Moment of Inertia given Maximum Stress for Column with Eccentric Load Calculator

✖Maximum stress at crack tip due to the applied nominal stress.ⓘ Maximum Stress at Crack Tip [σ_max]			+10% -10%
✖Eccentric load on column is the load that causes direct stress as well as bending stress.ⓘ Eccentric load on column [P]			+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%
✖Section Modulus for Column is a geometric property for a given cross-section used in the design of beams or flexural members.ⓘ Section Modulus for Column [S]			+10% -10%
✖Eccentricity is the distance from point of application of resultant to center of base.ⓘ Eccentricity [e]			+10% -10%
✖Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.ⓘ Effective Column Length [L_e]			+10% -10%
✖Modulus of elasticity of column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of elasticity of column [ε_column]			+10% -10%

✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia given Maximum Stress for Column with Eccentric Load [I]

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Formula

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Moment of Inertia given Maximum Stress for Column with Eccentric Load

Formula

`"I" = ((asech((("σ"_{"max"}-("P"/"A"_{"sectional"}))*"S")/("P"*"e"))/("L"_{"e"}))^2)/("P"/("ε"_{"column"}))`

Example

`"1.1E^6kg·m²"=((asech((("0.00006MPa"-("40N"/"1.4m²"))*"13m³")/("40N"*"15000mm"))/("200mm"))^2)/("40N"/("2MPa"))`

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Moment of Inertia given Maximum Stress for Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia = ((asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(Effective Column Length))^2)/(Eccentric load on column/(Modulus of elasticity of column))
I = ((asech(((σ_max-(P/A_sectional))*S)/(P*e))/(L_e))^2)/(P/(ε_column))
This formula uses 2 Functions, 8 Variables

Functions Used

sech - The hyperbolic secant function is a hyperbolic function that is the reciprocal of the hyperbolic cosine function., sech(Number)
asech - The hyperbolic secant function is defined as sech(x) = 1/cosh(x), where cosh(x) is the hyperbolic cosine function., asech(Number)

Variables Used

Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum stress at crack tip due to the applied nominal stress.
Eccentric load on column - (Measured in Newton) - Eccentric load on column is the load that causes direct stress as well as bending stress.
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.
Section Modulus for Column - (Measured in Cubic Meter) - Section Modulus for Column is a geometric property for a given cross-section used in the design of beams or flexural members.
Eccentricity - (Measured in Meter) - Eccentricity is the distance from point of application of resultant to center of base.
Effective Column Length - (Measured in Meter) - Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.
Modulus of elasticity of column - (Measured in Pascal) - Modulus of elasticity of column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

STEP 1: Convert Input(s) to Base Unit

Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion here)
Eccentric load on column: 40 Newton --> 40 Newton No Conversion Required
Column Cross Sectional Area: 1.4 Square Meter --> 1.4 Square Meter No Conversion Required
Section Modulus for Column: 13 Cubic Meter --> 13 Cubic Meter No Conversion Required
Eccentricity: 15000 Millimeter --> 15 Meter (Check conversion here)
Effective Column Length: 200 Millimeter --> 0.2 Meter (Check conversion here)
Modulus of elasticity of column: 2 Megapascal --> 2000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = ((asech(((σ_max-(P/A_sectional))*S)/(P*e))/(L_e))^2)/(P/(ε_column)) --> ((asech(((60-(40/1.4))*13)/(40*15))/(0.2))^2)/(40/(2000000))

Evaluating ... ...

I = 1089812.05899143

STEP 3: Convert Result to Output's Unit

1089812.05899143 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

1089812.05899143 ≈ 1.1E+6 Kilogram Square Meter <-- Moment of Inertia

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Columns With Eccentric Load » Moment of Inertia given Maximum Stress for Column with Eccentric Load

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< 16 Columns With Eccentric Load Calculators

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load

Go Column Cross Sectional Area = (Eccentric load on column)/(Maximum Stress at Crack Tip-(((Eccentric load on column*Eccentricity of Load*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))/2)/Section Modulus for Column))

Effective Length of Column given Maximum Stress for Column with Eccentric Load

Go Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2)

Eccentricity given Maximum Stress for Column with Eccentric Load

Go Eccentricity = ((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/((Eccentric load on column*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))/2)

Section Modulus given Maximum Stress for Column with Eccentric Load

Go Section Modulus for Column = ((Eccentric load on column*Eccentricity*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))/2)/(Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))

Maximum Stress for Column with Eccentric Load

Go Maximum Stress at Crack Tip = (Eccentric load on column/Column Cross Sectional Area)+(((Eccentric load on column*Eccentricity*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))/2)/Section Modulus for Column)

Modulus of Elasticity given Maximum Stress for Column with Eccentric Load

Go Modulus of elasticity of column = ((asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(Effective Column Length))^2)/(Eccentric load on column/(Moment of Inertia))

Moment of Inertia given Maximum Stress for Column with Eccentric Load

Go Moment of Inertia = ((asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(Effective Column Length))^2)/(Eccentric load on column/(Modulus of elasticity of column))

Eccentricity given Deflection at Section of Column with Eccentric load

Go Eccentricity = (Deflection of Column/(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))))-Deflection of Free End

Modulus of Elasticity given Deflection at Section of Column with Eccentric Load

Go Modulus of elasticity of column = (Eccentric load on column/(Moment of Inertia*(((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w fixed end and deflection point)^2)))

Moment of Inertia given Deflection at Section of Column with Eccentric Load

Go Moment of Inertia = (Eccentric load on column/(Modulus of elasticity of column*(((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w fixed end and deflection point)^2)))

Eccentric Load given Deflection at Section of Column with Eccentric Load

Go Eccentric load on column = (((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w fixed end and deflection point)^2)*(Modulus of elasticity of column*Moment of Inertia)

Eccentricity given Deflection at Free End of Column with Eccentric load

Go Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load at column/(Modulus of elasticity of column*Moment of Inertia)))-1)

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load

Go Modulus of elasticity of column = Eccentric load on column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))

Moment of Inertia given Deflection at Free End of Column with Eccentric Load

Go Moment of Inertia = Eccentric load on column/(Modulus of elasticity of column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))

Moment at Section of Column with Eccentric Load

Go Moment of force = Eccentric load on column*(Deflection of Free End+Eccentricity of Load-Deflection of Column)

Eccentricity given Moment at Section of Column with Eccentric Load

Go Eccentricity = (Moment of force/Eccentric load on column)-Deflection of Free End+Deflection of Column

Moment of Inertia given Maximum Stress for Column with Eccentric Load Formula

What is buckling or crippling load?

Buckling Load is the highest load at which the column will buckle. Crippling load is the max load beyond that load, it cant use further it becomes disable to use.

How to Calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load?

Moment of Inertia given Maximum Stress for Column with Eccentric Load calculator uses Moment of Inertia = ((asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(Effective Column Length))^2)/(Eccentric load on column/(Modulus of elasticity of column)) to calculate the Moment of Inertia, The Moment of inertia given maximum stress for column with eccentric 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 is denoted by I symbol.

How to calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load using this online calculator? To use this online calculator for Moment of Inertia given Maximum Stress for Column with Eccentric Load, enter Maximum Stress at Crack Tip (σ_max), Eccentric load on column (P), Column Cross Sectional Area (A_sectional), Section Modulus for Column (S), Eccentricity (e), Effective Column Length (L_e) & Modulus of elasticity of column (ε_column) and hit the calculate button. Here is how the Moment of Inertia given Maximum Stress for Column with Eccentric Load calculation can be explained with given input values -> 1.1E+6 = ((asech(((60-(40/1.4))*13)/(40*15))/(0.2))^2)/(40/(2000000)).

FAQ

What is Moment of Inertia given Maximum Stress for Column with Eccentric Load?

The Moment of inertia given maximum stress for column with eccentric 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 = ((asech(((σ_max-(P/A_sectional))*S)/(P*e))/(L_e))^2)/(P/(ε_column)) or Moment of Inertia = ((asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(Effective Column Length))^2)/(Eccentric load on column/(Modulus of elasticity of column)). Maximum stress at crack tip due to the applied nominal stress, Eccentric load on column is the load that causes direct stress as well as bending stress, 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, Section Modulus for Column is a geometric property for a given cross-section used in the design of beams or flexural members, Eccentricity is the distance from point of application of resultant to center of base, Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration & Modulus of elasticity of column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

How to calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load?

The Moment of inertia given maximum stress for column with eccentric 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 = ((asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(Effective Column Length))^2)/(Eccentric load on column/(Modulus of elasticity of column)). To calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load, you need Maximum Stress at Crack Tip (σ_max), Eccentric load on column (P), Column Cross Sectional Area (A_sectional), Section Modulus for Column (S), Eccentricity (e), Effective Column Length (L_e) & Modulus of elasticity of column (ε_column). With our tool, you need to enter the respective value for Maximum Stress at Crack Tip, Eccentric load on column, Column Cross Sectional Area, Section Modulus for Column, Eccentricity, Effective Column Length & Modulus of elasticity of column 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 Moment of Inertia?

In this formula, Moment of Inertia uses Maximum Stress at Crack Tip, Eccentric load on column, Column Cross Sectional Area, Section Modulus for Column, Eccentricity, Effective Column Length & Modulus of elasticity of column. We can use 2 other way(s) to calculate the same, which is/are as follows -

Moment of Inertia = (Eccentric load on column/(Modulus of elasticity of column*(((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w fixed end and deflection point)^2)))
Moment of Inertia = Eccentric load on column/(Modulus of elasticity of column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))

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