Concept: Influence line diagram: An influence line for a given function, such as a reaction, axial force, shear force, or bending moment, is a graph that shows the variation of that function at any given point on a structure due to the applicationof a unit load at any point on the structure.
ILD can be drawn for statically determinate as well as indeterminate structures. Advantages of drawing ILD are as follows: i) To determine the value of a quantity (shear force, bending moment, deflection, etc.) for a given system of loads on the span of the structure.
ii) To determine the position of a live load for the quantity to have the maximum value and hence to compute the maximum value of the quantity.
Explanation:
Rolling load = 40 kN
Maximum positive shear force:
When rolling load will be acting at point A then the shear force will be maximum.
Maximum shear force = Magnitude of load × ordinate of ILD under the load
= 40 × 1 = 40 kN (+)
Maximum negative shear force:
When rolling load will be acting at point B then the shear force will be maximum.
Maximum shear force = Magnitude of load × ordinate of ILD under the load
= 40 × 1 = 40 kN (-).