Slenderness Ratio given Allowable Axial Compression Stress Calculator

✖Specified minimum yield stress for column represents the minimum tensile stress or yield stress required by the flexural member, say, web.ⓘ Specified minimum yield stress for column [F_yw]			+10% -10%
✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety [f_s]			+10% -10%
✖Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material.ⓘ Allowable compression stress [F_a]			+10% -10%
✖Column Compressive load is the load applied to a column that is compressive in nature.ⓘ Column Compressive load [P_compressive]			+10% -10%
✖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.ⓘ Modulus of Elasticity Column [ε_column]			+10% -10%

✖The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section.ⓘ Slenderness Ratio given Allowable Axial Compression Stress [λ]

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Slenderness Ratio given Allowable Axial Compression Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness Ratio = ((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column)))))
λ = ((F_yw/(f_s*F_a))-1)/(0.20*((sqrt(f_s*P_compressive/(4*ε_column)))))
This formula uses 1 Functions, 6 Variables

Functions Used

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., sqrt(Number)

Variables Used

Slenderness Ratio - The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
Specified minimum yield stress for column - (Measured in Pascal) - Specified minimum yield stress for column represents the minimum tensile stress or yield stress required by the flexural member, say, web.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Allowable compression stress - (Measured in Pascal) - Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material.
Column Compressive load - (Measured in Newton) - Column Compressive load is the load applied to a column that is compressive in nature.
Modulus of Elasticity Column - (Measured in Pascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Specified minimum yield stress for column: 2.7 Megapascal --> 2700000 Pascal (Check conversion here)
Factor of Safety: 2.8 --> No Conversion Required
Allowable compression stress: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Column Compressive load: 0.4 Kilonewton --> 400 Newton (Check conversion here)
Modulus of Elasticity Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = ((F_yw/(f_s*F_a))-1)/(0.20*((sqrt(f_s*P_compressive/(4*ε_column))))) --> ((2700000/(2.8*10000000))-1)/(0.20*((sqrt(2.8*400/(4*10560000)))))

Evaluating ... ...

λ = -877.375368039899

STEP 3: Convert Result to Output's Unit

-877.375368039899 --> No Conversion Required

FINAL ANSWER

-877.375368039899 ≈ -877.375368 <-- Slenderness Ratio

(Calculation completed in 00.004 seconds)

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< Formula By I.S. Code For Mild Steel Calculators

Effective Column Length given Allowable Axial Compression Stress

LaTeX Go Effective Column Length = (((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))))*Least Radius of Gyration Column

Allowable Axial Compression Stress for Slenderness Ratio 0 to 160

LaTeX Go 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))))))

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

LaTeX Go Specified minimum yield stress for column = Allowable compression stress*(1+(0.20*((Effective Interest Rate/Least Radius of Gyration Column)*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))))*Factor of Safety

Allowable Axial Compression Stress for Slenderness Ratio greater than 160

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

Slenderness Ratio given Allowable Axial Compression Stress Formula

LaTeX Go

Which is example of eccentric loading?

Examples of eccentric loading activities include performing a calf raise off the ledge of a stair, an exercise that has been shown to decrease the risk of Achilles tendon injuries. Another example is the nordic curl exercise, which has been shown to help reduce the risk of hamstring strains.

How to Calculate Slenderness Ratio given Allowable Axial Compression Stress?

Slenderness Ratio given Allowable Axial Compression Stress calculator uses Slenderness Ratio = ((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))) to calculate the Slenderness Ratio, Slenderness Ratio given Allowable Axial Compression Stress formula is defined as a measure of the structural efficiency of a column, which is a critical parameter in determining the load-carrying capacity of a column under axial compression, and is used to ensure the safety and stability of structures. Slenderness Ratio is denoted by λ symbol.

How to calculate Slenderness Ratio given Allowable Axial Compression Stress using this online calculator? To use this online calculator for Slenderness Ratio given Allowable Axial Compression Stress, enter Specified minimum yield stress for column (F_yw), Factor of Safety (f_s), Allowable compression stress (F_a), Column Compressive load (P_compressive) & Modulus of Elasticity Column (ε_column) and hit the calculate button. Here is how the Slenderness Ratio given Allowable Axial Compression Stress calculation can be explained with given input values -> -877.375368 = ((2700000/(2.8*10000000))-1)/(0.20*((sqrt(2.8*400/(4*10560000))))).

FAQ

What is Slenderness Ratio given Allowable Axial Compression Stress?

Slenderness Ratio given Allowable Axial Compression Stress formula is defined as a measure of the structural efficiency of a column, which is a critical parameter in determining the load-carrying capacity of a column under axial compression, and is used to ensure the safety and stability of structures and is represented as λ = ((F_yw/(f_s*F_a))-1)/(0.20*((sqrt(f_s*P_compressive/(4*ε_column))))) or Slenderness Ratio = ((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))). Specified minimum yield stress for column represents the minimum tensile stress or yield stress required by the flexural member, say, web, Factor of Safety expresses how much stronger a system is than it needs to be for an intended load, Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material, Column Compressive load is the load applied to a column that is compressive in nature & 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.

How to calculate Slenderness Ratio given Allowable Axial Compression Stress?

Slenderness Ratio given Allowable Axial Compression Stress formula is defined as a measure of the structural efficiency of a column, which is a critical parameter in determining the load-carrying capacity of a column under axial compression, and is used to ensure the safety and stability of structures is calculated using Slenderness Ratio = ((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))). To calculate Slenderness Ratio given Allowable Axial Compression Stress, you need Specified minimum yield stress for column (F_yw), Factor of Safety (f_s), Allowable compression stress (F_a), Column Compressive load (P_compressive) & Modulus of Elasticity Column (ε_column). With our tool, you need to enter the respective value for Specified minimum yield stress for column, Factor of Safety, Allowable compression stress, Column Compressive load & Modulus of Elasticity Column 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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