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Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Formula

GoAllowable Axial Compression Stress for Slenderness Ratio greater than 160 Formula

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Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material. Check FAQs

F a = \frac{\frac{F yw}{f s}}{1 + (0.20 \cdot ((\frac{EAR}{r least}) \cdot (\sqrt{f s \cdot \frac{P compressive}{4 \cdot ε column}})))}

F_a - Allowable compression stress?F_yw - Specified minimum yield stress for column?f_s - Factor of Safety?EAR - Effective Interest Rate?r_least - Least Radius of Gyration Column?P_compressive - Column Compressive load?ε_column - Modulus of Elasticity Column?

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Example

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Here is how the Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 equation looks like with Values.

Here is how the Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 equation looks like with Units.

Here is how the Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 equation looks like.

0.8523 = \frac{\frac{2.7}{2.8}}{1 + (0.20 \cdot ((\frac{6}{47.02}) \cdot (\sqrt{2.8 \cdot \frac{0.4}{4 \cdot 10.56}})))}

0.8523MPa = \frac{\frac{2.7MPa}{2.8}}{1 + (0.20 \cdot ((\frac{6}{47.02mm}) \cdot (\sqrt{2.8 \cdot \frac{0.4kN}{4 \cdot 10.56MPa}})))}

0.8523 = \frac{\frac{2.7}{2.8}}{1 + (0.20 \cdot ((\frac{6}{47.02}) \cdot (\sqrt{2.8 \cdot \frac{0.4}{4 \cdot 10.56}})))}

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Home » Physics » Mechanical » Strength of Materials » Allowable Axial Compression Stress for Slenderness Ratio 0 to 160

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Solution

Follow our step by step solution on how to calculate Allowable Axial Compression Stress for Slenderness Ratio 0 to 160?

FIRST Step Consider the formula

F a = \frac{\frac{F yw}{f s}}{1 + (0.20 \cdot ((\frac{EAR}{r least}) \cdot (\sqrt{f s \cdot \frac{P compressive}{4 \cdot ε column}})))}

Next Step Substitute values of Variables

∴

F a = \frac{\frac{2.7MPa}{2.8}}{1 + (0.20 \cdot ((\frac{6}{47.02mm}) \cdot (\sqrt{2.8 \cdot \frac{0.4kN}{4 \cdot 10.56MPa}})))}

Next Step Convert Units

∴

F a = \frac{\frac{2.7E+6Pa}{2.8}}{1 + (0.20 \cdot ((\frac{6}{0.047m}) \cdot (\sqrt{2.8 \cdot \frac{400N}{4 \cdot 1.1E+7Pa}})))}

Next Step Prepare to Evaluate

∴

F a = \frac{\frac{2.7E+6}{2.8}}{1 + (0.20 \cdot ((\frac{6}{0.047}) \cdot (\sqrt{2.8 \cdot \frac{400}{4 \cdot 1.1E+7}})))}

Next Step Evaluate

∴

F a = 852282.782042558Pa

Next Step Convert to Output's Unit

∴

F a = 0.852282782042558MPa

LAST Step Rounding Answer

∴

F a = 0.8523MPa

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Formula Elements

Variables

Functions

Allowable compression stress

Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material.

Symbol: F_a

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Specified minimum yield stress for column

Specified minimum yield stress for column represents the minimum tensile stress or yield stress required by the flexural member, say, web.

Symbol: F_yw

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Factor of Safety

Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Effective Interest Rate

The effective interest rate is the true rate of interest earned.

Symbol: EAR

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

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 can be positive or negative.

Column Compressive load

Column Compressive load is the load applied to a column that is compressive in nature.

Symbol: P_compressive

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Modulus of Elasticity Column

Modulus of Elasticity 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.

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)

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Formula and 2000+ more formulas!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Formula and 1900+ more formulas!

Other Formulas to find Allowable compression stress

Go Allowable Axial Compression Stress for Slenderness Ratio greater than 160

F a = σ c' \cdot (1.2 - (\frac{L eff}{800 \cdot r least}))

Other formulas in Formula By I.S. Code For Mild Steel category

Go Minimum Yield Stress for Allowable Axial Compression Stress for Slenderness Ratio between 0 to 160

F yw = F a \cdot (1 + (0.20 \cdot ((\frac{EAR}{r least}) \cdot (\sqrt{f s \cdot \frac{P compressive}{4 \cdot ε column}})))) \cdot f s

Go Effective Column Length given Allowable Axial Compression Stress

L eff = (\frac{(\frac{F yw}{f s \cdot F a}) - 1}{0.20 \cdot ((\sqrt{f s \cdot \frac{P compressive}{4 \cdot ε column}}))}) \cdot r least

How to Evaluate Allowable Axial Compression Stress for Slenderness Ratio 0 to 160?

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 evaluator uses Allowable compression stress = (Specified minimum yield stress for column/Factor of Safety)/(1+(0.20*((Effective Interest Rate/Least Radius of Gyration Column)*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column)))))) to evaluate the Allowable compression stress, Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 formula is defined as the maximum compressive stress that a mild steel column can withstand without buckling, considering the slenderness ratio, yield strength, and compressive load, ensuring safe design and construction of steel structures. Allowable compression stress is denoted by F_a symbol.

How to evaluate Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 using this online evaluator? To use this online evaluator for Allowable Axial Compression Stress for Slenderness Ratio 0 to 160, enter Specified minimum yield stress for column (F_yw), Factor of Safety (f_s), Effective Interest Rate (EAR), Least Radius of Gyration Column (r_least), Column Compressive load (P_compressive) & Modulus of Elasticity Column (ε_column) and hit the calculate button.

FAQs on Allowable Axial Compression Stress for Slenderness Ratio 0 to 160

What is the formula to find Allowable Axial Compression Stress for Slenderness Ratio 0 to 160?

The formula of Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 is expressed as Allowable compression stress = (Specified minimum yield stress for column/Factor of Safety)/(1+(0.20*((Effective Interest Rate/Least Radius of Gyration Column)*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column)))))). Here is an example- 8.5E-7 = (2700000/2.8)/(1+(0.20*((6/0.04702)*(sqrt(2.8*400/(4*10560000)))))).

How to calculate Allowable Axial Compression Stress for Slenderness Ratio 0 to 160?

With Specified minimum yield stress for column (F_yw), Factor of Safety (f_s), Effective Interest Rate (EAR), Least Radius of Gyration Column (r_least), Column Compressive load (P_compressive) & Modulus of Elasticity Column (ε_column) we can find Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 using the formula - Allowable compression stress = (Specified minimum yield stress for column/Factor of Safety)/(1+(0.20*((Effective Interest Rate/Least Radius of Gyration Column)*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column)))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Allowable compression stress?

Here are the different ways to Calculate Allowable compression stress-

Allowable compression stress=Value obtained from Secant Formula*(1.2-(Effective Column Length/(800*Least Radius of Gyration Column)))

Can the Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 be negative?

Yes, the Allowable Axial Compression Stress for Slenderness Ratio 0 to 160, measured in Pressure can be negative.

Which unit is used to measure Allowable Axial Compression Stress for Slenderness Ratio 0 to 160?

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 can be measured.

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Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Formula

​GoAllowable Axial Compression Stress for Slenderness Ratio greater than 160 Formula

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Example

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Solution

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Formula Elements

Credits

Other Formulas to find Allowable compression stress

Other formulas in Formula By I.S. Code For Mild Steel category

How to Evaluate Allowable Axial Compression Stress for Slenderness Ratio 0 to 160?

FAQs on Allowable Axial Compression Stress for Slenderness Ratio 0 to 160

Variable Name

GoAllowable Axial Compression Stress for Slenderness Ratio greater than 160 Formula