An analytic solution for the stress distribution in a semi- infinite strip loaded on the transverse edge

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Virginia Polytechnic Institute

This thesis presents an analytic solution for the stress distribution in a semi-infinite strip subjected to symmetrical loads on the transverse edge. Three different types of loading on the transverse edge are considered: (i) a segment of uniform load, (ii) two concentrated normal loads, and (iii) two concentrated tangential loads. The solution is constructed by the method of images. Under successive reflections the given strip and the resulting images become a semi-infinite plate with a series of periodic loads on the edge. The stress function for such a plate is constructed by superposing the known solutions of a simple nature. To satisfy the boundary conditions along the longitudinal edges of the semi-infinite strip, additional stress functions are introduced. When the boundary conditions are adjusted, a system of integral equations and a system of algebraic equations are obtained, which are further reduced. to a single system of algebraic equations. The latter system is solved by the method of successive approximations. In each case, the expressions for normal stresses along the longitudinal axis are derived and numerical values for these stresses are given.