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Maximum Initial Deflection given Initial Deflection at Distance X from A Formula

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

GoMaximum Initial Deflection given Maximum Deflection for Columns with Initial Curvature Formula

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Maximum Initial Deflection is the degree to which a structural element is displaced under a load. Check FAQs

C = \frac{y'}{\sin (\frac{π \cdot x}{l})}

C - Maximum Initial Deflection?y' - Initial Deflection?x - Distance of Deflection from end A?l - Length of Column?π - Archimedes' constant?

Maximum Initial Deflection given Initial Deflection at Distance X from A Example

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Here is how the Maximum Initial Deflection given Initial Deflection at Distance X from A equation looks like with Values.

Here is how the Maximum Initial Deflection given Initial Deflection at Distance X from A equation looks like with Units.

Here is how the Maximum Initial Deflection given Initial Deflection at Distance X from A equation looks like.

2728.5904 = \frac{60}{\sin (\frac{3.1416 \cdot 35}{5000})}

2728.5904mm = \frac{60mm}{\sin (\frac{3.1416 \cdot 35mm}{5000mm})}

2728.5904 = \frac{60}{\sin (\frac{3.1416 \cdot 35}{5000})}

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Maximum Initial Deflection given Initial Deflection at Distance X from A Solution

Follow our step by step solution on how to calculate Maximum Initial Deflection given Initial Deflection at Distance X from A?

FIRST Step Consider the formula

C = \frac{y'}{\sin (\frac{π \cdot x}{l})}

Next Step Substitute values of Variables

∴

C = \frac{60mm}{\sin (\frac{π \cdot 35mm}{5000mm})}

Next Step Substitute values of Constants

∴

C = \frac{60mm}{\sin (\frac{3.1416 \cdot 35mm}{5000mm})}

Next Step Convert Units

∴

C = \frac{0.06m}{\sin (\frac{3.1416 \cdot 0.035m}{5m})}

Next Step Prepare to Evaluate

∴

C = \frac{0.06}{\sin (\frac{3.1416 \cdot 0.035}{5})}

Next Step Evaluate

∴

C = 2.72859037689798m

Next Step Convert to Output's Unit

∴

C = 2728.59037689798mm

LAST Step Rounding Answer

∴

C = 2728.5904mm

Maximum Initial Deflection given Initial Deflection at Distance X from A Formula Elements

Variables

Constants

Functions

Maximum Initial Deflection

Maximum Initial Deflection is the degree to which a structural element is displaced under a load.

Symbol: C

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Maximum Initial Deflection

Initial Deflection

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.

Symbol: y'

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Initial Deflection

Distance of Deflection from end A

Distance of Deflection from end A is the distance x of deflection from end A.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance of Deflection from end A

Length of Column

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.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Column

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

Other Formulas to find Maximum Initial Deflection

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

C = \frac{δ c}{(\frac{1}{1 - (\frac{P}{P E})}) \cdot \sin (\frac{π \cdot x}{l})}

Go Maximum Initial Deflection given Maximum Deflection for Columns with Initial Curvature

C = \frac{δ c}{\frac{1}{1 - (\frac{P}{P E})}}

Go Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature

C = (1 - (\frac{σ}{σ E})) \cdot ((\frac{σ max}{σ}) - 1) \cdot \frac{{k G}^{2}}{c}

Other formulas in Columns With Initial Curvature category

Go Value of Distance 'X' given Initial Deflection at Distance X from end A

x = (a \sin (\frac{y'}{C})) \cdot \frac{l}{π}

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

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

Go Euler Load

P E = \frac{(π^{2}) \cdot ε column \cdot I}{l^{2}}

Go Modulus of Elasticity given Euler Load

ε column = \frac{P E \cdot (l^{2})}{π^{2} \cdot I}

How to Evaluate Maximum Initial Deflection given Initial Deflection at Distance X from A?

Maximum Initial Deflection given Initial Deflection at Distance X from A evaluator uses Maximum Initial Deflection = Initial Deflection/sin((pi*Distance of Deflection from end A)/Length of Column) to evaluate the Maximum Initial Deflection, The Maximum Initial Deflection given Initial Deflection at Distance X from A formula is defined as a measure of the maximum deflection of a column from its original position due to an initial curvature, providing insights into the structural behavior of columns under various loads. Maximum Initial Deflection is denoted by C symbol.

How to evaluate Maximum Initial Deflection given Initial Deflection at Distance X from A using this online evaluator? To use this online evaluator for Maximum Initial Deflection given Initial Deflection at Distance X from A, enter Initial Deflection (y'), Distance of Deflection from end A (x) & Length of Column (l) and hit the calculate button.

FAQs on Maximum Initial Deflection given Initial Deflection at Distance X from A

What is the formula to find Maximum Initial Deflection given Initial Deflection at Distance X from A?

The formula of Maximum Initial Deflection given Initial Deflection at Distance X from A is expressed as Maximum Initial Deflection = Initial Deflection/sin((pi*Distance of Deflection from end A)/Length of Column). Here is an example- 2.7E+6 = 0.06/sin((pi*0.035)/5).

How to calculate Maximum Initial Deflection given Initial Deflection at Distance X from A?

With Initial Deflection (y'), Distance of Deflection from end A (x) & Length of Column (l) we can find Maximum Initial Deflection given Initial Deflection at Distance X from A using the formula - Maximum Initial Deflection = Initial Deflection/sin((pi*Distance of Deflection from end A)/Length of Column). This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Maximum Initial Deflection?

Here are the different ways to Calculate Maximum Initial Deflection-

Maximum Initial Deflection=Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*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

Can the Maximum Initial Deflection given Initial Deflection at Distance X from A be negative?

Yes, the Maximum Initial Deflection given Initial Deflection at Distance X from A, measured in Length can be negative.

Which unit is used to measure Maximum Initial Deflection given Initial Deflection at Distance X from A?

Maximum Initial Deflection given Initial Deflection at Distance X from A is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Maximum Initial Deflection given Initial Deflection at Distance X from A can be measured.

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Maximum Initial Deflection given Initial Deflection at Distance X from A Formula

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

​GoMaximum Initial Deflection given Maximum Deflection for Columns with Initial Curvature Formula

Maximum Initial Deflection given Initial Deflection at Distance X from A Example

Maximum Initial Deflection given Initial Deflection at Distance X from A Solution

Maximum Initial Deflection given Initial Deflection at Distance X from A Formula Elements

Other Formulas to find Maximum Initial Deflection

Other formulas in Columns With Initial Curvature category

How to Evaluate Maximum Initial Deflection given Initial Deflection at Distance X from A?

FAQs on Maximum Initial Deflection given Initial Deflection at Distance X from A

Variable Name

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

GoMaximum Initial Deflection given Maximum Deflection for Columns with Initial Curvature Formula