Theory of structure:

Study of Applied Mechanics and Strength of Materials have enabled you to compute the reactions, shear force (SF), bending moments (BM), deflections etc. in a beam and bar forces in a pin-jointed truss, subjected to a given static load system which remains stationary. Quite often, a beam or a truss is subjected to a load which is not exactly stationary and may be moving along a certain path (which may be the length of the beam or top or bottom chord of a truss etc.). Such moving loads are called live loads as opposed to stationary loads which may be known as dead loads. Examples of live loads are quite common, e.g. a railway train moving across a rail bridge or a vehicle moving along a road bridge. Obviously, the value of any of the desired quantities (e.g., shear force, bending moment or bar force) depends upon the position of the load. For the design of the members, it is important to find out the position of the loads for which the stresses caused in the structure is maximum at any point or in any member. For this purpose, a graphical representation (or a curve), depicting a values of the desired quantity for various load positions and is drawn and is used for calculation. Such curves or lines are called influence lines for the quantity.

Objectives

After studying this unit, you should be able to

• Conceptualise and define influence line,
• Compute the variation of a particular quantity (BM, SF, axial force etc.) due to a unit load moving across a structure,
• Depict the variation of the quantity, graphically, through influence lines,
• Describe the properties of the influence line and to interpret it for direct use in structural analysis, and
• Compute the magnitude of the quantity under a given system of live loads moving across the structure.