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Engineering Sciences • Statics

Resultants & Equivalent Force Systems

5 min read

Worked: a loaded girder

A 12 ft member, measured from its left end. An 8 kip point load acts downward 3 ft from the left end. A uniform load of 2 kip/ft acts downward from 6 ft to the right end at 12 ft. Distances are from the left end.

The uniform load is 2 × 6 = 12 kips acting at its midpoint, 9 ft from the left. R = 8 + 12 = 20 kips. Moments about the left end: 8 × 3 + 12 × 9 = 24 + 108 = 132 ft-kips, so x̄ = 132/20 = 6.6 ft.

Equivalently, at the left end the system is a 20 kip downward force plus a 132 ft-kip clockwise couple. Either description gives the same support reactions.

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