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Cross-Sectional Area of Column given Crippling Load and Rankine's Constant Formula

GoCross-Sectional Area of Column given Crushing Load Formula

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Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point. Check FAQs

A = \frac{P \cdot (1 + α \cdot {(\frac{L eff}{r least})}^{2})}{σ c}

A - Column Cross Sectional Area?P - Crippling Load?α - Rankine's Constant?L_eff - Effective Column Length?r_least - Least Radius of Gyration Column?σ_c - Column Crushing Stress?

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant Example

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Here is how the Cross-Sectional Area of Column given Crippling Load and Rankine's Constant equation looks like with Values.

Here is how the Cross-Sectional Area of Column given Crippling Load and Rankine's Constant equation looks like with Units.

Here is how the Cross-Sectional Area of Column given Crippling Load and Rankine's Constant equation looks like.

2000 = \frac{588.9524 \cdot (1 + 0.0004 \cdot {(\frac{3000}{47.02})}^{2})}{750}

2000mm² = \frac{588.9524kN \cdot (1 + 0.0004 \cdot {(\frac{3000mm}{47.02mm})}^{2})}{750MPa}

2000 = \frac{588.9524 \cdot (1 + 0.0004 \cdot {(\frac{3000}{47.02})}^{2})}{750}

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Cross-Sectional Area of Column given Crippling Load and Rankine's Constant Solution

Follow our step by step solution on how to calculate Cross-Sectional Area of Column given Crippling Load and Rankine's Constant?

FIRST Step Consider the formula

A = \frac{P \cdot (1 + α \cdot {(\frac{L eff}{r least})}^{2})}{σ c}

Next Step Substitute values of Variables

∴

A = \frac{588.9524kN \cdot (1 + 0.0004 \cdot {(\frac{3000mm}{47.02mm})}^{2})}{750MPa}

Next Step Convert Units

∴

A = \frac{588952.4N \cdot (1 + 0.0004 \cdot {(\frac{3m}{0.047m})}^{2})}{7.5E+8Pa}

Next Step Prepare to Evaluate

∴

A = \frac{588952.4 \cdot (1 + 0.0004 \cdot {(\frac{3}{0.047})}^{2})}{7.5E+8}

Next Step Evaluate

∴

A = 0.00199999995518706m²

Next Step Convert to Output's Unit

∴

A = 1999.99995518706mm²

LAST Step Rounding Answer

∴

A = 2000mm²

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant Formula Elements

Variables

Column Cross Sectional Area

Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Column Cross Sectional Area

Crippling Load

Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Symbol: P

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Crippling Load

Rankine's Constant

Rankine's Constant is the constant of Rankine's empirical formula.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Rankine's Constant

Effective Column Length

Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

Symbol: L_eff

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

Least Radius of Gyration Column

Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.

Symbol: r_least

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Least Radius of Gyration Column

Column Crushing Stress

Column Crushing Stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest.

Symbol: σ_c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Column Crushing Stress

Other Formulas to find Column Cross Sectional Area

Go Cross-Sectional Area of Column given Crushing Load

A = \frac{P c}{σ c}

Other formulas in Euler and Rankine's Theory category

Go Crippling Load by Rankine's

P r = \frac{P c \cdot P E}{P c + P E}

Go Crippling Load given Rankine's Constant

P = \frac{σ c \cdot A}{1 + α \cdot {(\frac{L eff}{r least})}^{2}}

Go Crushing Load by Rankine's Formula

P c = \frac{P r \cdot P E}{P E - P r}

Go Crushing Load given Ultimate Crushing Stress

P c = σ c \cdot A

How to Evaluate Cross-Sectional Area of Column given Crippling Load and Rankine's Constant?

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant evaluator uses Column Cross Sectional Area = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Crushing Stress to evaluate the Column Cross Sectional Area, The Cross-Sectional Area of Column given Crippling Load and Rankine's Constant formula is defined as a measure of the internal area of a column that resists external forces, calculated based on the crippling load and Rankine's constant, providing a critical value for structural integrity in engineering design. Column Cross Sectional Area is denoted by A symbol.

How to evaluate Cross-Sectional Area of Column given Crippling Load and Rankine's Constant using this online evaluator? To use this online evaluator for Cross-Sectional Area of Column given Crippling Load and Rankine's Constant, enter Crippling Load (P), Rankine's Constant (α), Effective Column Length (L_eff), Least Radius of Gyration Column (r_least) & Column Crushing Stress (σ_c) and hit the calculate button.

FAQs on Cross-Sectional Area of Column given Crippling Load and Rankine's Constant

What is the formula to find Cross-Sectional Area of Column given Crippling Load and Rankine's Constant?

The formula of Cross-Sectional Area of Column given Crippling Load and Rankine's Constant is expressed as Column Cross Sectional Area = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Crushing Stress. Here is an example- 2E+9 = (588952.4*(1+0.00038*(3/0.04702)^2))/750000000.

How to calculate Cross-Sectional Area of Column given Crippling Load and Rankine's Constant?

With Crippling Load (P), Rankine's Constant (α), Effective Column Length (L_eff), Least Radius of Gyration Column (r_least) & Column Crushing Stress (σ_c) we can find Cross-Sectional Area of Column given Crippling Load and Rankine's Constant using the formula - Column Cross Sectional Area = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Crushing Stress.

What are the other ways to Calculate Column Cross Sectional Area?

Here are the different ways to Calculate Column Cross Sectional Area-

Column Cross Sectional Area=Crushing Load/Column Crushing Stress

Can the Cross-Sectional Area of Column given Crippling Load and Rankine's Constant be negative?

No, the Cross-Sectional Area of Column given Crippling Load and Rankine's Constant, measured in Area cannot be negative.

Which unit is used to measure Cross-Sectional Area of Column given Crippling Load and Rankine's Constant?

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant is usually measured using the Square Millimeter[mm²] for Area. Square Meter[mm²], Square Kilometer[mm²], Square Centimeter[mm²] are the few other units in which Cross-Sectional Area of Column given Crippling Load and Rankine's Constant can be measured.

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Cross-Sectional Area of Column given Crippling Load and Rankine's Constant Formula

​GoCross-Sectional Area of Column given Crushing Load Formula

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant Example

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant Solution

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant Formula Elements

Other Formulas to find Column Cross Sectional Area

Other formulas in Euler and Rankine's Theory category

How to Evaluate Cross-Sectional Area of Column given Crippling Load and Rankine's Constant?

FAQs on Cross-Sectional Area of Column given Crippling Load and Rankine's Constant

Variable Name

GoCross-Sectional Area of Column given Crushing Load Formula