Question

4.5-7 A simply supported beam ABC is loaded by a verti- cal load P acting at the end of a bracket BDE (see figure). (a) Draw the shear-force and bending-moment dia- grams for beam ABC. (b) Now assume that load P at Eis directed to the right. The vertical dimension BD is LIS. Draw axial-force, shear-force, and bending-moment diagrams for ABC 2 PROB. 4.5-7

In (b), how to obtain bending moment at x = L/4. Plz explain specifically.

Answer 1

The load at E produces a moment of magnitude P times L/4 = PL/4 at point B, and also produces a vertical force equal to P(downarrow) at B. So we can redraw the beam as Reactions at A and C: Sigma M_A = 0 = > -PL/4 - PL/4 + R_B times L = 0 = > R_B = P/2 Sigma F_y = 0 = > R_A = P - P/2 = P/2 = > R_A = P/2 Moment equations: section AB: V(x) = -P/2 M(x) = Px/2 x = L/4 = > M(x) = PL/8 section CB: V(x) = P/2 M(x) = P/2x x = 3L/4 = > M(x) = 3PL/8 \r\n SFD and BMD: If load P is towards the right, there will be an equivalent moment = P times L/5 = PL/5 and a force P (rightarrow) at point B, so the beam can be drawn as, Find reactions at A and B: Sigma M_A =