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

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Minor Principal Stress is the minimum normal stress acting on the Principal plane. Check FAQs

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

σ_minor - Minor Principal Stress?σ_x - Stress Acting Along X Direction?σ_y - Stress Acting Along Y Direction?𝜏 - Shear Stress?

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

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

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

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

-1.7547 = \frac{0.5 + 0.8}{2} - \sqrt{{(\frac{0.5 - 0.8}{2})}^{2} + {2.4}^{2}}

-1.7547MPa = \frac{0.5MPa + 0.8MPa}{2} - \sqrt{{(\frac{0.5MPa - 0.8MPa}{2})}^{2} + {2.4MPa}^{2}}

-1.7547 = \frac{0.5 + 0.8}{2} - \sqrt{{(\frac{0.5 - 0.8}{2})}^{2} + {2.4}^{2}}

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Minor 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 Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

σ minor = -1754682.93128221Pa

Next Step Convert to Output's Unit

∴

σ minor = -1.75468293128221MPa

LAST Step Rounding Answer

∴

σ minor = -1.7547MPa

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

Variables

Functions

Minor Principal Stress

Minor Principal Stress is the minimum normal stress acting on the Principal plane.

Symbol: σ_minor

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Minor Principal Stress

Stress Acting Along X Direction

Stress Acting Along X Direction is 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

Stress Acting Along Y Direction is stress acting along y direction is denoted by σy.

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 a}{A}

Go Maximum Axial Force

P a = σ \cdot A

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

Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress evaluator uses Minor 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 Minor Principal Stress, Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress formula is defined as a measure of the minimum normal stress experienced by a member when it is subjected to two perpendicular direct stresses and a shear stress, providing a critical value for structural analysis and design. Minor Principal Stress is denoted by σ_minor symbol.

How to evaluate Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress using this online evaluator? To use this online evaluator for Minor 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 Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress

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

The formula of Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress is expressed as Minor 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- -1.8E-6 = (500000+800000)/2-sqrt(((500000-800000)/2)^2+2400000^2).

How to calculate Minor 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 Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress using the formula - Minor 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 Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress be negative?

Yes, the Minor 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 Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

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

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

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

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

Minor 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 Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

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

Variable Name