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Normal Stress on Oblique Section given Stress in Perpendicular Directions Formula

GoNormal Stress across Oblique Section Formula

GoNormal Stress for Principal Planes at Angle of 0 Degrees given Major and Minor Tensile Stress Formula

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Normal Stress is stress that occurs when a member is loaded by an axial force. Check FAQs

σ n = \frac{σ 1 + σ 2}{2} + \frac{σ 1 - σ 2}{2} \cdot \cos (2 \cdot θ o)

σ_n - Normal Stress?σ₁ - Major Tensile Stress?σ₂ - Minor Tensile Stress?θ_o - Angle Made By Oblique Section With Normal?

Normal Stress on Oblique Section given Stress in Perpendicular Directions Example

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Here is how the Normal Stress on Oblique Section given Stress in Perpendicular Directions equation looks like with Values.

Here is how the Normal Stress on Oblique Section given Stress in Perpendicular Directions equation looks like with Units.

Here is how the Normal Stress on Oblique Section given Stress in Perpendicular Directions equation looks like.

0.0007 = \frac{1.2E-7 + 11196}{2} + \frac{1.2E-7 - 11196}{2} \cdot \cos (2 \cdot 15)

0.0007MPa = \frac{1.2E-7N/m² + 11196N/m²}{2} + \frac{1.2E-7N/m² - 11196N/m²}{2} \cdot \cos (2 \cdot 15°)

0.0007 = \frac{1.2E-7 + 11196}{2} + \frac{1.2E-7 - 11196}{2} \cdot \cos (2 \cdot 15)

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Normal Stress on Oblique Section given Stress in Perpendicular Directions Solution

Follow our step by step solution on how to calculate Normal Stress on Oblique Section given Stress in Perpendicular Directions?

FIRST Step Consider the formula

σ n = \frac{σ 1 + σ 2}{2} + \frac{σ 1 - σ 2}{2} \cdot \cos (2 \cdot θ o)

Next Step Substitute values of Variables

∴

σ n = \frac{1.2E-7N/m² + 11196N/m²}{2} + \frac{1.2E-7N/m² - 11196N/m²}{2} \cdot \cos (2 \cdot 15°)

Next Step Convert Units

∴

σ n = \frac{1.2E-7Pa + 11196Pa}{2} + \frac{1.2E-7Pa - 11196Pa}{2} \cdot \cos (2 \cdot 0.2618rad)

Next Step Prepare to Evaluate

∴

σ n = \frac{1.2E-7 + 11196}{2} + \frac{1.2E-7 - 11196}{2} \cdot \cos (2 \cdot 0.2618)

Next Step Evaluate

∴

σ n = 749.989789730407Pa

Next Step Convert to Output's Unit

∴

σ n = 0.000749989789730407MPa

LAST Step Rounding Answer

∴

σ n = 0.0007MPa

Normal Stress on Oblique Section given Stress in Perpendicular Directions Formula Elements

Variables

Functions

Normal Stress

Normal Stress is stress that occurs when a member is loaded by an axial force.

Symbol: σ_n

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Normal Stress

Major Tensile Stress

Major Tensile Stress is the stress acting along the longitudinal direction.

Symbol: σ₁

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Major Tensile Stress

Minor Tensile Stress

Minor Tensile Stress is the stress acting along lateral direction.

Symbol: σ₂

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Minor Tensile Stress

Angle Made By Oblique Section With Normal

Angle Made By Oblique Section with Normal cross-section, it is denoted by symbol θ.

Symbol: θ_o

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle Made By Oblique Section With Normal

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Normal Stress

Go Normal Stress across Oblique Section

σ n = σ \cdot {(\cos (θ o))}^{2}

Go Normal Stress for Principal Planes at Angle of 0 Degrees given Major and Minor Tensile Stress

σ n = \frac{σ 1 + σ 2}{2} + \frac{σ 1 - σ 2}{2}

Go Normal Stress for Principal Planes at Angle of 90 degrees

σ n = \frac{σ 1 + σ 2}{2} - \frac{σ 1 - σ 2}{2}

Go Normal Stress for Principal Planes when Planes are at Angle of 0 Degree

σ n = \frac{σ 1 + σ 2}{2} + \frac{σ 1 - σ 2}{2}

Other formulas in Normal Stress category

Go Equivalent Stress by Distortion Energy Theory

σ e = \frac{1}{\sqrt{2}} \cdot \sqrt{{(σ' 1 - σ' 2)}^{2} + {(σ' 2 - σ 3)}^{2} + {(σ 3 - σ' 1)}^{2}}

Go Stress Amplitude

σ a = \frac{σ max - σ min}{2}

How to Evaluate Normal Stress on Oblique Section given Stress in Perpendicular Directions?

Normal Stress on Oblique Section given Stress in Perpendicular Directions evaluator uses Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2*cos(2*Angle Made By Oblique Section With Normal) to evaluate the Normal Stress, Normal Stress on Oblique Section given Stress in Perpendicular Directions formula is defined as a measure of the normal stress on an oblique section of a material, considering the principal stresses in perpendicular directions, which is essential in understanding the material's behavior under different loading conditions. Normal Stress is denoted by σ_n symbol.

How to evaluate Normal Stress on Oblique Section given Stress in Perpendicular Directions using this online evaluator? To use this online evaluator for Normal Stress on Oblique Section given Stress in Perpendicular Directions, enter Major Tensile Stress (σ₁), Minor Tensile Stress (σ₂) & Angle Made By Oblique Section With Normal (θ_o) and hit the calculate button.

FAQs on Normal Stress on Oblique Section given Stress in Perpendicular Directions

What is the formula to find Normal Stress on Oblique Section given Stress in Perpendicular Directions?

The formula of Normal Stress on Oblique Section given Stress in Perpendicular Directions is expressed as Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2*cos(2*Angle Made By Oblique Section With Normal). Here is an example- 7.5E-10 = (1.24E-07+11196)/2+(1.24E-07-11196)/2*cos(2*0.2617993877991).

How to calculate Normal Stress on Oblique Section given Stress in Perpendicular Directions?

With Major Tensile Stress (σ₁), Minor Tensile Stress (σ₂) & Angle Made By Oblique Section With Normal (θ_o) we can find Normal Stress on Oblique Section given Stress in Perpendicular Directions using the formula - Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2*cos(2*Angle Made By Oblique Section With Normal). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Normal Stress?

Here are the different ways to Calculate Normal Stress-

Normal Stress=Stress in Bar*(cos(Angle Made By Oblique Section With Normal))^2
Normal Stress=(Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2
Normal Stress=(Major Tensile Stress+Minor Tensile Stress)/2-(Major Tensile Stress-Minor Tensile Stress)/2

Can the Normal Stress on Oblique Section given Stress in Perpendicular Directions be negative?

No, the Normal Stress on Oblique Section given Stress in Perpendicular Directions, measured in Stress cannot be negative.

Which unit is used to measure Normal Stress on Oblique Section given Stress in Perpendicular Directions?

Normal Stress on Oblique Section given Stress in Perpendicular Directions 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 Normal Stress on Oblique Section given Stress in Perpendicular Directions can be measured.

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Normal Stress on Oblique Section given Stress in Perpendicular Directions Formula

​GoNormal Stress across Oblique Section Formula

​GoNormal Stress for Principal Planes at Angle of 0 Degrees given Major and Minor Tensile Stress Formula

Normal Stress on Oblique Section given Stress in Perpendicular Directions Example

Normal Stress on Oblique Section given Stress in Perpendicular Directions Solution

Normal Stress on Oblique Section given Stress in Perpendicular Directions Formula Elements

Other Formulas to find Normal Stress

Other formulas in Normal Stress category

How to Evaluate Normal Stress on Oblique Section given Stress in Perpendicular Directions?

FAQs on Normal Stress on Oblique Section given Stress in Perpendicular Directions

Variable Name

GoNormal Stress across Oblique Section Formula

GoNormal Stress for Principal Planes at Angle of 0 Degrees given Major and Minor Tensile Stress Formula