Differential Equations of the Deflection Curve The beams described in the problems for Section 9.2 have constant flexural rigidity EI. Problem 9.2-1 The deflection curve for a simple beam AB (see figure) is given by the following equation: v =- (7L 4 - 10L 2 x 2 + 3x 4 ) Describe the load acting on the beam. Solution 9.2-1 Simple beam q 0 x  360LEI 9 Deflections of Beams y x A B L Take four consecutive derivatives and obtain: From Eq. (9-12c): The load is a downward triangular load of maximum intensity q 0 . q =-EIv –– = q 0 x L v –– =- q 0 x LEI v =- q 0 x 360 LEI (7L 4 - 10 L 2 x 2 + 3x 4 ) L q 0 Problem 9.2-2 The deflection curve for a simple beam AB (see figure) is given by the following equation: v =- sin   L x  (a) Describe the load acting on the beam. (b) Determine the reactions R A and R B at the supports. (c) Determine the maximum bending moment M max . q 0 L 4   4 EI Probs. 9.2-1 and 9.2-2