FormulaDen.com

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

Shear Stress Induced in Oblique Plane due to Biaxial Loading Formula

Fx Copy

LaTeX Copy

The Shear Stress on Oblique Plane is the shear stress experienced by a body at any θ angle. Check FAQs

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

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

Shear Stress Induced in Oblique Plane due to Biaxial Loading Example

With values

With units

Only example

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

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

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

31.7458 = - (\frac{1}{2} \cdot (45 - 110) \cdot \sin (2 \cdot 30)) + (7.2 \cdot \cos (2 \cdot 30))

31.7458MPa = - (\frac{1}{2} \cdot (45MPa - 110MPa) \cdot \sin (2 \cdot 30°)) + (7.2MPa \cdot \cos (2 \cdot 30°))

31.7458 = - (\frac{1}{2} \cdot (45 - 110) \cdot \sin (2 \cdot 30)) + (7.2 \cdot \cos (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 Shear Stress Induced in Oblique Plane due to Biaxial Loading

Shear Stress Induced in Oblique Plane due to Biaxial Loading Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

τ θ = 31745825.6229923Pa

Next Step Convert to Output's Unit

∴

τ θ = 31.7458256229923MPa

LAST Step Rounding Answer

∴

τ θ = 31.7458MPa

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

Variables

Functions

Shear Stress on Oblique Plane

The Shear Stress on Oblique Plane is the shear stress experienced by a body at any θ angle.

Symbol: τ_θ

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear 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 Normal Stress Induced in Oblique Plane due to Biaxial Loading

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))

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

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

How to evaluate Shear Stress Induced in Oblique Plane due to Biaxial Loading using this online evaluator? To use this online evaluator for Shear 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 Shear Stress Induced in Oblique Plane due to Biaxial Loading

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

The formula of Shear Stress Induced in Oblique Plane due to Biaxial Loading is expressed as Shear Stress on Oblique Plane = -(1/2*(Stress along x Direction-Stress along y Direction)*sin(2*Theta))+(Shear Stress xy*cos(2*Theta)). Here is an example- 3.2E-5 = -(1/2*(45000000-110000000)*sin(2*0.5235987755982))+(7200000*cos(2*0.5235987755982)).

How to calculate Shear 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 Shear Stress Induced in Oblique Plane due to Biaxial Loading using the formula - Shear Stress on Oblique Plane = -(1/2*(Stress along x Direction-Stress along y Direction)*sin(2*Theta))+(Shear Stress xy*cos(2*Theta)). This formula also uses Sine (sin), Cosine (cos) function(s).

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

No, the Shear Stress Induced in Oblique Plane due to Biaxial Loading, measured in Stress cannot be negative.

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

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

Let Others Know

✖

Facebook

Twitter

Copied!

Shear Stress Induced in Oblique Plane due to Biaxial Loading Formula

Shear Stress Induced in Oblique Plane due to Biaxial Loading Example

Shear Stress Induced in Oblique Plane due to Biaxial Loading Solution

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

Other formulas in Stresses in Bi Axial Loading category

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

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

Variable Name