Shearing Stress Calculator

✖The Shearing force are unaligned forces pushing one part of a body in one specific direction, and another part of the body in the opposite direction.ⓘ Shearing Force [V]			+10% -10%
✖The First Moment of Area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σ(a × d)].ⓘ First Moment of Area [Ay]			+10% -10%
✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%
✖The Thickness of Material is the distance through an object.ⓘ Thickness of Material [t]			+10% -10%

✖The Shearing Stress is a type of stress that acts coplanar with cross section of material.ⓘ Shearing Stress [𝜏]

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Formula

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Shearing Stress

Formula

`"𝜏" = ("V"*"Ay")/("I"*"t")`

Example

`"3.6Pa"=("42N"*"4500mm³")/("3.5kg·m²"*"0.015mm")`

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Shearing Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shearing Stress = (Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)
𝜏 = (V*Ay)/(I*t)
This formula uses 5 Variables

Variables Used

Shearing Stress - (Measured in Pascal) - The Shearing Stress is a type of stress that acts coplanar with cross section of material.
Shearing Force - (Measured in Newton) - The Shearing force are unaligned forces pushing one part of a body in one specific direction, and another part of the body in the opposite direction.
First Moment of Area - (Measured in Cubic Meter) - The First Moment of Area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σ(a × d)].
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
Thickness of Material - (Measured in Meter) - The Thickness of Material is the distance through an object.

STEP 1: Convert Input(s) to Base Unit

Shearing Force: 42 Newton --> 42 Newton No Conversion Required
First Moment of Area: 4500 Cubic Millimeter --> 4.5E-06 Cubic Meter (Check conversion here)
Moment of Inertia: 3.5 Kilogram Square Meter --> 3.5 Kilogram Square Meter No Conversion Required
Thickness of Material: 0.015 Millimeter --> 1.5E-05 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = (V*Ay)/(I*t) --> (42*4.5E-06)/(3.5*1.5E-05)

Evaluating ... ...

𝜏 = 3.6

STEP 3: Convert Result to Output's Unit

3.6 Pascal --> No Conversion Required

FINAL ANSWER

3.6 Pascal <-- Shearing Stress

(Calculation completed in 00.020 seconds)

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Created by Pragati Jaju

College Of Engineering (COEP), Pune

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Verified by Kethavath Srinath

Osmania University (OU), Hyderabad

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< 16 Stress Calculators

Stress due to Impact Loading

Go Stress due to Loading = Load*(1+sqrt(1+(2*Cross sectional area*Bending Stress*Height at which load falls)/(Load*Length of Weld)))/Cross sectional area

Brinell Hardness Number

Go Brinell Hardness Number = Load/((0.5*pi*Diameter of Ball Indentor)*(Diameter of Ball Indentor-(Diameter of Ball Indentor^2-Diameter of Indentation^2)^0.5))

Thermal Stress in Tapered Bar

Go Thermal Stress = (4*Load*Length of Weld)/(pi*Diameter of Bigger End*Diameter of Smaller End*Bending Stress)

Beam Shear Stress

Go Shearing Stress = (Total Shear Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)

Shearing Stress

Go Shearing Stress = (Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)

Shear Stress in Double Parallel Fillet Weld

Go Shearing Stress = Load on Double Parallel Fillet Weld/(0.707*Length of Weld*Leg of Weld)

Thermal Stress

Go Thermal Stress = Coefficient of Thermal Expansion*Bending Stress*Change in Temperature

Bending Stress

Go Bending Stress = Bending Moment*Distance from Neutral Axis/Moment of Inertia

Torsional Shear Stress

Go Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia

Shear Stress of Circular Beam

Go Stress on Body = (4*Shearing Force)/(3*Cross sectional area)

Stress due to Gradual Loading

Go Stress due to Gradual Loading = Force/Cross sectional area

Maximum Shearing Stress

Go Stress on Body = (1.5*Shearing Force)/Cross sectional area

Shear Stress

Go Shearing Stress = Tangential Force/Cross sectional area

Bulk Stress

Go Bulk Stress = Normal Inward Force/Cross sectional area

Direct Stress

Go Direct Stress = Axial Thrust/Cross sectional area

Stress due to Sudden Loading

Go Stress on Body = 2*Force/Cross sectional area

Shearing Stress Formula

Shearing Stress = (Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)
𝜏 = (V*Ay)/(I*t)

What is Shearing Stress?

When an external force acts on an object, It undergoes deformation. If the direction of the force is parallel to the plane of the object. The deformation will be along that plane. The stress experienced by the object here is shear stress or tangential stress.

It arises when the force vector components which are parallel to the cross-sectional area of the material. In the case of normal/longitudinal stress, The force vectors will be perpendicular to the cross-sectional area on which it acts.

How to Calculate Shearing Stress?

Shearing Stress calculator uses Shearing Stress = (Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material) to calculate the Shearing Stress, The Shearing Stress formula is defined as the type of stress that acts coplanar with a cross-section of material. Shearing Stress is denoted by 𝜏 symbol.

How to calculate Shearing Stress using this online calculator? To use this online calculator for Shearing Stress, enter Shearing Force (V), First Moment of Area (Ay), Moment of Inertia (I) & Thickness of Material (t) and hit the calculate button. Here is how the Shearing Stress calculation can be explained with given input values -> 0.0036 = (42*4.5E-06)/(3.5*1.5E-05).

FAQ

What is Shearing Stress?

The Shearing Stress formula is defined as the type of stress that acts coplanar with a cross-section of material and is represented as 𝜏 = (V*Ay)/(I*t) or Shearing Stress = (Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material). The Shearing force are unaligned forces pushing one part of a body in one specific direction, and another part of the body in the opposite direction, The First Moment of Area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σ(a × d)], Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis & The Thickness of Material is the distance through an object.

How to calculate Shearing Stress?

The Shearing Stress formula is defined as the type of stress that acts coplanar with a cross-section of material is calculated using Shearing Stress = (Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material). To calculate Shearing Stress, you need Shearing Force (V), First Moment of Area (Ay), Moment of Inertia (I) & Thickness of Material (t). With our tool, you need to enter the respective value for Shearing Force, First Moment of Area, Moment of Inertia & Thickness of Material and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Shearing Stress?

In this formula, Shearing Stress uses Shearing Force, First Moment of Area, Moment of Inertia & Thickness of Material. We can use 3 other way(s) to calculate the same, which is/are as follows -

Shearing Stress = (Total Shear Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)
Shearing Stress = Tangential Force/Cross sectional area
Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia

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