Structural and Stress Analysis - Theories, Tutorials and by J. Ye

By J. Ye

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Example text

7), determine the shear stresses at the corners of the cross-section. [Solution] This question tests your conceptual understanding of shear stresses. They always appear in pair on planes that are perpendicular to each other. They are equal in magnitude, but in an opposite sense. 7 Take an infinitesimal element around a corner point and assume that on the plane of the cross-section there are two shear stresses perpendicular to either the horizontal or the vertical boundary. The two assumed shear stresses must be equal to the shear stresses acting on the Torsion 49 top and the left-hand-side surfaces.

For a structure system, if the number of independent equilibrium equations is less than the number of unknown forces, the system is termed as an indeterminate system. • To solve a statically indeterminate system, geometrical compatibility of deformation must be considered along with the equilibrium conditions. • Replacing a load applied on a material by an alternative, but statically equivalent load will affect only the stress field in the vicinity. • An abrupt change of geometry of a structural member will cause stress concentration near the region of the change.

Solution] This is a statically indeterminate structure and hence the reaction torques on the cross-sections at A and D cannot be uniquely determined by considering the equilibrium of the system. 4(a)). Under the action of the three twist moments, the angle of twist of section D must be zero (fixed end condition). After the end moment at D is found, the system is equivalent to a statically determinate system. The procedure shown in previous examples can then be followed to determine the final solution.

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