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 deformation that a structural component experiences before any external load is applied or due to inherent imperfections such as residual stresses etc.ⓘ Initial Deflection at Distance X from end A [y']

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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 deformation that a structural component experiences before any external load is applied or due to inherent imperfections such as residual stresses etc.
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 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Initial Curvature » Initial Deflection at Distance X from end A

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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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< Columns With Initial Curvature Calculators

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

LaTeX 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

LaTeX Go Distance of Deflection from end A = (asin(Initial Deflection/Maximum Initial Deflection))*Length of Column/pi

Modulus of Elasticity given Euler Load

LaTeX Go Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia)

Euler Load

LaTeX Go Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)

Initial Deflection at Distance X from end A Formula

LaTeX Go

Initial Deflection = Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)
y' = C*sin((pi*x)/l)

What is Deflection?

Deflection refers to the displacement or deformation of a structural element, such as a beam, column, or cantilever, under an applied load. It is the distance by which a point on the element moves from its original, unloaded position due to the forces or moments acting on it.

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 a measure of the initial curvature of a column at a specific distance from one end, providing insight into the column's deformation under load, essential for structural analysis and design in civil engineering. 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 a measure of the initial curvature of a column at a specific distance from one end, providing insight into the column's deformation under load, essential for structural analysis and design in civil engineering 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 a measure of the initial curvature of a column at a specific distance from one end, providing insight into the column's deformation under load, essential for structural analysis and design in civil engineering 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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