31 A beam is loaded and supported as shown in Fig. P7-31. Using the coordinate axes shown, write equations for the shear force V, and the bending moment M, for any section of the beam in the interval 4 ft < x < 8 ft.

Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Additionally: Let a = 3.1 m, b = 5.9 m, w = 34 kN/m, P = 48 kN, Q = 34 kN, and Mc = 155 kN-m. Construct the shear-force and bending-moment diagrams P A В E Mc a b a а Determine the shear force acting at each of the following locations: (a)x = 3.1 – m (i.e., just to the left of support B) (b) x = 3.1 + m (i.e., just to the right of support B) (c)x = 12.1 – m (i.e., just to the left of support D) (d) x = 12.1 + m (i.e., just to the right of support D)

Draw the shear force and Bending Moment Diagram for the following beam. 25 KN 32 KN 17 KN 28 KN A B 35 75 90 125 160 All Dimensions are in mm