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

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Distance b/w Fixed End and Deflection Point is the distance x between the point of deflection at section and fixed point. Check FAQs

X d = \frac{a \cos (1 - (\frac{δ c}{a crippling + e load}))}{\sqrt{\frac{F}{ε column \cdot I}}}

X_d - Distance b/w Fixed End and Deflection Point?δ_c - Deflection of Column?a_crippling - Deflection of Free End?e_load - Eccentricity of Load?F - Eccentric Load on Column?ε_column - Modulus of Elasticity of Column?I - Moment of Inertia?

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

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Here is how the Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load equation looks like with Values.

Here is how the Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load equation looks like with Units.

Here is how the Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load equation looks like.

26905.3175 = \frac{a \cos (1 - (\frac{18.4711}{14 + 2.5}))}{\sqrt{\frac{40}{0.009 \cdot 1.125}}}

26905.3175mm = \frac{a \cos (1 - (\frac{18.4711mm}{14mm + 2.5mm}))}{\sqrt{\frac{40N}{0.009MPa \cdot 1.125kg·m²}}}

26905.3175 = \frac{a \cos (1 - (\frac{18.4711}{14 + 2.5}))}{\sqrt{\frac{40}{0.009 \cdot 1.125}}}

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Home » Physics » Mechanical » Strength of Materials » 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 Solution

Follow our step by step solution on how to calculate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load?

FIRST Step Consider the formula

X d = \frac{a \cos (1 - (\frac{δ c}{a crippling + e load}))}{\sqrt{\frac{F}{ε column \cdot I}}}

Next Step Substitute values of Variables

∴

X d = \frac{a \cos (1 - (\frac{18.4711mm}{14mm + 2.5mm}))}{\sqrt{\frac{40N}{0.009MPa \cdot 1.125kg·m²}}}

Next Step Convert Units

∴

X d = \frac{a \cos (1 - (\frac{0.0185m}{0.014m + 0.0025m}))}{\sqrt{\frac{40N}{9006Pa \cdot 1.125kg·m²}}}

Next Step Prepare to Evaluate

∴

X d = \frac{a \cos (1 - (\frac{0.0185}{0.014 + 0.0025}))}{\sqrt{\frac{40}{9006 \cdot 1.125}}}

Next Step Evaluate

∴

X d = 26.9053174852866m

Next Step Convert to Output's Unit

∴

X d = 26905.3174852866mm

LAST Step Rounding Answer

∴

X d = 26905.3175mm

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

Variables

Functions

Distance b/w Fixed End and Deflection Point

Distance b/w Fixed End and Deflection Point is the distance x between the point of deflection at section and fixed point.

Symbol: X_d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Deflection of Column

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.

Symbol: δ_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Deflection of Free End

Deflection of Free End is the deflection caused due to crippling load at the free end.

Symbol: a_crippling

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Eccentricity of Load

Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.

Symbol: e_load

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Eccentric Load on Column

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.

Symbol: F

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Modulus of Elasticity of Column

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.

Symbol: ε_column

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Moment of Inertia

Moment of Inertia is a physical quantity that describes how mass is distributed in relation to an axis of rotation.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

Syntax: sqrt(Number)

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Formula and 2000+ more formulas!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Formula and 1900+ more formulas!

Other formulas in Columns With Initial Curvature category

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

x = (a \sin (\frac{y'}{C})) \cdot \frac{l}{π}

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

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

How to Evaluate 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 evaluator 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 evaluate 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 evaluate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load using this online evaluator? To use this online evaluator 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.

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

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

The formula of Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load is expressed as 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))). Here is an example- 9.2E+8 = (acos(1-(0.01847108/(0.014+0.0025))))/(sqrt(40/(9006*1.125))).

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

With 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) we can find Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load using the formula - 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))). This formula also uses Cosine (cos)Inverse Cosine (acos), Square Root (sqrt) function(s).

Can the Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load be negative?

No, the Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load, measured in Length cannot be negative.

Which unit is used to measure 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 is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load can be measured.

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

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

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

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

Credits

Other formulas in Columns With Initial Curvature category

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

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

Variable Name