Mechanical Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 8 (Q.No. 46)
46.
A shear stress across a plane, is always accompanied by a balancing shear stress across the plane and normal to it.
Discussion:
11 comments Page 2 of 2.
Dheeraj Kumar said:
11 months ago
@All.
That's correct.
This is a fundamental concept in solid mechanics often referred to as **complementary shear stress**.
Here's a breakdown of why this happens:
Equilibrium: For a body to be in equilibrium, all forces and moments acting on it must balance. This applies to internal stresses as well.
Shear Stress: Shear stress acts parallel to a surface. If you have shear stress acting on one plane, it creates an unbalanced moment (a twisting force).
Complementary Shear Stress: To counteract this moment and maintain equilibrium, equal and opposite shear stress must exist on a perpendicular plane.
For Eg;
Imagine holding a book between your hands and trying to slide the top cover to the right. To prevent the book from rotating, you instinctively apply an equal and opposite force with your other hand, sliding the bottom cover to the left. These opposing forces are analogous to complementary shear stresses.
Key Points:-
Magnitude: The complementary shear stresses are equal in magnitude.
Direction: They act in opposite directions.
Planes: They act on planes that are perpendicular to each other.
This principle of complementary shear stress is crucial in understanding how materials behave under load and is essential for analyzing and designing structures.
That's correct.
This is a fundamental concept in solid mechanics often referred to as **complementary shear stress**.
Here's a breakdown of why this happens:
Equilibrium: For a body to be in equilibrium, all forces and moments acting on it must balance. This applies to internal stresses as well.
Shear Stress: Shear stress acts parallel to a surface. If you have shear stress acting on one plane, it creates an unbalanced moment (a twisting force).
Complementary Shear Stress: To counteract this moment and maintain equilibrium, equal and opposite shear stress must exist on a perpendicular plane.
For Eg;
Imagine holding a book between your hands and trying to slide the top cover to the right. To prevent the book from rotating, you instinctively apply an equal and opposite force with your other hand, sliding the bottom cover to the left. These opposing forces are analogous to complementary shear stresses.
Key Points:-
Magnitude: The complementary shear stresses are equal in magnitude.
Direction: They act in opposite directions.
Planes: They act on planes that are perpendicular to each other.
This principle of complementary shear stress is crucial in understanding how materials behave under load and is essential for analyzing and designing structures.
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