Deflection at Free End of Column with Eccentric load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1)
acrippling = eload*(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
Deflection of Free End - (Measured in Meter) - Deflection of Free End is the deflection caused due to crippling load at the free end.
Eccentricity of Load - (Measured in Meter) - Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.
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 on column - (Measured in Newton) - Eccentric load on 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
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Column Length: 5000 Millimeter --> 5 Meter (Check conversion here)
Eccentric load on column: 40 Newton --> 40 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
acrippling = eload*(sec(lcolumn*sqrt(P/(εcolumn*I)))-1) --> 0.0025*(sec(5*sqrt(40/(2000000*0.000168)))-1)
Evaluating ... ...
acrippling = -0.018759610370341
STEP 3: Convert Result to Output's Unit
-0.018759610370341 Meter -->-18.759610370341 Millimeter (Check conversion here)
FINAL ANSWER
-18.759610370341 -18.75961 Millimeter <-- Deflection of Free End
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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5 Deflection Calculators

Deflection at Free End given Deflection at Section of Column with Eccentric load
Go Deflection of Free End = (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)))))-Eccentricity of Load
Deflection at Section of Column with Eccentric Load
Go Deflection of Column = (Deflection of Free End+Eccentricity)*(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))
Deflection at Free End of Column with Eccentric load
Go Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1)
Deflection at Free End given Moment at Section of Column with Eccentric load
Go Deflection of Column = (Moment of force/Eccentric load on column)-(Eccentricity of Load+Deflection of Free End)
Deflection at Section of Column with Eccentric Load given Moment at Section
Go Deflection of Column = -(Moment of force/Eccentric load on column)+Deflection of Free End+Eccentricity

Deflection at Free End of Column with Eccentric load Formula

Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1)
acrippling = eload*(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 Deflection at Free End of Column with Eccentric load?

Deflection at Free End of Column with Eccentric load calculator uses Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1) to calculate the Deflection of Free End, Deflection at Free end of Column with Eccentric load is defined as the movement of a beam or node from its original position due to the forces and loads. Deflection of Free End is denoted by acrippling symbol.

How to calculate Deflection at Free End of Column with Eccentric load using this online calculator? To use this online calculator for Deflection at Free End of Column with Eccentric load, enter Eccentricity of Load (eload), Column Length (lcolumn), Eccentric load on column (P), Modulus of elasticity of column column) & Moment of Inertia (I) and hit the calculate button. Here is how the Deflection at Free End of Column with Eccentric load calculation can be explained with given input values -> -18759.61037 = 0.0025*(sec(5*sqrt(40/(2000000*0.000168)))-1).

FAQ

What is Deflection at Free End of Column with Eccentric load?
Deflection at Free end of Column with Eccentric load is defined as the movement of a beam or node from its original position due to the forces and loads and is represented as acrippling = eload*(sec(lcolumn*sqrt(P/(εcolumn*I)))-1) or Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1). Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load, 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 on 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 Deflection at Free End of Column with Eccentric load?
Deflection at Free end of Column with Eccentric load is defined as the movement of a beam or node from its original position due to the forces and loads is calculated using Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1). To calculate Deflection at Free End of Column with Eccentric load, you need Eccentricity of Load (eload), Column Length (lcolumn), Eccentric load on column (P), Modulus of elasticity of column column) & Moment of Inertia (I). With our tool, you need to enter the respective value for Eccentricity of Load, Column Length, Eccentric load on 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 Deflection of Free End?
In this formula, Deflection of Free End uses Eccentricity of Load, Column Length, Eccentric load on column, Modulus of elasticity of column & Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Deflection of Free End = (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)))))-Eccentricity of Load
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