Maximum Stress for Columns with Initial Curvature Calculator

✖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 to Extreme Point [c]			+10% -10%
✖Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.ⓘ Least Radius of Gyration Column [r_least]			+10% -10%
✖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 for Columns with Initial Curvature [σ_max]

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Formula

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Maximum Stress for Columns with Initial Curvature

Formula

σ max = ((\frac{C \cdot \frac{c}{{r least}^{2}}}{1 - (\frac{σ}{σ E})}) + 1) \cdot σ

Example

1.9E-5 MPa = ((\frac{300 mm \cdot \frac{10 mm}{{47.02 mm}^{2}}}{1 - (\frac{0.000008 MPa}{0.3 MPa})}) + 1) \cdot 0.000008 MPa

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Maximum Stress for Columns with Initial Curvature Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
σ_max = (((C*c/(r_least^2))/(1-(σ/σ_E)))+1)*σ
This formula uses 6 Variables

Variables Used

Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum stress at crack tip due to the applied nominal stress.
Maximum initial deflection - (Measured in Meter) - Maximum initial deflection is the degree to which a structural element is displaced under a load.
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.
Least Radius of Gyration Column - (Measured in Meter) - Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.
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.

STEP 1: Convert Input(s) to Base Unit

Maximum initial deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)
Distance from Neutral Axis to Extreme Point: 10 Millimeter --> 0.01 Meter (Check conversion here)
Least Radius of Gyration Column: 47.02 Millimeter --> 0.04702 Meter (Check conversion here)
Direct stress: 8E-06 Megapascal --> 8 Pascal (Check conversion here)
Euler Stress: 0.3 Megapascal --> 300000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_max = (((C*c/(r_least^2))/(1-(σ/σ_E)))+1)*σ --> (((0.3*0.01/(0.04702^2))/(1-(8/300000)))+1)*8

Evaluating ... ...

σ_max = 18.8556935133475

STEP 3: Convert Result to Output's Unit

18.8556935133475 Pascal -->1.88556935133475E-05 Megapascal (Check conversion here)

FINAL ANSWER

1.88556935133475E-05 ≈ 1.9E-5 Megapascal <-- Maximum Stress at Crack Tip

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Columns With Initial Curvature Calculators

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

Modulus of Elasticity given Euler Load

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

Euler Load

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

Maximum Stress for Columns with Initial Curvature 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 Maximum Stress for Columns with Initial Curvature?

Maximum Stress for Columns with Initial Curvature calculator uses 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 to calculate the Maximum Stress at Crack Tip, The Maximum stress for columns with initial curvature formula is defined as one of the most extensively used failure criteria to predict the failure of composite materials as this criterion is less complicated. Maximum Stress at Crack Tip is denoted by σ_max symbol.

How to calculate Maximum Stress for Columns with Initial Curvature using this online calculator? To use this online calculator for Maximum Stress for Columns with Initial Curvature, enter Maximum initial deflection (C), Distance from Neutral Axis to Extreme Point (c), Least Radius of Gyration Column (r_least), Direct stress (σ) & Euler Stress (σ_E) and hit the calculate button. Here is how the Maximum Stress for Columns with Initial Curvature calculation can be explained with given input values -> 1.9E-11 = (((0.3*0.01/(0.04702^2))/(1-(8/300000)))+1)*8.

FAQ

What is Maximum Stress for Columns with Initial Curvature?

The Maximum stress for columns with initial curvature formula is defined as one of the most extensively used failure criteria to predict the failure of composite materials as this criterion is less complicated and is represented as σ_max = (((C*c/(r_least^2))/(1-(σ/σ_E)))+1)*σ or 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. Maximum initial deflection is the degree to which a structural element is displaced under a load, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point, Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations, 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.

How to calculate Maximum Stress for Columns with Initial Curvature?

The Maximum stress for columns with initial curvature formula is defined as one of the most extensively used failure criteria to predict the failure of composite materials as this criterion is less complicated is calculated using 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. To calculate Maximum Stress for Columns with Initial Curvature, you need Maximum initial deflection (C), Distance from Neutral Axis to Extreme Point (c), Least Radius of Gyration Column (r_least), Direct stress (σ) & Euler Stress (σ_E). With our tool, you need to enter the respective value for Maximum initial deflection, Distance from Neutral Axis to Extreme Point, Least Radius of Gyration Column, Direct stress & Euler Stress 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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