Final answer:
To draw the shear and bending-moment diagrams, we analyze the beam and loading. The shear diagram shows the shear force along the beam, while the bending-moment diagram shows the bending moment. The maximum absolute values of the shear and bending moment can be found from the diagrams.
Step-by-step explanation:
To draw the shear and bending-moment diagrams, we need to analyze the beam and loading shown. We start by calculating the reactions at the supports. From the given information, the total load on the beam is 5 lb + 16 lb + 12 lb + 16 lb + 5 lb = 54 lb. The reactions at points A and E are half of this total load, so RA = RE = 54 lb / 2 = 27 lb.
We can now construct the shear diagram. Starting from point A, the shear force decreases by 27 lb (the reaction at A) and remains constant until we reach point B. At B, the shear force increases by 5 lb (the first load). Then, it decreases by 16 lb (the second load) until we reach point C. At C, the shear force increases by 12 lb (the third load) and remains constant until we reach point D. At D, the shear force decreases by 16 lb (the fourth load) until we reach point E. Finally, at E, the shear force increases by 5 lb (the fifth load) and remains constant until the end of the beam.
To construct the bending-moment diagram, we start by calculating the moments at points A and E. The moment at A is zero since there are no loads to the left of A. The moment at E is the reaction at E (27 lb) multiplied by the distance from A to E (12 in). Therefore, ME = 27 lb * 12 in = 324 lb.in.
From point A to B, the bending moment increases linearly from 0 to 27 lb * 9 in = 243 lb.in. From point B to C, the bending moment remains constant at 243 lb.in. From point C to D, the bending moment increases linearly from 243 lb.in to 243 lb.in + 12 lb * 9 in = 351 lb.in. From point D to E, the bending moment remains constant at 351 lb.in. Finally, from point E to the end of the beam, the bending moment decreases linearly from 351 lb.in to 351 lb.in - 5 lb * 9 in = 306 lb.in.
(a) The maximum absolute value of the shear is 27 lb, which occurs at points A and E.
(b) The maximum absolute value of the bending moment is 351 lb.in, which occurs at points C and D.