Moment of Inertia given Deflection at Free End 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*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))
I = P/(εcolumn*(((arcsec((δ/eload)+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
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 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.
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 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
Modulus of elasticity of column: 2 Megapascal --> 2000000 Pascal (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)
Column Length: 5000 Millimeter --> 5 Meter (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = P/(εcolumn*(((arcsec((δ/eload)+1))/L)^2)) --> 40/(2000000*(((arcsec((0.014/0.0025)+1))/5)^2))
Evaluating ... ...
I = 0.000248422937198531
STEP 3: Convert Result to Output's Unit
0.000248422937198531 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
0.000248422937198531 0.000248 Kilogram Square Meter <-- Moment of Inertia
(Calculation completed in 00.020 seconds)

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Columns With Eccentric Load Calculators

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)))
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 Moment at Section of Column with Eccentric Load
​ 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
​ Go Moment of force = Eccentric Load on Column*(Deflection of Free End+Eccentricity of Load-Deflection of Column)

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

​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))
I = P/(εcolumn*(((arcsec((δ/eload)+1))/L)^2))

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 Free End of Column with Eccentric Load?

Moment of Inertia given Deflection at Free End of Column with Eccentric Load calculator uses Moment of Inertia = Eccentric Load on Column/(Modulus of elasticity of column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)) to calculate the Moment of Inertia, Moment of Inertia given Deflection at Free End of Column with Eccentric Load formula is defined as a measure of the tendency of an object to resist changes in its rotation, specifically in columns subjected to eccentric loads, providing valuable insights into the structural integrity of such systems. Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia given Deflection at Free End of Column with Eccentric Load using this online calculator? To use this online calculator for Moment of Inertia given Deflection at Free End of Column with Eccentric Load, enter Eccentric Load on Column (P), Modulus of elasticity of column column), Deflection of Free End (δ), Eccentricity of Load (eload) & Column Length (L) and hit the calculate button. Here is how the Moment of Inertia given Deflection at Free End of Column with Eccentric Load calculation can be explained with given input values -> 0.000248 = 40/(2000000*(((arcsec((0.014/0.0025)+1))/5)^2)).

FAQ

What is Moment of Inertia given Deflection at Free End of Column with Eccentric Load?
Moment of Inertia given Deflection at Free End of Column with Eccentric Load formula is defined as a measure of the tendency of an object to resist changes in its rotation, specifically in columns subjected to eccentric loads, providing valuable insights into the structural integrity of such systems and is represented as I = P/(εcolumn*(((arcsec((δ/eload)+1))/L)^2)) or Moment of Inertia = Eccentric Load on Column/(Modulus of elasticity of column*(((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, 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 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 Moment of Inertia given Deflection at Free End of Column with Eccentric Load?
Moment of Inertia given Deflection at Free End of Column with Eccentric Load formula is defined as a measure of the tendency of an object to resist changes in its rotation, specifically in columns subjected to eccentric loads, providing valuable insights into the structural integrity of such systems is calculated using Moment of Inertia = Eccentric Load on Column/(Modulus of elasticity of column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)). To calculate Moment of Inertia given Deflection at Free End of Column with Eccentric Load, you need Eccentric Load on Column (P), Modulus of elasticity of column column), Deflection of Free End (δ), Eccentricity of Load (eload) & Column Length (L). With our tool, you need to enter the respective value for Eccentric Load on Column, Modulus of elasticity of column, 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 Moment of Inertia?
In this formula, Moment of Inertia uses Eccentric Load on Column, Modulus of elasticity of column, 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 -
  • 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 = ((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/(Modulus of elasticity of column))
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