Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber Calculator

✖Distance from Neutral Axis is measured between N.A. and the extreme point.ⓘ Distance from Neutral Axis [y]			+10% -10%
✖Moment of Resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress.ⓘ Moment of Resistance [M_r]			+10% -10%
✖Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.ⓘ Bending Stress [σ_b]			+10% -10%

✖Area Moment of Inertia is a property of a two-dimensional plane shape where it shows how its points are dispersed in an arbitrary axis in the cross-sectional plane.ⓘ Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber [I]

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Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber

Formula

`"I" = ("y"*"M"_{"r"})/"σ"_{"b"}`

Example

`"0.0016m⁴"=("25mm"*"4.608kN*m")/"0.072MPa"`

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Download Combined Axial and Bending Loads Formulas PDF

Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress
I = (y*M_r)/σ_b
This formula uses 4 Variables

Variables Used

Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a property of a two-dimensional plane shape where it shows how its points are dispersed in an arbitrary axis in the cross-sectional plane.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is measured between N.A. and the extreme point.
Moment of Resistance - (Measured in Newton Meter) - Moment of Resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress.
Bending Stress - (Measured in Pascal) - Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

STEP 1: Convert Input(s) to Base Unit

Distance from Neutral Axis: 25 Millimeter --> 0.025 Meter (Check conversion here)
Moment of Resistance: 4.608 Kilonewton Meter --> 4608 Newton Meter (Check conversion here)
Bending Stress: 0.072 Megapascal --> 72000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (y*M_r)/σ_b --> (0.025*4608)/72000

Evaluating ... ...

I = 0.0016

STEP 3: Convert Result to Output's Unit

0.0016 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.0016 Meter⁴ <-- Area Moment of Inertia

(Calculation completed in 00.004 seconds)

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< 19 Combined Axial and Bending Loads Calculators

Neutral Axis to Outermost Fiber Distance given Maximum Stress for Short Beams

Go Distance from Neutral Axis = ((Maximum Stress*Cross Sectional Area*Area Moment of Inertia)-(Axial Load*Area Moment of Inertia))/(Maximum Bending Moment*Cross Sectional Area)

Maximum Stress in Short Beams for Large Deflection

Go Maximum Stress = (Axial Load/Cross Sectional Area)+(((Maximum Bending Moment+Axial Load*Deflection of Beam)*Distance from Neutral Axis)/Area Moment of Inertia)

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams

Go Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load))

Axial Load given Maximum Stress for Short Beams

Go Axial Load = Cross Sectional Area*(Maximum Stress -((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia))

Maximum Bending Moment given Maximum Stress for Short Beams

Go Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis

Cross-Sectional Area given Maximum Stress for Short Beams

Go Cross Sectional Area = Axial Load/(Maximum Stress-((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia))

Maximum Stress for Short Beams

Go Maximum Stress = (Axial Load/Cross Sectional Area)+((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia)

Young's Modulus given Distance from Extreme Fiber along with Radius and Stress Induced

Go Young's Modulus = ((Radius of Curvature*Fibre Stress at Distance ‘y’ from NA)/Distance from Neutral Axis)

Stress Induced with known Distance from Extreme Fiber, Young's Modulus and Radius of curvature

Go Fibre Stress at Distance ‘y’ from NA = (Young's Modulus*Distance from Neutral Axis)/Radius of Curvature

Distance from Extreme Fiber given Young's Modulus along with Radius and Stress Induced

Go Distance from Neutral Axis = (Radius of Curvature*Fibre Stress at Distance ‘y’ from NA)/Young's Modulus

Deflection for Transverse Loading given Deflection for Axial Bending

Go Deflection for Transverse Loading Alone = Deflection of Beam*(1-(Axial Load/Critical Buckling Load))

Deflection for Axial Compression and Bending

Go Deflection of Beam = Deflection for Transverse Loading Alone/(1-(Axial Load/Critical Buckling Load))

Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress

Go Distance from Neutral Axis = (Area Moment of Inertia*Bending Stress)/Moment of Resistance

Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber

Go Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress

Stress Induced using Moment of Resistance, Moment of Inertia and Distance from Extreme Fiber

Go Bending Stress = (Distance from Neutral Axis*Moment of Resistance)/Area Moment of Inertia

Moment of Resistance in Bending Equation

Go Moment of Resistance = (Area Moment of Inertia*Bending Stress)/Distance from Neutral Axis

Young's Modulus using Moment of Resistance, Moment of Inertia and Radius

Go Young's Modulus = (Moment of Resistance*Radius of Curvature)/Area Moment of Inertia

Moment of Resistance given Young's Modulus, Moment of Inertia and Radius

Go Moment of Resistance = (Area Moment of Inertia*Young's Modulus)/Radius of Curvature

Moment of Inertia given Young's Modulus, Moment of Resistance and Radius

Go Area Moment of Inertia = (Moment of Resistance*Radius of Curvature)/Young's Modulus

Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber Formula

Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress
I = (y*M_r)/σ_b

What is Simple Bending?

The Bending will be called as simple bending when it occurs because of beam self-load and external load. This type of bending is also known as ordinary bending and in this type of bending results both shear stress and normal stress in the beam.

Define Stress.

Stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. Thus, Stress is defined as “The restoring force per unit area of the material”. It is a tensor quantity. Denoted by the Greek letter σ. Measured using Pascal or N/m2.

How to Calculate Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber?

Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber calculator uses Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress to calculate the Area Moment of Inertia, The Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber formula is defined as moment of inertia of the material when the cross section is undergoing simple bending. Area Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber using this online calculator? To use this online calculator for Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber, enter Distance from Neutral Axis (y), Moment of Resistance (M_r) & Bending Stress (σ_b) and hit the calculate button. Here is how the Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber calculation can be explained with given input values -> 0.0016 = (0.025*4608)/72000.

FAQ

What is Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber?

The Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber formula is defined as moment of inertia of the material when the cross section is undergoing simple bending and is represented as I = (y*M_r)/σ_b or Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress. Distance from Neutral Axis is measured between N.A. and the extreme point, Moment of Resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress & Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

How to calculate Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber?

The Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber formula is defined as moment of inertia of the material when the cross section is undergoing simple bending is calculated using Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress. To calculate Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber, you need Distance from Neutral Axis (y), Moment of Resistance (M_r) & Bending Stress (σ_b). With our tool, you need to enter the respective value for Distance from Neutral Axis, Moment of Resistance & Bending Stress 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 Area Moment of Inertia?

In this formula, Area Moment of Inertia uses Distance from Neutral Axis, Moment of Resistance & Bending Stress. We can use 2 other way(s) to calculate the same, which is/are as follows -

Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load))
Area Moment of Inertia = (Moment of Resistance*Radius of Curvature)/Young's Modulus

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