Maximum Value of Shear Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
τmax = sqrt(((σx-σy)/2)^2+τ^2)
This formula uses 1 Functions, 4 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
Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.
Stress Along x Direction - (Measured in Pascal) - Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.
Stress Along y Direction - (Measured in Pascal) - Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.
Shear Stress in Mpa - (Measured in Pascal) - Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
STEP 1: Convert Input(s) to Base Unit
Stress Along x Direction: 95 Megapascal --> 95000000 Pascal (Check conversion here)
Stress Along y Direction: 22 Megapascal --> 22000000 Pascal (Check conversion here)
Shear Stress in Mpa: 41.5 Megapascal --> 41500000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τmax = sqrt(((σxy)/2)^2+τ^2) --> sqrt(((95000000-22000000)/2)^2+41500000^2)
Evaluating ... ...
τmax = 55267531.1552814
STEP 3: Convert Result to Output's Unit
55267531.1552814 Pascal -->55.2675311552814 Megapascal (Check conversion here)
FINAL ANSWER
55.2675311552814 55.26753 Megapascal <-- Maximum Shear Stress
(Calculation completed in 00.020 seconds)

Credits

Created by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
Vaibhav Malani has created this Calculator and 600+ more calculators!
Verified by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has verified this Calculator and 2500+ more calculators!

7 Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress Calculators

Maximum Value of Normal Stress
Go Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Minimum Value of Normal Stress
Go Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses
Go Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)
Maximum Value of Shear Stress
Go Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress
Go Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)
Condition for Maximum Value of Normal Stress
Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2
Condition for Minimum Normal Stress
Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

7 When a Body is subjected to two Mutual Perpendicular Principal Tensile stresses along with Simple Shear Stress Calculators

Maximum Value of Normal Stress
Go Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Minimum Value of Normal Stress
Go Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses
Go Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)
Maximum Value of Shear Stress
Go Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress
Go Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)
Condition for Maximum Value of Normal Stress
Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2
Condition for Minimum Normal Stress
Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

Maximum Value of Shear Stress Formula

Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
τmax = sqrt(((σx-σy)/2)^2+τ^2)

What is Shear 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 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 Maximum Value of Shear Stress?

Maximum Value of Shear Stress calculator uses Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2) to calculate the Maximum Shear Stress, The Maximum Value of Shear Stress formula is defined as the square root of the sum of the square of half the value of the difference of stress along the x-axis and stress along the y-axis and square of shear stress. Maximum Shear Stress is denoted by τmax symbol.

How to calculate Maximum Value of Shear Stress using this online calculator? To use this online calculator for Maximum Value of Shear Stress, enter Stress Along x Direction x), Stress Along y Direction y) & Shear Stress in Mpa (τ) and hit the calculate button. Here is how the Maximum Value of Shear Stress calculation can be explained with given input values -> 5.5E-5 = sqrt(((95000000-22000000)/2)^2+41500000^2).

FAQ

What is Maximum Value of Shear Stress?
The Maximum Value of Shear Stress formula is defined as the square root of the sum of the square of half the value of the difference of stress along the x-axis and stress along the y-axis and square of shear stress and is represented as τmax = sqrt(((σxy)/2)^2+τ^2) or Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2). Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation, Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure & Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
How to calculate Maximum Value of Shear Stress?
The Maximum Value of Shear Stress formula is defined as the square root of the sum of the square of half the value of the difference of stress along the x-axis and stress along the y-axis and square of shear stress is calculated using Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2). To calculate Maximum Value of Shear Stress, you need Stress Along x Direction x), Stress Along y Direction y) & Shear Stress in Mpa (τ). With our tool, you need to enter the respective value for Stress Along x Direction, Stress Along y Direction & Shear Stress in Mpa and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!