Strain Energy Stored in Rod Subjected to Bending Moment Calculator

✖The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering.ⓘ Bending Moment [M_b]			+10% -10%
✖The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions.ⓘ Modulus of Elasticity [E]			+10% -10%
✖The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.ⓘ Area Moment of Inertia [I]			+10% -10%

✖The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.ⓘ 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 = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Area Moment of Inertia)
U = M_b^2*L/(2*E*I)
This formula uses 5 Variables

Variables Used

Strain Energy - (Measured in Joule) - The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.
Bending Moment - (Measured in Newton Meter) - The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering.
Length of Rod or Shaft - (Measured in Meter) - The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.
Modulus of Elasticity - (Measured in Pascal) - The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions.
Area Moment of Inertia - (Measured in Meter⁴) - The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 55001 Newton Millimeter --> 55.001 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1432.449 Millimeter --> 1.432449 Meter (Check conversion here)
Modulus of Elasticity: 105548.9 Newton per Square Millimeter --> 105548900000 Pascal (Check conversion here)
Area Moment of Inertia: 552.5 Millimeter⁴ --> 5.525E-10 Meter⁴ (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = M_b^2*L/(2*E*I) --> 55.001^2*1.432449/(2*105548900000*5.525E-10)

Evaluating ... ...

U = 37.1538950799147

STEP 3: Convert Result to Output's Unit

37.1538950799147 Joule --> No Conversion Required

FINAL ANSWER

37.1538950799147 ≈ 37.1539 Joule <-- Strain Energy

(Calculation completed in 00.007 seconds)

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Osmania University (OU), Hyderabad

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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*2*Cross Sectional Area of Rod*Modulus of Elasticity/Length of Rod or Shaft)

Strain Energy Stored in Tension Rod

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

Modulus of Elasticity of Rod given Strain Energy Stored

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

Length of Rod given Strain Energy Stored

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

Strain Energy Stored in Rod Subjected to Bending Moment Formula

LaTeX Go

Strain Energy = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Area Moment of Inertia)
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 = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Area Moment of Inertia) to calculate the Strain Energy, Strain Energy Stored in Rod Subjected to Bending Moment formula is defined as a representation of the energy accumulated in a rod when it experiences bending. This energy is crucial for understanding the material's behavior under stress and for ensuring structural integrity in engineering applications. Strain Energy 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 (M_b), Length of Rod or Shaft (L), Modulus of Elasticity (E) & Area Moment of Inertia (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 -> 0.19889 = 55.001^2*1.432449/(2*105548900000*5.525E-10).

FAQ

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

Strain Energy Stored in Rod Subjected to Bending Moment formula is defined as a representation of the energy accumulated in a rod when it experiences bending. This energy is crucial for understanding the material's behavior under stress and for ensuring structural integrity in engineering applications and is represented as U = M_b^2*L/(2*E*I) or Strain Energy = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Area Moment of Inertia). The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering, The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis, The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions & The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.

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

Strain Energy Stored in Rod Subjected to Bending Moment formula is defined as a representation of the energy accumulated in a rod when it experiences bending. This energy is crucial for understanding the material's behavior under stress and for ensuring structural integrity in engineering applications is calculated using Strain Energy = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Area Moment of Inertia). To calculate Strain Energy Stored in Rod Subjected to Bending Moment, you need Bending Moment (M_b), Length of Rod or Shaft (L), Modulus of Elasticity (E) & Area Moment of Inertia (I). With our tool, you need to enter the respective value for Bending Moment, Length of Rod or Shaft, Modulus of Elasticity & Area Moment of Inertia 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 this formula, Strain Energy uses Bending Moment, Length of Rod or Shaft, Modulus of Elasticity & Area Moment of Inertia. We can use 2 other way(s) to calculate the same, which is/are as follows -

Strain Energy = (Axial Force on Beam^2*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of Elasticity)
Strain Energy = Torque^2*Length of Rod or Shaft/(2*Polar Moment of Inertia*Modulus of Rigidity)

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