Eccentricity given Deflection at Section of Column with Eccentric load Calculator

✖Deflection of column refers to the degree to which a column bends or displaces under the influence of external forces such as weight, wind, or seismic activity.ⓘ 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%
✖Deflection of Free End is the deflection caused due to crippling load at the free end.ⓘ Deflection of Free End [a_crippling]			+10% -10%

✖Eccentricity is the distance from point of application of resultant to center of base.ⓘ Eccentricity given Deflection at Section of Column with Eccentric load [e]

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Eccentricity given Deflection at Section of Column with Eccentric load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
e = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-a_crippling
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

Eccentricity - (Measured in Meter) - Eccentricity is the distance from point of application of resultant to center of base.
Deflection of Column - (Measured in Meter) - Deflection of column refers to the degree to which a column bends or displaces under the influence of external forces such as weight, wind, or seismic activity.
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.
Deflection of Free End - (Measured in Meter) - Deflection of Free End is the deflection caused due to crippling load at the free end.

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
Deflection of Free End: 14 Millimeter --> 0.014 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-a_crippling --> (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.014

Evaluating ... ...

e = 0.189611961236572

STEP 3: Convert Result to Output's Unit

0.189611961236572 Meter -->189.611961236572 Millimeter (Check conversion here)

FINAL ANSWER

189.611961236572 ≈ 189.612 Millimeter <-- Eccentricity

(Calculation completed in 00.020 seconds)

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

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National Institute Of Technology (NIT), Hamirpur

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< Columns With Eccentric Load Calculators

Modulus of Elasticity given Deflection at Section of Column with Eccentric Load

LaTeX 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)))

Eccentric Load given Deflection at Section of Column with Eccentric Load

LaTeX 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)

Moment at Section of Column with Eccentric Load

LaTeX 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

LaTeX Go Eccentricity = (Moment of force/Eccentric load on column)-Deflection of Free End+Deflection of Column

Eccentricity given Deflection at Section of Column with Eccentric load Formula

LaTeX Go

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 Section of Column with Eccentric load?

Eccentricity given Deflection at Section of Column with Eccentric load calculator uses 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 to calculate the Eccentricity, Eccentricity given Deflection at Section of Column with Eccentric load formula is defined as a measure of how much the column is deviating from its vertical axis due to the eccentric load, which affects the structural integrity and stability of the column. Eccentricity is denoted by e symbol.

How to calculate Eccentricity given Deflection at Section of Column with Eccentric load using this online calculator? To use this online calculator for Eccentricity 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) & Deflection of Free End (a_crippling) and hit the calculate button. Here is how the Eccentricity given Deflection at Section of Column with Eccentric load calculation can be explained with given input values -> 189612 = (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.014.

FAQ

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

Eccentricity given Deflection at Section of Column with Eccentric load formula is defined as a measure of how much the column is deviating from its vertical axis due to the eccentric load, which affects the structural integrity and stability of the column and is represented as e = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-a_crippling or 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. Deflection of column refers to the degree to which a column bends or displaces under the influence of external forces such as weight, wind, or seismic activity, 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 & Deflection of Free End is the deflection caused due to crippling load at the free end.

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

Eccentricity given Deflection at Section of Column with Eccentric load formula is defined as a measure of how much the column is deviating from its vertical axis due to the eccentric load, which affects the structural integrity and stability of the column is calculated using 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. To calculate Eccentricity 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) & Deflection of Free End (a_crippling). 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 & Deflection of Free End 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 Column, Distance b/w fixed end and deflection point, Eccentric load on column, Modulus of elasticity of column, Moment of Inertia & Deflection of Free End. We can use 2 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 = ((Maximum Stress at Crack Tip-(Eccentric load on column/Cross-Sectional Area of Column))*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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