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Eccentricity given Maximum Stress for Column with Eccentric Load Formula

GoEccentricity given Moment at Section of Column with Eccentric Load Formula

GoEccentricity given Deflection at Section of Column with Eccentric load Formula

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Eccentricity of column refers to the distance between the line of action of the applied load and the centroidal axis of the column’s cross-section. Check FAQs

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}}

e - Eccentricity of Column?σ_max - Maximum Stress at Crack Tip?P - Eccentric Load on Column?A_sectional - Cross-Sectional Area of Column?S - Section Modulus for Column?l_e - Effective Column Length?ε_column - Modulus of Elasticity of Column?I - Moment of Inertia?

Eccentricity given Maximum Stress for Column with Eccentric Load Example

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Here is how the Eccentricity given Maximum Stress for Column with Eccentric Load equation looks like with Values.

Here is how the Eccentricity given Maximum Stress for Column with Eccentric Load equation looks like with Units.

Here is how the Eccentricity given Maximum Stress for Column with Eccentric Load equation looks like.

2.5288 = \frac{(6E-5 - (\frac{40}{0.6667})) \cdot 13}{\frac{40 \cdot \sec (200 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}})}{2}}

2.5288mm = \frac{(6E-5MPa - (\frac{40N}{0.6667m²})) \cdot 13m³}{\frac{40N \cdot \sec (200mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}{2}}

2.5288 = \frac{(6E-5 - (\frac{40}{0.6667})) \cdot 13}{\frac{40 \cdot \sec (200 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}})}{2}}

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Eccentricity given Maximum Stress for Column with Eccentric Load Solution

Follow our step by step solution on how to calculate Eccentricity given Maximum Stress for Column with Eccentric Load?

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

e = \frac{(6E-5MPa - (\frac{40N}{0.6667m²})) \cdot 13m³}{\frac{40N \cdot \sec (200mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}{2}}

Next Step Convert Units

∴

e = \frac{(60Pa - (\frac{40N}{0.6667m²})) \cdot 13m³}{\frac{40N \cdot \sec (0.2m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}})}{2}}

Next Step Prepare to Evaluate

∴

e = \frac{(60 - (\frac{40}{0.6667})) \cdot 13}{\frac{40 \cdot \sec (0.2 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}})}{2}}

Next Step Evaluate

∴

e = 0.00252880230831189m

Next Step Convert to Output's Unit

∴

e = 2.52880230831189mm

LAST Step Rounding Answer

∴

e = 2.5288mm

Eccentricity given Maximum Stress for Column with Eccentric Load Formula Elements

Variables

Functions

Eccentricity of Column

Eccentricity of column refers to the distance between the line of action of the applied load and the centroidal axis of the column’s cross-section.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity of Column

Maximum Stress at Crack Tip

Maximum stress at crack tip refers to the highest stress concentration that occurs at the very tip of a crack in a material.

Symbol: σ_max

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Stress at Crack Tip

Eccentric Load on Column

Eccentric load on column refers to a load that is applied at a point away from the centroidal axis of the column’s cross-section where loading introduces both axial stress and bending stress.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Eccentric Load on Column

Cross-Sectional Area of Column

Cross-sectional area of column is the area of the shape we get when we cut through the column perpendicular to its length, helps in determining the column’s ability to bear loads and resist stresses.

Symbol: A_sectional

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross-Sectional Area of Column

Section Modulus for Column

Section modulus for column is a geometric property of a cross-section that measures the ability of a section to resist bending and is crucial for determining the bending stress in structural elements.

Symbol: S

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Section Modulus for Column

Effective Column Length

Effective column length, often that represents the length of a column that influences its buckling behavior.

Symbol: l_e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

Modulus of Elasticity of Column

Modulus of elasticity of column is a measure of a material’s stiffness or rigidity, is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit of a material.

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 also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific 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 of Column

Go Eccentricity given Moment at Section of Column with Eccentric Load

e = (\frac{M}{P}) - δ + δ c

Go Eccentricity given Deflection at Section of Column with Eccentric load

e = (\frac{δ c}{1 - \cos (x \cdot \sqrt{\frac{P}{ε column \cdot I}})}) - δ

Other formulas in Columns With Eccentric Load category

Go Moment at Section of Column with Eccentric Load

M = P \cdot (δ + e load - δ c)

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

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

How to Evaluate Eccentricity given Maximum Stress for Column with Eccentric Load?

Eccentricity given Maximum Stress for Column with Eccentric Load evaluator uses Eccentricity of Column = ((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) to evaluate the Eccentricity of Column, Eccentricity given Maximum Stress for Column with Eccentric Load formula is defined as a measure of how much a column's load is offset from its central axis, which affects the column's ability to withstand stress and compression. It is a critical parameter in structural engineering to ensure the stability and safety of columns under eccentric loads. Eccentricity of Column is denoted by e symbol.

How to evaluate Eccentricity given Maximum Stress for Column with Eccentric Load using this online evaluator? To use this online evaluator for Eccentricity given Maximum Stress for Column with Eccentric Load, enter Maximum Stress at Crack Tip (σ_max), Eccentric Load on Column (P), Cross-Sectional Area of Column (A_sectional), Section Modulus for Column (S), Effective Column Length (l_e), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) and hit the calculate button.

FAQs on Eccentricity given Maximum Stress for Column with Eccentric Load

What is the formula to find Eccentricity given Maximum Stress for Column with Eccentric Load?

The formula of Eccentricity given Maximum Stress for Column with Eccentric Load is expressed as Eccentricity of Column = ((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). Here is an example- 2E+7 = ((60-(40/0.66671))*13)/((40*sec(0.2*sqrt(40/(2000000*0.000168))))/2).

How to calculate Eccentricity given Maximum Stress for Column with Eccentric Load?

With Maximum Stress at Crack Tip (σ_max), Eccentric Load on Column (P), Cross-Sectional Area of Column (A_sectional), Section Modulus for Column (S), Effective Column Length (l_e), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) we can find Eccentricity given Maximum Stress for Column with Eccentric Load using the formula - Eccentricity of Column = ((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). This formula also uses Secant (sec), Square Root (sqrt) function(s).

What are the other ways to Calculate Eccentricity of Column?

Here are the different ways to Calculate Eccentricity of Column-

Eccentricity of Column=(Moment of Force/Eccentric Load on Column)-Deflection of Free End+Deflection of Column
Eccentricity of Column=(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

Can the Eccentricity given Maximum Stress for Column with Eccentric Load be negative?

No, the Eccentricity given Maximum Stress for Column with Eccentric Load, measured in Length cannot be negative.

Which unit is used to measure Eccentricity given Maximum Stress for Column with Eccentric Load?

Eccentricity given Maximum Stress for 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 Maximum Stress for Column with Eccentric Load can be measured.

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Eccentricity given Maximum Stress for Column with Eccentric Load Formula

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

​GoEccentricity given Deflection at Section of Column with Eccentric load Formula

Eccentricity given Maximum Stress for Column with Eccentric Load Example

Eccentricity given Maximum Stress for Column with Eccentric Load Solution

Eccentricity given Maximum Stress for Column with Eccentric Load Formula Elements

Other Formulas to find Eccentricity of Column

Other formulas in Columns With Eccentric Load category

How to Evaluate Eccentricity given Maximum Stress for Column with Eccentric Load?

FAQs on Eccentricity given Maximum Stress for Column with Eccentric Load

Variable Name

GoEccentricity given Moment at Section of Column with Eccentric Load Formula

GoEccentricity given Deflection at Section of Column with Eccentric load Formula