Test: ILD & Rolling Loads - 3 - Civil Engineering (CE) MCQ

Using Castigliano’s second theorem

There is no force in member (1) - (2),

Maximum shear force is at either of the support due to a point load

The load should be positioned such that section divides the span and load in the same ratio.

The ILD for support reaction at D can be obtained by:giving unit displacement in the direction of reaction. The deflected shape of beam will represent ILD as in figure (c).

ILD for BM at fixed end will have maximum ordinate when the unit load is at free end. While the BMD due to unit load at free end will have zero ordinate at free end and maximum ordinate at fixed end.

We must first draw the influence line diagram for the SF at the section D,

For maximum positive SF at D, the loading should be applied as shown in the figure.
Maximum positive = load x area of ILD SF at D intensity covered by the load

To find the maximum bending moment at a section 6 meters from the left end of a 16-meter span girder with loads of 200 kN and 80 kN spaced 2 meters apart:

- Position the Loads: Place the 200 kN load at 6 meters from the left end.
- Calculate Reactions:
- Use equilibrium equations to find reactions at supports.
- Bending Moment at 6m:
- Calculate moment due to 200 kN directly at 6m.
- Add moment due to 80 kN, 2m away.

Maximum bending moment at 6m is 990 kNm. Thus, the correct answer is A.