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Eccentricity given Deflection at Section of Column with Eccentric load Formula

GoEccentricity given Moment at Section of Column with Eccentric Load Formula

GoEccentricity given Maximum Stress for Column with Eccentric Load Formula

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Eccentricity is the distance from point of application of resultant to center of base. Check FAQs

e = \frac{a crippling}{\sec (L \cdot \sqrt{\frac{P}{ε column \cdot I}}) - 1}

e - Eccentricity?a_crippling - Deflection of Free End?L - Column Length?P - Eccentric load on column?ε_column - Modulus of elasticity of column?I - Moment of Inertia?

Eccentricity given Deflection at Section of Column with Eccentric load Example

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

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

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

-1.8657 = \frac{14}{\sec (5000 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}}) - 1}

-1.8657mm = \frac{14mm}{\sec (5000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}) - 1}

-1.8657 = \frac{14}{\sec (5000 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}}) - 1}

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Eccentricity given Deflection at Section of Column with Eccentric load Solution

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

FIRST Step Consider the formula

e = \frac{a crippling}{\sec (L \cdot \sqrt{\frac{P}{ε column \cdot I}}) - 1}

Next Step Substitute values of Variables

∴

e = \frac{14mm}{\sec (5000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}) - 1}

Next Step Convert Units

∴

e = \frac{0.014m}{\sec (5m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}}) - 1}

Next Step Prepare to Evaluate

∴

e = \frac{0.014}{\sec (5 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}}) - 1}

Next Step Evaluate

∴

e = -0.00186571039105029m

Next Step Convert to Output's Unit

∴

e = -1.86571039105029mm

LAST Step Rounding Answer

∴

e = -1.8657mm

Eccentricity given Deflection at Section of Column with Eccentric load Formula Elements

Variables

Functions

Eccentricity

Eccentricity is the distance from point of application of resultant to center of base.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity

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

Column Length

Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

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

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

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(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.

Syntax: sqrt(Number)

Other Formulas to find Eccentricity

Go Eccentricity given Moment at Section of Column with Eccentric Load

e = (\frac{M}{P}) - a crippling + δ c

Go Eccentricity given Maximum Stress for Column with Eccentric Load

e = \frac{(σ max - (\frac{P}{A sectional})) \cdot S}{\frac{P \cdot \sec (L e \cdot \sqrt{\frac{P}{ε column \cdot I}})}{2}}

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 Eccentric Load given Deflection at Section of Column with Eccentric Load

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

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

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

Go Moment of Inertia given Deflection at Section of Column with Eccentric Load

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

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

Eccentricity given Deflection at Section of Column with Eccentric load evaluator uses Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1) to evaluate 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 evaluate Eccentricity given Deflection at Section of Column with Eccentric load using this online evaluator? To use this online evaluator for Eccentricity given Deflection at Section of Column with Eccentric load, enter Deflection of Free End (a_crippling), Column Length (L), Eccentric load on column (P), Modulus of elasticity of column (ε_column) & Moment of Inertia (I) and hit the calculate button.

FAQs on Eccentricity given Deflection at Section of Column with Eccentric load

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

The formula of Eccentricity given Deflection at Section of Column with Eccentric load is expressed as Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1). Here is an example- 189612 = (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.014.

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

With Deflection of Free End (a_crippling), Column Length (L), Eccentric load on column (P), Modulus of elasticity of column (ε_column) & Moment of Inertia (I) we can find Eccentricity given Deflection at Section of Column with Eccentric load using the formula - Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))-1). This formula also uses Secant Function, Square Root Function function(s).

What are the other ways to Calculate Eccentricity?

Here are the different ways to Calculate Eccentricity-

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)

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

No, the Eccentricity given Deflection at Section of Column with Eccentric load, measured in Length cannot be negative.

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

Eccentricity 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 Eccentricity given Deflection at Section of Column with Eccentric load can be measured.

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Eccentricity given Deflection at Section of Column with Eccentric load Formula

​GoEccentricity given Moment at Section of Column with Eccentric Load Formula

​GoEccentricity given Maximum Stress for Column with Eccentric Load Formula

Eccentricity given Deflection at Section of Column with Eccentric load Example

Eccentricity given Deflection at Section of Column with Eccentric load Solution

Eccentricity given Deflection at Section of Column with Eccentric load Formula Elements

Other Formulas to find Eccentricity

Other formulas in Columns With Eccentric Load category

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

FAQs on Eccentricity given Deflection at Section of Column with Eccentric load

Variable Name

GoEccentricity given Moment at Section of Column with Eccentric Load Formula

GoEccentricity given Maximum Stress for Column with Eccentric Load Formula