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Moment of inertia in terms of deflection at the 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*(((arcsec((Deflection of free end/Eccentricity)+1))/Length of column)^2))
I = P/(E*(((arcsec((a/e)+1))/l)^2))
This formula uses 1 Constants, 2 Functions, 5 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
sec - Trigonometric secant function, sec(Angle)
arcsec - Inverse trignometric secant function, arcsec
Variables Used
Eccentric load on column - Eccentric load on column is the load that causes direct stress as well as bending stress. (Measured in Newton)
Modulus Of Elasticity - Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it. (Measured in Kilonewton per Square Meter)
Deflection of free end - Deflection of free end is the deflection caused due to crippling load at free end. (Measured in Meter)
Eccentricity - Eccentricity of an ellipse is a non-negative real number that uniquely characterizes its shape. (Measured in Centimeter)
Length of column - Length of column is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Eccentric load on column: 60 Newton --> 60 Newton No Conversion Required
Modulus Of Elasticity: 10 Kilonewton per Square Meter --> 10000 Pascal (Check conversion here)
Deflection of free end: 0 Meter --> 0 Meter No Conversion Required
Eccentricity: 10 Centimeter --> 0.1 Meter (Check conversion here)
Length of column: 5 Meter --> 5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = P/(E*(((arcsec((a/e)+1))/l)^2)) --> 60/(10000*(((arcsec(((0)/0.1)+1))/5)^2))
Evaluating ... ...
I = NaN
STEP 3: Convert Result to Output's Unit
NaN Kilogram Meter² --> No Conversion Required
FINAL ANSWER
NaN Kilogram Meter² <-- Moment of Inertia
(Calculation completed in 00.031 seconds)

10+ Columns With Eccentric Load Calculators

Deflection at free end in terms of deflection at the section of column with eccentric load
deflection_of_free_end = (Deflection at section/(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus Of Elasticity*Moment of Inertia)))))-Eccentricity Go
Eccentricity in terms of deflection at the section of column with eccentric load
eccentricity = (Deflection at section/(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus Of Elasticity*Moment of Inertia)))))-Deflection of free end Go
Deflection at the section of column with eccentric load
deflection_at_section = (Deflection of free end+Eccentricity)*(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus Of Elasticity*Moment of Inertia)))) Go
Modulus of elasticity in terms of deflection at the section of the column with eccentric load
modulus_of_elasticity = (Eccentric load on column/(Moment of Inertia*(((acos(1-(Deflection at section/(Deflection of free end+Eccentricity))))/Distance b/w fixed end and deflection point)^2))) Go
Moment of inertia in terms of deflection at the section of column with eccentric load
moment_of_inertia = (Eccentric load on column/(Modulus Of Elasticity*(((acos(1-(Deflection at section/(Deflection of free end+Eccentricity))))/Distance b/w fixed end and deflection point)^2))) Go
Eccentric load in terms of deflection at the section of column with eccentric load
eccentric_load_on_column = (((acos(1-(Deflection at section/(Deflection of free end+Eccentricity))))/Distance b/w fixed end and deflection point)^2)*(Modulus Of Elasticity*Moment of Inertia) Go
Deflection at the section of column with eccentric load in terms of moment at section
deflection_at_section = -(Moment of force/Eccentric load on column)+Deflection of free end+Eccentricity Go
Eccentricity in terms of moment at the section of the column with eccentric load
eccentricity = (Moment of force/Eccentric load on column)-Deflection of free end+Deflection at section Go
Moment at the section of column with eccentric load
moment_of_force = Eccentric load on column*(Deflection of free end+Eccentricity-Deflection at section) Go
Deflection at free end in terms of moment at the section of column with eccentric load
deflection_of_spring = (Moment of force/Eccentric load on column)-Eccentricity+Deflection at section Go

Moment of inertia in terms of deflection at the free end of column with eccentric load Formula

moment_of_inertia = Eccentric load on column/(Modulus Of Elasticity*(((arcsec((Deflection of free end/Eccentricity)+1))/Length of column)^2))
I = P/(E*(((arcsec((a/e)+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 in terms of deflection at the free end of column with eccentric load?

Moment of inertia in terms of deflection at the free end of column with eccentric load calculator uses moment_of_inertia = Eccentric load on column/(Modulus Of Elasticity*(((arcsec((Deflection of free end/Eccentricity)+1))/Length of column)^2)) to calculate the Moment of Inertia, The Moment of inertia in terms of deflection at the free end 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 and is denoted by I symbol.

How to calculate Moment of inertia in terms of deflection at the free end of column with eccentric load using this online calculator? To use this online calculator for Moment of inertia in terms of deflection at the free end of column with eccentric load, enter Eccentric load on column (P), Modulus Of Elasticity (E), Deflection of free end (a), Eccentricity (e) and Length of column (l) and hit the calculate button. Here is how the Moment of inertia in terms of deflection at the free end of column with eccentric load calculation can be explained with given input values -> NaN = 60/(10000*(((arcsec(((0)/0.1)+1))/5)^2)).

FAQ

What is Moment of inertia in terms of deflection at the free end of column with eccentric load?
The Moment of inertia in terms of deflection at the free end 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/(E*(((arcsec((a/e)+1))/l)^2)) or moment_of_inertia = Eccentric load on column/(Modulus Of Elasticity*(((arcsec((Deflection of free end/Eccentricity)+1))/Length of column)^2)). Eccentric load on column is the load that causes direct stress as well as bending stress, Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it, Deflection of free end is the deflection caused due to crippling load at free end, Eccentricity of an ellipse is a non-negative real number that uniquely characterizes its shape and Length of column is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
How to calculate Moment of inertia in terms of deflection at the free end of column with eccentric load?
The Moment of inertia in terms of deflection at the free end 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*(((arcsec((Deflection of free end/Eccentricity)+1))/Length of column)^2)). To calculate Moment of inertia in terms of deflection at the free end of column with eccentric load, you need Eccentric load on column (P), Modulus Of Elasticity (E), Deflection of free end (a), Eccentricity (e) and Length of column (l). With our tool, you need to enter the respective value for Eccentric load on column, Modulus Of Elasticity, Deflection of free end, Eccentricity and Length 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 Eccentric load on column, Modulus Of Elasticity, Deflection of free end, Eccentricity and Length of column. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • moment_of_force = Eccentric load on column*(Deflection of free end+Eccentricity-Deflection at section)
  • deflection_of_spring = (Moment of force/Eccentric load on column)-Eccentricity+Deflection at section
  • eccentricity = (Moment of force/Eccentric load on column)-Deflection of free end+Deflection at section
  • deflection_at_section = (Deflection of free end+Eccentricity)*(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus Of Elasticity*Moment of Inertia))))
  • deflection_at_section = -(Moment of force/Eccentric load on column)+Deflection of free end+Eccentricity
  • deflection_of_free_end = (Deflection at section/(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus Of Elasticity*Moment of Inertia)))))-Eccentricity
  • eccentricity = (Deflection at section/(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus Of Elasticity*Moment of Inertia)))))-Deflection of free end
  • eccentric_load_on_column = (((acos(1-(Deflection at section/(Deflection of free end+Eccentricity))))/Distance b/w fixed end and deflection point)^2)*(Modulus Of Elasticity*Moment of Inertia)
  • modulus_of_elasticity = (Eccentric load on column/(Moment of Inertia*(((acos(1-(Deflection at section/(Deflection of free end+Eccentricity))))/Distance b/w fixed end and deflection point)^2)))
  • moment_of_inertia = (Eccentric load on column/(Modulus Of Elasticity*(((acos(1-(Deflection at section/(Deflection of free end+Eccentricity))))/Distance b/w fixed end and deflection point)^2)))
Where is the Moment of inertia in terms of deflection at the free end of column with eccentric load calculator used?
Among many, Moment of inertia in terms of deflection at the free end of column with eccentric load calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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