Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load Calculator

✖Deflection of Column is the displacement or bending of a column from its original, vertical position when subjected to an external load, particularly a compressive load.ⓘ Deflection of Column [δ_c]			+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 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%
✖Eccentric Load on Column is a load that is applied at a point away from the centroid of the column's cross-section, causing the column to experience both direct compressive stress and bending stress.ⓘ Eccentric Load on Column [F]			+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 a physical quantity that describes how mass is distributed in relation to an axis of rotation.ⓘ Moment of Inertia [I]			+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 of Section from Fixed End given Deflection at Section of Column with Eccentric Load [X_d]

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Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance b/w Fixed End and Deflection Point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))
X_d = (acos(1-(δ_c/(a_crippling+e_load))))/(sqrt(F/(ε_column*I)))
This formula uses 3 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)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)
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

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.
Deflection of Column - (Measured in Meter) - Deflection of Column is the displacement or bending of a column from its original, vertical position when subjected to an external load, particularly a compressive load.
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.
Eccentric Load on Column - (Measured in Newton) - Eccentric Load on Column is a load that is applied at a point away from the centroid of the column's cross-section, causing the column to experience both direct compressive stress and 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 a physical quantity that describes how mass is distributed in relation to an axis of rotation.

STEP 1: Convert Input(s) to Base Unit

Deflection of Column: 18.47108 Millimeter --> 0.01847108 Meter (Check conversion here)
Deflection of Free End: 14 Millimeter --> 0.014 Meter (Check conversion here)
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Eccentric Load on Column: 40 Newton --> 40 Newton No Conversion Required
Modulus of Elasticity of Column: 0.009006 Megapascal --> 9006 Pascal (Check conversion here)
Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

X_d = (acos(1-(δ_c/(a_crippling+e_load))))/(sqrt(F/(ε_column*I))) --> (acos(1-(0.01847108/(0.014+0.0025))))/(sqrt(40/(9006*1.125)))

Evaluating ... ...

X_d = 26.9053174852866

STEP 3: Convert Result to Output's Unit

26.9053174852866 Meter -->26905.3174852866 Millimeter (Check conversion here)

FINAL ANSWER

26905.3174852866 ≈ 26905.32 Millimeter <-- Distance b/w Fixed End and Deflection Point

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Initial Curvature » Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load

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< Columns With Initial Curvature Calculators

Length of Column given Initial Deflection at Distance X from end A

LaTeX Go Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection))

Value of Distance 'X' given Initial Deflection at Distance X from end A

LaTeX Go Distance of Deflection from end A = (asin(Initial Deflection/Maximum Initial Deflection))*Length of Column/pi

Modulus of Elasticity given Euler Load

LaTeX Go Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia)

Euler Load

LaTeX Go Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)

Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load Formula

LaTeX Go

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 Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load?

Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load calculator uses Distance b/w Fixed End and Deflection Point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))) to calculate the Distance b/w Fixed End and Deflection Point, The Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the distance from the fixed end of a column to a section where deflection occurs due to an eccentric load, providing insight into the column's structural behavior under load. Distance b/w Fixed End and Deflection Point is denoted by X_d symbol.

How to calculate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load using this online calculator? To use this online calculator for Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load, enter Deflection of Column (δ_c), Deflection of Free End (a_crippling), Eccentricity of Load (e_load), Eccentric Load on Column (F), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) and hit the calculate button. Here is how the Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load calculation can be explained with given input values -> 9.2E+8 = (acos(1-(0.01847108/(0.014+0.0025))))/(sqrt(40/(9006*1.125))).

FAQ

What is Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load?

The Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the distance from the fixed end of a column to a section where deflection occurs due to an eccentric load, providing insight into the column's structural behavior under load and is represented as X_d = (acos(1-(δ_c/(a_crippling+e_load))))/(sqrt(F/(ε_column*I))) or Distance b/w Fixed End and Deflection Point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))). Deflection of Column is the displacement or bending of a column from its original, vertical position when subjected to an external load, particularly a compressive load, Deflection of Free End is the deflection caused due to crippling load at the free end, Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load, Eccentric Load on Column is a load that is applied at a point away from the centroid of the column's cross-section, causing the column to experience both direct compressive stress and 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 a physical quantity that describes how mass is distributed in relation to an axis of rotation.

How to calculate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load?

The Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the distance from the fixed end of a column to a section where deflection occurs due to an eccentric load, providing insight into the column's structural behavior under load is calculated using Distance b/w Fixed End and Deflection Point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))). To calculate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load, you need Deflection of Column (δ_c), Deflection of Free End (a_crippling), Eccentricity of Load (e_load), Eccentric Load on Column (F), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I). With our tool, you need to enter the respective value for Deflection of Column, Deflection of Free End, Eccentricity of Load, 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.

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