The 9.75 m long beam is simply supported at A and B shown below with a uniformly distributed load (UDL) between A and C of 4.75 kN/m and a concentrated point load of 12.50 kN at point D (i.e., midpoint between C & B). Determine the bending moment in kilonewton metres (kNm) at the midpoint of AB (i.e., mid-beam). Assume the beam is weightless and give your answer in kilonewtons (kN) to 2 decimal places.

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Influence Lines

The graphs that show the variation of a function at a specific point on a beam or truss due to a unit load placed at any point along the structure are known as influence lines in engineering. Some common functions that are studied with influence lines are shear, moment, and deflection. In designing beams and trusses, it is important to use influence lines in structures where loads would move along their span such as bridges, crane rails, conveyor belts, floor girders, etc. The influence lines help to study where a load will create the maximum effect for any of the functions.