An introduction Shear Stress, Modulus of Rigidity and Strain Energy.
Shear StressIf the applied load consists of two equal and opposite parallel forces which do not share the same line of action, then there will be a tendency for one part of the body to slide over, or shear from the other part. In the figure below, if the section LM is parallel to the forces and has an area A, then the average Shear Stress . If the Shear Force varies then at a point Note : The Shear Stress is tangential to the area over which it acts, and is expressed in the same units as Direct Stress, i.e. Load per unit Area. See Also the section on Shear Force and Bending Moment
Complementary Shear Stress.A,B,C,D is a small rectangular element whose sides are x, y and z which are perpendicular to the figure. A Shear Stress S acts on the planes A,B and C,D It can be seen that these Stresses form a Couple which can only be balanced by tangential Stresses on the planes A,D and B,C. These are known as Complementary Shear Stresses. Let S' be the Complementary Shear Stress induced on planes A,D and B,C. Then as the element is in equilibrium:
Example - Shear stress on shaft bolts
A Flange Coupling which joins two sections of a Shaft is required to transmit 250 h.p. at 1000 r.p.m. If six bolts are used on a pitch circle of 6 ins. find the diameter of the bolts. The allowable mean Shear Stress is 5 tons/in2.
Torque to be transmitted s given by:
Diameter of bolt,
Shear StrainThe distortion produced by Shear Stress on an element or Rectangular Block is shown in the following diagram. The Shear Strain or "Slide" is and can be defined as the change in the right angle. It is measured in Radians and is dimensionless.
The Modulus Of RigidityFor Elastic materials it is found that within certain limits, Shear Strain is proportional to the Shear Stress producing it. The Ratio is called the Modulus of Rigidity and is denoted by C. and in the Imperial system is in
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