Stiffness of Cantilever Beam Calculator

✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of Inertia of Beam About Bending Axis is the moment of inertia of the cross-section of the beam about the bending axis.ⓘ Moment of Inertia of Beam About Bending Axis [Ι]			+10% -10%
✖Total Length is the measurement or extent of something from end to end.ⓘ Total Length [L]			+10% -10%

✖Spring Constant of Cantilever Beam is defined as the equivalent spring constant of a cantilever beam when subjected to some load.ⓘ Stiffness of Cantilever Beam [κ]

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Stiffness of Cantilever Beam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3
κ = (3*E*Ι)/L^3
This formula uses 4 Variables

Variables Used

Spring Constant of Cantilever Beam - (Measured in Newton per Meter) - Spring Constant of Cantilever Beam is defined as the equivalent spring constant of a cantilever beam when subjected to some load.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Moment of Inertia of Beam About Bending Axis - (Measured in Kilogram Square Meter) - Moment of Inertia of Beam About Bending Axis is the moment of inertia of the cross-section of the beam about the bending axis.
Total Length - (Measured in Meter) - Total Length is the measurement or extent of something from end to end.

STEP 1: Convert Input(s) to Base Unit

Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of Inertia of Beam About Bending Axis: 48.5 Kilogram Square Meter --> 48.5 Kilogram Square Meter No Conversion Required
Total Length: 1300 Millimeter --> 1.3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

κ = (3*E*Ι)/L^3 --> (3*15*48.5)/1.3^3

Evaluating ... ...

κ = 993.400091033227

STEP 3: Convert Result to Output's Unit

993.400091033227 Newton per Meter --> No Conversion Required

FINAL ANSWER

993.400091033227 ≈ 993.4001 Newton per Meter <-- Spring Constant of Cantilever Beam

(Calculation completed in 00.020 seconds)

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< Stiffness Calculators

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LaTeX Go Stiffness Constant = (pi*Young's Modulus*End Diameter 1*End Diameter 2)/(4*Total Length)

Stiffness of Cantilever Beam

LaTeX Go Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3

Stiffness of Rod under Axial Load

LaTeX Go Stiffness Constant = (Young's Modulus*Rod Cross Sectional Area)/Total Length

Stiffness of Fixed-Fixed Beam with Load at Middle

LaTeX Go Stiffness Constant = (192*Young's Modulus*Moment of Inertia)/Total Length^3

Stiffness of Cantilever Beam Formula

LaTeX Go

Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3
κ = (3*E*Ι)/L^3

Assumptions of the formula

For simplicity, we assume the self-weight of the beam is negligible and the concentrated load F acts at the end of the beam due to the weight of a point mass.

Direction of Moment of Inertia

It is possible for a cantilever beam to be subjected to concentrated loads in two directions at its end.
When the load is applied along the y-direction, the beam bends about the z-axis and vice versa. Then the I will be Izz or Iyy according to the situation.

How to Calculate Stiffness of Cantilever Beam?

Stiffness of Cantilever Beam calculator uses Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3 to calculate 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 calculate Stiffness of Cantilever Beam using this online calculator? To use this online calculator 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. Here is how the Stiffness of Cantilever Beam calculation can be explained with given input values -> 993.4001 = (3*15*48.5)/1.3^3.

FAQ

What is Stiffness 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 and is represented as κ = (3*E*Ι)/L^3 or Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3. Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Moment of Inertia of Beam About Bending Axis is the moment of inertia of the cross-section of the beam about the bending axis & Total Length is the measurement or extent of something from end to end.

How to calculate Stiffness 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 is calculated using Spring Constant of Cantilever Beam = (3*Young's Modulus*Moment of Inertia of Beam About Bending Axis)/Total Length^3. To calculate Stiffness of Cantilever Beam, you need Young's Modulus (E), Moment of Inertia of Beam About Bending Axis (Ι) & Total Length (L). With our tool, you need to enter the respective value for Young's Modulus, Moment of Inertia of Beam About Bending Axis & Total Length and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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