The maximum bending moment due to a train of wheel loads on a simply supported girder

Concept:

Suppose 4 loads P1, P2, P3, P4 move in a series. Maximum bending moment will occur under P2 when the centre of span is midway between the centre of gravity of the load system R and the wheel load P2.

A maximum bending moment under the wheel load is always below some point load. To find maximum bending moment below a point load, the point load should be placed so that the resultant load and the point load are equidistant from the mid-span.

To find absolute bending moment following steps are followed:

Step 1: Find the resultant of all the loads.

Step 2: Place the individual load as per the condition of absolute maximum bending moment and compute the bending moment under the concentrated load.

Step 3: The maximum of all the possible cases will give the absolute maximum bending moment.

Here the maximum bending moment below the load is obtained.

Important point:

The influence line diagram represents the variation of the stress function at a specified point in a member as a concentrated load moves over the member.

To find the value of stress function, the value of the ordinate of ILD at the location of point load is multiplied by the value of point load.