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Tham khảo tài liệu 'fundamentals of structural analysis episode 1 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Beam and Frame Analysis Force Method Part II by S. T. Mau To find the expression for strain energy we noted that M x Mo U f 1 M 2 dx 1 M o2 L 2 EI 2 EI Equating Wext to U yields n _ MoL t o EI It is clear that the principle of conservation of mechanical energy can only be use to find the deflection under a single external load. A more general method is the unit load method which is based on the principle of virtual force. The principle of virtual force states that the virtual work done by an external virtual force upon a real displacement system is equal to the virtual work done by internal virtual forces which are in equilibrium with the external virtual force upon the real deformation. Denoting the external virtual work by ÔW and the internal virtual work by ÔU we can express the principle of virtual force as ÔW ÔU 16 In view of Eq. 15 which defines the strain energy as work done by internal forces we can call ÔU as the virtual strain energy. When applying the principle of virtual force to find a particular deflection at a point we apply a fictitious unit load at the point of interest and in the direction of the deflection we are to find. This unit load is the external virtual force. The internal virtual force for a beam corresponding to the unit load is the bending moment in equlibrium with the unit load and is denoted by m x . Denoting the internal moment induced by the real applied load as M x the real deformation corresponding to the virtual moment m x is then de M x dx EI The strain energy of an infinitesimal element is m x dỡ and the integration of m x dỡ over the length of the beam gives the virtual strain energy. ÔU J m x MEd EI The external virtual work is the product of the unit load and the deflection we want denoted by A 135 Beam and Frame Analysis Force Method Part II by S. T. Mau 0W 1 A The principle of virtual force then leads to the following useful formula of the unit load method. t t 1 A J- m x M x dx t I EI 17 In Eq. 17 we have indicated the .
