Eccentricity given Deflection at Free End of Column with Eccentric load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load at column/(Modulus of elasticity of column*Moment of Inertia)))-1)
e = acrippling/(sec(lcolumn*sqrt(P/(εcolumn*I)))-1)
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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., 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.
Column Length - (Measured in Meter) - Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
Eccentric load at column - (Measured in Newton) - Eccentric load at 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.
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.
STEP 1: Convert Input(s) to Base Unit
Deflection of Free End: 14 Millimeter --> 0.014 Meter (Check conversion here)
Column Length: 5000 Millimeter --> 5 Meter (Check conversion here)
Eccentric load at column: 25 Newton --> 25 Newton No Conversion Required
Modulus of elasticity of column: 2 Megapascal --> 2000000 Pascal (Check conversion here)
Moment of Inertia: 0.000168 Kilogram Square Meter --> 0.000168 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
e = acrippling/(sec(lcolumn*sqrt(P/(εcolumn*I)))-1) --> 0.014/(sec(5*sqrt(25/(2000000*0.000168)))-1)
Evaluating ... ...
e = 0.00362027564564687
STEP 3: Convert Result to Output's Unit
0.00362027564564687 Meter -->3.62027564564687 Millimeter (Check conversion here)
FINAL ANSWER
3.62027564564687 3.620276 Millimeter <-- Eccentricity
(Calculation completed in 00.004 seconds)

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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

Eccentricity given Deflection at Free End of Column with Eccentric load Formula

Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load at column/(Modulus of elasticity of column*Moment of Inertia)))-1)
e = acrippling/(sec(lcolumn*sqrt(P/(εcolumn*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 given Deflection at Free End of Column with Eccentric load?

Eccentricity given Deflection at Free End of Column with Eccentric load calculator uses Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load at column/(Modulus of elasticity of column*Moment of Inertia)))-1) to calculate the Eccentricity, The Eccentricity given 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 given Deflection at Free End of Column with Eccentric load using this online calculator? To use this online calculator for Eccentricity given Deflection at Free End of Column with Eccentric load, enter Deflection of Free End (acrippling), Column Length (lcolumn), Eccentric load at column (P), Modulus of elasticity of column column) & Moment of Inertia (I) and hit the calculate button. Here is how the Eccentricity given Deflection at Free End of Column with Eccentric load calculation can be explained with given input values -> -1865.710391 = 0.014/(sec(5*sqrt(25/(2000000*0.000168)))-1).

FAQ

What is Eccentricity given Deflection at Free End of Column with Eccentric load?
The Eccentricity given 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 = acrippling/(sec(lcolumn*sqrt(P/(εcolumn*I)))-1) or Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load at column/(Modulus of elasticity of column*Moment of Inertia)))-1). Deflection of Free End is the deflection caused due to crippling load at the free end, Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions, Eccentric load at 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 & Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
How to calculate Eccentricity given Deflection at Free End of Column with Eccentric load?
The Eccentricity given 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(Column Length*sqrt(Eccentric load at column/(Modulus of elasticity of column*Moment of Inertia)))-1). To calculate Eccentricity given Deflection at Free End of Column with Eccentric load, you need Deflection of Free End (acrippling), Column Length (lcolumn), Eccentric load at column (P), Modulus of elasticity of column column) & Moment of Inertia (I). With our tool, you need to enter the respective value for Deflection of Free End, Column Length, Eccentric load at column, Modulus of elasticity of column & 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, Column Length, Eccentric load at column, Modulus of elasticity of column & 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 of Column
  • 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
  • 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)
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