4-24 - CHAP 4 Finite Element Analysis for Beams and Frames...

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CHAP 4 Finite Element Analysis for Beams and Frames 247 24. The frame shown in the figure is clamped at the left end and supported on a hinged roller at the right end. The radius of circular cross-section r = 0.05 m. An axial force P and a couple C act at the right end. Assume the following numerical values: L = 1 m, E = 80 GPa, P = 15,000 N, C = 1,000 Nm. (a) Use one element to determine the rotation at the right support. (b) What is the deflection of the beam at x = L /2 (c) What is the maximum tensile stress? Where does it occur? Solution: (a) The frame element has 6 DOFs. 1 1 1 2 2 2 { } { , , , , , } T u v u v  Q . Since u 1 , v 1 , 1 , and v 2 are fixed, we can construct element matrix equations for only free-DOFs: u 2 and 2 . From Eq. (5.80), we have 2 2 0 4 0 EA uP L EI C L  
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