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

✖Eccentric load on column is the load that causes direct stress as well as bending stress.ⓘ Eccentric load on column [P]			+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%
✖Deflection of Column at free end in terms of moment at the section of column with eccentric load.ⓘ Deflection of Column [δ_c]			+10% -10%
✖Deflection of Free End is the deflection caused due to crippling load at the free end.ⓘ Deflection of Free End [a_crippling]			+10% -10%
✖Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.ⓘ Eccentricity of Load [e_load]			+10% -10%
✖Distance b/w fixed end and deflection point is the distance x between the point of deflection at section and fixed point.ⓘ Distance b/w fixed end and deflection point [x]			+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 Deflection at Section of Column with Eccentric Load [I]

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Formula

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

Formula

`"I" = ("P"/("ε"_{"column"}*(((acos(1-("δ"_{"c"}/("a"_{"crippling"}+"e"_{"load"}))))/"x")^2)))`

Example

`"1.2E^-5kg·m²"=("40N"/("2MPa"*(((acos(1-("12mm"/("14mm"+"2.5mm"))))/"1000mm")^2)))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
I = (P/(ε_column*(((acos(1-(δ_c/(a_crippling+e_load))))/x)^2)))
This formula uses 2 Functions, 7 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(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.
Eccentric load on column - (Measured in Newton) - Eccentric load on column is the load that causes direct stress as well as bending stress.
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.
Deflection of Column - (Measured in Meter) - Deflection of Column at free end in terms of moment at the section of column with eccentric load.
Deflection of Free End - (Measured in Meter) - Deflection of Free End is the deflection caused due to crippling load at the free end.
Eccentricity of Load - (Measured in Meter) - Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.
Distance b/w fixed end and deflection point - (Measured in Meter) - Distance b/w fixed end and deflection point is the distance x between the point of deflection at section and fixed point.

STEP 1: Convert Input(s) to Base Unit

Eccentric load on column: 40 Newton --> 40 Newton No Conversion Required
Modulus of elasticity of column: 2 Megapascal --> 2000000 Pascal (Check conversion here)
Deflection of Column: 12 Millimeter --> 0.012 Meter (Check conversion here)
Deflection of Free End: 14 Millimeter --> 0.014 Meter (Check conversion here)
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Distance b/w fixed end and deflection point: 1000 Millimeter --> 1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (P/(ε_column*(((acos(1-(δ_c/(a_crippling+e_load))))/x)^2))) --> (40/(2000000*(((acos(1-(0.012/(0.014+0.0025))))/1)^2)))

Evaluating ... ...

I = 1.19338100921898E-05

STEP 3: Convert Result to Output's Unit

1.19338100921898E-05 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

1.19338100921898E-05 ≈ 1.2E-5 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 Deflection at Section of 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 Deflection at Section of Column with Eccentric Load Formula

Which is example of eccentric loading?

Examples of eccentric loading activities include performing a calf raise off the ledge of a stair, an exercise that has been shown to decrease the risk of Achilles tendon injuries. Another example is the nordic curl exercise, which has been shown to help reduce the risk of hamstring strains.

How to Calculate Moment of Inertia given Deflection at Section of Column with Eccentric Load?

Moment of Inertia given Deflection at Section of Column with Eccentric Load calculator uses 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))) to calculate the Moment of Inertia, The Moment of inertia given deflection at section of 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 Deflection at Section of Column with Eccentric Load using this online calculator? To use this online calculator for Moment of Inertia given Deflection at Section of Column with Eccentric Load, enter Eccentric load on column (P), Modulus of elasticity of column (ε_column), Deflection of Column (δ_c), Deflection of Free End (a_crippling), Eccentricity of Load (e_load) & Distance b/w fixed end and deflection point (x) and hit the calculate button. Here is how the Moment of Inertia given Deflection at Section of Column with Eccentric Load calculation can be explained with given input values -> 1.2E-5 = (40/(2000000*(((acos(1-(0.012/(0.014+0.0025))))/1)^2))).

FAQ

What is Moment of Inertia given Deflection at Section of Column with Eccentric Load?

The Moment of inertia given deflection at section of 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 = (P/(ε_column*(((acos(1-(δ_c/(a_crippling+e_load))))/x)^2))) or 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 on column is the load that causes direct stress as well as bending stress, 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, Deflection of Column at free end in terms of moment at the section of column with eccentric load, Deflection of Free End is the deflection caused due to crippling load at the free end, Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load & Distance b/w fixed end and deflection point is the distance x between the point of deflection at section and fixed point.

How to calculate Moment of Inertia given Deflection at Section of Column with Eccentric Load?

The Moment of inertia given deflection at section of 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 = (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))). To calculate Moment of Inertia given Deflection at Section of Column with Eccentric Load, you need Eccentric load on column (P), Modulus of elasticity of column (ε_column), Deflection of Column (δ_c), Deflection of Free End (a_crippling), Eccentricity of Load (e_load) & Distance b/w fixed end and deflection point (x). With our tool, you need to enter the respective value for Eccentric load on column, Modulus of elasticity of column, Deflection of Column, Deflection of Free End, Eccentricity of Load & Distance b/w fixed end and deflection point 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 Eccentric load on column, Modulus of elasticity of column, Deflection of Column, Deflection of Free End, Eccentricity of Load & Distance b/w fixed end and deflection point. 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*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))
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))

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