Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

From the positive root, the maximum rod deformation can now be expressed in
terms of the static deformation and the drop height h as
δ = δ + δ + 2δ
h
(a)
max st st 2 st
The maximum axial deformation of the rod if the collar is dropped from the height
of 30 mm can now be computed:
2
δ = 0.025465 mm + (0.025465 mm) + 2(0.025465 mm)(30 mm)
max
= 0.025465 mm + 1.236345 mm
= 1.261810 mm = 1.262 mm
Ans.
(c) The maximum dynamic force exerted on the rod is calculated from the maximum
dynamic deformation. If it is assumed that the rod behaves elastically and that the
stress–strain curve applicable to this dynamic load is the same as the stress–strain
curve for a static load, the relationship of the force exerted on the rod and the deformation
caused by the dynamic load is
FmaxL
δ max =
AE
Therefore, the maximum dynamic force is
F
max
AE
= δmax
L
2 2
(176.7146 mm )(200,000 N/mm )
= (1.261810 mm)
750 mm
= 59,461.4 N = 59,500 N
Ans.
The maximum dynamic normal stress in the rod is thus
Fmax
59,461.4 N
σ max = = = 336 MPa
2
A 176.7146 mm
(e) The impact factor n is simply the ratio of the dynamic effect to the static effect:
Hence,
n
Fmax
δmax
σ
n = = =
F δ σ
st
st
max
st
Ans.
= 1.261810 mm
0.025465 mm = 49.551
Ans.
SiMPliFiED SolutioN
An equation similar to Equation (17.23) can be derived for the impact factor n. Recall
Equation (a):
δ = δ + δ + 2δ
h
max st st 2 st
Multiplying the second term under the radical by δ st /δ st (i.e., 1), factoring and taking
δ ( = δ ) out of the radical, and factoring again yields
st 2
st
2h 2h ⎡ 2h
⎤
δmax = δst + δst 2 + δst 2 = δst
+ δst
1 + = δst
⎢1+ 1+
⎥
δ st
δst
⎣ δst
⎦
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