Draw influence lines for the reactions at A and C and for the bending moment at E in the beam system shown in Fig. P.20.8. Note that the beam AB is supported on the lower beam at D by a roller. If two 10 kN loads, 5 m apart, cross the upper beam AB, determine the maximum values of the reactions at A and C and the bending moment at E. Ans. Ra(max)=16.7 kN, R(max)=17.5 kN, Mµ(max) =58.3 kNm.

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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.