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Eccentric Load given Deflection at Section of Column with Eccentric Load Formula

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Eccentric load on column is the load that causes direct stress as well as bending stress. Check FAQs

P = ({(\frac{a \cos (1 - (\frac{δ c}{a crippling + e load}))}{x})}^{2}) \cdot (ε column \cdot I)

P - Eccentric load on column?δ_c - Deflection of Column?a_crippling - Deflection of Free End?e_load - Eccentricity of Load?x - Distance b/w fixed end and deflection point?ε_column - Modulus of elasticity of column?I - Moment of Inertia?

Eccentric Load given Deflection at Section of Column with Eccentric Load Example

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

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

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

563.106 = ({(\frac{a \cos (1 - (\frac{12}{14 + 2.5}))}{1000})}^{2}) \cdot (2 \cdot 0.0002)

563.106N = ({(\frac{a \cos (1 - (\frac{12mm}{14mm + 2.5mm}))}{1000mm})}^{2}) \cdot (2MPa \cdot 0.0002kg·m²)

563.106 = ({(\frac{a \cos (1 - (\frac{12}{14 + 2.5}))}{1000})}^{2}) \cdot (2 \cdot 0.0002)

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Eccentric Load given Deflection at Section of Column with Eccentric Load Solution

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

FIRST Step Consider the formula

P = ({(\frac{a \cos (1 - (\frac{δ c}{a crippling + e load}))}{x})}^{2}) \cdot (ε column \cdot I)

Next Step Substitute values of Variables

∴

P = ({(\frac{a \cos (1 - (\frac{12mm}{14mm + 2.5mm}))}{1000mm})}^{2}) \cdot (2MPa \cdot 0.0002kg·m²)

Next Step Convert Units

∴

P = ({(\frac{a \cos (1 - (\frac{0.012m}{0.014m + 0.0025m}))}{1m})}^{2}) \cdot (2E+6Pa \cdot 0.0002kg·m²)

Next Step Prepare to Evaluate

∴

P = ({(\frac{a \cos (1 - (\frac{0.012}{0.014 + 0.0025}))}{1})}^{2}) \cdot (2E+6 \cdot 0.0002)

Next Step Evaluate

∴

P = 563.105994488549N

LAST Step Rounding Answer

∴

P = 563.106N

Eccentric Load given Deflection at Section of Column with Eccentric Load Formula Elements

Variables

Functions

Eccentric load on column

Eccentric load on column is the load that causes direct stress as well as bending stress.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Eccentric load on column

Deflection of Column

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.

Symbol: δ_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Column

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.

Formulas to find Deflection of Free End

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.

Formulas to find Eccentricity of Load

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

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance b/w fixed end and deflection point

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.

Formulas to find Modulus of elasticity of column

Moment of Inertia

Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

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)

Other formulas in Columns With Eccentric Load category

Go Moment at Section of Column with Eccentric Load

M = P \cdot (a crippling + e load - δ c)

Go Eccentricity given Moment at Section of Column with Eccentric Load

e = (\frac{M}{P}) - a crippling + δ c

How to Evaluate Eccentric Load given Deflection at Section of Column with Eccentric Load?

Eccentric Load given Deflection at Section of Column with Eccentric Load evaluator uses 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) to evaluate the Eccentric load on column, Eccentric Load given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the load applied at a distance from the central axis of a column, causing bending and deflection, which is critical in determining the column's stability and structural integrity. Eccentric load on column is denoted by P symbol.

How to evaluate Eccentric Load given Deflection at Section of Column with Eccentric Load using this online evaluator? To use this online evaluator for Eccentric Load 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), Distance b/w fixed end and deflection point (x), Modulus of elasticity of column (ε_column) & Moment of Inertia (I) and hit the calculate button.

FAQs on Eccentric Load given Deflection at Section of Column with Eccentric Load

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

The formula of Eccentric Load given Deflection at Section of Column with Eccentric Load is expressed as 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). Here is an example- 563.106 = (((acos(1-(0.012/(0.014+0.0025))))/1)^2)*(2000000*0.000168).

How to calculate Eccentric Load 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), Distance b/w fixed end and deflection point (x), Modulus of elasticity of column (ε_column) & Moment of Inertia (I) we can find Eccentric Load given Deflection at Section of Column with Eccentric Load using the formula - 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). This formula also uses Cosine, Inverse Cosine function(s).

Can the Eccentric Load given Deflection at Section of Column with Eccentric Load be negative?

No, the Eccentric Load given Deflection at Section of Column with Eccentric Load, measured in Force cannot be negative.

Which unit is used to measure Eccentric Load given Deflection at Section of Column with Eccentric Load?

Eccentric Load given Deflection at Section of Column with Eccentric Load is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Eccentric Load given Deflection at Section of Column with Eccentric Load can be measured.

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Eccentric Load given Deflection at Section of Column with Eccentric Load Formula

Eccentric Load given Deflection at Section of Column with Eccentric Load Example

Eccentric Load given Deflection at Section of Column with Eccentric Load Solution

Eccentric Load given Deflection at Section of Column with Eccentric Load Formula Elements

Other formulas in Columns With Eccentric Load category

How to Evaluate Eccentric Load given Deflection at Section of Column with Eccentric Load?

FAQs on Eccentric Load given Deflection at Section of Column with Eccentric Load

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