How is the modulus of rigidity mathematically defined as a ratio_________________?
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Answer: D. shear stress and shear strain
Explanation
Modulus of rigidity, also known as shear modulus, is formally defined as the ratio of shear stress to corresponding shear strain. This fundamental elastic constant measures a material resistance to shape change under planar shearing forces without volume alteration. Hooke law for shear states that shear stress is directly proportional to shear strain through this specific rigidity modulus constant. Shear stress represents the force component parallel to the material cross-sectional area divided by the total area. Shear strain measures the angular deformation or distortion experienced by the stressed material element under applied loads. Isotropic material elasticity can be completely characterized using elastic modulus, rigidity modulus, bulk modulus, and Poisson ratio.
The ratio of longitudinal stress to longitudinal strain defines Young modulus of elasticity for axial tensile or compressive loads. Volumetric stress divided by volumetric strain defines the bulk modulus, which characterizes resistance to uniform hydrostatic compression. Lateral stress and strain ratios are not used directly to define standard primary engineering material elasticity moduli.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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