# Building Construction Handbook PDF

### Building Construction

Damping in structures, resulting from friction and other causes, resists motion imposed by dynamic loads. Generally, the effect is to decrease the amplitude and lengthen the period of vibrations.

If damping is large enough, vibration may be eliminated. When maximum stress and displacement are the prime concern, damping may not be of great significance for short-time loads.

These maximums usually occur under such loads at the first peek of the response, and damping. unless unusually large. has little effect in a short period of time.

But under conditions close to resonance, damping has a considerable effect. Resonance is the condition of a vibrating system under a varying load such that the amplitude of successive vibrations increases.

Unless limited by damping or changes in the condition of the system, amplitudes may become very large. Two forms of damping generally are assumed in structural analysis, viscous or constant (Coulombs. For viscous damping.

the damping force is taken proportional to the velocity but opposite in ddırection. For Coulomb damping, the damping force is assumed constant and opposed in direction to the velocity

Viscous Damping. For a one-degree system (Arts 5.18.2 to 5. 18.4), the equation of motion for a mass weighing W and subjected to a force Varying with time as opposed to Vince damping is.

The response of the beam then is given by Eq. (5.278), and the dynamic deflection is the sum of the modal components, EA 6,(x).

Nonlinear Responses. When the structure does not react linearly to loads, the equations of motion can be solved by numerical analysis if resistance is a unique function of displacement.

Sometimes, the behavior of the structure can be represented by an idealized resistance-displacement diagram that makes possible a solution in closed form. Figure 5.112a shows such a diagram.

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