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Ultimate Crushing Stress given Crippling Load and Rankine's Constant Formula

GoUltimate Crushing Stress given Crushing Load Formula

GoUltimate Crushing Stress given Rankine's Constant Formula

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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. Check FAQs

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

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

Ultimate Crushing Stress given Crippling Load and Rankine's Constant Example

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Here is how the Ultimate Crushing Stress given Crippling Load and Rankine's Constant equation looks like with Values.

Here is how the Ultimate Crushing Stress given Crippling Load and Rankine's Constant equation looks like with Units.

Here is how the Ultimate Crushing Stress given Crippling Load and Rankine's Constant equation looks like.

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

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

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

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Ultimate Crushing Stress given Crippling Load and Rankine's Constant Solution

Follow our step by step solution on how to calculate Ultimate Crushing Stress given Crippling Load and Rankine's Constant?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

σ c = \frac{588952.4N \cdot (1 + 0.0004 \cdot {(\frac{3m}{0.047m})}^{2})}{0.002m²}

Next Step Prepare to Evaluate

∴

σ c = \frac{588952.4 \cdot (1 + 0.0004 \cdot {(\frac{3}{0.047})}^{2})}{0.002}

Next Step Evaluate

∴

σ c = 749999983.195147Pa

Next Step Convert to Output's Unit

∴

σ c = 749.999983195147MPa

LAST Step Rounding Answer

∴

σ c = 750MPa

Ultimate Crushing Stress given Crippling Load and Rankine's Constant Formula Elements

Variables

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

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 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

Other Formulas to find Column Crushing Stress

Go Ultimate Crushing Stress given Crushing Load

σ c = \frac{P c}{A}

Go Ultimate Crushing Stress given Rankine's Constant

σ c = α \cdot π^{2} \cdot E

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

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

Go Cross-Sectional Area of Column given Crushing Load

A = \frac{P c}{σ c}

How to Evaluate Ultimate Crushing Stress given Crippling Load and Rankine's Constant?

Ultimate Crushing Stress given Crippling Load and Rankine's Constant evaluator uses Column Crushing Stress = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Cross Sectional Area to evaluate the Column Crushing Stress, The Ultimate Crushing Stress given Crippling Load and Rankine's Constant formula is defined as a measure of the maximum stress a column can withstand without collapsing, considering the crippling load and Rankine's constant, which is essential in Euler and Rankine's theory for structural analysis and design. Column Crushing Stress is denoted by σ_c symbol.

How to evaluate Ultimate Crushing Stress given Crippling Load and Rankine's Constant using this online evaluator? To use this online evaluator for Ultimate Crushing Stress 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 Cross Sectional Area (A) and hit the calculate button.

FAQs on Ultimate Crushing Stress given Crippling Load and Rankine's Constant

What is the formula to find Ultimate Crushing Stress given Crippling Load and Rankine's Constant?

The formula of Ultimate Crushing Stress given Crippling Load and Rankine's Constant is expressed as Column Crushing Stress = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Cross Sectional Area. Here is an example- 0.00075 = (588952.4*(1+0.00038*(3/0.04702)^2))/0.002.

How to calculate Ultimate Crushing Stress 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 Cross Sectional Area (A) we can find Ultimate Crushing Stress given Crippling Load and Rankine's Constant using the formula - Column Crushing Stress = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Cross Sectional Area.

What are the other ways to Calculate Column Crushing Stress?

Here are the different ways to Calculate Column Crushing Stress-

Column Crushing Stress=Crushing Load/Column Cross Sectional Area
Column Crushing Stress=Rankine's Constant*pi^2*Modulus of Elasticity Column

Can the Ultimate Crushing Stress given Crippling Load and Rankine's Constant be negative?

No, the Ultimate Crushing Stress given Crippling Load and Rankine's Constant, measured in Pressure cannot be negative.

Which unit is used to measure Ultimate Crushing Stress given Crippling Load and Rankine's Constant?

Ultimate Crushing Stress given Crippling Load and Rankine's Constant is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Ultimate Crushing Stress given Crippling Load and Rankine's Constant can be measured.

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Ultimate Crushing Stress given Crippling Load and Rankine's Constant Formula

​GoUltimate Crushing Stress given Crushing Load Formula

​GoUltimate Crushing Stress given Rankine's Constant Formula

Ultimate Crushing Stress given Crippling Load and Rankine's Constant Example

Ultimate Crushing Stress given Crippling Load and Rankine's Constant Solution

Ultimate Crushing Stress given Crippling Load and Rankine's Constant Formula Elements

Other Formulas to find Column Crushing Stress

Other formulas in Euler and Rankine's Theory category

How to Evaluate Ultimate Crushing Stress given Crippling Load and Rankine's Constant?

FAQs on Ultimate Crushing Stress given Crippling Load and Rankine's Constant

Variable Name

GoUltimate Crushing Stress given Crushing Load Formula

GoUltimate Crushing Stress given Rankine's Constant Formula