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

✖Eccentric load on column refers to a load that is applied at a point away from the centroidal axis of the column’s cross-section where loading introduces both axial stress and bending stress.ⓘ Eccentric Load on Column [P]			+10% -10%
✖Moment of inertia also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific axis.ⓘ Moment of Inertia [I]			+10% -10%
✖Deflection of free end of a beam refers to the displacement or movement of the beam’s free end from its original position due to applied loads or crippling load at the free end.ⓘ Deflection of Free End [δ]			+10% -10%
✖Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column.ⓘ Eccentricity of Load [e_load]			+10% -10%
✖Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity.ⓘ Column Length [L]			+10% -10%

✖Modulus of elasticity of column is a measure of a material’s stiffness or rigidity, is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit of a material.ⓘ Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load [ε_column]

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

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of Elasticity of Column = Eccentric Load on Column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))
ε_column = P/(I*(((arcsec((δ/e_load)+1))/L)^2))
This formula uses 2 Functions, 6 Variables

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
arcsec - Inverse trigonometric secant – Unary function., arcsec(x)

Variables Used

Modulus of Elasticity of Column - (Measured in Pascal) - Modulus of elasticity of column is a measure of a material’s stiffness or rigidity, is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit of a material.
Eccentric Load on Column - (Measured in Newton) - Eccentric load on column refers to a load that is applied at a point away from the centroidal axis of the column’s cross-section where loading introduces both axial stress and bending stress.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of inertia also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific axis.
Deflection of Free End - (Measured in Meter) - Deflection of free end of a beam refers to the displacement or movement of the beam’s free end from its original position due to applied loads or crippling load at the free end.
Eccentricity of Load - (Measured in Meter) - Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column.
Column Length - (Measured in Meter) - Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity.

STEP 1: Convert Input(s) to Base Unit

Eccentric Load on Column: 40 Newton --> 40 Newton No Conversion Required
Moment of Inertia: 0.000168 Kilogram Square Meter --> 0.000168 Kilogram Square Meter No Conversion Required
Deflection of Free End: 201.112 Millimeter --> 0.201112 Meter (Check conversion here)
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Column Length: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_column = P/(I*(((arcsec((δ/e_load)+1))/L)^2)) --> 40/(0.000168*(((arcsec((0.201112/0.0025)+1))/5)^2))

Evaluating ... ...

ε_column = 2450570.52196348

STEP 3: Convert Result to Output's Unit

2450570.52196348 Pascal -->2.45057052196348 Megapascal (Check conversion here)

FINAL ANSWER

2.45057052196348 ≈ 2.450571 Megapascal <-- Modulus of Elasticity of Column

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Eccentric Load » Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load

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< Columns With Eccentric Load Calculators

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

LaTeX 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)))

Eccentric Load given Deflection at Section of Column with Eccentric Load

LaTeX 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 Moment at Section of Column with Eccentric Load

LaTeX Go Eccentricity of Column = (Moment of Force/Eccentric Load on Column)-Deflection of Free End+Deflection of Column

Moment at Section of Column with Eccentric Load

LaTeX Go Moment of Force = Eccentric Load on Column*(Deflection of Free End+Eccentricity of Load-Deflection of Column)

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

LaTeX Go

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

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load calculator uses Modulus of Elasticity of Column = Eccentric Load on Column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)) to calculate the Modulus of Elasticity of Column, Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load formula is defined as a measure of the ratio of stress and strain of a material, specifically in columns subjected to eccentric loads, providing insight into the material's ability to resist deformation under such conditions. Modulus of Elasticity of Column is denoted by ε_column symbol.

How to calculate Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load using this online calculator? To use this online calculator for Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load, enter Eccentric Load on Column (P), Moment of Inertia (I), Deflection of Free End (δ), Eccentricity of Load (e_load) & Column Length (L) and hit the calculate button. Here is how the Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load calculation can be explained with given input values -> 3E-6 = 40/(0.000168*(((arcsec((0.201112/0.0025)+1))/5)^2)).

FAQ

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

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load formula is defined as a measure of the ratio of stress and strain of a material, specifically in columns subjected to eccentric loads, providing insight into the material's ability to resist deformation under such conditions and is represented as ε_column = P/(I*(((arcsec((δ/e_load)+1))/L)^2)) or Modulus of Elasticity of Column = Eccentric Load on Column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)). Eccentric load on column refers to a load that is applied at a point away from the centroidal axis of the column’s cross-section where loading introduces both axial stress and bending stress, Moment of inertia also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific axis, Deflection of free end of a beam refers to the displacement or movement of the beam’s free end from its original position due to applied loads or crippling load at the free end, Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column & Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity.

How to calculate Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load?

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load formula is defined as a measure of the ratio of stress and strain of a material, specifically in columns subjected to eccentric loads, providing insight into the material's ability to resist deformation under such conditions is calculated using Modulus of Elasticity of Column = Eccentric Load on Column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)). To calculate Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load, you need Eccentric Load on Column (P), Moment of Inertia (I), Deflection of Free End (δ), Eccentricity of Load (e_load) & Column Length (L). With our tool, you need to enter the respective value for Eccentric Load on Column, Moment of Inertia, Deflection of Free End, Eccentricity of Load & Column Length 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 Modulus of Elasticity of Column?

In this formula, Modulus of Elasticity of Column uses Eccentric Load on Column, Moment of Inertia, Deflection of Free End, Eccentricity of Load & Column Length. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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