Draw the shear and bending-moment diagrams for the beam and loading shown and determine the maximum normal stress due to bending. Shear Diagram Step 1: Determine the reactions at A and B. Step 2: Draw out the shear diagram The shear at A is equal to the reaction at A. A uniformly distributed load (w) corresponds to a linearly sloped line of the shear diagram. In this problem, there is a line between points A and C with a negative slope of 16 kN/m. First let's determine the shear at point C. Connect these two points. There are no loads or supports between points C and B, therefore there is no change in shear. There is an upward reaction of 7.2 kN at B, so the shear increases by 7.2 kN at B. The shear diagram ends at 0. This is our final shear diagram. Moment Diagram Step 1: Divide the shear diagram into 3 areas. Step 2: Use similar triangles to determine x. Step 3: Since the moment is the area under the shear diagram, determine the area of each section under the shear diagram. Step 4: Draw out the moment diagram. The moment at "x" is equal to the area of the 1st section. A linearly sloped line on the shear diagram corresponds to a curved line on the moment diagram. Since the area of the second section was -1.62 kN-m (it's negative because the area is below 0 on the shear diagram) the moment is decreases by 1.62 kN-m. 8.82 - 1.62 = 7.2 KN/m Since the area of the third section was -7.2 kN-m, the moment is decreases by 7.2 kN-m. A flat line on the shear diagram corresponds to a linearly sloped line on the moment diagram. This is our final moment diagram. Maximum Stress According to the moment diagram the maximum moment on the beam is 8.82 kN-m. Look up the section modulus (S) for an S150x16.5 (be sure to use metric) and use the bending stress formula to determine the maximum bending stress. ANS = norm. stress: 73.5 MPa
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January 2023
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