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Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Formula

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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. Check FAQs

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

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

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Example

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Here is how the Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load equation looks like with Values.

Here is how the Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load equation looks like with Units.

Here is how the Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load equation looks like.

0.6667 = \frac{40}{6E-5 - (\frac{\frac{40 \cdot 2.5 \cdot \sec (200 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}})}{2}}{13})}

0.6667m² = \frac{40N}{6E-5MPa - (\frac{\frac{40N \cdot 2.5mm \cdot \sec (200mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}{2}}{13m³})}

0.6667 = \frac{40}{6E-5 - (\frac{\frac{40 \cdot 2.5 \cdot \sec (200 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}})}{2}}{13})}

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Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Solution

Follow our step by step solution on how to calculate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A sectional = \frac{40N}{6E-5MPa - (\frac{\frac{40N \cdot 2.5mm \cdot \sec (200mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}{2}}{13m³})}

Next Step Convert Units

∴

A sectional = \frac{40N}{60Pa - (\frac{\frac{40N \cdot 0.0025m \cdot \sec (0.2m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}})}{2}}{13m³})}

Next Step Prepare to Evaluate

∴

A sectional = \frac{40}{60 - (\frac{\frac{40 \cdot 0.0025 \cdot \sec (0.2 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}})}{2}}{13})}

Next Step Evaluate

∴

A sectional = 0.666709506414469m²

LAST Step Rounding Answer

∴

A sectional = 0.6667m²

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Formula Elements

Variables

Functions

Cross-Sectional Area of Column

Symbol: A_sectional

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross-Sectional Area of Column

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

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

Eccentricity of Load

Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column.

Symbol: e_load

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity of Load

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

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

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 in Columns With Eccentric Load category

Go Moment at Section of Column with Eccentric Load

M = P \cdot (δ + e load - δ c)

Go Eccentricity given Moment at Section of Column with Eccentric Load

e = (\frac{M}{P}) - δ + δ c

How to Evaluate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load evaluator uses Cross-Sectional Area of Column = (Eccentric Load on Column)/(Maximum Stress at Crack Tip-(((Eccentric Load on Column*Eccentricity of Load*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/Section Modulus for Column)) to evaluate the Cross-Sectional Area of Column, Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the area of a column's cross-section when subjected to an eccentric load, taking into account the maximum stress, load eccentricity, and column properties, providing a critical design parameter for structural integrity. Cross-Sectional Area of Column is denoted by A_sectional symbol.

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

FAQs on Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load

What is the formula to find Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

The formula of Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load is expressed as Cross-Sectional Area of Column = (Eccentric Load on Column)/(Maximum Stress at Crack Tip-(((Eccentric Load on Column*Eccentricity of Load*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/Section Modulus for Column)). Here is an example- 0.66671 = (40)/(60-(((40*0.0025*sec(0.2*sqrt(40/(2000000*0.000168))))/2)/13)).

How to calculate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

With Eccentric Load on Column (P), Maximum Stress at Crack Tip (σ_max), Eccentricity of Load (e_load), Effective Column Length (l_e), Modulus of Elasticity of Column (ε_column), Moment of Inertia (I) & Section Modulus for Column (S) we can find Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load using the formula - Cross-Sectional Area of Column = (Eccentric Load on Column)/(Maximum Stress at Crack Tip-(((Eccentric Load on Column*Eccentricity of Load*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/Section Modulus for Column)). This formula also uses Secant (sec), Square Root (sqrt) function(s).

Can the Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load be negative?

No, the Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load, measured in Area cannot be negative.

Which unit is used to measure Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load can be measured.

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Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Formula

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Example

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Solution

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Formula Elements

Other formulas in Columns With Eccentric Load category

How to Evaluate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

FAQs on Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load

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