Initial Deflection at Distance X from end A Calculator

✖Maximum initial deflection is the degree to which a structural element is displaced under a load.ⓘ Maximum initial deflection [C]			+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%

✖Initial Deflection is the deflection caused in the column at a distance x from end A.ⓘ Initial Deflection at Distance X from end A [y']

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Formula

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Initial Deflection at Distance X from end A

Formula

`"y'" = "C"*sin((pi*"x")/"l")`

Example

`"6.596813mm"="300mm"*sin((pi*"35mm")/"5000mm")`

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Initial Deflection at Distance X from end A Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Deflection = Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)
y' = C*sin((pi*x)/l)
This formula uses 1 Constants, 1 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)

Variables Used

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.
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

Maximum initial deflection: 300 Millimeter --> 0.3 Meter (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

y' = C*sin((pi*x)/l) --> 0.3*sin((pi*0.035)/5)

Evaluating ... ...

y' = 0.00659681282775153

STEP 3: Convert Result to Output's Unit

0.00659681282775153 Meter -->6.59681282775153 Millimeter (Check conversion here)

FINAL ANSWER

6.59681282775153 ≈ 6.596813 Millimeter <-- Initial Deflection

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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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

Initial Deflection at Distance X from end A Formula

Initial Deflection = Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)
y' = C*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 Initial Deflection at Distance X from end A?

Initial Deflection at Distance X from end A calculator uses Initial Deflection = Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column) to calculate the Initial Deflection, The Initial deflection at distance x from end A formula is defined as the degree to which a structural element is displaced under a load. Initial Deflection is denoted by y' symbol.

How to calculate Initial Deflection at Distance X from end A using this online calculator? To use this online calculator for Initial Deflection at Distance X from end A, enter Maximum initial deflection (C), Distance of deflection from end A (x) & Length of column (l) and hit the calculate button. Here is how the Initial Deflection at Distance X from end A calculation can be explained with given input values -> 6596.813 = 0.3*sin((pi*0.035)/5).

FAQ

What is Initial Deflection at Distance X from end A?

The Initial deflection at distance x from end A formula is defined as the degree to which a structural element is displaced under a load and is represented as y' = C*sin((pi*x)/l) or Initial Deflection = Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column). Maximum initial deflection is the degree to which a structural element is displaced under a load, 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 Initial Deflection at Distance X from end A?

The Initial deflection at distance x from end A formula is defined as the degree to which a structural element is displaced under a load is calculated using Initial Deflection = Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column). To calculate Initial Deflection at Distance X from end A, you need Maximum initial deflection (C), Distance of deflection from end A (x) & Length of column (l). With our tool, you need to enter the respective value for Maximum initial deflection, 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.

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