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MACHINE DESIGN  An
3111
PROBLEM 311
Statement:
Determine the impact force and dynamic deflection that will result when the 100kg person
in Problem 310 jumps up 250 mm and lands back on the board.
Assume that the board weighs 29 kg and
deflects 131 mm statically when the person stands on it.
Find the reaction forces and construct the shear and
moment diagrams for this dynamic loading. Determine the maximum shear force, maximum moment and their
locations along the length of the board.
700 = a
2000
= L
R
R
1
2
F
i
Units:
N
newton
kN
10
3
newton
.
Given:
Beam length
L
2000
mm
.
Distance to support
a
700
mm
.
Mass of person
m
pers
100
kg
.
Mass of board
m
board
29
kg
.
Static deflection
δ
st
131
mm
.
Height of jump
h
250
mm
.
FIGURE 311A
Free Body Diagram for Problem 311
Assumptions:
1. Equation (3.15) can be used to approximate a mass correction factor.
Solution:
See Figure 311 and Mathcad file P0311.
1.
The person is the moving object and the board is the struck object.
The mass ratio to be used in equation (3.15) for
the correction factor is
massratio
m
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 Spring '10
 N/A
 Machine Design

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