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Maximum Principal Stress Formula

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Maximum principal stress is the maximum stress acting on principal plane due to applied normal load. Check FAQs

σ max = \frac{σ x + σ y}{2} + \sqrt{{(\frac{σ x - σ y}{2})}^{2} + {ζ xy}^{2}}

σ_max - Maximum Principal Stress?σ_x - Normal Stress along x Direction?σ_y - Normal Stress along y Direction?ζ_xy - Shear Stress acting in xy Plane?

Maximum Principal Stress Example

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Here is how the Maximum Principal Stress equation looks like with Values.

Here is how the Maximum Principal Stress equation looks like with Units.

Here is how the Maximum Principal Stress equation looks like.

9.6E+7 = \frac{80 + 40}{2} + \sqrt{{(\frac{80 - 40}{2})}^{2} + 30^{2}}

9.6E+7Pa = \frac{80MPa + 40MPa}{2} + \sqrt{{(\frac{80MPa - 40MPa}{2})}^{2} + {30MPa}^{2}}

9.6E+7 = \frac{80 + 40}{2} + \sqrt{{(\frac{80 - 40}{2})}^{2} + 30^{2}}

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Maximum Principal Stress Solution

Follow our step by step solution on how to calculate Maximum Principal Stress?

FIRST Step Consider the formula

σ max = \frac{σ x + σ y}{2} + \sqrt{{(\frac{σ x - σ y}{2})}^{2} + {ζ xy}^{2}}

Next Step Substitute values of Variables

∴

σ max = \frac{80MPa + 40MPa}{2} + \sqrt{{(\frac{80MPa - 40MPa}{2})}^{2} + {30MPa}^{2}}

Next Step Convert Units

∴

σ max = \frac{8E+7Pa + 4E+7Pa}{2} + \sqrt{{(\frac{8E+7Pa - 4E+7Pa}{2})}^{2} + {3E+7Pa}^{2}}

Next Step Prepare to Evaluate

∴

σ max = \frac{8E+7 + 4E+7}{2} + \sqrt{{(\frac{8E+7 - 4E+7}{2})}^{2} + {3E+7}^{2}}

Next Step Evaluate

∴

σ max = 96055512.7546399Pa

LAST Step Rounding Answer

∴

σ max = 9.6E+7Pa

Maximum Principal Stress Formula Elements

Variables

Functions

Maximum Principal Stress

Maximum principal stress is the maximum stress acting on principal plane due to applied normal load.

Symbol: σ_max

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Maximum Principal Stress

Normal Stress along x Direction

Normal stress along x direction is the internal resistive force acting longitudinally.

Symbol: σ_x

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Normal Stress along x Direction

Normal Stress along y Direction

Normal stress along y direction is the internal resistive force per unit area acting along y direction.

Symbol: σ_y

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Normal Stress along y Direction

Shear Stress acting in xy Plane

Shear stress acting in xy plane is the shear stress on xy plane.

Symbol: ζ_xy

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Shear Stress acting in xy Plane

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.

Syntax: sqrt(Number)

Other formulas in Stress category

Go Beam Shear Stress

𝜏 = \frac{ΣS \cdot Ay}{I \cdot t}

Go Bending Stress

σ b = M b \cdot \frac{y}{I}

Go Bulk Stress

B stress = \frac{N.F}{A cs}

Go Direct Stress

σ = \frac{P axial}{A cs}

How to Evaluate Maximum Principal Stress?

Maximum Principal Stress evaluator 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 evaluate the Maximum Principal Stress, The Maximum principal stress formula is defined as the measure of the component's ability to sustain the maximum amount of force. Maximum Principal Stress is denoted by σ_max symbol.

How to evaluate Maximum Principal Stress using this online evaluator? To use this online evaluator 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.

FAQs on Maximum Principal Stress

What is the formula to find Maximum Principal Stress?

The formula of Maximum Principal Stress is expressed as 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). Here is an example- 9.6E-5 = (80000000+40000000)/2+sqrt(((80000000-40000000)/2)^2+30000000^2).

How to calculate Maximum Principal Stress?

With Normal Stress along x Direction (σ_x), Normal Stress along y Direction (σ_y) & Shear Stress acting in xy Plane (ζ_xy) we can find Maximum Principal Stress using the formula - 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). This formula also uses Square Root (sqrt) function(s).

Can the Maximum Principal Stress be negative?

Yes, the Maximum Principal Stress, measured in Pressure can be negative.

Which unit is used to measure Maximum Principal Stress?

Maximum Principal Stress is usually measured using the Pascal[Pa] for Pressure. Kilopascal[Pa], Bar[Pa], Pound Per Square Inch[Pa] are the few other units in which Maximum Principal Stress can be measured.

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Maximum Principal Stress Formula

Maximum Principal Stress Example

Maximum Principal Stress Solution

Maximum Principal Stress Formula Elements

Other formulas in Stress category

How to Evaluate Maximum Principal Stress?

FAQs on Maximum Principal Stress

Variable Name