Determining the maximal effect of distributed load

The definition says that in order to obtain the maximal effect of the load from the influence line in a fixed section, the ordinate of the influence line in the x-coordinate is multiplied by the size of the load. According to this definition, the effect of the distributed load means the calculation of the area under the influence line between every change of sign, and its multiplication by the load size. If the influence line is defined by several positive and negative parts, the area is calculated for each part considering the sign. The overall effect is the sum of all loaded parts. The maximal effect is caused by a distributed load positioned on the positive part of the influence line. The load is therefore divided between each of the parts according to the following picture.

Qm,pos&neg – mobile load in the positive or negative part

Qb,pos&neg – distributed load between load groups (interrupted)

Each line below the influence line shows the possible division of the load system. E.g. the first line represents the distributed load Qm,pos positioned only on the first positive part. The third line is the represents the distributed load Qm,pos divided between the first and second positive part and the unloading of the distributed load Qb,neg that causes an important reduction of the overall effect in the summation of loaded parts. It can be seen from the picture that the maximal effect is reached if the load is positioned only on positive or only on negative parts of the influence line. Each of them results in an extreme. The critical position is therefore determined separately for the positive and negative part.