Primary Shear Stress given Resultant Shear Stress Calculator

✖Resultant shear stress in weld is defined as the resultant stress-induced by two or more forces acting on the welded joint.ⓘ Resultant shear stress in weld [τ]			+10% -10%
✖Bending stress in welded joint is the normal stress that is induced at a point in a welded joint subjected to loads that cause it to bend.ⓘ Bending stress in welded joint [σ_b]			+10% -10%

✖Primary shear stress in weld is defined as the force tending to cause deformation of the welded joint by slippage along a plane or planes parallel to the imposed stress.ⓘ Primary Shear Stress given Resultant Shear Stress [τ₁]

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Formula

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Primary Shear Stress given Resultant Shear Stress

Formula

`"τ"_{"1"} = sqrt(("τ"^2)-("σ"_{"b"}^2)/4)`

Example

`"25.98076N/mm²"=sqrt((("70N/mm²")^2)-(("130N/mm²")^2)/4)`

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Primary Shear Stress given Resultant Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Primary shear stress in weld = sqrt((Resultant shear stress in weld^2)-(Bending stress in welded joint^2)/4)
τ₁ = sqrt((τ^2)-(σ_b^2)/4)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Primary shear stress in weld - (Measured in Pascal) - Primary shear stress in weld is defined as the force tending to cause deformation of the welded joint by slippage along a plane or planes parallel to the imposed stress.
Resultant shear stress in weld - (Measured in Pascal) - Resultant shear stress in weld is defined as the resultant stress-induced by two or more forces acting on the welded joint.
Bending stress in welded joint - (Measured in Pascal) - Bending stress in welded joint is the normal stress that is induced at a point in a welded joint subjected to loads that cause it to bend.

STEP 1: Convert Input(s) to Base Unit

Resultant shear stress in weld: 70 Newton per Square Millimeter --> 70000000 Pascal (Check conversion here)
Bending stress in welded joint: 130 Newton per Square Millimeter --> 130000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ₁ = sqrt((τ^2)-(σ_b^2)/4) --> sqrt((70000000^2)-(130000000^2)/4)

Evaluating ... ...

τ₁ = 25980762.1135332

STEP 3: Convert Result to Output's Unit

25980762.1135332 Pascal -->25.9807621135332 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

25.9807621135332 ≈ 25.98076 Newton per Square Millimeter <-- Primary shear stress in weld

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 8 Welded Joints Subjected to Bending Moment Calculators

Distance of Point in Weld from Neutral Axis given Bending Stress in Weld

Go Distance of Point in Weld to Neutral Axis = Moment of Inertia of Weld about Neutral Axis*Bending stress in welded joint/Bending moment in welded joint

Moment of Inertia of all Welds given Bending Moment

Go Moment of Inertia of Weld about Neutral Axis = Bending moment in welded joint*Distance of Point in Weld to Neutral Axis/Bending stress in welded joint

Bending Stress Caused Due to Bending Moment

Go Bending stress in welded joint = Bending moment in welded joint*Distance of Point in Weld to Neutral Axis/Moment of Inertia of Weld about Neutral Axis

Bending Moment given Bending Stress

Go Bending moment in welded joint = Moment of Inertia of Weld about Neutral Axis*Bending stress in welded joint/Distance of Point in Weld to Neutral Axis

Bending Stress given Resultant Shear Stress in Weld

Go Bending stress in welded joint = sqrt(2*(Resultant shear stress in weld^2)-(Primary shear stress in weld^2))

Primary Shear Stress given Resultant Shear Stress

Go Primary shear stress in weld = sqrt((Resultant shear stress in weld^2)-(Bending stress in welded joint^2)/4)

Resultant Shear Stress in Weld

Go Resultant shear stress in weld = sqrt((Bending stress in welded joint^2)/4+(Primary shear stress in weld^2))

Primary Shear Stress-induced due to Eccentric Load

Go Primary shear stress in weld = Eccentric load on weld/Throat Area of Welds

Primary Shear Stress given Resultant Shear Stress Formula

Primary shear stress in weld = sqrt((Resultant shear stress in weld^2)-(Bending stress in welded joint^2)/4)
τ₁ = sqrt((τ^2)-(σ_b^2)/4)

Define Shear Stress?

Shear stress, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. The resultant shear is of great importance in nature, being intimately related to the downslope movement of earth materials and to earthquakes

How to Calculate Primary Shear Stress given Resultant Shear Stress?

Primary Shear Stress given Resultant Shear Stress calculator uses Primary shear stress in weld = sqrt((Resultant shear stress in weld^2)-(Bending stress in welded joint^2)/4) to calculate the Primary shear stress in weld, The Primary Shear Stress given Resultant Shear Stress formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Primary shear stress in weld is denoted by τ₁ symbol.

How to calculate Primary Shear Stress given Resultant Shear Stress using this online calculator? To use this online calculator for Primary Shear Stress given Resultant Shear Stress, enter Resultant shear stress in weld (τ) & Bending stress in welded joint (σ_b) and hit the calculate button. Here is how the Primary Shear Stress given Resultant Shear Stress calculation can be explained with given input values -> 2.6E-5 = sqrt((70000000^2)-(130000000^2)/4).

FAQ

What is Primary Shear Stress given Resultant Shear Stress?

The Primary Shear Stress given Resultant Shear Stress formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress and is represented as τ₁ = sqrt((τ^2)-(σ_b^2)/4) or Primary shear stress in weld = sqrt((Resultant shear stress in weld^2)-(Bending stress in welded joint^2)/4). Resultant shear stress in weld is defined as the resultant stress-induced by two or more forces acting on the welded joint & Bending stress in welded joint is the normal stress that is induced at a point in a welded joint subjected to loads that cause it to bend.

How to calculate Primary Shear Stress given Resultant Shear Stress?

The Primary Shear Stress given Resultant Shear Stress formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress is calculated using Primary shear stress in weld = sqrt((Resultant shear stress in weld^2)-(Bending stress in welded joint^2)/4). To calculate Primary Shear Stress given Resultant Shear Stress, you need Resultant shear stress in weld (τ) & Bending stress in welded joint (σ_b). With our tool, you need to enter the respective value for Resultant shear stress in weld & Bending stress in welded joint 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 Primary shear stress in weld?

In this formula, Primary shear stress in weld uses Resultant shear stress in weld & Bending stress in welded joint. We can use 1 other way(s) to calculate the same, which is/are as follows -

Primary shear stress in weld = Eccentric load on weld/Throat Area of Welds

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