Maximum Principal Stress Calculator

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✖Normal stress along x direction is the internal resistive force acting longitudinally.ⓘ Normal stress along x direction [σ_x]			+10% -10%
✖Normal stress along y direction is the internal resistive force per unit area acting along y direction.ⓘ Normal stress along y direction [σ_y]			+10% -10%
✖Shear stress acting in xy plane is the shear stress on xy plane.ⓘ Shear stress acting in xy plane [ζ_xy]			+10% -10%

✖Maximum principal stress is the maximum stress acting on principal plane due to applied normal load.ⓘ Maximum Principal Stress [σ_max]

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Formula

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Maximum Principal Stress

Formula

`"σ"_{"max"} = ("σ"_{"x"}+"σ"_{"y"})/2+sqrt((("σ"_{"x"}-"σ"_{"y"})/2)^2+"ζ"_{"xy"}^2)`

Example

`"96.05551MPa"=("80MPa"+"40MPa")/2+sqrt((("80MPa"-"40MPa")/2)^2+("30MPa")^2)`

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Maximum Principal Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum principal stress = (Normal stress along x direction+Normal stress along y direction)/2+sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2)
σ_max = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+ζ_xy^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 principal stress - (Measured in Pascal) - Maximum principal stress is the maximum stress acting on principal plane due to applied normal load.
Normal stress along x direction - (Measured in Pascal) - Normal stress along x direction is the internal resistive force acting longitudinally.
Normal stress along y direction - (Measured in Pascal) - Normal stress along y direction is the internal resistive force per unit area acting along y direction.
Shear stress acting in xy plane - (Measured in Pascal) - Shear stress acting in xy plane is the shear stress on xy plane.

STEP 1: Convert Input(s) to Base Unit

Normal stress along x direction: 80 Megapascal --> 80000000 Pascal (Check conversion here)
Normal stress along y direction: 40 Megapascal --> 40000000 Pascal (Check conversion here)
Shear stress acting in xy plane: 30 Megapascal --> 30000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_max = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+ζ_xy^2) --> (80000000+40000000)/2+sqrt(((80000000-40000000)/2)^2+30000000^2)

Evaluating ... ...

σ_max = 96055512.7546399

STEP 3: Convert Result to Output's Unit

96055512.7546399 Pascal -->96.0555127546399 Megapascal (Check conversion here)

FINAL ANSWER

96.0555127546399 ≈ 96.05551 Megapascal <-- Maximum principal stress

(Calculation completed in 00.011 seconds)

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BMS COLLEGE OF ENGINEERING (BMSCE), BANGALORE

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< 6 Analysis of Stresses Calculators

Maximum Principal Stress

Go Maximum principal stress = (Normal stress along x direction+Normal stress along y direction)/2+sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2)

Minimum Principal Stress

Go Minimum principal stress = (Normal stress along x direction+Normal stress along y direction)/2-sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2)

Shear Stress on Inclined Plane

Go Shear stress on inclined plane = -Tensile load*sin(Theta)*cos(Theta)/Area of inclined plane

Area of Inclined Plane given Stress

Go Area of inclined plane = (Tensile load*(cos(Theta))^2)/Stress on inclined plane

Load of Inclined Plane given Stress

Go Tensile load = (Stress on inclined plane*Area of inclined plane)/(cos(Theta))^2

Stress on Inclined Plane

Go Stress on inclined plane = (Tensile load*(cos(Theta))^2)/Area of inclined plane

Maximum Principal Stress Formula

Importance of principal stresses

Principal Stress shows the maximum and minimum normal stress. Maximum normal Stress shows the component's ability to sustain the maximum amount of force.

How to Calculate Maximum Principal Stress?

Maximum Principal Stress calculator uses Maximum principal stress = (Normal stress along x direction+Normal stress along y direction)/2+sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2) to calculate the Maximum principal stress, The Maximum principal stress formula is defined as the component's ability to sustain the maximum amount of force. Maximum principal stress is denoted by σ_max symbol.

How to calculate Maximum Principal Stress using this online calculator? To use this online calculator for Maximum Principal Stress, enter Normal stress along x direction (σ_x), Normal stress along y direction (σ_y) & Shear stress acting in xy plane (ζ_xy) and hit the calculate button. Here is how the Maximum Principal Stress calculation can be explained with given input values -> 9.6E-5 = (80000000+40000000)/2+sqrt(((80000000-40000000)/2)^2+30000000^2).

FAQ

What is Maximum Principal Stress?

The Maximum principal stress formula is defined as the component's ability to sustain the maximum amount of force and is represented as σ_max = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+ζ_xy^2) or Maximum principal stress = (Normal stress along x direction+Normal stress along y direction)/2+sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2). Normal stress along x direction is the internal resistive force acting longitudinally, Normal stress along y direction is the internal resistive force per unit area acting along y direction & Shear stress acting in xy plane is the shear stress on xy plane.

How to calculate Maximum Principal Stress?

The Maximum principal stress formula is defined as the component's ability to sustain the maximum amount of force is calculated using Maximum principal stress = (Normal stress along x direction+Normal stress along y direction)/2+sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2). To calculate Maximum Principal Stress, you need Normal stress along x direction (σ_x), Normal stress along y direction (σ_y) & Shear stress acting in xy plane (ζ_xy). With our tool, you need to enter the respective value for Normal stress along x direction, Normal stress along y direction & Shear stress acting in xy plane 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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