Safety Factor for Allowable Compressive Stress Calculator

✖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.ⓘ Effective Length Factor [k]			+10% -10%
✖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.ⓘ Effective Column Length [l]			+10% -10%
✖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.ⓘ Radius of Gyration [r]			+10% -10%
✖Factor for Allowable Stress Design is the usual term used to demarcate between inelastic and elastic member buckling.ⓘ Factor for Allowable Stress Design [C_c]			+10% -10%

✖Safety factor otherwise called as factor of safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Safety Factor for Allowable Compressive Stress [F_s]

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Formula

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Safety Factor for Allowable Compressive Stress

Formula

`"F"_{"s"} = 5/3+((3*(("k"*"l")/"r"))/(8*"C"_{"c"}))-(((("k"*"l")/"r")^3)/(8*"C"_{"c"}^3))`

Example

`"1.742756"=5/3+((3*(("0.75"*"3000mm")/"87mm"))/(8*"125.66"))-(((("0.75"*"3000mm")/"87mm")^3)/(8*("125.66")^3))`

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Safety Factor for Allowable Compressive Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
F_s = 5/3+((3*((k*l)/r))/(8*C_c))-((((k*l)/r)^3)/(8*C_c^3))
This formula uses 5 Variables

Variables Used

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.
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.
Effective Column Length - (Measured in Meter) - 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.
Radius of Gyration - (Measured in Meter) - 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.
Factor for Allowable Stress Design - Factor for Allowable Stress Design is the usual term used to demarcate between inelastic and elastic member buckling.

STEP 1: Convert Input(s) to Base Unit

Effective Length Factor: 0.75 --> No Conversion Required
Effective Column Length: 3000 Millimeter --> 3 Meter (Check conversion here)
Radius of Gyration: 87 Millimeter --> 0.087 Meter (Check conversion here)
Factor for Allowable Stress Design: 125.66 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_s = 5/3+((3*((k*l)/r))/(8*C_c))-((((k*l)/r)^3)/(8*C_c^3)) --> 5/3+((3*((0.75*3)/0.087))/(8*125.66))-((((0.75*3)/0.087)^3)/(8*125.66^3))

Evaluating ... ...

F_s = 1.74275566576299

STEP 3: Convert Result to Output's Unit

1.74275566576299 --> No Conversion Required

FINAL ANSWER

1.74275566576299 ≈ 1.742756 <-- Safety Factor

(Calculation completed in 00.007 seconds)

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Home » Engineering » Civil » Design of Steel Structures » Allowable-Stress Design » Allowable-Stress Design for Building Columns » Safety Factor for Allowable Compressive Stress

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 6 Allowable-Stress Design for Building Columns Calculators

Safety Factor for Allowable Compressive Stress

Go 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))

Allowable Compressive Stress when Slenderness Ratio is Less than Cc

Go Allowable Compression Stress = ((1-((((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2)/(2*Factor for Allowable Stress Design^2)))*Yield Stress of Steel)/Safety Factor

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc

Go Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2)

Slenderness Ratio Used for Separation

Go Factor for Allowable Stress Design = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Yield Stress of Steel)

Factor for Unbraced Segment of any Cross-Section

Go Factor for Allowable Stress Design = 1986.66/sqrt(Yield Stress of Steel)

Effective Length Factor

Go Effective Length Factor = Effective Column Length/Actual Unbraced Length

Safety Factor for Allowable Compressive Stress Formula

What is Allowable Stress Design or ASD?

In the Allowable Stress (or working stress) Design, member stresses computed under the action of service (or working) loads are compared to some predesignated stresses called allowable stresses. The allowable stresses are usually expressed as a function of the yield stress or tensile stress of the material.

Define Radius of Gyration & Slenderness Ratio.

The radius of gyration is defined as the imaginary distance from the centroid at which the area of the cross-section is imagined to be focused on a point to obtain the same moment of inertia. It is the perpendicular distance from point mass to the axis of rotation.
The slenderness ratio can also be defined as the ratio of the effective length of the column to the minimum radius of gyration1. It serves as a measure of the column’s ability to withstand buckling pressure. In structural engineering, slenderness is a measure of the propensity of a column to buckle.

How to Calculate Safety Factor for Allowable Compressive Stress?

Safety Factor for Allowable Compressive Stress calculator 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 calculate 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 calculate Safety Factor for Allowable Compressive Stress using this online calculator? To use this online calculator 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. Here is how the Safety Factor for Allowable Compressive Stress calculation can be explained with given input values -> 1.742756 = 5/3+((3*((0.75*3)/0.087))/(8*125.66))-((((0.75*3)/0.087)^3)/(8*125.66^3)).

FAQ

What is Safety Factor for Allowable Compressive Stress?

The Safety Factor for Allowable Compressive Stress formula is defined as the value which we provide in order to make the section more safe and is represented as F_s = 5/3+((3*((k*l)/r))/(8*C_c))-((((k*l)/r)^3)/(8*C_c^3)) or 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)). 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, 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, 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 & Factor for Allowable Stress Design is the usual term used to demarcate between inelastic and elastic member buckling.

How to calculate Safety Factor for Allowable Compressive Stress?

The Safety Factor for Allowable Compressive Stress formula is defined as the value which we provide in order to make the section more safe is calculated using 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 calculate Safety Factor for Allowable Compressive Stress, you need Effective Length Factor (k), Effective Column Length (l), Radius of Gyration (r) & Factor for Allowable Stress Design (C_c). With our tool, you need to enter the respective value for Effective Length Factor, Effective Column Length, Radius of Gyration & Factor for Allowable Stress Design and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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