Strain Energy Stored in Rod Subjected to Bending Moment Calculator

✖Bending Moment in Shaft or Beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Shaft or Beam [M_b]			+10% -10%
✖Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of elasticity of rod or shaft [E]			+10% -10%
✖Area Moment of Inertia of rod or shaft is the measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.ⓘ Area Moment of Inertia of rod or shaft [I]			+10% -10%

✖Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.ⓘ Strain Energy Stored in Rod Subjected to Bending Moment [U]

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Strain Energy Stored in Rod Subjected to Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft)
U = (M_b^2)*L/(2*E*I)
This formula uses 5 Variables

Variables Used

Strain Energy in Rod or Shaft - (Measured in Joule) - Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.
Bending Moment in Shaft or Beam - (Measured in Newton Meter) - Bending Moment in Shaft or Beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
Length of Rod or Shaft - (Measured in Meter) - Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.
Modulus of elasticity of rod or shaft - (Measured in Pascal) - Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Area Moment of Inertia of rod or shaft - (Measured in Meter⁴) - Area Moment of Inertia of rod or shaft is the measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Shaft or Beam: 780000 Newton Millimeter --> 780 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1330 Millimeter --> 1.33 Meter (Check conversion here)
Modulus of elasticity of rod or shaft: 98000 Newton per Square Millimeter --> 98000000000 Pascal (Check conversion here)
Area Moment of Inertia of rod or shaft: 103000 Millimeter⁴ --> 1.03E-07 Meter⁴ (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = (M_b^2)*L/(2*E*I) --> (780^2)*1.33/(2*98000000000*1.03E-07)

Evaluating ... ...

U = 40.0818307905687

STEP 3: Convert Result to Output's Unit

40.0818307905687 Joule --> No Conversion Required

FINAL ANSWER

40.0818307905687 ≈ 40.08183 Joule <-- Strain Energy in Rod or Shaft

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Castigliano's Theorem for Deflection in Complex Structures Calculators

Force Applied on Rod given Strain Energy Stored in Tension Rod

LaTeX Go Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft)

Strain Energy Stored in Tension Rod

LaTeX Go Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft)

Modulus of Elasticity of Rod given Strain Energy Stored

LaTeX Go Modulus of elasticity of rod or shaft = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy in Rod or Shaft)

Length of Rod given Strain Energy Stored

LaTeX Go Length of Rod or Shaft = Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Axial Force on Beam^2

Strain Energy Stored in Rod Subjected to Bending Moment Formula

LaTeX Go

Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft)
U = (M_b^2)*L/(2*E*I)

Define Bending Moment?

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam.

How to Calculate Strain Energy Stored in Rod Subjected to Bending Moment?

Strain Energy Stored in Rod Subjected to Bending Moment calculator uses Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft) to calculate the Strain Energy in Rod or Shaft, The Strain Energy Stored in Rod Subjected to Bending Moment formula is defined as type of potential energy that is stored in structural member as result of elastic deformation. Strain Energy in Rod or Shaft is denoted by U symbol.

How to calculate Strain Energy Stored in Rod Subjected to Bending Moment using this online calculator? To use this online calculator for Strain Energy Stored in Rod Subjected to Bending Moment, enter Bending Moment in Shaft or Beam (M_b), Length of Rod or Shaft (L), Modulus of elasticity of rod or shaft (E) & Area Moment of Inertia of rod or shaft (I) and hit the calculate button. Here is how the Strain Energy Stored in Rod Subjected to Bending Moment calculation can be explained with given input values -> 40.08183 = (780^2)*1.33/(2*98000000000*1.03E-07).

FAQ

What is Strain Energy Stored in Rod Subjected to Bending Moment?

The Strain Energy Stored in Rod Subjected to Bending Moment formula is defined as type of potential energy that is stored in structural member as result of elastic deformation and is represented as U = (M_b^2)*L/(2*E*I) or Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft). Bending Moment in Shaft or Beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend, Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom, Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it & Area Moment of Inertia of rod or shaft is the measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.

How to calculate Strain Energy Stored in Rod Subjected to Bending Moment?

The Strain Energy Stored in Rod Subjected to Bending Moment formula is defined as type of potential energy that is stored in structural member as result of elastic deformation is calculated using Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft). To calculate Strain Energy Stored in Rod Subjected to Bending Moment, you need Bending Moment in Shaft or Beam (M_b), Length of Rod or Shaft (L), Modulus of elasticity of rod or shaft (E) & Area Moment of Inertia of rod or shaft (I). With our tool, you need to enter the respective value for Bending Moment in Shaft or Beam, Length of Rod or Shaft, Modulus of elasticity of rod or shaft & Area Moment of Inertia of rod or shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Strain Energy in Rod or Shaft?

In this formula, Strain Energy in Rod or Shaft uses Bending Moment in Shaft or Beam, Length of Rod or Shaft, Modulus of elasticity of rod or shaft & Area Moment of Inertia of rod or shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft)
Strain Energy in Rod or Shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)

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