Theoretical Maximum Stress for Johnson Code Steels Calculator

✖Stress at any Point y is unit stress S, at any point y where y is positive for points on the same side of center of gravity.ⓘ Stress at any Point y [S_y]			+10% -10%
✖Coefficient for Column End Conditions is defined as the multiplicative factor for different column end conditions.ⓘ Coefficient for Column End Conditions [n]			+10% -10%
✖The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.ⓘ Modulus of Elasticity [E]			+10% -10%
✖The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.ⓘ Effective Length of Column [L]			+10% -10%
✖The Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.ⓘ Radius of Gyration of Column [r_gyration]			+10% -10%

✖The Theoretical Maximum Stress is when a material will fail or yield when its maximum stress equals or exceeds the shear stress value at the yield point in the uniaxial tensile test.ⓘ Theoretical Maximum Stress for Johnson Code Steels [S_cr]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Eccentric Loads on Columns Formulas PDF PDF Image

Theoretical Maximum Stress for Johnson Code Steels Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theoretical Maximum Stress = Stress at any Point y*(1-(Stress at any Point y/(4*Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity))*(Effective Length of Column/Radius of Gyration of Column)^2)
S_cr = S_y*(1-(S_y/(4*n*(pi^2)*E))*(L/r_gyration)^2)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Theoretical Maximum Stress - (Measured in Pascal) - The Theoretical Maximum Stress is when a material will fail or yield when its maximum stress equals or exceeds the shear stress value at the yield point in the uniaxial tensile test.
Stress at any Point y - (Measured in Pascal) - Stress at any Point y is unit stress S, at any point y where y is positive for points on the same side of center of gravity.
Coefficient for Column End Conditions - Coefficient for Column End Conditions is defined as the multiplicative factor for different column end conditions.
Modulus of Elasticity - (Measured in Pascal) - The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.
Effective Length of Column - (Measured in Meter) - The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.
Radius of Gyration of Column - (Measured in Meter) - The Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.

STEP 1: Convert Input(s) to Base Unit

Stress at any Point y: 35000 Pascal --> 35000 Pascal No Conversion Required
Coefficient for Column End Conditions: 2 --> No Conversion Required
Modulus of Elasticity: 50 Megapascal --> 50000000 Pascal (Check conversion here)
Effective Length of Column: 3000 Millimeter --> 3 Meter (Check conversion here)
Radius of Gyration of Column: 26 Millimeter --> 0.026 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_cr = S_y*(1-(S_y/(4*n*(pi^2)*E))*(L/r_gyration)^2) --> 35000*(1-(35000/(4*2*(pi^2)*50000000))*(3/0.026)^2)

Evaluating ... ...

S_cr = 30868.8385737545

STEP 3: Convert Result to Output's Unit

30868.8385737545 Pascal --> No Conversion Required

FINAL ANSWER

30868.8385737545 ≈ 30868.84 Pascal <-- Theoretical Maximum Stress

(Calculation completed in 00.020 seconds)

You are here -

Home » Engineering » Civil » Columns » Eccentric Loads on Columns » Typical Short Column Formulas » Theoretical Maximum Stress for Johnson Code Steels

Credits

Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

Rudrani Tidke has created this Calculator and 100+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< Typical Short Column Formulas Calculators

Theoretical Maximum Stress for Johnson Code Steels

LaTeX Go Theoretical Maximum Stress = Stress at any Point y*(1-(Stress at any Point y/(4*Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity))*(Effective Length of Column/Radius of Gyration of Column)^2)

Theoretical Maximum Stress for ANC Code 2017ST Aluminium

LaTeX Go Theoretical Maximum Stress = 34500-(245/sqrt(End Fixity Coefficient))*(Effective Length of Column/Radius of Gyration of Column)

Theoretical Maximum Stress for ANC Code Alloy Steel Tubing

LaTeX Go Theoretical Maximum Stress = 135000-(15.9/End Fixity Coefficient)*(Effective Length of Column/Radius of Gyration of Column)^2

Theoretical Maximum Stress for ANC Code Spruce

LaTeX Go Theoretical Maximum Stress = 5000-(0.5/End Fixity Coefficient)*(Effective Length of Column/Radius of Gyration of Column)^2

Theoretical Maximum Stress for Johnson Code Steels Formula

LaTeX Go

What is Steel?

Steel is an alloy of iron with typically a few percent of carbon to improve its strength and fracture resistance compared to iron. Many other elements may be present or added. Stainless steels that are corrosion- and oxidation-resistant need typically an additional 11% chromium.

How to Calculate Theoretical Maximum Stress for Johnson Code Steels?

Theoretical Maximum Stress for Johnson Code Steels calculator uses Theoretical Maximum Stress = Stress at any Point y*(1-(Stress at any Point y/(4*Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity))*(Effective Length of Column/Radius of Gyration of Column)^2) to calculate the Theoretical Maximum Stress, The Theoretical Maximum Stress for Johnson Code Steels formula is defined as maximum possible stress a perfect solid can withstand, when short blocks or short column are loaded eccentrically in compression or in tension (not through the center of gravity). Theoretical Maximum Stress is denoted by S_cr symbol.

How to calculate Theoretical Maximum Stress for Johnson Code Steels using this online calculator? To use this online calculator for Theoretical Maximum Stress for Johnson Code Steels, enter Stress at any Point y (S_y), Coefficient for Column End Conditions (n), Modulus of Elasticity (E), Effective Length of Column (L) & Radius of Gyration of Column (r_gyration) and hit the calculate button. Here is how the Theoretical Maximum Stress for Johnson Code Steels calculation can be explained with given input values -> 30868.84 = 35000*(1-(35000/(4*2*(pi^2)*50000000))*(3/0.026)^2).

FAQ

What is Theoretical Maximum Stress for Johnson Code Steels?

The Theoretical Maximum Stress for Johnson Code Steels formula is defined as maximum possible stress a perfect solid can withstand, when short blocks or short column are loaded eccentrically in compression or in tension (not through the center of gravity) and is represented as S_cr = S_y*(1-(S_y/(4*n*(pi^2)*E))*(L/r_gyration)^2) or Theoretical Maximum Stress = Stress at any Point y*(1-(Stress at any Point y/(4*Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity))*(Effective Length of Column/Radius of Gyration of Column)^2). Stress at any Point y is unit stress S, at any point y where y is positive for points on the same side of center of gravity, Coefficient for Column End Conditions is defined as the multiplicative factor for different column end conditions, The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality, The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration & The Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.

How to calculate Theoretical Maximum Stress for Johnson Code Steels?

The Theoretical Maximum Stress for Johnson Code Steels formula is defined as maximum possible stress a perfect solid can withstand, when short blocks or short column are loaded eccentrically in compression or in tension (not through the center of gravity) is calculated using Theoretical Maximum Stress = Stress at any Point y*(1-(Stress at any Point y/(4*Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity))*(Effective Length of Column/Radius of Gyration of Column)^2). To calculate Theoretical Maximum Stress for Johnson Code Steels, you need Stress at any Point y (S_y), Coefficient for Column End Conditions (n), Modulus of Elasticity (E), Effective Length of Column (L) & Radius of Gyration of Column (r_gyration). With our tool, you need to enter the respective value for Stress at any Point y, Coefficient for Column End Conditions, Modulus of Elasticity, Effective Length of Column & Radius of Gyration of Column and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Theoretical Maximum Stress?

In this formula, Theoretical Maximum Stress uses Stress at any Point y, Coefficient for Column End Conditions, Modulus of Elasticity, Effective Length of Column & Radius of Gyration of Column. We can use 3 other way(s) to calculate the same, which is/are as follows -

Theoretical Maximum Stress = 135000-(15.9/End Fixity Coefficient)*(Effective Length of Column/Radius of Gyration of Column)^2
Theoretical Maximum Stress = 34500-(245/sqrt(End Fixity Coefficient))*(Effective Length of Column/Radius of Gyration of Column)
Theoretical Maximum Stress = 5000-(0.5/End Fixity Coefficient)*(Effective Length of Column/Radius of Gyration of Column)^2

Home

FREE PDFs

🔍 Search