A shear stress in a given direction cannot exist without a balancing shear stress of equal intensity in a direction at right angle to it. The balancing shear stress is known as:

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  1. compound shear stress 
  2. complimentary shear stress
  3. principal shear stress
  4. torsional shear stress

Answer (Detailed Solution Below)

Option 2 : complimentary shear stress
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Explanation:

Complimentary Shear Stress:

  • When a shear stress is applied on an element, it induces two planes of shear stress. One is the direction of the applied shear stress and the other is the direction perpendicular (or at a 90-degree angle) to the applied shear stress.
  • These shear stresses balance each other out and maintain the equilibrium of the stressed body, thus, they are named as "complimentary".
  • The concept of complimentary shear stress is based on the equilibrium condition for a body.
  • For a body to be in equilibrium, the net force and net moment should be zero. So, the summation of all stresses acting on the element should be zero. Therefore, if a shear stress tau acts on one plane, there must be an equal and opposite shear stress acting on an adjacent plane (which is perpendicular) to keep the object in equilibrium.
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