Q.3 A simply-supported prestressed concrete beam ABCDE is pinned at support A and supported on a roller at E, as shown in Figure Q.3. (a) Draw the Influence Lines for (i) the vertical reaction Va at support A, (ii) the vertical reaction VE at support E, (iii) the shear force FyB at point B, (iv) the bending moment Mg at point B. (b) Using these Influence Lines, determine the values of Va, Ve, FvB and MB when the beam is loaded as indicated with three point loads at points B, C and D and a distributed load between points B and C. (c) Using these Influence Lines, determine the maximum values for Va, VE, FVB and MB when the total uniformly distributed load of 240 kN over a 4.0 m length and the single point load of 100 kN traverse across the prestressed concrete beam independently. 80 kN 100 kN 80 kN 60 kN/m A B D E НА VA VE 4.0 m 4.0 m 4.0 m 4.0 m 16.0 m Figure Q.3

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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.