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

STEP 0: Pre-Calculation Summary
Formula Used
Length of column = (pi*Distance of deflection from end A)/(asin(Initial Deflection/Maximum initial deflection))
l = (pi*x)/(asin(y'/C))
This formula uses 1 Constants, 2 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)
Variables Used
Length of column - (Measured in Meter) - Length of column is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
Distance of deflection from end A - (Measured in Meter) - Distance of deflection from end A is the distance x of deflection from end A.
Initial Deflection - (Measured in Meter) - Initial Deflection is the deflection caused in the column at a distance x from end A.
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
Distance of deflection from end A: 35 Millimeter --> 0.035 Meter (Check conversion here)
Initial Deflection: 60 Millimeter --> 0.06 Meter (Check conversion here)
Maximum initial deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = (pi*x)/(asin(y'/C)) --> (pi*0.035)/(asin(0.06/0.3))
Evaluating ... ...
l = 0.54607110782663
STEP 3: Convert Result to Output's Unit
0.54607110782663 Meter -->546.07110782663 Millimeter (Check conversion here)
FINAL ANSWER
546.07110782663 โ‰ˆ 546.0711 Millimeter <-- Length of column
(Calculation completed in 00.020 seconds)

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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))

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

Length of column = (pi*Distance of deflection from end A)/(asin(Initial Deflection/Maximum initial deflection))
l = (pi*x)/(asin(y'/C))

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

Length of Column given Initial Deflection at Distance X from end A calculator uses Length of column = (pi*Distance of deflection from end A)/(asin(Initial Deflection/Maximum initial deflection)) to calculate the Length of column, The Length of column given initial deflection at distance x from end A formula is defined as the vertical distance between two floors or between two tie levels. Length of column is denoted by l symbol.

How to calculate Length of Column given Initial Deflection at Distance X from end A using this online calculator? To use this online calculator for Length of Column given Initial Deflection at Distance X from end A, enter Distance of deflection from end A (x), Initial Deflection (y') & Maximum initial deflection (C) and hit the calculate button. Here is how the Length of Column given Initial Deflection at Distance X from end A calculation can be explained with given input values -> 546071.1 = (pi*0.035)/(asin(0.06/0.3)).

FAQ

What is Length of Column given Initial Deflection at Distance X from end A?
The Length of column given initial deflection at distance x from end A formula is defined as the vertical distance between two floors or between two tie levels and is represented as l = (pi*x)/(asin(y'/C)) or Length of column = (pi*Distance of deflection from end A)/(asin(Initial Deflection/Maximum initial deflection)). Distance of deflection from end A is the distance x of deflection from end A, Initial Deflection is the deflection caused in the column at a distance x from end A & Maximum initial deflection is the degree to which a structural element is displaced under a load.
How to calculate Length of Column given Initial Deflection at Distance X from end A?
The Length of column given initial deflection at distance x from end A formula is defined as the vertical distance between two floors or between two tie levels is calculated using Length of column = (pi*Distance of deflection from end A)/(asin(Initial Deflection/Maximum initial deflection)). To calculate Length of Column given Initial Deflection at Distance X from end A, you need Distance of deflection from end A (x), Initial Deflection (y') & Maximum initial deflection (C). With our tool, you need to enter the respective value for Distance of deflection from end A, Initial Deflection & Maximum initial deflection 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 Length of column?
In this formula, Length of column uses Distance of deflection from end A, Initial Deflection & Maximum initial deflection. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Length of column = sqrt(((pi^2)*Modulus of elasticity of column*Moment of Inertia)/(Euler Load))
  • Length of column = (pi*Distance of deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))
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