FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Normal Stress Induced in Oblique Plane due to Biaxial Loading Formula

Fx Copy

LaTeX Copy

Normal Stress on Oblique Plane is the stress acting normally to its oblique plane. Check FAQs

σ θ = (\frac{1}{2} \cdot (σ x + σ y)) + (\frac{1}{2} \cdot (σ x - σ y) \cdot (\cos (2 \cdot θ))) + (τ xy \cdot \sin (2 \cdot θ))

σ_θ - Normal Stress on Oblique Plane?σ_x - Stress along x Direction?σ_y - Stress along y Direction?θ - Theta?τ_xy - Shear Stress xy?

Normal Stress Induced in Oblique Plane due to Biaxial Loading Example

With values

With units

Only example

Here is how the Normal Stress Induced in Oblique Plane due to Biaxial Loading equation looks like with Values.

Here is how the Normal Stress Induced in Oblique Plane due to Biaxial Loading equation looks like with Units.

Here is how the Normal Stress Induced in Oblique Plane due to Biaxial Loading equation looks like.

67.4854 = (\frac{1}{2} \cdot (45 + 110)) + (\frac{1}{2} \cdot (45 - 110) \cdot (\cos (2 \cdot 30))) + (7.2 \cdot \sin (2 \cdot 30))

67.4854MPa = (\frac{1}{2} \cdot (45MPa + 110MPa)) + (\frac{1}{2} \cdot (45MPa - 110MPa) \cdot (\cos (2 \cdot 30°))) + (7.2MPa \cdot \sin (2 \cdot 30°))

67.4854 = (\frac{1}{2} \cdot (45 + 110)) + (\frac{1}{2} \cdot (45 - 110) \cdot (\cos (2 \cdot 30))) + (7.2 \cdot \sin (2 \cdot 30))

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Civil » Category

Strength of Materials » fx Normal Stress Induced in Oblique Plane due to Biaxial Loading

Normal Stress Induced in Oblique Plane due to Biaxial Loading Solution

Follow our step by step solution on how to calculate Normal Stress Induced in Oblique Plane due to Biaxial Loading?

FIRST Step Consider the formula

σ θ = (\frac{1}{2} \cdot (σ x + σ y)) + (\frac{1}{2} \cdot (σ x - σ y) \cdot (\cos (2 \cdot θ))) + (τ xy \cdot \sin (2 \cdot θ))

Next Step Substitute values of Variables

∴

σ θ = (\frac{1}{2} \cdot (45MPa + 110MPa)) + (\frac{1}{2} \cdot (45MPa - 110MPa) \cdot (\cos (2 \cdot 30°))) + (7.2MPa \cdot \sin (2 \cdot 30°))

Next Step Convert Units

∴

σ θ = (\frac{1}{2} \cdot (4.5E+7Pa + 1.1E+8Pa)) + (\frac{1}{2} \cdot (4.5E+7Pa - 1.1E+8Pa) \cdot (\cos (2 \cdot 0.5236rad))) + (7.2E+6Pa \cdot \sin (2 \cdot 0.5236rad))

Next Step Prepare to Evaluate

∴

σ θ = (\frac{1}{2} \cdot (4.5E+7 + 1.1E+8)) + (\frac{1}{2} \cdot (4.5E+7 - 1.1E+8) \cdot (\cos (2 \cdot 0.5236))) + (7.2E+6 \cdot \sin (2 \cdot 0.5236))

Next Step Evaluate

∴

σ θ = 67485382.9072417Pa

Next Step Convert to Output's Unit

∴

σ θ = 67.4853829072417MPa

LAST Step Rounding Answer

∴

σ θ = 67.4854MPa

Normal Stress Induced in Oblique Plane due to Biaxial Loading Formula Elements

Variables

Functions

Normal Stress on Oblique Plane

Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.

Symbol: σ_θ

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Normal Stress on Oblique Plane

Stress along x Direction

The Stress along x Direction can be described as axial stress along the given direction.

Symbol: σ_x

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress along x Direction

Stress along y Direction

The Stress along y Direction can be described as axial stress along the given direction.

Symbol: σ_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress along y Direction

Theta

The Theta is the angle subtended by a plane of a body when stress is applied.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Theta

Shear Stress xy

Shear Stress xy is the Stress acting along xy plane.

Symbol: τ_xy

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress xy

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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 in Stresses in Bi Axial Loading category

Go Stress along X- Direction with known Shear Stress in Bi-Axial Loading

σ x = σ y - (\frac{τ θ \cdot 2}{\sin (2 \cdot θ)})

Go Stress along Y- Direction using Shear Stress in Bi-Axial Loading

σ y = σ x + (\frac{τ θ \cdot 2}{\sin (2 \cdot θ)})

Go Shear Stress Induced in Oblique Plane due to Biaxial Loading

τ θ = - (\frac{1}{2} \cdot (σ x - σ y) \cdot \sin (2 \cdot θ)) + (τ xy \cdot \cos (2 \cdot θ))

How to Evaluate Normal Stress Induced in Oblique Plane due to Biaxial Loading?

Normal Stress Induced in Oblique Plane due to Biaxial Loading evaluator uses Normal Stress on Oblique Plane = (1/2*(Stress along x Direction+Stress along y Direction))+(1/2*(Stress along x Direction-Stress along y Direction)*(cos(2*Theta)))+(Shear Stress xy*sin(2*Theta)) to evaluate the Normal Stress on Oblique Plane, The Normal Stress Induced in Oblique Plane due to Biaxial Loading formula is defined as calculating stress subjected to a combination of direct stresses (σx) and (σy) in two mutually perpendicular planes, accompanied by simple shear stress (τxy). Normal Stress on Oblique Plane is denoted by σ_θ symbol.

How to evaluate Normal Stress Induced in Oblique Plane due to Biaxial Loading using this online evaluator? To use this online evaluator for Normal Stress Induced in Oblique Plane due to Biaxial Loading, enter Stress along x Direction (σ_x), Stress along y Direction (σ_y), Theta (θ) & Shear Stress xy (τ_xy) and hit the calculate button.

FAQs on Normal Stress Induced in Oblique Plane due to Biaxial Loading

What is the formula to find Normal Stress Induced in Oblique Plane due to Biaxial Loading?

The formula of Normal Stress Induced in Oblique Plane due to Biaxial Loading is expressed as Normal Stress on Oblique Plane = (1/2*(Stress along x Direction+Stress along y Direction))+(1/2*(Stress along x Direction-Stress along y Direction)*(cos(2*Theta)))+(Shear Stress xy*sin(2*Theta)). Here is an example- 6.7E-5 = (1/2*(45000000+110000000))+(1/2*(45000000-110000000)*(cos(2*0.5235987755982)))+(7200000*sin(2*0.5235987755982)).

How to calculate Normal Stress Induced in Oblique Plane due to Biaxial Loading?

With Stress along x Direction (σ_x), Stress along y Direction (σ_y), Theta (θ) & Shear Stress xy (τ_xy) we can find Normal Stress Induced in Oblique Plane due to Biaxial Loading using the formula - Normal Stress on Oblique Plane = (1/2*(Stress along x Direction+Stress along y Direction))+(1/2*(Stress along x Direction-Stress along y Direction)*(cos(2*Theta)))+(Shear Stress xy*sin(2*Theta)). This formula also uses Sine (sin), Cosine (cos) function(s).

Can the Normal Stress Induced in Oblique Plane due to Biaxial Loading be negative?

Yes, the Normal Stress Induced in Oblique Plane due to Biaxial Loading, measured in Stress can be negative.

Which unit is used to measure Normal Stress Induced in Oblique Plane due to Biaxial Loading?

Normal Stress Induced in Oblique Plane due to Biaxial Loading 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 Induced in Oblique Plane due to Biaxial Loading can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Normal Stress Induced in Oblique Plane due to Biaxial Loading Formula

Normal Stress Induced in Oblique Plane due to Biaxial Loading Example

Normal Stress Induced in Oblique Plane due to Biaxial Loading Solution

Normal Stress Induced in Oblique Plane due to Biaxial Loading Formula Elements

Other formulas in Stresses in Bi Axial Loading category

How to Evaluate Normal Stress Induced in Oblique Plane due to Biaxial Loading?

FAQs on Normal Stress Induced in Oblique Plane due to Biaxial Loading

Variable Name