Resolved shear stress Calculator

✖Applied stress is denoted by the symbol σ.ⓘ Applied stress [σ]			+10% -10%
✖Slip plane angle is the angle between the normal to the slip plane and the applied stress direction.ⓘ Slip plane angle [ϕ]			+10% -10%
✖Slip direction angle is the angle between the slip and stress directions.ⓘ Slip direction angle [λ]			+10% -10%

✖Resolved shear stress is the shear component that exists at all but parallel or perpendicular alignments to the stress direction.ⓘ Resolved shear stress [𝛕_R]

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Formula

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Resolved shear stress

Formula

`"𝛕"_{"R"} = "σ"*cos("ϕ")*cos("λ")`

Example

`"7E^-5MPa"="93.3Pa"*cos("30°")*cos("30°")`

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Resolved shear stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Resolved shear stress = Applied stress*cos(Slip plane angle)*cos(Slip direction angle)
𝛕_R = σ*cos(ϕ)*cos(λ)
This formula uses 1 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Resolved shear stress - (Measured in Pascal) - Resolved shear stress is the shear component that exists at all but parallel or perpendicular alignments to the stress direction.
Applied stress - (Measured in Pascal) - Applied stress is denoted by the symbol σ.
Slip plane angle - (Measured in Radian) - Slip plane angle is the angle between the normal to the slip plane and the applied stress direction.
Slip direction angle - (Measured in Radian) - Slip direction angle is the angle between the slip and stress directions.

STEP 1: Convert Input(s) to Base Unit

Applied stress: 93.3 Pascal --> 93.3 Pascal No Conversion Required
Slip plane angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Slip direction angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛕_R = σ*cos(ϕ)*cos(λ) --> 93.3*cos(0.5235987755982)*cos(0.5235987755982)

Evaluating ... ...

𝛕_R = 69.975

STEP 3: Convert Result to Output's Unit

69.975 Pascal -->6.9975E-05 Megapascal (Check conversion here)

FINAL ANSWER

6.9975E-05 ≈ 7E-5 Megapascal <-- Resolved shear stress

(Calculation completed in 00.004 seconds)

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Created by Hariharan V S

Indian Institute of Technology (IIT), Chennai

Hariharan V S has created this Calculator and 25+ more calculators!

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< 10+ Stress and Strain Calculators

Strain hardening exponent

Go Strain hardening exponent = (ln(True stress)-ln(K value))/ln(True strain)

Resolved shear stress

Go Resolved shear stress = Applied stress*cos(Slip plane angle)*cos(Slip direction angle)

Engineering strain

Go Engineering strain = (Instantaneous length-Initial Length)/Initial Length

True strain

Go True strain = ln(Instantaneous length/Initial Length)

Maximum Shear Stress from Tresca Criterion

Go Maximum Shear Stress = (Largest principal stress-Smallest principal stress)/2

True stress

Go True stress = Engineering stress*(1+Engineering strain)

Engineering stress

Go Engineering stress = Load/Cross-sectional Area

Safe stress

Go Safe Stress = Yield Strength/Factor of Safety

True strain from Engineering strain

Go True strain = ln(1+Engineering strain)

Maximum Shear Stress from Von Mises Criterion

Go Maximum Shear Stress = 0.577*Yield Strength

Resolved shear stress Formula

Resolved shear stress = Applied stress*cos(Slip plane angle)*cos(Slip direction angle)
𝛕_R = σ*cos(ϕ)*cos(λ)

Resolved Shear Stress

Even though an applied stress may be pure tensile (or compressive), shear components exist at all but parallel or perpendicular alignments to the stress direction.These are termed resolved shear stresses, and their magnitudes depend not only on the applied stress, but also on the orientation of both the slip plane and direction within that plane.

How to Calculate Resolved shear stress?

Resolved shear stress calculator uses Resolved shear stress = Applied stress*cos(Slip plane angle)*cos(Slip direction angle) to calculate the Resolved shear stress, Resolved shear stress is the shear component that exists at all but parallel or perpendicular alignments to the stress direction. Resolved shear stress is denoted by 𝛕_R symbol.

How to calculate Resolved shear stress using this online calculator? To use this online calculator for Resolved shear stress, enter Applied stress (σ), Slip plane angle (ϕ) & Slip direction angle (λ) and hit the calculate button. Here is how the Resolved shear stress calculation can be explained with given input values -> 7E-11 = 93.3*cos(0.5235987755982)*cos(0.5235987755982).

FAQ

What is Resolved shear stress?

Resolved shear stress is the shear component that exists at all but parallel or perpendicular alignments to the stress direction and is represented as 𝛕_R = σ*cos(ϕ)*cos(λ) or Resolved shear stress = Applied stress*cos(Slip plane angle)*cos(Slip direction angle). Applied stress is denoted by the symbol σ, Slip plane angle is the angle between the normal to the slip plane and the applied stress direction & Slip direction angle is the angle between the slip and stress directions.

How to calculate Resolved shear stress?

Resolved shear stress is the shear component that exists at all but parallel or perpendicular alignments to the stress direction is calculated using Resolved shear stress = Applied stress*cos(Slip plane angle)*cos(Slip direction angle). To calculate Resolved shear stress, you need Applied stress (σ), Slip plane angle (ϕ) & Slip direction angle (λ). With our tool, you need to enter the respective value for Applied stress, Slip plane angle & Slip direction angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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