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 ¼ 1000 lb at its apex. The frame has a radius to
centerline cross section of R ¼ 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
10
6
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
:
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