Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Calculator

✖Maximum Bending Moment occurs where shear force is zero.ⓘ Maximum Bending Moment [M_max]			+10% -10%
✖The Cross Sectional Area is the breadth times the depth of the beam structure.ⓘ Cross Sectional Area [A]			+10% -10%
✖Distance from Neutral Axis is measured between N.A. and the extreme point.ⓘ Distance from Neutral Axis [y]			+10% -10%
✖Maximum Stress is the maximum amount of stress the taken by the beam/column before it breaks.ⓘ Maximum Stress [σ_max]			+10% -10%
✖Axial Load is a force applied on a structure directly along an axis of the structure.ⓘ Axial Load [P]			+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.ⓘ Neutral Axis Moment of Inertia given Maximum Stress for Short Beams [I]

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Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load))
I = (M_max*A*y)/((σ_max*A)-(P))
This formula uses 6 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.
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment occurs where shear force is zero.
Cross Sectional Area - (Measured in Square Meter) - The Cross Sectional Area is the breadth times the depth of the beam structure.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is measured between N.A. and the extreme point.
Maximum Stress - (Measured in Pascal) - Maximum Stress is the maximum amount of stress the taken by the beam/column before it breaks.
Axial Load - (Measured in Newton) - Axial Load is a force applied on a structure directly along an axis of the structure.

STEP 1: Convert Input(s) to Base Unit

Maximum Bending Moment: 7.7 Kilonewton Meter --> 7700 Newton Meter (Check conversion here)
Cross Sectional Area: 0.12 Square Meter --> 0.12 Square Meter No Conversion Required
Distance from Neutral Axis: 25 Millimeter --> 0.025 Meter (Check conversion here)
Maximum Stress: 0.136979 Megapascal --> 136979 Pascal (Check conversion here)
Axial Load: 2000 Newton --> 2000 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (M_max*A*y)/((σ_max*A)-(P)) --> (7700*0.12*0.025)/((136979*0.12)-(2000))

Evaluating ... ...

I = 0.00160000221645329

STEP 3: Convert Result to Output's Unit

0.00160000221645329 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00160000221645329 ≈ 0.0016 Meter⁴ <-- Area Moment of Inertia

(Calculation completed in 00.008 seconds)

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Osmania University (OU), Hyderabad

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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)

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Formula

LaTeX Go

Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load))
I = (M_max*A*y)/((σ_max*A)-(P))

Define Moment of Inertia?

Moment of Inertia is a measure of the resistance of a body to angular acceleration about a given axis that is equal to the sum of the products of each element of mass in the body and the square of the element's distance from the axis.

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 Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams calculator uses Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load)) to calculate the Area Moment of Inertia, The Neutral Axis Moment of Inertia given Maximum Stress for Short Beams formula is defined as a measure of the resistance of a body to angular acceleration about a given axis. Area Moment of Inertia is denoted by I symbol.

How to calculate Neutral Axis Moment of Inertia given Maximum Stress for Short Beams using this online calculator? To use this online calculator for Neutral Axis Moment of Inertia given Maximum Stress for Short Beams, enter Maximum Bending Moment (M_max), Cross Sectional Area (A), Distance from Neutral Axis (y), Maximum Stress (σ_max) & Axial Load (P) and hit the calculate button. Here is how the Neutral Axis Moment of Inertia given Maximum Stress for Short Beams calculation can be explained with given input values -> 0.0016 = (7700*0.12*0.025)/((136979*0.12)-(2000)).

FAQ

What is Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

The Neutral Axis Moment of Inertia given Maximum Stress for Short Beams formula is defined as a measure of the resistance of a body to angular acceleration about a given axis and is represented as I = (M_max*A*y)/((σ_max*A)-(P)) or Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load)). Maximum Bending Moment occurs where shear force is zero, The Cross Sectional Area is the breadth times the depth of the beam structure, Distance from Neutral Axis is measured between N.A. and the extreme point, Maximum Stress is the maximum amount of stress the taken by the beam/column before it breaks & Axial Load is a force applied on a structure directly along an axis of the structure.

How to calculate Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

The Neutral Axis Moment of Inertia given Maximum Stress for Short Beams formula is defined as a measure of the resistance of a body to angular acceleration about a given axis is calculated using Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load)). To calculate Neutral Axis Moment of Inertia given Maximum Stress for Short Beams, you need Maximum Bending Moment (M_max), Cross Sectional Area (A), Distance from Neutral Axis (y), Maximum Stress (σ_max) & Axial Load (P). With our tool, you need to enter the respective value for Maximum Bending Moment, Cross Sectional Area, Distance from Neutral Axis, Maximum Stress & Axial Load 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 Maximum Bending Moment, Cross Sectional Area, Distance from Neutral Axis, Maximum Stress & Axial Load. We can use 2 other way(s) to calculate the same, which is/are as follows -

Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress
Area Moment of Inertia = (Moment of Resistance*Radius of Curvature)/Young's Modulus

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