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

STEP 0: Pre-Calculation Summary
Formula Used
Distance of deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))*Length of column/pi
x = (asin(δc/((1/(1-(P/PE)))*C)))*l/pi
This formula uses 1 Constants, 2 Functions, 6 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
Distance of deflection from end A - (Measured in Meter) - Distance of deflection from end A is the distance x of deflection from end A.
Deflection of Column - (Measured in Meter) - Deflection of Column at free end in terms of moment at the section of column with eccentric load.
Crippling Load - (Measured in Newton) - Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.
Euler Load - (Measured in Newton) - Euler load is the compressive load at which a slender column will suddenly bend or buckle.
Maximum initial deflection - (Measured in Meter) - Maximum initial deflection is the degree to which a structural element is displaced under a load.
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.
STEP 1: Convert Input(s) to Base Unit
Deflection of Column: 12 Millimeter --> 0.012 Meter (Check conversion here)
Crippling Load: 3.6 Kilonewton --> 3600 Newton (Check conversion here)
Euler Load: 4 Kilonewton --> 4000 Newton (Check conversion here)
Maximum initial deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)
Length of column: 5000 Millimeter --> 5 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
x = (asin(δc/((1/(1-(P/PE)))*C)))*l/pi --> (asin(0.012/((1/(1-(3600/4000)))*0.3)))*5/pi
Evaluating ... ...
x = 0.00636621470032531
STEP 3: Convert Result to Output's Unit
0.00636621470032531 Meter -->6.36621470032531 Millimeter (Check conversion here)
FINAL ANSWER
6.36621470032531 6.366215 Millimeter <-- Distance of deflection from end A
(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))

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

Distance of deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))*Length of column/pi
x = (asin(δc/((1/(1-(P/PE)))*C)))*l/pi

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

Value of Distance 'X' given Final Deflection at Distance X from end A of Column calculator uses Distance of deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))*Length of column/pi to calculate the Distance of deflection from end A, The Value of distance 'x' given final deflection at distance x from end A of column formula is defined as the distance of deflection from end A of the column. Distance of deflection from end A is denoted by x symbol.

How to calculate Value of Distance 'X' given Final Deflection at Distance X from end A of Column using this online calculator? To use this online calculator for Value of Distance 'X' given Final Deflection at Distance X from end A of Column, enter Deflection of Column c), Crippling Load (P), Euler Load (PE), Maximum initial deflection (C) & Length of column (l) and hit the calculate button. Here is how the Value of Distance 'X' given Final Deflection at Distance X from end A of Column calculation can be explained with given input values -> 6366.215 = (asin(0.012/((1/(1-(3600/4000)))*0.3)))*5/pi.

FAQ

What is Value of Distance 'X' given Final Deflection at Distance X from end A of Column?
The Value of distance 'x' given final deflection at distance x from end A of column formula is defined as the distance of deflection from end A of the column and is represented as x = (asin(δc/((1/(1-(P/PE)))*C)))*l/pi or Distance of deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))*Length of column/pi. Deflection of Column at free end in terms of moment at the section of column with eccentric load, Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself, Euler load is the compressive load at which a slender column will suddenly bend or buckle, Maximum initial deflection is the degree to which a structural element is displaced under a load & 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.
How to calculate Value of Distance 'X' given Final Deflection at Distance X from end A of Column?
The Value of distance 'x' given final deflection at distance x from end A of column formula is defined as the distance of deflection from end A of the column is calculated using Distance of deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))*Length of column/pi. To calculate Value of Distance 'X' given Final Deflection at Distance X from end A of Column, you need Deflection of Column c), Crippling Load (P), Euler Load (PE), Maximum initial deflection (C) & Length of column (l). With our tool, you need to enter the respective value for Deflection of Column, Crippling Load, Euler Load, Maximum initial deflection & Length of column 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 Distance of deflection from end A?
In this formula, Distance of deflection from end A uses Deflection of Column, Crippling Load, Euler Load, Maximum initial deflection & Length of column. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Distance of deflection from end A = (asin(Initial Deflection/Maximum initial deflection))*Length of column/pi
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