5. Influence Lines

5.2 Solved Problems

• Example Set 1

• Example Set 2

Loads not applied directly to members

Sometimes loads are applied to one part of a structure, but an influence line is wanted for the resulting action in another part. When using the Muller-Breslau principle to draw the influence line, it is important to know that unit displacements are imposed at the appropriate part of the structure where the response is desired, but it is the displaced shape of the load-carrying portion that provides the influence line.

A common example is that of a bridge structure such as that shown above. The main load carrying girders are parallel to the road direction and span between piers, but there may be only two of these placed a considerable distance apart. If the deck slab had to span between the girders, it would be very thick and heavy. So cross beams are placed at regular intervals. Then stringers are placed close together, spanning between beams. The slab then only has to span between stringers and can be lighter as a result.

Wheel loads are transferred to the slab, then from the slab to the stringers, then from the stringers to the beams and finally from the beams to the girders and then into the supports.

Because environental loads are applied to the stringers, it is the displaced shape of the stringers that gives the influence line.

If you wish an influence line for an action, such as shear force in the girder, you must displace the girder appropriately then draw the resulting displaced shapes of the stringers.

This is shown in the above figure. It gives the influence line for shear in the girder just to the right of point $a$.

The above figure gives the influence line for bending moment in the girder at point $b$.