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Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Formula

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Major Principal Stress can be defined as the maximum normal stress acting on the principal plane. Check FAQs

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

σ_major - Major Principal Stress?σ_x - Stress acting along x-direction?σ_y - Stress acting along y-direction?𝜏 - Shear Stress?

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Example

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Here is how the Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress equation looks like with Values.

Here is how the Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress equation looks like with Units.

Here is how the Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress equation looks like.

3.0547 = \frac{0.5 + 0.8}{2} + \sqrt{{(\frac{0.5 - 0.8}{2})}^{2} + {2.4}^{2}}

3.0547MPa = \frac{0.5MPa + 0.8MPa}{2} + \sqrt{{(\frac{0.5MPa - 0.8MPa}{2})}^{2} + {2.4MPa}^{2}}

3.0547 = \frac{0.5 + 0.8}{2} + \sqrt{{(\frac{0.5 - 0.8}{2})}^{2} + {2.4}^{2}}

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Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Solution

Follow our step by step solution on how to calculate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ major = \frac{0.5MPa + 0.8MPa}{2} + \sqrt{{(\frac{0.5MPa - 0.8MPa}{2})}^{2} + {2.4MPa}^{2}}

Next Step Convert Units

∴

σ major = \frac{500000Pa + 800000Pa}{2} + \sqrt{{(\frac{500000Pa - 800000Pa}{2})}^{2} + {2.4E+6Pa}^{2}}

Next Step Prepare to Evaluate

∴

σ major = \frac{500000 + 800000}{2} + \sqrt{{(\frac{500000 - 800000}{2})}^{2} + {2.4E+6}^{2}}

Next Step Evaluate

∴

σ major = 3054682.93128221Pa

Next Step Convert to Output's Unit

∴

σ major = 3.05468293128221MPa

LAST Step Rounding Answer

∴

σ major = 3.0547MPa

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Formula Elements

Variables

Functions

Major Principal Stress

Major Principal Stress can be defined as the maximum normal stress acting on the principal plane.

Symbol: σ_major

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Major Principal Stress

Stress acting along x-direction

The stress acting along x-direction.

Symbol: σ_x

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress acting along x-direction

Stress acting along y-direction

The Stress acting along y-direction is denoted by the symbol σ_y.

Symbol: σ_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress acting along y-direction

Shear Stress

Shear Stress is 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

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 Relations category

Go Angle of Obliquity

ϕ = a \tan (\frac{𝜏}{σ n})

Go Resultant Stress on Oblique Section given Stress in Perpendicular Directions

σ R = \sqrt{{σ n}^{2} + 𝜏^{2}}

Go Stress along Maximum Axial Force

σ = \frac{P axial}{A}

Go Maximum Axial Force

P axial = σ \cdot A

How to Evaluate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress evaluator uses Major Principal Stress = (Stress acting along x-direction+Stress acting along y-direction)/2+sqrt(((Stress acting along x-direction-Stress acting along y-direction)/2)^2+Shear Stress^2) to evaluate the Major Principal Stress, The Major principal stress if Member is subjected to two perpendicular direct stress and shear stress is the maximum value of principal stress. Major Principal Stress is denoted by σ_major symbol.

How to evaluate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress using this online evaluator? To use this online evaluator for Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress, enter Stress acting along x-direction (σ_x), Stress acting along y-direction (σ_y) & Shear Stress (𝜏) and hit the calculate button.

FAQs on Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress

What is the formula to find Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

The formula of Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress is expressed as Major Principal Stress = (Stress acting along x-direction+Stress acting along y-direction)/2+sqrt(((Stress acting along x-direction-Stress acting along y-direction)/2)^2+Shear Stress^2). Here is an example- 3.1E-6 = (500000+800000)/2+sqrt(((500000-800000)/2)^2+2400000^2).

How to calculate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

With Stress acting along x-direction (σ_x), Stress acting along y-direction (σ_y) & Shear Stress (𝜏) we can find Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress using the formula - Major Principal Stress = (Stress acting along x-direction+Stress acting along y-direction)/2+sqrt(((Stress acting along x-direction-Stress acting along y-direction)/2)^2+Shear Stress^2). This formula also uses Square Root (sqrt) function(s).

Can the Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress be negative?

Yes, the Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress, measured in Stress can be negative.

Which unit is used to measure Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear 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 Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress can be measured.

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Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Formula

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Example

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Solution

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Formula Elements

Other formulas in Stress Relations category

How to Evaluate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

FAQs on Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress

Variable Name