Deflection at Free End given Deflection at Section of Column with Eccentric load Calculator

✖Deflection of Column at free end in terms of moment at the section of column with eccentric load.ⓘ Deflection of Column [δ_c]			+10% -10%
✖Distance b/w fixed end and deflection point is the distance x between the point of deflection at section and fixed point.ⓘ Distance b/w fixed end and deflection point [x]			+10% -10%
✖Eccentric load on column is the load that causes direct stress as well as bending stress.ⓘ Eccentric load on column [P]			+10% -10%
✖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.ⓘ Modulus of elasticity of column [ε_column]			+10% -10%
✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%
✖Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.ⓘ Eccentricity of Load [e_load]			+10% -10%

✖Deflection of Free End is the deflection caused due to crippling load at the free end.ⓘ Deflection at Free End given Deflection at Section of Column with Eccentric load [a_crippling]

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Formula

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Deflection at Free End given Deflection at Section of Column with Eccentric load

Formula

`"a"_{"crippling"} = ("δ"_{"c"}/(1-cos("x"*sqrt("P"/("ε"_{"column"}*"I")))))-"e"_{"load"}`

Example

`"201.112mm"=("12mm"/(1-cos("1000mm"*sqrt("40N"/("2MPa"*"0.000168kg·m²")))))-"2.5mm"`

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

STEP 0: Pre-Calculation Summary

Formula Used

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
a_crippling = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-e_load
This formula uses 2 Functions, 7 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(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.
Deflection of Column - (Measured in Meter) - Deflection of Column at free end in terms of moment at the section of column with eccentric load.
Distance b/w fixed end and deflection point - (Measured in Meter) - Distance b/w fixed end and deflection point is the distance x between the point of deflection at section and fixed point.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Deflection of Column: 12 Millimeter --> 0.012 Meter (Check conversion here)
Distance b/w fixed end and deflection point: 1000 Millimeter --> 1 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
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_crippling = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-e_load --> (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.0025

Evaluating ... ...

a_crippling = 0.201111961236572

STEP 3: Convert Result to Output's Unit

0.201111961236572 Meter -->201.111961236572 Millimeter (Check conversion here)

FINAL ANSWER

201.111961236572 ≈ 201.112 Millimeter <-- Deflection of Free End

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Columns With Eccentric Load » Deflection » Deflection at Free End given Deflection at Section of Column with Eccentric load

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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 given Deflection at Section of Column with Eccentric load Formula

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 given Deflection at Section of Column with Eccentric load?

Deflection at Free End given Deflection at Section of Column with Eccentric load calculator uses 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 to calculate the Deflection of Free End, Deflection at Free end given Deflection at section 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 a_crippling symbol.

How to calculate Deflection at Free End given Deflection at Section of Column with Eccentric load using this online calculator? To use this online calculator for Deflection at Free End given Deflection at Section of Column with Eccentric load, enter Deflection of Column (δ_c), Distance b/w fixed end and deflection point (x), Eccentric load on column (P), Modulus of elasticity of column (ε_column), Moment of Inertia (I) & Eccentricity of Load (e_load) and hit the calculate button. Here is how the Deflection at Free End given Deflection at Section of Column with Eccentric load calculation can be explained with given input values -> 201112 = (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.0025.

FAQ

What is Deflection at Free End given Deflection at Section of Column with Eccentric load?

Deflection at Free end given Deflection at section 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 a_crippling = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-e_load or 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 of Column at free end in terms of moment at the section of column with eccentric load, Distance b/w fixed end and deflection point is the distance x between the point of deflection at section and fixed point, 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 & Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.

How to calculate Deflection at Free End given Deflection at Section of Column with Eccentric load?

Deflection at Free end given Deflection at section 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 = (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. To calculate Deflection at Free End given Deflection at Section of Column with Eccentric load, you need Deflection of Column (δ_c), Distance b/w fixed end and deflection point (x), Eccentric load on column (P), Modulus of elasticity of column (ε_column), Moment of Inertia (I) & Eccentricity of Load (e_load). With our tool, you need to enter the respective value for Deflection of Column, Distance b/w fixed end and deflection point, Eccentric load on column, Modulus of elasticity of column, Moment of Inertia & Eccentricity of Load 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 Deflection of Column, Distance b/w fixed end and deflection point, Eccentric load on column, Modulus of elasticity of column, Moment of Inertia & Eccentricity of Load. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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