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This vibrating glass beam may be modeled as a cantilever beam with acceleration, variable linear density, variable section modulus, some kind of dissipation, springy end loading, and possibly a point mass at the free end. Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the ...
Simply supported beam with a single eccentric concentrated load. An illustration of the Macaulay method considers a simply supported beam with a single eccentric concentrated load as shown in the adjacent figure. The first step is to find . The reactions at the supports A and C are determined from the balance of forces and moments as
Free body diagram of a statically indeterminate beam In the beam construction on the right, the four unknown reactions are V A , V B , V C , and H A . The equilibrium equations are: [ 2 ]
For most boundary conditions several solutions exist simultaneously. When small deflections of a structure are to be analyzed, elastica theory is not required and an approximate solution may be found using the simpler linear elasticity theory or (for 1-dimensional components) beam theory .
Consequently, from Theorems 1 and 2, the conjugate beam must be supported by a pin or a roller, since this support has zero moment but has a shear or end reaction. When the real beam is fixed supported, both the slope and displacement are zero. Here the conjugate beam has a free end, since at this end there is zero shear and zero moment.
The moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. It was published in 1930 in an ASCE journal. [ 1 ] The method only accounts for flexural effects and ignores axial and shear effects.
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The structure’s unknown displacements and forces can then be determined by solving this equation. The direct stiffness method forms the basis for most commercial and free source finite element software. The direct stiffness method originated in the field of aerospace. Researchers looked at various approaches for analysis of complex airplane ...