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Maximum Value of Normal Stress Formula

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Maximum Normal Stress is defined as stress acting on a plane normally. Check FAQs

σ n,max = \frac{σ x + σ y}{2} + \sqrt{{(\frac{σ x - σ y}{2})}^{2} + τ^{2}}

σ_n,max - Maximum Normal Stress?σ_x - Stress Along x Direction?σ_y - Stress Along y Direction?τ - Shear Stress in Mpa?

Maximum Value of Normal Stress Example

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Here is how the Maximum Value of Normal Stress equation looks like with Values.

Here is how the Maximum Value of Normal Stress equation looks like with Units.

Here is how the Maximum Value of Normal Stress equation looks like.

113.7675 = \frac{95 + 22}{2} + \sqrt{{(\frac{95 - 22}{2})}^{2} + {41.5}^{2}}

113.7675MPa = \frac{95MPa + 22MPa}{2} + \sqrt{{(\frac{95MPa - 22MPa}{2})}^{2} + {41.5MPa}^{2}}

113.7675 = \frac{95 + 22}{2} + \sqrt{{(\frac{95 - 22}{2})}^{2} + {41.5}^{2}}

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Maximum Value of Normal Stress Solution

Follow our step by step solution on how to calculate Maximum Value of Normal Stress?

FIRST Step Consider the formula

σ n,max = \frac{σ x + σ y}{2} + \sqrt{{(\frac{σ x - σ y}{2})}^{2} + τ^{2}}

Next Step Substitute values of Variables

∴

σ n,max = \frac{95MPa + 22MPa}{2} + \sqrt{{(\frac{95MPa - 22MPa}{2})}^{2} + {41.5MPa}^{2}}

Next Step Convert Units

∴

σ n,max = \frac{9.5E+7Pa + 2.2E+7Pa}{2} + \sqrt{{(\frac{9.5E+7Pa - 2.2E+7Pa}{2})}^{2} + {4.2E+7Pa}^{2}}

Next Step Prepare to Evaluate

∴

σ n,max = \frac{9.5E+7 + 2.2E+7}{2} + \sqrt{{(\frac{9.5E+7 - 2.2E+7}{2})}^{2} + {4.2E+7}^{2}}

Next Step Evaluate

∴

σ n,max = 113767531.155281Pa

Next Step Convert to Output's Unit

∴

σ n,max = 113.767531155281MPa

LAST Step Rounding Answer

∴

σ n,max = 113.7675MPa

Maximum Value of Normal Stress Formula Elements

Variables

Functions

Maximum Normal Stress

Maximum Normal Stress is defined as stress acting on a plane normally.

Symbol: σ_n,max

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Normal Stress

Stress Along x Direction

Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.

Symbol: σ_x

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress Along x Direction

Stress Along y Direction

Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.

Symbol: σ_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress Along y Direction

Shear Stress in Mpa

Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: τ

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress in Mpa

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

Go Condition for Maximum Value of Normal Stress

θ plane = \frac{a \tan (\frac{2 \cdot τ}{σ x - σ y})}{2}

Go Condition for Minimum Normal Stress

θ plane = \frac{a \tan (\frac{2 \cdot τ}{σ x - σ y})}{2}

Go Maximum Value of Shear Stress

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

Go Minimum Value of Normal Stress

σ n,min = \frac{σ x + σ y}{2} - \sqrt{{(\frac{σ x - σ y}{2})}^{2} + τ^{2}}

How to Evaluate Maximum Value of Normal Stress?

Maximum Value of Normal Stress evaluator uses 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) to evaluate the Maximum Normal Stress, The Maximum Value of Normal Stress formula is defined as equal to the major principal stress value or maximum principal stress value. Maximum Normal Stress is denoted by σ_n,max symbol.

How to evaluate Maximum Value of Normal Stress using this online evaluator? To use this online evaluator for Maximum Value of Normal Stress, enter Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ) and hit the calculate button.

FAQs on Maximum Value of Normal Stress

What is the formula to find Maximum Value of Normal Stress?

The formula of Maximum Value of Normal Stress is expressed as 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). Here is an example- 0.000114 = (95000000+22000000)/2+sqrt(((95000000-22000000)/2)^2+41500000^2).

How to calculate Maximum Value of Normal Stress?

With Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ) we can find Maximum Value of Normal Stress using the formula - 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). This formula also uses Square Root (sqrt) function(s).

Can the Maximum Value of Normal Stress be negative?

No, the Maximum Value of Normal Stress, measured in Stress cannot be negative.

Which unit is used to measure Maximum Value of Normal Stress?

Maximum Value of Normal Stress is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Maximum Value of Normal Stress can be measured.

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Maximum Value of Normal Stress Formula

Maximum Value of Normal Stress Example

Maximum Value of Normal Stress Solution

Maximum Value of Normal Stress Formula Elements

Other formulas in Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress category

How to Evaluate Maximum Value of Normal Stress?

FAQs on Maximum Value of Normal Stress

Variable Name