The Influence Line Diagram (ILD) for a force in a truss member is shown in figure. If a Uniformly Distributed Load (UDL) of intensity of 30 kN/m longer than span traverses, n maximum compression in member is

(Upper Triangular area is of Tension, Lower Triangle is of Compression)

Approach: To get the maximum compressive force place the UDL only up to the region of compressive force

Concept:

ILD (Influence lines are important in designing beams and trusses used in bridges, etc. Where loads will move along their span.

The influence lines show where a load will create the maximum effect for any of the functions studied.)

Calculations:

Given, ILD of the truss member

The intensity of UDL = 30 kN/m.

From the ILD figure, we know that the upper triangle is in the tension part and the bottom triangle is in the compression part.

The length of the compression span needs to be determined

From the similarity of triangles:

$\frac{0.29}{x}=\frac{0.58}{4-x}$

$x=\frac{4}{3}$

In the above figure,

In order to get the maximum compressive force, UDL is placed till the compressive zone.   

 Force = UDL × (Area of the Compression triangle of ILD)

 Maximum compressive force = 30 × ($\frac{1}{2}\times 0.29\times \left(4+\frac{4}{3}\right)$ ) kN

 = 30 × 0.7733

 = 23.2 kN. 

∴ Maximum compressive force = 23.2 kN.