Learning Goal: To analyze the deformations in a straight rod with a uniform cros

Question

Learning Goal: To analyze the deformations in a straight rod with a uniform cross-sectional area made out of a homogeneous material that is subjected to an externally applied bending moment. As shown, a cantilevered beam of length L = 5 rn is fixed at A. It has a moment of M = 35.0 kN. m applied at B and a diameter of d = 600 mm Bending moment diagram The cantilevered beam shown is subjected to a 35.0 kN . m moment at B. Draw the bending moment diagram for this beam. Begin by placing the lines of discontinuity. Normal strain at a point above the neutral axis A small segment of the beam located a distance x along the beam's length and having a thickness delta x is shown below (in profile view) in the undeformed and deformed positions, respectively. If the radius of curvature is rho = 2.5in, find the normal strain at y = 206rmn above the neutral axis. Express your answer to three significant figures in units of millimeters per millimeter. Maximum normal strain The normal strain distribution of an isolated segment of the beam is shown. If c = 300 mm, y = 206mm, and rho = 2.5m, what is the maximum normal strain in the beam? Express your answer in millimeters per millimeters.

Explanation / Answer

Part A: Since only moment is applied and no other forces, the bending moment diagram will be a horizontal straight line with value 35kn.m

Part B: normal strain epsilon = -y/rho = -206/2500 = -0.0824 (-ve indicates compression)

Part C: As can be seen from the profile, the maximum normal strain occurs at the boundary

epsilon_max = -ymax/rho = -300/2500 = -0.12 (-ve indicates compression)

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