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Stiffness of Cantilever Beam Formula

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Spring Constant of Cantilever Beam is defined as the equivalent spring constant of a cantilever beam when subjected to some load. Check FAQs

κ = \frac{3 \cdot E \cdot Ι}{L^{3}}

κ - Spring Constant of Cantilever Beam?E - Young's Modulus?Ι - Moment of Inertia of Beam About Bending Axis?L - Total Length?

Stiffness of Cantilever Beam Example

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Here is how the Stiffness of Cantilever Beam equation looks like with Values.

Here is how the Stiffness of Cantilever Beam equation looks like with Units.

Here is how the Stiffness of Cantilever Beam equation looks like.

993.4001 = \frac{3 \cdot 15 \cdot 48.5}{1300^{3}}

993.4001N/m = \frac{3 \cdot 15N/m \cdot 48.5kg·m²}{{1300mm}^{3}}

993.4001 = \frac{3 \cdot 15 \cdot 48.5}{1300^{3}}

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Stiffness of Cantilever Beam Solution

Follow our step by step solution on how to calculate Stiffness of Cantilever Beam?

FIRST Step Consider the formula

κ = \frac{3 \cdot E \cdot Ι}{L^{3}}

Next Step Substitute values of Variables

∴

κ = \frac{3 \cdot 15N/m \cdot 48.5kg·m²}{{1300mm}^{3}}

Next Step Convert Units

∴

κ = \frac{3 \cdot 15N/m \cdot 48.5kg·m²}{{1.3m}^{3}}

Next Step Prepare to Evaluate

∴

κ = \frac{3 \cdot 15 \cdot 48.5}{{1.3}^{3}}

Next Step Evaluate

∴

κ = 993.400091033227N/m

LAST Step Rounding Answer

∴

κ = 993.4001N/m

Stiffness of Cantilever Beam Formula Elements

Variables

Spring Constant of Cantilever Beam

Spring Constant of Cantilever Beam is defined as the equivalent spring constant of a cantilever beam when subjected to some load.

Symbol: κ

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Spring Constant of Cantilever Beam

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Moment of Inertia of Beam About Bending Axis

Moment of Inertia of Beam About Bending Axis is the moment of inertia of the cross-section of the beam about the bending axis.

Symbol: Ι

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Beam About Bending Axis

Total Length

Total Length is the measurement or extent of something from end to end.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Total Length

Other formulas in Stiffness category

Go Stiffness of Rod under Axial Load

K = \frac{E \cdot A c}{L}

Go Stiffness of Tapered Rod under Axial Load

K = \frac{π \cdot E \cdot d 1 \cdot d 2}{4 \cdot L}

Go Stiffness of Fixed-Fixed Beam with Load at Middle

K = \frac{192 \cdot E \cdot I}{L^{3}}

How to Evaluate Stiffness of Cantilever Beam?

Stiffness of Cantilever Beam evaluator uses Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3 to evaluate the Spring Constant of Cantilever Beam, Stiffness of Cantilever Beam formula is defined as a measure of the resistance of the beam to deformation under an applied load, providing a way to quantify the beam's ability to resist bending and deflection, which is essential in engineering design and analysis of cantilever beam structures. Spring Constant of Cantilever Beam is denoted by κ symbol.

How to evaluate Stiffness of Cantilever Beam using this online evaluator? To use this online evaluator for Stiffness of Cantilever Beam, enter Young's Modulus (E), Moment of Inertia of Beam About Bending Axis (Ι) & Total Length (L) and hit the calculate button.

FAQs on Stiffness of Cantilever Beam

What is the formula to find Stiffness of Cantilever Beam?

The formula of Stiffness of Cantilever Beam is expressed as Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3. Here is an example- 993.4001 = (3*15*48.5)/1.3^3.

How to calculate Stiffness of Cantilever Beam?

With Young's Modulus (E), Moment of Inertia of Beam About Bending Axis (Ι) & Total Length (L) we can find Stiffness of Cantilever Beam using the formula - Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3.

Can the Stiffness of Cantilever Beam be negative?

No, the Stiffness of Cantilever Beam, measured in Surface Tension cannot be negative.

Which unit is used to measure Stiffness of Cantilever Beam?

Stiffness of Cantilever Beam is usually measured using the Newton per Meter[N/m] for Surface Tension. Millinewton per Meter[N/m], Gram-Force per Centimeter[N/m], Dyne per Centimeter[N/m] are the few other units in which Stiffness of Cantilever Beam can be measured.

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Stiffness of Cantilever Beam Formula

Stiffness of Cantilever Beam Example

Stiffness of Cantilever Beam Solution

Stiffness of Cantilever Beam Formula Elements

Other formulas in Stiffness category

How to Evaluate Stiffness of Cantilever Beam?

FAQs on Stiffness of Cantilever Beam

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