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Shearing stress is the deforming force that acts per unit area on the object. When an external force acts along with an object, deformation takes place. If the direction of the force is parallel to the plane of the object, stress will be experienced by the object. This stress is Shearing Stress or Tangential Stress.
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Key Terms: Shear Stress, Strain, Force, Shear Force, Tangential Force, Bending Stress, Vector, Pascal, Angular Changes
What is Shearing Stress?
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Shearing stress is defined as the stress that acts coplanar with the cross-section area of the material. Shear Forces lead to Shear Stress. It is a vector quantity, thus both the direction and the magnitude of the force are involved. Shear Stress is denoted by the Greek alphabet “\(\tau\)”.
The units of shearing stress are similar to that of any other type of stress. The SI unit for shearing stress is N/m2 or Pa (Pascal).
Also Check:
| Important Concept Related Topics | ||
|---|---|---|
| Elastic Limit | Beam Deflection Formula | Plastic Deformation |
| Stress | Fluid Friction | Unit of Viscosity |
How is Shearing Stress Calculated?
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The formula for calculating Shearing Stress is:
| \(\tau\) = F/A |
Where,
- \(\tau\) = Shearing Stress
- F = Force acting on the body
- A = Area of the cross-section of the body, which is parallel to the force vector
Shearing Stress in our Daily Lives
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Shearing stress is a regular phenomenon that we all experience unknowingly every day. Some of the real-life shearing stress examples are:
- Painting, Brushing or applying lotions
- While making Indian bread such as Dosa or Roti
- While sliding the screen of our smartphones
- While sliding through a slide in a park
- Writing on a blackboard with a chalk
- When a vehicle suddenly stops after a break, the seat surface experiences a shear force
- Any forms of cutting (cutting vegetables, fruits, paper, or cloth)
- When someone steps on a sandcastle leading to its collapse
How is Shear Stress different from Bending Stress?Shear stress is the deforming force that acts per unit area and in the direction perpendicular to the axle of the member. Whereas, Bending Stress acts parallel to the axle of the member. It is also known as Flexural Stress. |
Difference Between Shear Stress and Shear Strain
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Shear Stress and Shear Strain are different from one another. Some of their major differences include:
| Shear Stress | Shear Strain |
|---|---|
| Shear Stress is defined as the stress that acts coplanar with the cross-section area of the material. | Shear Strain is the ratio of the length of the transverse deformation occurring in the object to that of the perpendicular length in the plane of the applied force. |
| Shear stress unit is N/m2 or Pa (Pascal). | Shear Strain does not have any unit. |
| Shear Stress, \(\tau\) = ꬾ × G (here, \(\tau\) = Shear stress, ꬾ = Shear strain, and G = Modulus of rigidity) | Shear Strain, ꬾ = \(\tau\) /G (here, \(\tau\) = Shear stress, ꬾ = Shear strain, and G = Modulus of rigidity) |
| Shear stress is usually measured as per the Tangential force quantity. | Shear strain is usually measured as per the Angular changes of body. |
Shearing Stress in Fluids
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Shear stress takes place in fluids too. When any kind of fluid flows within a solid structure, the shear stress is observed along with the point of contact between fluid and boundary. Fluid comprises various levels, each level moves at a different speed.
The layers of the same height from the boundary experience the same speed whereas levels of different heights experience different speeds. This varying speed between the layers is a result of shearing stress.
Solved Examples Related to Shearing StressQues. Why is the shearing stress in a beam are maximum? (1 mark) Ans. Shearing stress in a beam is maximum when it is at the neutral axis. Shearing stress is the stress that acts coplanar with the cross-section area of the material. Ques. A steel rod, round in shape, of 100 mm diameter is bent to form an arc of the radius of 100 m. Determine its maximum stress in the rod. (Consider, E = 2×105 N/mm2). (2 marks) Ans. As given in the question, |
Previous Year Questions
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- A copper wire and a steel wire of the same diameter and length … [BHU UET]
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Things to Remember Based on Shearing Stress
- Shearing stress is defined as the type of stress that acts coplanar with the cross-section area of the material.
- It is a Vector quantity and denoted by the Greek alphabet ‘\(\tau\)’.
- The SI unit of shearing stress is N/m2 or Pa (Pascal).
- The formula for Shearing Stress is, \(\tau\) = F/A (where \(\tau\) is shearing stress, F is the force acting on the body and A is area of the cross-section of the body, which is parallel to the force vector.)
- Bending Stress is the force that acts parallel to the axle of the member.
- Shear Strain is the ratio of the length of the transverse deformation occurring in the object to that of the perpendicular length in the plane of the applied force.
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Sample Questions Based on Shearing Stress
Ques: Give an example of pure shear. (1 Mark)
Ans: Pure shear is produced by the twisting of a cylinder.
Ques: Define tangential or shearing stress. (1 Mark)
Ans: Shearing Stress or tangential stress is defined as the deforming force acting per unit area tangential to the surface.
Ques: In Calculate shearing stress on PQ, when the shearing stress can be maximum? (2 Marks)
Ans: Shearing stress = Fsin2θ/2a
sin2θ must be maximum for maximum shearing stress
\(i.e. \cos (2\theta) = 1 = \sin (\frac{\pi}{2})\)
Therefore, \(2\theta = \frac{\pi}{2} or \theta = \frac{\pi}{4} = 45^o\)
Ques: What is the difference between shear stress and shear strain? (2 Marks)
Ans: Shear Stress is the ratio of shear force to that of the area of the surface and is tangential and applied along the surface. Shear stress is denoted by ‘?’.
Shear Strain is the ratio of the length of the transverse deformation occurring in the object to that of the perpendicular length in the plane of the applied force. It is denoted by ‘y’.
Ques: Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 x 107 Pa? Assume that each rivet is to carry one-quarter of the load. (2 Marks)
Ans: Given that: Diameter = 6mm
Radius, r = 3 x 10-3 m;
Maximum stress = 6.9 x 107 Pa
Maximum load on a rivet = Maximum stress x cross-sectional area
= 6.9 x 107 x 22/7 (3 x 10-3)2 N = 1952 N
Maximum tension = 4 x 1951.7 N = 7.8 x 103 N.
Ques: Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 x 107 Pa? Assume that each rivet is to carry one-quarter of the load. (3 Marks)
Ans: Diameter of the metal strip, d = 6.0 mm = 6.0 x 10-3 m
Radius, r = d/2 = 3.0 x 10-3 m
Maximum shearing stress = 6.9 x 107 Pa
Maximum stress = Maximum Load or force / Area
Maximum force = Maximum stress x Area
= 6.9 x 107 x π x (r)2
= 6.9 x 107 x π x (3 x 10-3)2
= 1949.94 N
Each rivet carries one-quarter of the load.
∴ Maximum tension on each rivet = 4 x 1949.94 = 7799.76 N
Ques: A bar of cross-section A is subjected to equal and opposite tensile force F at its ends. If there is a plane through the bar making an angle Q, with the plane at right angles to the bar in the figure
a. Find the tensile stress at this plane in terms of F, A and Q
b. What is the shearing stress at the plane in terms of F, and Q.
i. For what value of Q is tensile stress a maximum. (3 Marks)
Ans: a) Tensile stress = Normal Stress / Area
Normal force = F cos θ
Tensile Stress = F cos θ / (A/ cos θ)
Tensile Stress = F cos2θ / A
b) Shearing Stress = Tangential Stress / Area
Tangential force = F Sinθ
Area = A/Cos θ
Shearing Stress = F Sinθ / (A/cos θ)
= F(Sinθ Cosθ)/A
Divide & Multiply by 2
= F 2Sinθ Cosθ) / 2A
Since, Sin2θ = 2Sinθ Cosθ
= F Sin2θ / 2A
c) Tensile Stress = F Cos2θ / 2A
Tensile stress ∝ cos2θ
cos2θ = Maximum = 1
cos2θ = 1
θ = cos-1(1)
θ = 0°
Tensile stress a maximum when the plane is parallel to the bar.
Ques: A cube of aluminum of each side 4 cm is subjected to a tangential (shearing) force. The top of the cube is sheared through 0.012 cm with respect to the bottom face.
Find (a) shearing strain,
(b) shearing stress,
(c) shearing force. Given η = 2.08 × 1011 dyne cm-2. (3 Marks)
Ans: Here,
length of each side, L = 4 cm
Lateral displacement, x = 0.012 cm ,
η = 2.08 × 1011 dyne cm-2.
Ques: Explain shear stress in fluids. (3 Marks)
Ans: The fluid movement along the boundary of the solid exerts shear stress at the boundary of the solid. The speed of the fluid with respect to the boundary is zero. At a point from the boundary, the speed of flow of the fluid will be equal to that of the fluid.
The shear stress is directly proportional to the shear strain in the fluid for all the Newtonian fluids under the laminar flow. In this, the viscosity of the fluid is a constant of proportionality and the viscosity is not constant for all Non-Newtonian fluids. The shear stress exerted on the boundary of the solid result in the loss of velocity of the fluid. For the Newtonian Fluids, the shear stress is given by, \(\tau\)= μ (du/dy)
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