Maximum Initial Deflection given Final Deflection at Distance X from End A of Column Calculator

✖Deflection of Column at free end in terms of moment at the section of column with eccentric load.ⓘ Deflection of Column [δ_c]			+10% -10%
✖Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.ⓘ Crippling Load [P]			+10% -10%
✖Euler load is the compressive load at which a slender column will suddenly bend or buckle.ⓘ Euler Load [P_E]			+10% -10%
✖Distance of deflection from end A is the distance x of deflection from end A.ⓘ Distance of deflection from end A [x]			+10% -10%
✖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.ⓘ Length of column [l]			+10% -10%

✖Maximum initial deflection is the degree to which a structural element is displaced under a load.ⓘ Maximum Initial Deflection given Final Deflection at Distance X from End A of Column [C]

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Maximum Initial Deflection given Final Deflection at Distance X from End A of Column

Formula

`"C" = "δ"_{"c"}/((1/(1-("P"/"P"_{"E"})))*sin((pi*"x")/"l"))`

Example

`"54.57181mm"="12mm"/((1/(1-("3.6kN"/"4kN")))*sin((pi*"35mm")/"5000mm"))`

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Maximum Initial Deflection given Final Deflection at Distance X from End A of Column Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum initial deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of deflection from end A)/Length of column))
C = δ_c/((1/(1-(P/P_E)))*sin((pi*x)/l))
This formula uses 1 Constants, 1 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)

Variables Used

Maximum initial deflection - (Measured in Meter) - Maximum initial deflection is the degree to which a structural element is displaced under a load.
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.
Distance of deflection from end A - (Measured in Meter) - Distance of deflection from end A is the distance x of deflection from end A.
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)
Distance of deflection from end A: 35 Millimeter --> 0.035 Meter (Check conversion here)
Length of column: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = δ_c/((1/(1-(P/P_E)))*sin((pi*x)/l)) --> 0.012/((1/(1-(3600/4000)))*sin((pi*0.035)/5))

Evaluating ... ...

C = 0.0545718075379596

STEP 3: Convert Result to Output's Unit

0.0545718075379596 Meter -->54.5718075379596 Millimeter (Check conversion here)

FINAL ANSWER

54.5718075379596 ≈ 54.57181 Millimeter <-- Maximum initial deflection

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Columns With Initial Curvature » Deflection » Maximum Initial Deflection given Final Deflection at Distance X from End A of Column

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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< 8 Deflection Calculators

Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load

Go Distance b/w fixed end and deflection point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))

Maximum Initial Deflection given Final Deflection at Distance X from End A of Column

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

Final Deflection at Distance X from end A of Column

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

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature

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

Maximum Initial Deflection given Initial Deflection at Distance X from A

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

Initial Deflection at Distance X from end A

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

Maximum Initial Deflection given Maximum Deflection for Columns with Initial Curvature

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

Maximum Deflection for Columns with Initial Curvature

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

Maximum Initial Deflection given Final Deflection at Distance X from End A of Column Formula

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

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 Initial Deflection given Final Deflection at Distance X from End A of Column?

Maximum Initial Deflection given Final Deflection at Distance X from End A of Column calculator uses Maximum initial deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of deflection from end A)/Length of column)) to calculate the Maximum initial deflection, The Maximum initial deflection given final deflection at distance x from end A of column formula is defined as the degree to which a structural element is displaced under a load. Maximum initial deflection is denoted by C symbol.

How to calculate Maximum Initial Deflection given Final Deflection at Distance X from End A of Column using this online calculator? To use this online calculator for Maximum Initial Deflection given Final Deflection at Distance X from End A of Column, enter Deflection of Column (δ_c), Crippling Load (P), Euler Load (P_E), Distance of deflection from end A (x) & Length of column (l) and hit the calculate button. Here is how the Maximum Initial Deflection given Final Deflection at Distance X from End A of Column calculation can be explained with given input values -> 54571.81 = 0.012/((1/(1-(3600/4000)))*sin((pi*0.035)/5)).

FAQ

What is Maximum Initial Deflection given Final Deflection at Distance X from End A of Column?

The Maximum initial deflection given final deflection at distance x from end A of column formula is defined as the degree to which a structural element is displaced under a load and is represented as C = δ_c/((1/(1-(P/P_E)))*sin((pi*x)/l)) or Maximum initial deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of deflection from end A)/Length of column)). 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, Distance of deflection from end A is the distance x of deflection from end A & 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 Maximum Initial Deflection given Final Deflection at Distance X from End A of Column?

The Maximum initial deflection given final deflection at distance x from end A of column formula is defined as the degree to which a structural element is displaced under a load is calculated using Maximum initial deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of deflection from end A)/Length of column)). To calculate Maximum Initial Deflection given Final Deflection at Distance X from End A of Column, you need Deflection of Column (δ_c), Crippling Load (P), Euler Load (P_E), Distance of deflection from end A (x) & Length of column (l). With our tool, you need to enter the respective value for Deflection of Column, Crippling Load, Euler Load, Distance of deflection from end A & 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 Maximum initial deflection?

In this formula, Maximum initial deflection uses Deflection of Column, Crippling Load, Euler Load, Distance of deflection from end A & Length of column. We can use 3 other way(s) to calculate the same, which is/are as follows -

Maximum initial deflection = Initial Deflection/sin((pi*Distance of deflection from end A)/Length of column)
Maximum initial deflection = Deflection of Column/(1/(1-(Crippling Load/Euler Load)))
Maximum initial deflection = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point

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