31. The figure shown below depicts a load cell made of aluminum. The ring and the stem both have square cross-section: 0.1 x 0.1 m2. Assume the Young's modulus is 72 GPa. The mean radius of the ring is 0.05 m. In a load cell, the axial load is measured from the average of strains at points P, <2, R, and S, as shown in the figure. Points P and S are on the outside surface, and Q and R are on the inside surface of the ring. Model the load cell using plane frame elements. The step portions may be modeled using one element each. Use about 20 elements to model the entire ring. Compute the axial strain evv at locations P, Q, R, and S for a load of 1,000 N. Draw the axial force, shear force, and bending moment diagrams for one quarter of the ring. The strain can be computed using the beam formula:
Chapter 5 Oxv = E8xx P Mc A T where P is the axial force, M the bending moment, A the cross-sectional area, I the moment of ;
inertia, and c the distance from the midplane.
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