________________________________________________________________________
PROBLEM (12.92) A 20-kg block falls from a height h = 50 mm onto the midspan of a simply
supported 2-m-long beam of rectangular cross section 40 mm wide and 60 mm deep. For E = 70 GPa,
calculate:
(a) The maximum deflection.
(b) The maximum stress.
SOLUTION
B
A
1
m
C
1 m 80 mm
40 mm
h
W
(a) max 1
20 9.81 196.2 4
WNM=× = =
WL
36
1(0.04)(0.06) 0.72 10
12 4
I
m
==×
Midspan deflection
33
96
196.2(2) 0.65
48 48(70 10 )(0.72 10 )
st WL mm
EI
δ
== =
××
Equation (12.55):
3
2(0.05)
1 1 13.44
0.65 10
K
=+ + =
×
Thus,
max 13.44(0.65) 8.74vm==m
(b) Maximum static stress, at midspan:
6
196.2(2)(0.03)
4(0.72 10 )
st Mc
I
σ
== ×
and
max 13.44(4.09) 55
M
Pa
σ
==
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