Normal Stress on Oblique Section given Stress in Perpendicular Directions Calculator

✖Major Tensile Stress is the stress acting along the longitudinal direction.ⓘ Major Tensile Stress [σ₁]			+10% -10%
✖Minor Tensile Stress is the stress acting along lateral direction.ⓘ Minor Tensile Stress [σ₂]			+10% -10%
✖Angle made by Oblique Section with Normal cross-section, it is denoted by symbol θ.ⓘ Angle made by Oblique Section with Normal [θ_oblique]			+10% -10%

✖Normal Stress is stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress on Oblique Section given Stress in Perpendicular Directions [σ_n]

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Formula

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Normal Stress on Oblique Section given Stress in Perpendicular Directions

Formula

`"σ"_{"n"} = ("σ"_{"1"}+"σ"_{"2"})/2+("σ"_{"1"}-"σ"_{"2"})/2*cos(2*"θ"_{"oblique"})`

Example

`"118.909MPa"=("124MPa"+"48MPa")/2+("124MPa"-"48MPa")/2*cos(2*"15°")`

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Normal Stress on Oblique Section given Stress in Perpendicular Directions Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
σ_n = (σ₁+σ₂)/2+(σ₁-σ₂)/2*cos(2*θ_oblique)
This formula uses 1 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Normal Stress - (Measured in Pascal) - Normal Stress is stress that occurs when a member is loaded by an axial force.
Major Tensile Stress - (Measured in Pascal) - Major Tensile Stress is the stress acting along the longitudinal direction.
Minor Tensile Stress - (Measured in Pascal) - Minor Tensile Stress is the stress acting along lateral direction.
Angle made by Oblique Section with Normal - (Measured in Radian) - Angle made by Oblique Section with Normal cross-section, it is denoted by symbol θ.

STEP 1: Convert Input(s) to Base Unit

Major Tensile Stress: 124 Megapascal --> 124000000 Pascal (Check conversion here)
Minor Tensile Stress: 48 Megapascal --> 48000000 Pascal (Check conversion here)
Angle made by Oblique Section with Normal: 15 Degree --> 0.2617993877991 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_n = (σ₁+σ₂)/2+(σ₁-σ₂)/2*cos(2*θ_oblique) --> (124000000+48000000)/2+(124000000-48000000)/2*cos(2*0.2617993877991)

Evaluating ... ...

σ_n = 118908965.343809

STEP 3: Convert Result to Output's Unit

118908965.343809 Pascal -->118.908965343809 Megapascal (Check conversion here)

FINAL ANSWER

118.908965343809 ≈ 118.909 Megapascal <-- Normal Stress

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Stress and Strain » Principal Stresses and Strains » Principal Stresses » Normal Stress » Normal Stress on Oblique Section given Stress in Perpendicular Directions

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< 6 Normal Stress Calculators

Normal Stress on Oblique Section given Stress in Perpendicular Directions

Go 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)

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

Go Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2

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

Go Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2

Normal Stress for Principal Planes at Angle of 90 degrees

Go Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2-(Major Tensile Stress-Minor Tensile Stress)/2

Normal Stress across Oblique Section

Go Normal Stress = Stress in Bar*(cos(Angle made by Oblique Section with Normal))^2

Normal Stress using Obliquity

Go Normal Stress = Shear Stress/tan(Angle of Obliquity)

Normal Stress on Oblique Section given Stress in Perpendicular Directions Formula

What is normal stress?

Stress is said to be normal stress when the direction of the deforming force is perpendicular to the cross-sectional area of the body.

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

Normal Stress on Oblique Section given Stress in Perpendicular Directions calculator 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 calculate the Normal Stress, The Normal Stress on Oblique Section given Stress in Perpendicular Directions formula is defined as the sum of the average of major tensile stress, minor tensile stress, and product of cos(2θ), half of the difference between major tensile stress and minor tensile stress. Normal Stress is denoted by σ_n symbol.

How to calculate Normal Stress on Oblique Section given Stress in Perpendicular Directions using this online calculator? To use this online calculator 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_oblique) and hit the calculate button. Here is how the Normal Stress on Oblique Section given Stress in Perpendicular Directions calculation can be explained with given input values -> 0.000119 = (124000000+48000000)/2+(124000000-48000000)/2*cos(2*0.2617993877991).

FAQ

What is Normal Stress on Oblique Section given Stress in Perpendicular Directions?

The Normal Stress on Oblique Section given Stress in Perpendicular Directions formula is defined as the sum of the average of major tensile stress, minor tensile stress, and product of cos(2θ), half of the difference between major tensile stress and minor tensile stress and is represented as σ_n = (σ₁+σ₂)/2+(σ₁-σ₂)/2*cos(2*θ_oblique) or 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). Major Tensile Stress is the stress acting along the longitudinal direction, Minor Tensile Stress is the stress acting along lateral direction & Angle made by Oblique Section with Normal cross-section, it is denoted by symbol θ.

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

The Normal Stress on Oblique Section given Stress in Perpendicular Directions formula is defined as the sum of the average of major tensile stress, minor tensile stress, and product of cos(2θ), half of the difference between major tensile stress and minor tensile stress is calculated using 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 calculate Normal Stress on Oblique Section given Stress in Perpendicular Directions, you need Major Tensile Stress (σ₁), Minor Tensile Stress (σ₂) & Angle made by Oblique Section with Normal (θ_oblique). With our tool, you need to enter the respective value for Major Tensile Stress, Minor Tensile Stress & Angle made by Oblique Section with Normal and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Normal Stress?

In this formula, Normal Stress uses Major Tensile Stress, Minor Tensile Stress & Angle made by Oblique Section with Normal. We can use 5 other way(s) to calculate the same, which is/are as follows -

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
Normal Stress = (Major Tensile Stress+Minor Tensile Stress)/2+(Major Tensile Stress-Minor Tensile Stress)/2
Normal Stress = Shear Stress/tan(Angle of Obliquity)

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