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Shear Modulus Formula

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Shear Modulus is the slope of the linear elastic region of the shear stress-strain curve. Check FAQs

G pa = \frac{𝜏}{𝜂}

G_pa - Shear Modulus?𝜏 - Shear Stress?𝜂 - Shear Strain?

Shear Modulus Example

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With units

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Here is how the Shear Modulus equation looks like with Values.

Here is how the Shear Modulus equation looks like with Units.

Here is how the Shear Modulus equation looks like.

34.8571 = \frac{61}{1.75}

34.8571Pa = \frac{61Pa}{1.75}

34.8571 = \frac{61}{1.75}

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Shear Modulus Solution

Follow our step by step solution on how to calculate Shear Modulus?

FIRST Step Consider the formula

G pa = \frac{𝜏}{𝜂}

Next Step Substitute values of Variables

∴

G pa = \frac{61Pa}{1.75}

Next Step Prepare to Evaluate

∴

G pa = \frac{61}{1.75}

Next Step Evaluate

∴

G pa = 34.8571428571429Pa

LAST Step Rounding Answer

∴

G pa = 34.8571Pa

Shear Modulus Formula Elements

Variables

Shear Modulus

Shear Modulus is the slope of the linear elastic region of the shear stress-strain curve.

Symbol: G_pa

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Modulus

Shear Stress

Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: 𝜏

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Stress

Shear Strain

The Shear Strain is the ratio of the change in deformation to its original length perpendicular to the axes of the member due to shear stress.

Symbol: 𝜂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Shear Strain

Other formulas in Stress and Strain category

Go Elongation Circular Tapered Bar

Δ c = \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 h = \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

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

How to Evaluate Shear Modulus?

Shear Modulus evaluator uses Shear Modulus = Shear Stress/Shear Strain to evaluate the Shear Modulus, The Shear Modulus formula is defined as a measure of the rigidity of a material, describing its tendency to deform under shear stress, which is a crucial property in understanding the behavior of materials under different types of loading, particularly in mechanical engineering and materials science applications. Shear Modulus is denoted by G_pa symbol.

How to evaluate Shear Modulus using this online evaluator? To use this online evaluator for Shear Modulus, enter Shear Stress (𝜏) & Shear Strain (𝜂) and hit the calculate button.

FAQs on Shear Modulus

What is the formula to find Shear Modulus?

The formula of Shear Modulus is expressed as Shear Modulus = Shear Stress/Shear Strain. Here is an example- 34.85714 = 61/1.75.

How to calculate Shear Modulus?

With Shear Stress (𝜏) & Shear Strain (𝜂) we can find Shear Modulus using the formula - Shear Modulus = Shear Stress/Shear Strain.

Can the Shear Modulus be negative?

No, the Shear Modulus, measured in Stress cannot be negative.

Which unit is used to measure Shear Modulus?

Shear Modulus is usually measured using the Pascal[Pa] for Stress. Newton per Square Meter[Pa], Newton per Square Millimeter[Pa], Kilonewton per Square Meter[Pa] are the few other units in which Shear Modulus can be measured.

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