 )
C
vm
−
==
×× m
3
22(0.1)
11 11
38.93 10
C
h
Kv
−
=+ + =+ + ×3.48
=
(a) max ( ) 3.48(38.93)
CC
vKv== 135.5 mm
=
↓
(b)
max 3.48(392.4) 1366PKW== = N
max max ( ) 1366(2.5) 3415
M
PL Nm== =⋅
max max 6
3415(0.03)
4.5 10
s
Mc
nI
σ
−
==
×22.77
M
Pa
=
or
60 2.64
22.77
s
n==
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