Use a computer program to assist in the design problems in Problem 5.73. The curved se...

Use a computer program to assist in the design problems in Problem 5.73.

The curved semi-circular frame shown in Figure P5–73 is supported by a pin on the left end and a roller on the right end and is subjected to a load P = 1000 lb at its apex. The frame has a radius to centerline cross section of R = 120 in. Select a structural steel W shape from Appendix F such that the maximum stress does not exceed 20 ksi. Perform a finite element analysis using 4, 8, and then 16 elements in your finite element model. Also, determine the maximum deflection for each model. It is suggested that the finite element answers for deflection be compared to the solution obtained by classical methods, such as using Castigliano’s theorem. The expression for deflection under the load is given by using Castigliano’s theorem as

where A is the cross sectional area of the W shape, Av is the shear area of the W shape (use depth of web times thickness of web for the shear area); E = 30 × 10⁶ psi; and G = 11.5 × 10⁶ psi: Now change the radius of the frame to 20 in. and repeat the problem. Run the finite element model with the shear area included in your computer program input and then without. Comment on the difference in results and compare to the predicted analytical deflection by using the equation above for d_y: