10 k 8 ft D 6 k 20 ft B 16 ft

Solve the problem by the moment-area method. The beam has constant flexural rigidity EI. A simple beam AB supports two concentrated loads P at the positions shown in the figure. B C 4. 4 A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d = 12 mm, L = 5.4 m, E = 200 GPa, and I = 193 x 10° mm, calculate the magnitude of the loads P (in kN) so that the beam just touches the support at C. 163.87 x kN

For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=1.50 m, b=5.00 m, PA = 75kN, and PC = 90kN. Construct the shear-force and bending-moment diagrams. Calculate the reaction forces By and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below.

Beam AC with constant EI has a roller support at point B and slider support at point A as shown in the figure below. Using the conjugate beam method to determine the magnitude of the couple moment M0 in terms of P if the displacement at point C is zero. Hint: the slider support can be considered as a fixed support but can move freely in the vertical direction. Use these properties to find the corresponding conjugate support for this problem.