Building Design and Construction Handbook - Merritt - Ventech!

For smaller values of �, it is given approximately by
STRUCTURAL THEORY 5.151
�2�
ƒ � 2ƒ o(1
� e ) (5.267)
� �
1
ƒ � ƒ 1 � (5.268)
o ��
Duration of impact, time it takes for the impact stress at the struck end to drop
to zero, is approximately
�L
T � (5.269)
c��
for small values of �.
When Wm is the weight of a falling body, velocity at impact is �2gh,
when it
falls a distance h, in. Substitution in Eq. (5.265) yields ƒo � �2EhW /AL,
since
b
Wb � pAL is the weight of the bar. Putting Wb � �Wm; Wm/A � ƒ�, the stress
produced by Wm when applied gradually, and E � ƒ�L/e�, where e� is the elongation
for the static load, gives ƒo � ƒ� �2h�/e� . Then, for values of � smaller than 0.2,
the maximum stress, from Eq. (5.268), is
� �
� �
2h� 2h
ƒ � ƒ� � (5.270)
e� e�
For larger values of �, the stress wave due to gravity acting on W m during impact
should be added to Eq. (5.267). Thus, for � larger than 0.2,
2h�
�2� �2�
ƒ � 2ƒ�(1 � e ) � 2ƒ � (1 � e ) (5.271)
e�
Equations (5.270) and (5.271) correspond to Eq. (5.261), which was developed
without wave effects being taken into account. For a sudden load, h � 0, Eq. (5.271)
�2�
gives for the maximum stress 2ƒ�(1 � e ), not quite double the static stress, the
result indicated by Eq. (5.261). (See also Art. 5.18.4.)
(S. Timoshenko and J. N. Goodier, ‘‘Theory of Elasticity,’’ McGraw-Hill Book
Company, New York; S. Timoshenko and D. H. Young, ‘‘Engineering Mechanics,’’
John Wiley & Sons, Inc., New York.)
5.18.4 Dynamic Analysis of Simple Structures
Articles 5.181 to 5.18.3 present a theoretic basis for analysis of structures under
dynamic loads. As noted in Art. 5.18.2, an approximate solution based on an idealized
representation of an actual member of structure is advisable for dynamic
analysis and design. Generally, the actual structure may be conveniently represented
by a system of masses and massless springs, with additional resistances to account
for damping. In simple cases, the masses may be set equal to the actual masses;
otherwise, equivalent masses may be substituted for the actual masses (Art. 5.18.6).
The spring constants are the ratios of forces to deflections (see Art. 5.18.2).
Usually, for structural purposes the data sought are the maximum stresses in the
springs and their maximum displacements and the time of occurrence of the max-