A simple beam has 14.8m distance between the supports and with free end at bothsupports as shown in figure. With the aid of influence lines, determine the maximum upward and maximum downward leftand rightreactions, the maximum positive shear and maximum negative shear 8m from the right support and the maximum positive and maximum negative moment 5m from the left support due to: a. Uniformly distributed moving load (w)of magnitude 12KN/m of indefinite length. b. 3 concentrated loads (P) of magnitude 45KN, 5KN and30KNeach 3m apart. (threedecimal places in the final answers)

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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.