4.1.5 Relation of Induced System Loads to Applied Loads
As shown above, the internal system response loads may be quite different than the
dynamically applied external loads. The response can be classified by calculating the ratio
of the system response to the applied load (or to the system response expected for a static load of the same magnitude) — this ratio is called the Dynamic Load Factor, or DLF.
This concept is illustrated in Figure 4-15. In Figure 4-15a, a weight rests on a spring, and
the spring compresses 1 inch. In Figure 4-15b, the same weight is suddenly applied to the
spring. In this case, the spring oscillates, eventually coming to rest at the static deflection.
However, initially the maximum deflection overshoots the static compression by an
additional 1 inch.
The Dynamic Load Factor for this case is the maximum dynamic response (2.0 inches) divided by the static response under the same load (1.0 inch):
In fact, the DLF for an instantaneously applied constant load (not a harmonic or impact load)
is always exactly 2.0. This is easily proven by equating work done by a weight while compressing a spring with the energy stored by the compressed spring:
WX = KX^2/2, or:
2W = KX (twice static weight load)
W = weight, lb.
X = spring compression, in.
K = spring stiffness, lb/in
Note: The force in the spring is KX, which, equal to 2W, is exactly twice the static load, for
a DLF of 2.0.
System responses may be classified based upon the value of the resulting DLF. Possible
system responses are:
The system response may be much lower than the applied load. In this case, the DLF will be much smaller than 1.0. This type of response is called a flexible response. Example: When one end of a rope lying on the floor is pulled quickly, most of the rope will not feel the pull and will continue to lie undisturbed in the pile on the floor.
The system response may be much higher than the applied load. In this case, the DLF will be much greater than 1.0. This type of response is called a resonant response. Example: When one end of a whip is swung over a small distance, the other end of the whip moves in a large arc and cracks with a great force.
The system response may be about the same as the applied load. In this case, the DLF will be approximately equal to 1.0. This type of response is called a rigid response. Example: When one end of a baseball bat is swung, the free end follows along simultaneously, over roughly the same distance as the batter's hands.
In which of these categories a system's response falls is dependent upon the relation
between the system characteristics (system response speed) and load characteristics (force
time profile). A system, in and of itself, is not flexible, resonant, or rigid. For example, in
the first example above, the rope no longer has a flexible response if the duration of the
applied load is increased significantly — i.e., if someone pulls indefinitely, eventually the entire rope will get up and follow the pulled end.
Introduction to Dynamic Theory
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