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Normal Stress 2 Formula

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A normal stress 2 is a stress that occurs when a member is loaded by an axial force. Check FAQs

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

σ₂ - Normal Stress 2?σ_x - Principal Stress along x?σ_y - Principal Stress along y?τ - Shear Stress on Upper Surface?

Normal Stress 2 Example

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With units

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Here is how the Normal Stress 2 equation looks like with Values.

Here is how the Normal Stress 2 equation looks like with Units.

Here is how the Normal Stress 2 equation looks like.

-0.5188 = \frac{100 + 0.2}{2} - \sqrt{{(\frac{100 - 0.2}{2})}^{2} + {8.5}^{2}}

-0.5188N/m² = \frac{100N/m² + 0.2N/m²}{2} - \sqrt{{(\frac{100N/m² - 0.2N/m²}{2})}^{2} + {8.5N/m²}^{2}}

-0.5188 = \frac{100 + 0.2}{2} - \sqrt{{(\frac{100 - 0.2}{2})}^{2} + {8.5}^{2}}

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Normal Stress 2 Solution

Follow our step by step solution on how to calculate Normal Stress 2?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ 2 = \frac{100N/m² + 0.2N/m²}{2} - \sqrt{{(\frac{100N/m² - 0.2N/m²}{2})}^{2} + {8.5N/m²}^{2}}

Next Step Convert Units

∴

σ 2 = \frac{100Pa + 0.2Pa}{2} - \sqrt{{(\frac{100Pa - 0.2Pa}{2})}^{2} + {8.5Pa}^{2}}

Next Step Prepare to Evaluate

∴

σ 2 = \frac{100 + 0.2}{2} - \sqrt{{(\frac{100 - 0.2}{2})}^{2} + {8.5}^{2}}

Next Step Evaluate

∴

σ 2 = -0.518771221751322Pa

Next Step Convert to Output's Unit

∴

σ 2 = -0.518771221751322N/m²

LAST Step Rounding Answer

∴

σ 2 = -0.5188N/m²

Normal Stress 2 Formula Elements

Variables

Functions

Normal Stress 2

A normal stress 2 is a stress that occurs when a member is loaded by an axial force.

Symbol: σ₂

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Normal Stress 2

Principal Stress along x

Principal stress along x is stress along x-axis.

Symbol: σ_x

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Principal Stress along x

Principal Stress along y

Principal stress along y is stress along y-axis.

Symbol: σ_y

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Principal Stress along y

Shear Stress on Upper Surface

Shear stress on upper surface refers to the amount of shear force that acts on a small element of the surface parallel to a given fluid particle. .

Symbol: τ

Measurement: StressUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Shear Stress on Upper Surface

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 and Strain category

Go Elongation Circular Tapered Bar

∆ = \frac{4 \cdot W load \cdot L bar}{π \cdot D 1 \cdot D 2 \cdot e}

Go Moment of Inertia for Hollow Circular Shaft

J = \frac{π}{32} \cdot ({d ho}^{4} - {d hi}^{4})

Go Moment of Inertia about Polar Axis

J = \frac{π \cdot {d s}^{4}}{32}

Go Elongation of Prismatic Bar due to its Own Weight

∆ = \frac{2 \cdot W load \cdot L bar}{A \cdot e}

How to Evaluate Normal Stress 2?

Normal Stress 2 evaluator uses Normal Stress 2 = (Principal Stress along x+Principal Stress along y)/2-sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2) to evaluate the Normal Stress 2, A normal stress 2 is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross-sectional area. Normal Stress 2 is denoted by σ₂ symbol.

How to evaluate Normal Stress 2 using this online evaluator? To use this online evaluator for Normal Stress 2, enter Principal Stress along x (σ_x), Principal Stress along y (σ_y) & Shear Stress on Upper Surface (τ) and hit the calculate button.

FAQs on Normal Stress 2

What is the formula to find Normal Stress 2?

The formula of Normal Stress 2 is expressed as Normal Stress 2 = (Principal Stress along x+Principal Stress along y)/2-sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2). Here is an example- -0.518771 = (100+0.2)/2-sqrt(((100-0.2)/2)^2+8.5^2).

How to calculate Normal Stress 2?

With Principal Stress along x (σ_x), Principal Stress along y (σ_y) & Shear Stress on Upper Surface (τ) we can find Normal Stress 2 using the formula - Normal Stress 2 = (Principal Stress along x+Principal Stress along y)/2-sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2). This formula also uses Square Root Function function(s).

Can the Normal Stress 2 be negative?

Yes, the Normal Stress 2, measured in Pressure can be negative.

Which unit is used to measure Normal Stress 2?

Normal Stress 2 is usually measured using the Newton per Square Meter[N/m²] for Pressure. Pascal[N/m²], Kilopascal[N/m²], Bar[N/m²] are the few other units in which Normal Stress 2 can be measured.

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Normal Stress 2 Formula

Normal Stress 2 Example

Normal Stress 2 Solution

Normal Stress 2 Formula Elements

Other formulas in Stress and Strain category

How to Evaluate Normal Stress 2?

FAQs on Normal Stress 2

Variable Name