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 = (Mmax*A*y)/((σmax*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 = (Mmax*A*y)/((σmax*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 00.004 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

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

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