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Problem 2.2-7 Two rigid bars, AB and CD, rest on a smooth horizontal surface (see figure). Bar AB is pivoted end A and bar CD is pivoted at end D. The bars are connected to each other by two linearly elastic springs of stiffness k. Before the load P is applied, the lengths of the springs are such that the bars are parallel and the springs are without stress. Derive a formula for the displacement C at point C when the load P is acting. (Assume that the bars rotate through very small angles under the action of the load P.) 67 b b A B C P D b Solution 2.2-7
b A Two bars connected by springs
b B DISPLACEMENT DIAGRAMS
B A b C P b D 2 B
C C D 2 k
C stiffness of springs displacement at point C due to load P B C 1 displacement of point B displacement of point C elongation of first spring
B C FREE-BODY DIAGRAMS
A b F1 F1 C P F2 b B F2 2 shortening of second spring
C 2 B b b D 2 1 F1 k 4P ; 3k 2 F2 k 2P 3k Also, SOLVE THE EQUATIONS: F1 F2 tensile force in first spring compressive force in second spring 1 2 bF1 2bP 4P 3 2bF1 F2 2bF2 bF2 2P 3 0 0 F1 F2 2F2 2F1 2P
C 1 2 B C 2
C 4P 3k 2P 3k
C: EQUILIBRIUM MA MD 0 0 B 2 Eliminate 20P 9k B and obtain Solving, F1 ...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.
- Spring '08