sm12 91

________________________________________________________________________
PROBLEM (12.91) A block of weight W = 50 N is dropped from a height h onto the end B of a
cantilever beam which is supported by a spring of stiffness k = 180 kN/m (Fig. P12.91). Using E = 200
GPa, determine the maximum stress for two cases:
(a) The height h = 40 mm.
(b) The height h = 250 mm.
SOLUTION
A
d=80 mm
R
b=40 mm
k
R
B
L
h
P
δ
W
W
st
R
k
δ
=
k
Referring to Example 12.22
33
3
()
0.2 10
33
st WRL RL R
vEI EI k
−
−
==×−
=
or
33
633
11(1.6)
200 10 ( ) ( )
3 180 10 3 200 10 1.7
L
RR
kEI
−
×=+ = +
××××
or
200 , (5.5556 4.0157)
R=+ 20.9
R
N
=
and 29.1WR N
−
=
Then
3
3
29.1 0.16 10 0.16
180 10
st mm
δ
−
==×=
×m
6
29.1(1.6)(0.04) 1.1
1.7 10
st
M
Pa σ
−
==
×
(
a) hm. 40 m=
3
2(0.04)
1 1 23.4
0.16 10
K− =+ + =
×
Thus
vm
max 23.4(0.16) 3.7 m==
max 23.4(1.1) 25.7
M
Pa
σ
==
Continued on next slide
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.

(b) h=250 mm.
()
3
20.25
11
0.16 10
K
−
=+ + ×=56.9
max 56.9(0.16) 9.1vm==m
max 59.6(1.1) 62.3
M
Pa
σ
==
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.