# Forces24.pdf - An arbitrary strip of the beam with length...

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An arbitrary strip of the beam with length dx is subjected to a force d p dx = − F j The position vector of the strip relative to A is x = r i The force acting on the strip therefore exerts a moment ( ) A d x p dx px dx = × − = − M i j k The total moment follows by summing (integrating) the forces over the entire length of the beam 2 0 ( / 2) L A p xdx pL = = M k k The position vector of the strip relative to B is ( ) L x = r i The force acting on the strip exerts a moment ( ) ( ) ( ) B d L x p dx p L x dx = × − = − M i j k The total moment follows by summing (integrating) the forces over the entire length of the beam 2 0 ( ) ( / 2) L A p L x dx pL =− = M k k 2.2.4 The Physical Significance of a Moment A force acting on a solid object has two effects: (i) it tends to accelerate the object (making the object’s center of mass move); and (ii) it tends to cause the object to rotate . 1. The moment of a force about some point quantifies its tendency to rotate an object about that
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