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

GoMaximum Initial Deflection given Initial Deflection at Distance X from A 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{δ c}{(\frac{1}{1 - (\frac{P}{P E})}) \cdot \sin (\frac{π \cdot x}{l})}

C - Maximum Initial Deflection?δ_c - Deflection of Column?P - Crippling Load?P_E - Euler Load?x - Distance of Deflection from end A?l - Length of Column?π - Archimedes' constant?

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

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

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

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

300 = \frac{18.4711}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot \sin (\frac{3.1416 \cdot 35}{5000})}

300mm = \frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot \sin (\frac{3.1416 \cdot 35mm}{5000mm})}

300 = \frac{18.4711}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot \sin (\frac{3.1416 \cdot 35}{5000})}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C = \frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot \sin (\frac{π \cdot 35mm}{5000mm})}

Next Step Substitute values of Constants

∴

C = \frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot \sin (\frac{3.1416 \cdot 35mm}{5000mm})}

Next Step Convert Units

∴

C = \frac{0.0185m}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot \sin (\frac{3.1416 \cdot 0.035m}{5m})}

Next Step Prepare to Evaluate

∴

C = \frac{0.0185}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot \sin (\frac{3.1416 \cdot 0.035}{5})}

Next Step Evaluate

∴

C = 0.299999976303032m

Next Step Convert to Output's Unit

∴

C = 299.999976303032mm

LAST Step Rounding Answer

∴

C = 300mm

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

Deflection of Column

Deflection of Column is the displacement or bending of a column from its original, vertical position when subjected to an external load, particularly a compressive load.

Symbol: δ_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Column

Crippling Load

Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Symbol: P

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Crippling Load

Euler Load

Euler load is the compressive load at which a slender column will suddenly bend or buckle.

Symbol: P_E

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Euler Load

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 Initial Deflection at Distance X from A

C = \frac{y'}{\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 Final Deflection at Distance X from End A of Column?

Maximum Initial Deflection given Final Deflection at Distance X from End A of Column evaluator 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 evaluate the Maximum Initial Deflection, The Maximum Initial Deflection given Final Deflection at Distance X from End A of Column formula is defined as a measure that determines the initial deflection of a column at a certain distance from its end, taking into account the final deflection and other parameters, providing valuable insights into the column's behavior under load. Maximum Initial Deflection is denoted by C symbol.

How to evaluate Maximum Initial Deflection given Final Deflection at Distance X from End A of Column using this online evaluator? To use this online evaluator 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.

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

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

The formula of Maximum Initial Deflection given Final Deflection at Distance X from End A of Column is expressed as Maximum Initial Deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of Deflection from end A)/Length of Column)). Here is an example- 194899.3 = 0.01847108/((1/(1-(2571.429/4000)))*sin((pi*0.035)/5)).

How to calculate Maximum Initial Deflection given Final Deflection at Distance X from End A of Column?

With Deflection of Column (δ_c), Crippling Load (P), Euler Load (P_E), Distance of Deflection from end A (x) & Length of Column (l) we can find Maximum Initial Deflection given Final Deflection at Distance X from End A of Column using the formula - Maximum Initial Deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*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=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

Can the Maximum Initial Deflection given Final Deflection at Distance X from End A of Column be negative?

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

Which unit is used to measure 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 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 Final Deflection at Distance X from End A of Column can be measured.

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

​GoMaximum Initial Deflection given Initial Deflection at Distance X from A Formula

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

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

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

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

Other Formulas to find Maximum Initial Deflection

Other formulas in Columns With Initial Curvature category

How to Evaluate Maximum Initial Deflection given Final Deflection at Distance X from End A of Column?

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

Variable Name

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

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