Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns Calculator

✖The direct stress is defined as axial thrust acting per unit area.ⓘ Direct stress [σ]			+10% -10%
✖Euler stress is the stress in column with curvature due to Euler load.ⓘ Euler Stress [σ_E]			+10% -10%
✖Maximum stress at crack tip due to the applied nominal stress.ⓘ Maximum Stress at Crack Tip [σ_max]			+10% -10%
✖The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.ⓘ Radius of Gyration [k_G]			+10% -10%
✖Maximum initial deflection is the degree to which a structural element is displaced under a load.ⓘ Maximum initial deflection [C]			+10% -10%

✖Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.ⓘ Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns [c]

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Formula

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Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns

Formula

`"c" = (1-("σ"/"σ"_{"E"}))*(("σ"_{"max"}/"σ")-1)*("k"_{"G"}^2)/"C"`

Example

`"49.91867mm"=(1-("0.000008MPa"/"0.3MPa"))*(("0.00006MPa"/"0.000008MPa")-1)*(("48mm")^2)/"300mm"`

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Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance from Neutral Axis to Extreme Point = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Maximum initial deflection
c = (1-(σ/σ_E))*((σ_max/σ)-1)*(k_G^2)/C
This formula uses 6 Variables

Variables Used

Distance from Neutral Axis to Extreme Point - (Measured in Meter) - Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.
Direct stress - (Measured in Pascal) - The direct stress is defined as axial thrust acting per unit area.
Euler Stress - (Measured in Pascal) - Euler stress is the stress in column with curvature due to Euler load.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum stress at crack tip due to the applied nominal stress.
Radius of Gyration - (Measured in Meter) - The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.
Maximum initial deflection - (Measured in Meter) - Maximum initial deflection is the degree to which a structural element is displaced under a load.

STEP 1: Convert Input(s) to Base Unit

Direct stress: 8E-06 Megapascal --> 8 Pascal (Check conversion here)
Euler Stress: 0.3 Megapascal --> 300000 Pascal (Check conversion here)
Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion here)
Radius of Gyration: 48 Millimeter --> 0.048 Meter (Check conversion here)
Maximum initial deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c = (1-(σ/σ_E))*((σ_max/σ)-1)*(k_G^2)/C --> (1-(8/300000))*((60/8)-1)*(0.048^2)/0.3

Evaluating ... ...

c = 0.0499186688

STEP 3: Convert Result to Output's Unit

0.0499186688 Meter -->49.9186688 Millimeter (Check conversion here)

FINAL ANSWER

49.9186688 ≈ 49.91867 Millimeter <-- Distance from Neutral Axis to Extreme Point

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Columns With Initial Curvature » Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns

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National Institute Of Technology (NIT), Hamirpur

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< 19 Columns With Initial Curvature Calculators

Radius of Gyration given Maximum Stress for Columns with Initial Curvature

Go Radius of Gyration = sqrt((Maximum initial deflection*Distance from Neutral Axis to Extreme Point)/(1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1))

Euler Stress given Maximum Stress for Columns with Initial Curvature

Go Euler Stress = Direct stress/(1-((Maximum initial deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/((Maximum Stress at Crack Tip/Direct stress)-1)))

Maximum Stress for Columns with Initial Curvature

Go Maximum Stress at Crack Tip = (((Maximum initial deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/(1-(Direct stress/Euler Stress)))+1)*Direct stress

Length of Column given Final Deflection at Distance X from End A of Column

Go Length of column = (pi*Distance of deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))

Value of Distance 'X' given Final Deflection at Distance X from end A of Column

Go Distance of deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))*Length of column/pi

Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns

Go Distance from Neutral Axis to Extreme Point = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Maximum initial deflection

Crippling Load given Final Deflection at Distance X from end A of Column

Go Crippling Load = (1-(Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)/Deflection of Column))*Euler Load

Euler Load given Final Deflection at Distance X from end A of Column

Go Euler Load = Crippling Load/(1-(Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)/Deflection of Column))

Length of Column given Initial Deflection at Distance X from end A

Go Length of column = (pi*Distance of deflection from end A)/(asin(Initial Deflection/Maximum initial deflection))

Value of Distance 'X' given Initial Deflection at Distance X from end A

Go Distance of deflection from end A = (asin(Initial Deflection/Maximum initial deflection))*Length of column/pi

Length of Column given Euler Load

Go Length of column = sqrt(((pi^2)*Modulus of elasticity of column*Moment of Inertia)/(Euler Load))

Modulus of Elasticity given Euler Load

Go Modulus of elasticity of column = (Euler Load*(Length of column^2))/((pi^2)*Moment of Inertia)

Moment of Inertia given Euler Load

Go Moment of Inertia = (Euler Load*(Length of column^2))/((pi^2)*Modulus of elasticity of column)

Euler Load

Go Euler Load = ((pi^2)*Modulus of elasticity of column*Moment of Inertia)/(Length of column^2)

Crippling Load given Maximum Deflection for Columns with Initial Curvature

Go Crippling Load = (1-(Maximum initial deflection/Deflection of Column))*Euler Load

Euler Load given Maximum Deflection for Columns with Initial Curvature

Go Euler Load = Crippling Load/(1-(Maximum initial deflection/Deflection of Column))

Crippling Load given Factor of Safety

Go Crippling Load = (1-(1/Factor of Safety))*Euler Load

Factor of Safety given Euler Load

Go Factor of Safety = 1/(1-(Crippling Load/Euler Load))

Euler Load given Factor of Safety

Go Euler Load = Crippling Load/(1-(1/Factor of Safety))

Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns Formula

What is buckling or crippling load?

Buckling Load is the highest load at which the column will buckle. Crippling load is the max load beyond that load, it cant use further it becomes disable to use.

How to Calculate Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns?

Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns calculator uses Distance from Neutral Axis to Extreme Point = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Maximum initial deflection to calculate the Distance from Neutral Axis to Extreme Point, The Distance from neutral axis of extreme layer given maximum stress for columns formula is defined as the distance of the extreme layer of the column from the neutral axis. Distance from Neutral Axis to Extreme Point is denoted by c symbol.

How to calculate Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns using this online calculator? To use this online calculator for Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns, enter Direct stress (σ), Euler Stress (σ_E), Maximum Stress at Crack Tip (σ_max), Radius of Gyration (k_G) & Maximum initial deflection (C) and hit the calculate button. Here is how the Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns calculation can be explained with given input values -> 49918.67 = (1-(8/300000))*((60/8)-1)*(0.048^2)/0.3.

FAQ

What is Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns?

The Distance from neutral axis of extreme layer given maximum stress for columns formula is defined as the distance of the extreme layer of the column from the neutral axis and is represented as c = (1-(σ/σ_E))*((σ_max/σ)-1)*(k_G^2)/C or Distance from Neutral Axis to Extreme Point = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Maximum initial deflection. The direct stress is defined as axial thrust acting per unit area, Euler stress is the stress in column with curvature due to Euler load, Maximum stress at crack tip due to the applied nominal stress, The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass & Maximum initial deflection is the degree to which a structural element is displaced under a load.

How to calculate Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns?

The Distance from neutral axis of extreme layer given maximum stress for columns formula is defined as the distance of the extreme layer of the column from the neutral axis is calculated using Distance from Neutral Axis to Extreme Point = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Maximum initial deflection. To calculate Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns, you need Direct stress (σ), Euler Stress (σ_E), Maximum Stress at Crack Tip (σ_max), Radius of Gyration (k_G) & Maximum initial deflection (C). With our tool, you need to enter the respective value for Direct stress, Euler Stress, Maximum Stress at Crack Tip, Radius of Gyration & Maximum initial deflection 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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