FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Theoretical Maximum Stress for Johnson Code Steels Formula

GoTheoretical Maximum Stress for ANC Code Alloy Steel Tubing Formula

GoTheoretical Maximum Stress for ANC Code 2017ST Aluminium Formula

Fx Copy

LaTeX Copy

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. Check FAQs

S cr = S y \cdot (1 - (\frac{S y}{4 \cdot n \cdot (π^{2}) \cdot E}) \cdot {(\frac{L}{r gyration})}^{2})

S_cr - Theoretical Maximum Stress?S_y - Stress at any Point y?n - Coefficient for Column End Conditions?E - Modulus of Elasticity?L - Effective Length of Column?r_gyration - Radius of Gyration of Column?π - Archimedes' constant?

Theoretical Maximum Stress for Johnson Code Steels Example

With values

With units

Only example

Here is how the Theoretical Maximum Stress for Johnson Code Steels equation looks like with Values.

Here is how the Theoretical Maximum Stress for Johnson Code Steels equation looks like with Units.

Here is how the Theoretical Maximum Stress for Johnson Code Steels equation looks like.

30868.8386 = 35000 \cdot (1 - (\frac{35000}{4 \cdot 2 \cdot ({3.1416}^{2}) \cdot 50}) \cdot {(\frac{3000}{26})}^{2})

30868.8386Pa = 35000Pa \cdot (1 - (\frac{35000Pa}{4 \cdot 2 \cdot ({3.1416}^{2}) \cdot 50MPa}) \cdot {(\frac{3000mm}{26mm})}^{2})

30868.8386 = 35000 \cdot (1 - (\frac{35000}{4 \cdot 2 \cdot ({3.1416}^{2}) \cdot 50}) \cdot {(\frac{3000}{26})}^{2})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Civil » Category

Columns » fx Theoretical Maximum Stress for Johnson Code Steels

Theoretical Maximum Stress for Johnson Code Steels Solution

Follow our step by step solution on how to calculate Theoretical Maximum Stress for Johnson Code Steels?

FIRST Step Consider the formula

S cr = S y \cdot (1 - (\frac{S y}{4 \cdot n \cdot (π^{2}) \cdot E}) \cdot {(\frac{L}{r gyration})}^{2})

Next Step Substitute values of Variables

∴

S cr = 35000Pa \cdot (1 - (\frac{35000Pa}{4 \cdot 2 \cdot (π^{2}) \cdot 50MPa}) \cdot {(\frac{3000mm}{26mm})}^{2})

Next Step Substitute values of Constants

∴

S cr = 35000Pa \cdot (1 - (\frac{35000Pa}{4 \cdot 2 \cdot ({3.1416}^{2}) \cdot 50MPa}) \cdot {(\frac{3000mm}{26mm})}^{2})

Next Step Convert Units

∴

S cr = 35000Pa \cdot (1 - (\frac{35000Pa}{4 \cdot 2 \cdot ({3.1416}^{2}) \cdot 5E+7Pa}) \cdot {(\frac{3m}{0.026m})}^{2})

Next Step Prepare to Evaluate

∴

S cr = 35000 \cdot (1 - (\frac{35000}{4 \cdot 2 \cdot ({3.1416}^{2}) \cdot 5E+7}) \cdot {(\frac{3}{0.026})}^{2})

Next Step Evaluate

∴

S cr = 30868.8385737545Pa

LAST Step Rounding Answer

∴

S cr = 30868.8386Pa

Theoretical Maximum Stress for Johnson Code Steels Formula Elements

Variables

Constants

Theoretical Maximum Stress

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.

Symbol: S_cr

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Theoretical Maximum Stress

Stress at any Point y

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.

Symbol: S_y

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Stress at any Point y

Coefficient for Column End Conditions

Coefficient for Column End Conditions is defined as the multiplicative factor for different column end conditions.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Coefficient for Column End Conditions

Modulus of Elasticity

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.

Symbol: E

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Effective Length of Column

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.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Radius of Gyration of Column

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.

Symbol: r_gyration

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration of Column

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Theoretical Maximum Stress

Go Theoretical Maximum Stress for ANC Code Alloy Steel Tubing

S cr = 135000 - (\frac{15.9}{c}) \cdot {(\frac{L}{r gyration})}^{2}

Go Theoretical Maximum Stress for ANC Code 2017ST Aluminium

S cr = 34500 - (\frac{245}{\sqrt{c}}) \cdot (\frac{L}{r gyration})

Go Theoretical Maximum Stress for ANC Code Spruce

S cr = 5000 - (\frac{0.5}{c}) \cdot {(\frac{L}{r gyration})}^{2}

Other formulas in Typical Short Column Formulas category

Go Critical Stress for Carbon Steel by AISC code

S w = 17000 - 0.485 \cdot {(\frac{L}{r gyration})}^{2}

Go Critical Stress for Carbon Steel by Chicago code

S w = 16000 - 70 \cdot (\frac{L}{r gyration})

Go Critical Stress for Carbon Steel by AREA code

S w = 15000 - 50 \cdot (\frac{L}{r gyration})

Go Critical Stress for Carbon Steel by Am. Br. Co. code

S w = 19000 - 100 \cdot (\frac{L}{r gyration})

How to Evaluate Theoretical Maximum Stress for Johnson Code Steels?

Theoretical Maximum Stress for Johnson Code Steels evaluator 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 evaluate 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 evaluate Theoretical Maximum Stress for Johnson Code Steels using this online evaluator? To use this online evaluator 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.

FAQs on Theoretical Maximum Stress for Johnson Code Steels

What is the formula to find Theoretical Maximum Stress for Johnson Code Steels?

The formula of Theoretical Maximum Stress for Johnson Code Steels is expressed as 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). Here is an example- 30868.84 = 35000*(1-(35000/(4*2*(pi^2)*50000000))*(3/0.026)^2).

How to calculate Theoretical Maximum Stress for Johnson Code Steels?

With 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) we can find Theoretical Maximum Stress for Johnson Code Steels using the formula - 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). This formula also uses Archimedes' constant .

What are the other ways to Calculate Theoretical Maximum Stress?

Here are the different ways to Calculate Theoretical Maximum Stress-

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

Can the Theoretical Maximum Stress for Johnson Code Steels be negative?

No, the Theoretical Maximum Stress for Johnson Code Steels, measured in Stress cannot be negative.

Which unit is used to measure Theoretical Maximum Stress for Johnson Code Steels?

Theoretical Maximum Stress for Johnson Code Steels is usually measured using the Pascal[Pa] for Stress. Newton per Square Meter[Pa], Newton per Square Millimeter[Pa], Kilonewton per Square Meter[Pa] are the few other units in which Theoretical Maximum Stress for Johnson Code Steels can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Theoretical Maximum Stress for Johnson Code Steels Formula

​GoTheoretical Maximum Stress for ANC Code Alloy Steel Tubing Formula

​GoTheoretical Maximum Stress for ANC Code 2017ST Aluminium Formula

Theoretical Maximum Stress for Johnson Code Steels Example

Theoretical Maximum Stress for Johnson Code Steels Solution

Theoretical Maximum Stress for Johnson Code Steels Formula Elements

Other Formulas to find Theoretical Maximum Stress

Other formulas in Typical Short Column Formulas category

How to Evaluate Theoretical Maximum Stress for Johnson Code Steels?

FAQs on Theoretical Maximum Stress for Johnson Code Steels

Variable Name

GoTheoretical Maximum Stress for ANC Code Alloy Steel Tubing Formula

GoTheoretical Maximum Stress for ANC Code 2017ST Aluminium Formula