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

✖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.ⓘ Area Moment of Inertia [I]			+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%
✖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%

✖Distance from Neutral Axis is measured between N.A. and the extreme point.ⓘ Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress [y]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is measured between N.A. and the extreme point.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required
Bending Stress: 0.072 Megapascal --> 72000 Pascal (Check conversion here)
Moment of Resistance: 4.608 Kilonewton Meter --> 4608 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y = (I*σ_b)/M_r --> (0.0016*72000)/4608

Evaluating ... ...

y = 0.025

STEP 3: Convert Result to Output's Unit

0.025 Meter -->25 Millimeter (Check conversion here)

FINAL ANSWER

25 Millimeter <-- Distance from Neutral Axis

(Calculation completed in 00.020 seconds)

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< Combined Axial and Bending Loads Calculators

Maximum Bending Moment given Maximum Stress for Short Beams

LaTeX 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

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

Axial Load given Maximum Stress for Short Beams

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

Maximum Stress for Short Beams

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

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

LaTeX Go

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

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

Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress calculator uses Distance from Neutral Axis = (Area Moment of Inertia*Bending Stress)/Moment of Resistance to calculate the Distance from Neutral Axis, The Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress formula is defined as the distance of the extreme fiber from the neutral axis when the beam is undergoing simple bending. Distance from Neutral Axis is denoted by y symbol.

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

FAQ

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

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

How to calculate Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress?

The Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress formula is defined as the distance of the extreme fiber from the neutral axis when the beam is undergoing simple bending is calculated using Distance from Neutral Axis = (Area Moment of Inertia*Bending Stress)/Moment of Resistance. To calculate Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress, you need Area Moment of Inertia (I), Bending Stress (σ_b) & Moment of Resistance (M_r). With our tool, you need to enter the respective value for Area Moment of Inertia, Bending Stress & Moment of Resistance 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 Distance from Neutral Axis?

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

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

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