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# 4-16 - CHAP 4 Finite Element Analysis for Beams and Frames...

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CHAP 4 Finite Element Analysis for Beams and Frames 235 16. Consider a cantilevered beam with spring support at the end, as shown in the figure. Assume E = 100 ksi, I = 1.0 in 4 , L = 10 in, k = 200 lb/in, beam height h = 10 in, and no gravity. The beam is subjected to a concentrated force F = 100 lb at the tip. (a) Using one beam element and one spring element, construct the structural matrix equation before applying boundary conditions. Clearly identify elements and nodes. Identify positive directions of all degrees of freedom. (b) Construct the global matrix equation after applying all the boundary conditions. (c) Solve the matrix equation and calculate the tip deflection. (d) Calculate the bending moment and shear force at the wall. Solution: For beam element, (1) 1 1 (1) 2 2 1 1 (1) 3 2 2 2 2 (1) 2 2 12 6 12 6 6 4 6 2 12 6 12 6 6 2 6 4 f L L v L L L L m EI L L v f L L L L L m  

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