Unformatted text preview: , , j , , r , respectively. Then, the external work done on the system from the gradual application of the external forces must be equal to the increment of strain energy, i.e., 1r
1 Q j j 1 2 Fe fe 2 j 1 (1) In which F is the internal force in an element of the structure and e is the corresponding deformation caused by the internal force, while f is the internal force in the same element due to the virtual unit load. (Note: the real work terms include a factor of 1 2 while those representing virtual work do not have such a factor because the virtual unit force P 1 is already on the structure when the external forces are gradually applied.) From conservation of energy, considering only the real forces, 1r
1 Q j j 2 Fe 2 j 1 (2) And, subtracting Equation (2) from Equation (1), the virtual work done by the virtual unit force can be obtained as: 1 fe (3) In the case of a plane truss, all members are subjected to bar forces only. Hence, for a truss consisting of n members, Equation (3) becomes: n fk Fk Lk k 1 Ak Ek 1 fe...
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This document was uploaded on 03/11/2014.
- Spring '14