More Complicated Beam Loads

Exponential Loads

An exponential load is a load whose force varies exponentially along the beam's length. In this document, we assume a force distribution of the form q (x ) = q0 exp(-x/L ) for a "left-handed" distribution, or q (x ) = q0 exp(-(L-x )/L ) for a "right-handed" distribution. If the total mass of the load is m , we leave the computation of q0 as an exercise for the reader.

Sine Load

A load whose force at the point x is q (x) = q0 sin(Pi x/L ) will be called a sine load. If the total mass of the load is m , a short computation shows that q0 = mg Pi/ (2L ).

Cosine Load

A load whose force at the point x is q (x) = q0 cos(Pi x/(2L)) will be called a cosine load. If the total mass of the load is m , then q0 = mg Pi/(2L) .

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The Geometry Center Calculus Development Team