Question

A simple beam AB supports a concentrated load P acting at distances a and b from the left-hand and right-hand supports, respectively (Fig. 9-12a). Determine the equations of the deflection curve, the angles of rota- tion a and at the supports, the maximum deflection 9mx, and the deflection &c at the midpoint C of the beam (Fig. 9-12b). (Note: The beam has length L and constant flexural rigidity El.) Fig. 9-12 Example 9-3: Deflections of a simple beam with a concentrated load CD 8 Solution Bending moments in the beam. In this example the bending moments are expressed by two equations, one for each part of the beam. Using the free- body diagrams of Fig. 9-13, we arive at the following equations: Fig. 9-13 Example 9-3: Free-body diagrams used in determining the bending moments Pbx (0 sx s a) (9-33a) Pbx Gi (9-33b)

Answer 1

Solution:- The solution for this problem can be obtained by using appropriate formulae as follows -

Calculation and Explanation as given below -

da- 6LEI ien a Past 6LET 6LET GLET