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Shear and Bulk Modulus

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Shear and Bulk Modulus - Lesson Summary

When a pair of equal and opposite forces is applied tangentially to opposite end faces of a cubical body, the shape of the body is distorted and the stress generated is called tangential stress or shear stress. Shear stress is measured as the ratio of applied tangential force (F) to the area of the face, (A).
Shear strain is defined as the ratio of the lateral displacement of the top layer of the solid with respect to its bottom layer, This is equal to the tangent of the angle g expressed in radians.
The ratio of shear stress to shear strain for a material is the shear modulus or the modulus of rigidity and is denoted by the symbol G. Shear modulus has units of newton per metre square or pascal. Most materials have shear modulus values lower than their Young’s Modulus, and typically about one-third of their Young’s Modulus value.
Bulk Modulus
 When deforming forces are applied perpendicular to a body’s surface at each point, thevolume of a body decreases and the stress generated is called bulk stress or volume stress.
Forces acting perpendicularly inward at each point on the surface of a body are equivalent to a uniform increase in external pressure. Therefore, bulk stress is defined as a change in pressure, D p, which is equal to the ratio of force (F) to area (A).
If the volume of a body (V), changes by D V, then the bulk strain or volume strain is equal to the ratio of D V to V.
The ratio of bulk stress to bulk strain is called bulk modulus and is denoted by the symbol B.
Bulk modulus is equal to the ratio of D p to DV/ V. An increase in pressure causes a decrease in volume, which means that a positive value of D p causes a negative value of delta V. Therefore, the expression has a negative sign to give a positive result for B.
Bulk modulus is measured in units of newton per metre square or pascal.
The reciprocal of bulk modulus is called compressibility and is denoted by k.
The values of bulk modulus for a few materials are shown. Data shows that solids have the highest values of bulk modulus followed by liquids and then gases. Gases have an extremely small bulk modulus.
As compressibility is the reciprocal of bulk modulus, this means that gases have very large compressibility compared to liquids and liquids have higher compressibility than solids.
The compressibility and bulk modulus of gases depend on the pressure and temperature of the gas.
The reason for the huge difference between compressibility of gases, liquids, and solids lies in the intermolecular forces of interaction in the three states of matter. 
The molecules of a gas are so far apart that there is a negligible interaction force between them.
Liquids have a strong intermolecular force of interaction whereas solids have the strongest interaction between their molecules.


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