Find the single force resultant and its location that is equivalent to the conce

Question

Find the single force resultant and its location that is equivalent to the
concentrated and distributed loads acting below.

Explanation / Answer

trapezoidal UDL force resultant = 0.5*(100+300)*12 = 2400 lb (downwards) concentrated force = 2500 lb (upwards) single resultant force = 2500 - 2400 = 100 lb (upwards) consider the origin at the left end of the rod. location of concentrated load on x-axis = 0 location of C.G. of trapezoidal UDL force on x-axis = 8 + [(100 + 2*300)/(100+300)]*(12/3) => location of C.G. of trapezoidal UDL force on x-axis = 15 ft location of single resultant force from the origin = location of C.G. of concentrated force and trapezoidal udl force = [(2500*0)+(2400*15)]/(2400+2500) = 12.414 ft So, magnitude of single resultant force = 100 lb location of single resultant force = 12.414 ft on the x-axis from the left end in the downwards direction

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