Eccentricity in terms of deflection at free end of column with eccentric load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Eccentricity = Deflection of Free End/(sec(Length of column*sqrt(Eccentric load on column/(Modulus of Elasticity*Moment of Inertia)))-1)
e = a/(sec(l*sqrt(P/(E*I)))-1)
This formula uses 1 Constants, 2 Functions, 6 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
sec - Trigonometric secant function, sec(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Eccentricity - (Measured in Meter) - Eccentricity is the distance from point of application of resultant to center of base.
Deflection of Free End - (Measured in Meter) - Deflection of Free End is the deflection caused due to crippling load at the free end.
Length of column - (Measured in Meter) - 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.
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 - (Measured in Pascal) - 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.
Moment of Inertia - (Measured in Kilogram Meter²) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
STEP 1: Convert Input(s) to Base Unit
Deflection of Free End: 0.05 Meter --> 0.05 Meter No Conversion Required
Length of column: 5 Meter --> 5 Meter No Conversion Required
Eccentric load on column: 60 Newton --> 60 Newton No Conversion Required
Modulus of Elasticity: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Moment of Inertia: 1.125 Kilogram Meter² --> 1.125 Kilogram Meter² No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
e = a/(sec(l*sqrt(P/(E*I)))-1) --> 0.05/(sec(5*sqrt(60/(10000000*1.125)))-1)
Evaluating ... ...
e = 749.95833338921
STEP 3: Convert Result to Output's Unit
749.95833338921 Meter --> No Conversion Required
FINAL ANSWER
749.95833338921 Meter <-- Eccentricity
(Calculation completed in 00.031 seconds)

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National Institute Of Technology (NIT), Hamirpur
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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 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 section of column with eccentric load
Modulus of elasticity = (Eccentric load on column/(Moment of Inertia*(((acos(1-(Deflection at section/(Deflection of Free End+Eccentricity of the load))))/Distance b/w fixed end and deflection point)^2))) Go
Moment of inertia in terms of deflection at 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 of the load))))/Distance b/w fixed end and deflection point)^2))) Go
Eccentric load in terms of deflection at section of column with eccentric load
Eccentric load on column = (((acos(1-(Deflection at section/(Deflection of Free End+Eccentricity of the load))))/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 section of 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

Eccentricity in terms of deflection at free end of column with eccentric load Formula

Eccentricity = Deflection of Free End/(sec(Length of column*sqrt(Eccentric load on column/(Modulus of Elasticity*Moment of Inertia)))-1)
e = a/(sec(l*sqrt(P/(E*I)))-1)

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 Eccentricity in terms of deflection at free end of column with eccentric load?

Eccentricity in terms of deflection at free end of column with eccentric load calculator uses Eccentricity = Deflection of Free End/(sec(Length of column*sqrt(Eccentric load on column/(Modulus of Elasticity*Moment of Inertia)))-1) to calculate the Eccentricity, The Eccentricity in terms of deflection at free end of column with eccentric load formula is defined as the distance from the center of gravity of the column section to the center of gravity of the applied load. Eccentricity is denoted by e symbol.

How to calculate Eccentricity in terms of deflection at free end of column with eccentric load using this online calculator? To use this online calculator for Eccentricity in terms of deflection at free end of column with eccentric load, enter Deflection of Free End (a), Length of column (l), Eccentric load on column (P), Modulus of Elasticity (E) & Moment of Inertia (I) and hit the calculate button. Here is how the Eccentricity in terms of deflection at free end of column with eccentric load calculation can be explained with given input values -> 749.9583 = 0.05/(sec(5*sqrt(60/(10000000*1.125)))-1).

FAQ

What is Eccentricity in terms of deflection at free end of column with eccentric load?
The Eccentricity in terms of deflection at free end of column with eccentric load formula is defined as the distance from the center of gravity of the column section to the center of gravity of the applied load and is represented as e = a/(sec(l*sqrt(P/(E*I)))-1) or Eccentricity = Deflection of Free End/(sec(Length of column*sqrt(Eccentric load on column/(Modulus of Elasticity*Moment of Inertia)))-1). Deflection of Free End is the deflection caused due to crippling load at the free end, 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, 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 & Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
How to calculate Eccentricity in terms of deflection at free end of column with eccentric load?
The Eccentricity in terms of deflection at free end of column with eccentric load formula is defined as the distance from the center of gravity of the column section to the center of gravity of the applied load is calculated using Eccentricity = Deflection of Free End/(sec(Length of column*sqrt(Eccentric load on column/(Modulus of Elasticity*Moment of Inertia)))-1). To calculate Eccentricity in terms of deflection at free end of column with eccentric load, you need Deflection of Free End (a), Length of column (l), Eccentric load on column (P), Modulus of Elasticity (E) & Moment of Inertia (I). With our tool, you need to enter the respective value for Deflection of Free End, Length of column, Eccentric load on column, Modulus of Elasticity & Moment of Inertia 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 Eccentricity?
In this formula, Eccentricity uses Deflection of Free End, Length of column, Eccentric load on column, Modulus of Elasticity & Moment of Inertia. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Eccentricity = (Moment of force/Eccentric load on column)-Deflection of free end+Deflection at section
  • 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
  • Eccentricity = ((Maximum Stress at Crack Tip-(Eccentric load on column/Cross Sectional Area))*Section Modulus)/((Eccentric load on column*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of Elasticity*Moment of Inertia))))/2)
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