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Safety Factor for Allowable Compressive Stress Formula

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Safety factor otherwise called as factor of safety expresses how much stronger a system is than it needs to be for an intended load. Check FAQs

F s = \frac{5}{3} + (\frac{3 \cdot (\frac{k \cdot l}{r})}{8 \cdot C c}) - (\frac{{(\frac{k \cdot l}{r})}^{3}}{8 \cdot {C c}^{3}})

F_s - Safety Factor?k - Effective Length Factor?l - Effective Column Length?r - Radius of Gyration?C_c - Factor for Allowable Stress Design?

Safety Factor for Allowable Compressive Stress Example

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Here is how the Safety Factor for Allowable Compressive Stress equation looks like with Values.

Here is how the Safety Factor for Allowable Compressive Stress equation looks like with Units.

Here is how the Safety Factor for Allowable Compressive Stress equation looks like.

1.7428 = \frac{5}{3} + (\frac{3 \cdot (\frac{0.75 \cdot 3000}{87})}{8 \cdot 125.66}) - (\frac{{(\frac{0.75 \cdot 3000}{87})}^{3}}{8 \cdot {125.66}^{3}})

1.7428 = \frac{5}{3} + (\frac{3 \cdot (\frac{0.75 \cdot 3000mm}{87mm})}{8 \cdot 125.66}) - (\frac{{(\frac{0.75 \cdot 3000mm}{87mm})}^{3}}{8 \cdot {125.66}^{3}})

1.7428 = \frac{5}{3} + (\frac{3 \cdot (\frac{0.75 \cdot 3000}{87})}{8 \cdot 125.66}) - (\frac{{(\frac{0.75 \cdot 3000}{87})}^{3}}{8 \cdot {125.66}^{3}})

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Safety Factor for Allowable Compressive Stress Solution

Follow our step by step solution on how to calculate Safety Factor for Allowable Compressive Stress?

FIRST Step Consider the formula

F s = \frac{5}{3} + (\frac{3 \cdot (\frac{k \cdot l}{r})}{8 \cdot C c}) - (\frac{{(\frac{k \cdot l}{r})}^{3}}{8 \cdot {C c}^{3}})

Next Step Substitute values of Variables

∴

F s = \frac{5}{3} + (\frac{3 \cdot (\frac{0.75 \cdot 3000mm}{87mm})}{8 \cdot 125.66}) - (\frac{{(\frac{0.75 \cdot 3000mm}{87mm})}^{3}}{8 \cdot {125.66}^{3}})

Next Step Convert Units

∴

F s = \frac{5}{3} + (\frac{3 \cdot (\frac{0.75 \cdot 3m}{0.087m})}{8 \cdot 125.66}) - (\frac{{(\frac{0.75 \cdot 3m}{0.087m})}^{3}}{8 \cdot {125.66}^{3}})

Next Step Prepare to Evaluate

∴

F s = \frac{5}{3} + (\frac{3 \cdot (\frac{0.75 \cdot 3}{0.087})}{8 \cdot 125.66}) - (\frac{{(\frac{0.75 \cdot 3}{0.087})}^{3}}{8 \cdot {125.66}^{3}})

Next Step Evaluate

∴

F s = 1.74275566576299

LAST Step Rounding Answer

∴

F s = 1.7428

Safety Factor for Allowable Compressive Stress Formula Elements

Variables

Safety Factor

Safety factor otherwise called as 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.

Formulas to find Safety Factor

Effective Length Factor

Effective Length Factor is the factor used for the members in the frame. It depends on the ratio of compression member stiffness to the end restraint stiffness.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Effective Length Factor

Effective Column Length

Effective Column Length of a column is the length of an equivalent pin-ended column that has the same load-carrying capacity and buckling behaviour as the actual column with different end conditions.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

Radius of Gyration

Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration

Factor for Allowable Stress Design

Factor for Allowable Stress Design is the usual term used to demarcate between inelastic and elastic member buckling.

Symbol: C_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor for Allowable Stress Design

Other formulas in Allowable Stress Design for Building Columns category

Go Slenderness Ratio Used for Separation

C c = \sqrt{\frac{2 \cdot (π^{2}) \cdot E s}{F y}}

Go Factor for Unbraced Segment of any Cross-Section

C c = \frac{1986.66}{\sqrt{F y}}

Go Allowable Compressive Stress when Slenderness Ratio is Greater than Cc

F a = \frac{12 \cdot π^{2} \cdot E s}{23 \cdot {(\frac{k \cdot l}{r})}^{2}}

Go Allowable Compressive Stress when Slenderness Ratio is Less than Cc

F a = \frac{(1 - (\frac{{(\frac{k \cdot l}{r})}^{2}}{2 \cdot {C c}^{2}})) \cdot F y}{F s}

How to Evaluate Safety Factor for Allowable Compressive Stress?

Safety Factor for Allowable Compressive Stress evaluator uses Safety Factor = 5/3+((3*((Effective Length Factor*Effective Column Length)/Radius of Gyration))/(8*Factor for Allowable Stress Design))-((((Effective Length Factor*Effective Column Length)/Radius of Gyration)^3)/(8*Factor for Allowable Stress Design^3)) to evaluate the Safety Factor, The Safety Factor for Allowable Compressive Stress formula is defined as the value which we provide in order to make the section more safe. Safety Factor is denoted by F_s symbol.

How to evaluate Safety Factor for Allowable Compressive Stress using this online evaluator? To use this online evaluator for Safety Factor for Allowable Compressive Stress, enter Effective Length Factor (k), Effective Column Length (l), Radius of Gyration (r) & Factor for Allowable Stress Design (C_c) and hit the calculate button.

FAQs on Safety Factor for Allowable Compressive Stress

What is the formula to find Safety Factor for Allowable Compressive Stress?

The formula of Safety Factor for Allowable Compressive Stress is expressed as Safety Factor = 5/3+((3*((Effective Length Factor*Effective Column Length)/Radius of Gyration))/(8*Factor for Allowable Stress Design))-((((Effective Length Factor*Effective Column Length)/Radius of Gyration)^3)/(8*Factor for Allowable Stress Design^3)). Here is an example- 1.742756 = 5/3+((3*((0.75*3)/0.087))/(8*125.66))-((((0.75*3)/0.087)^3)/(8*125.66^3)).

How to calculate Safety Factor for Allowable Compressive Stress?

With Effective Length Factor (k), Effective Column Length (l), Radius of Gyration (r) & Factor for Allowable Stress Design (C_c) we can find Safety Factor for Allowable Compressive Stress using the formula - Safety Factor = 5/3+((3*((Effective Length Factor*Effective Column Length)/Radius of Gyration))/(8*Factor for Allowable Stress Design))-((((Effective Length Factor*Effective Column Length)/Radius of Gyration)^3)/(8*Factor for Allowable Stress Design^3)).

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Safety Factor for Allowable Compressive Stress Formula

Safety Factor for Allowable Compressive Stress Example

Safety Factor for Allowable Compressive Stress Solution

Safety Factor for Allowable Compressive Stress Formula Elements

Other formulas in Allowable Stress Design for Building Columns category

How to Evaluate Safety Factor for Allowable Compressive Stress?

FAQs on Safety Factor for Allowable Compressive Stress

Variable Name