Moment of inertia given maximum stress for strut subjected to uniformly distributed load Calculator

✖Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment.ⓘ Maximum Bending Moment In Column [M]			+10% -10%
✖Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.ⓘ Distance from Neutral Axis to Extreme Point [c]			+10% -10%
✖Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.ⓘ Maximum bending stress [σb^max]			+10% -10%
✖The Axial Thrust is the resultant force of all the axial forces (F) acting on the object or material.ⓘ Axial Thrust [P_axial]			+10% -10%
✖Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.ⓘ Column Cross Sectional Area [A_sectional]			+10% -10%

✖Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of inertia given maximum stress for strut subjected to uniformly distributed load [I]

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Formula

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Moment of inertia given maximum stress for strut subjected to uniformly distributed load

Formula

`"I" = ("M"*"c"/(("σb"^{"max"}-("P"_{"axial"}/"A"_{"sectional"}))))`

Example

`"8.004288cm⁴"=("16N*m"*"10mm"/(("2MPa"-("1500N"/"1.4m²"))))`

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Moment of inertia given maximum stress for strut subjected to uniformly distributed load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia Column = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))))
I = (M*c/((σb^max-(P_axial/A_sectional))))
This formula uses 6 Variables

Variables Used

Moment of Inertia Column - (Measured in Meter⁴) - Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.
Maximum Bending Moment In Column - (Measured in Newton Meter) - Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment.
Distance from Neutral Axis to Extreme Point - (Measured in Meter) - Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.
Maximum bending stress - (Measured in Pascal) - Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.
Axial Thrust - (Measured in Newton) - The Axial Thrust is the resultant force of all the axial forces (F) acting on the object or material.
Column Cross Sectional Area - (Measured in Square Meter) - Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.

STEP 1: Convert Input(s) to Base Unit

Maximum Bending Moment In Column: 16 Newton Meter --> 16 Newton Meter No Conversion Required
Distance from Neutral Axis to Extreme Point: 10 Millimeter --> 0.01 Meter (Check conversion here)
Maximum bending stress: 2 Megapascal --> 2000000 Pascal (Check conversion here)
Axial Thrust: 1500 Newton --> 1500 Newton No Conversion Required
Column Cross Sectional Area: 1.4 Square Meter --> 1.4 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (M*c/((σb^max-(P_axial/A_sectional)))) --> (16*0.01/((2000000-(1500/1.4))))

Evaluating ... ...

I = 8.0042880114347E-08

STEP 3: Convert Result to Output's Unit

8.0042880114347E-08 Meter⁴ -->8.0042880114347 Centimeter⁴ (Check conversion here)

FINAL ANSWER

8.0042880114347 ≈ 8.004288 Centimeter⁴ <-- Moment of Inertia Column

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Strut With lateral load » Strut Subjected To Compressive Axial Thrust And A Transverse Uniformly Distributed Load » Moment of inertia given maximum stress for strut subjected to uniformly distributed load

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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< 25 Strut Subjected To Compressive Axial Thrust And A Transverse Uniformly Distributed Load Calculators

Maximum deflection for strut subjected to compressive axial and uniformly distributed load

Go Maximum initial deflection = (Load Intensity*(Modulus of Elasticity Column*Moment of Inertia Column/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust))

Load intensity given max deflection for strut subjected to uniformly distributed load

Go Load Intensity = Maximum initial deflection/((1*(Modulus of Elasticity Column*Moment of Inertia Column/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1))-(1*(Column Length^2)/(8*Axial Thrust)))

Maximum bending moment for strut subjected to compressive axial and uniformly distributed load

Go Maximum Bending Moment In Column = -Load Intensity*(Modulus of Elasticity Column*Moment of Inertia Column/Axial Thrust)*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1)

Load intensity given max bending moment for strut subjected to uniformly distributed load

Go Load Intensity = Maximum Bending Moment In Column/(Modulus of Elasticity Column*Moment of Inertia Column/Axial Thrust)*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1)

Bending moment at section for strut subjected to compressive axial and uniformly distributed load

Go Bending Moment in Column = -(Axial Thrust*Deflection at Section)+(Load Intensity*(((Distance of deflection from end A^2)/2)-(Column Length*Distance of deflection from end A/2)))

Deflection at section for strut subjected to compressive axial and uniformly distributed load

Go Deflection at Section = (-Bending Moment in Column+(Load Intensity*(((Distance of deflection from end A^2)/2)-(Column Length*Distance of deflection from end A/2))))/Axial Thrust

Axial thrust for strut subjected to compressive axial and uniformly distributed load

Go Axial Thrust = (-Bending Moment in Column+(Load Intensity*(((Distance of deflection from end A^2)/2)-(Column Length*Distance of deflection from end A/2))))/Deflection at Section

Length of column for strut subjected to compressive axial and uniformly distributed load

Go Column Length = (((Distance of deflection from end A^2)/2)-((Bending Moment in Column+(Axial Thrust*Deflection at Section))/Load Intensity))*2/Distance of deflection from end A

Load intensity for strut subjected to compressive axial and uniformly distributed load

Go Load Intensity = (Bending Moment in Column+(Axial Thrust*Deflection at Section))/(((Distance of deflection from end A^2)/2)-(Column Length*Distance of deflection from end A/2))

Moment of inertia given maximum stress for strut subjected to uniformly distributed load

Go Moment of Inertia Column = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))))

Distance of extreme layer from NA given max stress for strut under uniformly distributed load

Go Distance from Neutral Axis to Extreme Point = (Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))*Moment of Inertia Column/(Maximum Bending Moment In Column)

Maximum bending moment given max stress for strut subjected to uniformly distributed load

Go Maximum Bending Moment In Column = (Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))*Moment of Inertia Column/(Distance from Neutral Axis to Extreme Point)

Cross-sectional area given maximum stress for strut subjected to uniformly distributed load

Go Column Cross Sectional Area = Axial Thrust/(Maximum bending stress-(Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/Moment of Inertia Column))

Maximum stress for strut subjected to compressive axial and uniformly distributed load

Go Maximum bending stress = (Axial Thrust/Column Cross Sectional Area)+(Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/Moment of Inertia Column)

Axial thrust given maximum stress for strut subjected to uniformly distributed load

Go Axial Thrust = (Maximum bending stress-(Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/Moment of Inertia Column))*Column Cross Sectional Area

Length of column given max bending moment for strut subjected to uniformly distributed load

Go Column Length = sqrt(((Axial Thrust*Maximum initial deflection)-Maximum Bending Moment In Column)*8/(Load Intensity))

Maximum bending moment given elastic modulus for strut subjected to uniformly distributed load

Go Maximum Bending Moment In Column = (Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))*Modulus of Elasticity Column

Cross-sectional area given elastic modulus for strut subjected to uniformly distributed load

Go Column Cross Sectional Area = Axial Thrust/(Maximum bending stress-(Maximum Bending Moment In Column/Modulus of Elasticity Column))

Maximum stress given elastic modulus for strut subjected to uniformly distributed load

Go Maximum bending stress = (Axial Thrust/Column Cross Sectional Area)+(Maximum Bending Moment In Column/Modulus of Elasticity Column)

Elastic modulus given maximum stress for strut subjected to uniformly distributed load

Go Modulus of Elasticity Column = Maximum Bending Moment In Column/(Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))

Axial thrust given elastic modulus for strut subjected to uniformly distributed load

Go Axial Thrust = (Maximum bending stress-(Maximum Bending Moment In Column/Modulus of Elasticity Column))*Column Cross Sectional Area

Load intensity given maximum bending moment for strut subjected to uniformly distributed load

Go Load Intensity = (-(Axial Thrust*Maximum initial deflection)-Maximum Bending Moment In Column)*8/((Column Length^2))

Maximum deflection given max bending moment for strut subjected to uniformly distributed load

Go Maximum initial deflection = (-Maximum Bending Moment In Column-(Load Intensity*(Column Length^2)/8))/(Axial Thrust)

Axial thrust given maximum bending moment for strut subjected to uniformly distributed load

Go Axial Thrust = (-Maximum Bending Moment In Column-(Load Intensity*(Column Length^2)/8))/(Maximum initial deflection)

Maximum bending moment given max deflection for strut subjected to uniformly distributed load

Go Maximum Bending Moment In Column = -(Axial Thrust*Maximum initial deflection)-(Load Intensity*(Column Length^2)/8)

Moment of inertia given maximum stress for strut subjected to uniformly distributed load Formula

What is axial thrust?

Axial thrust refers to a propelling force applied along the axis (also called axial direction) of an object in order to push the object against a platform in a particular direction.

How to Calculate Moment of inertia given maximum stress for strut subjected to uniformly distributed load?

Moment of inertia given maximum stress for strut subjected to uniformly distributed load calculator uses Moment of Inertia Column = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum bending stress-(Axial Thrust/Column Cross Sectional Area)))) to calculate the Moment of Inertia Column, The Moment of inertia given maximum stress for strut subjected to uniformly distributed load formula is defined as a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of torque (turning force). Moment of Inertia Column is denoted by I symbol.

How to calculate Moment of inertia given maximum stress for strut subjected to uniformly distributed load using this online calculator? To use this online calculator for Moment of inertia given maximum stress for strut subjected to uniformly distributed load, enter Maximum Bending Moment In Column (M), Distance from Neutral Axis to Extreme Point (c), Maximum bending stress (σb^max), Axial Thrust (P_axial) & Column Cross Sectional Area (A_sectional) and hit the calculate button. Here is how the Moment of inertia given maximum stress for strut subjected to uniformly distributed load calculation can be explained with given input values -> 8E+8 = (16*0.01/((2000000-(1500/1.4)))).

FAQ

What is Moment of inertia given maximum stress for strut subjected to uniformly distributed load?

The Moment of inertia given maximum stress for strut subjected to uniformly distributed load formula is defined as a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of torque (turning force) and is represented as I = (M*c/((σb^max-(P_axial/A_sectional)))) or Moment of Inertia Column = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum bending stress-(Axial Thrust/Column Cross Sectional Area)))). Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point, Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend, The Axial Thrust is the resultant force of all the axial forces (F) acting on the object or material & Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.

How to calculate Moment of inertia given maximum stress for strut subjected to uniformly distributed load?

The Moment of inertia given maximum stress for strut subjected to uniformly distributed load formula is defined as a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of torque (turning force) is calculated using Moment of Inertia Column = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum bending stress-(Axial Thrust/Column Cross Sectional Area)))). To calculate Moment of inertia given maximum stress for strut subjected to uniformly distributed load, you need Maximum Bending Moment In Column (M), Distance from Neutral Axis to Extreme Point (c), Maximum bending stress (σb^max), Axial Thrust (P_axial) & Column Cross Sectional Area (A_sectional). With our tool, you need to enter the respective value for Maximum Bending Moment In Column, Distance from Neutral Axis to Extreme Point, Maximum bending stress, Axial Thrust & Column Cross Sectional Area and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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