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
ฯƒmax = (((C*c/(rleast^2))/(1-(ฯƒ/ฯƒE)))+1)*ฯƒ
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
ฯƒmax = (((C*c/(rleast^2))/(1-(ฯƒ/ฯƒE)))+1)*ฯƒ --> (((0.3*0.01/(0.04702^2))/(1-(8/300000)))+1)*8
Evaluating ... ...
ฯƒmax = 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 โ‰ˆ 1.9E-5 Megapascal <-- Maximum Stress at Crack Tip
(Calculation completed in 00.004 seconds)

Credits

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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))

Maximum Stress for Columns with Initial Curvature Formula

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
ฯƒmax = (((C*c/(rleast^2))/(1-(ฯƒ/ฯƒE)))+1)*ฯƒ

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 ฯƒmax 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 (rleast), Direct stress (ฯƒ) & Euler Stress (ฯƒE) 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 ฯƒmax = (((C*c/(rleast^2))/(1-(ฯƒ/ฯƒE)))+1)*ฯƒ 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 (rleast), Direct stress (ฯƒ) & Euler Stress (ฯƒE). 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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