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Maximum Deflection for Strut with Axial and Transverse Point Load at Center Formula

GoDeflection at Section for Strut with Axial and Transverse Point Load at Center Formula

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Deflection at Column Section is the lateral displacement at the section of the column. Check FAQs

δ = W p \cdot (((\frac{\sqrt{I \cdot \frac{ε column}{P compressive}}}{2 \cdot P compressive}) \cdot \tan ((\frac{l column}{2}) \cdot (\sqrt{\frac{P compressive}{I \cdot \frac{ε column}{P compressive}}}))) - (\frac{l column}{4 \cdot P compressive}))

δ - Deflection at Column Section?W_p - Greatest Safe Load?I - Moment of Inertia in Column?ε_column - Modulus of Elasticity?P_compressive - Column Compressive Load?l_column - Column Length?

Maximum Deflection for Strut with Axial and Transverse Point Load at Center Example

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Here is how the Maximum Deflection for Strut with Axial and Transverse Point Load at Center equation looks like with Values.

Here is how the Maximum Deflection for Strut with Axial and Transverse Point Load at Center equation looks like with Units.

Here is how the Maximum Deflection for Strut with Axial and Transverse Point Load at Center equation looks like.

-268.5854 = 0.1 \cdot (((\frac{\sqrt{5600 \cdot \frac{10.56}{0.4}}}{2 \cdot 0.4}) \cdot \tan ((\frac{5000}{2}) \cdot (\sqrt{\frac{0.4}{5600 \cdot \frac{10.56}{0.4}}}))) - (\frac{5000}{4 \cdot 0.4}))

-268.5854mm = 0.1kN \cdot (((\frac{\sqrt{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}}{2 \cdot 0.4kN}) \cdot \tan ((\frac{5000mm}{2}) \cdot (\sqrt{\frac{0.4kN}{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}}))) - (\frac{5000mm}{4 \cdot 0.4kN}))

-268.5854 = 0.1 \cdot (((\frac{\sqrt{5600 \cdot \frac{10.56}{0.4}}}{2 \cdot 0.4}) \cdot \tan ((\frac{5000}{2}) \cdot (\sqrt{\frac{0.4}{5600 \cdot \frac{10.56}{0.4}}}))) - (\frac{5000}{4 \cdot 0.4}))

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Maximum Deflection for Strut with Axial and Transverse Point Load at Center Solution

Follow our step by step solution on how to calculate Maximum Deflection for Strut with Axial and Transverse Point Load at Center?

FIRST Step Consider the formula

δ = W p \cdot (((\frac{\sqrt{I \cdot \frac{ε column}{P compressive}}}{2 \cdot P compressive}) \cdot \tan ((\frac{l column}{2}) \cdot (\sqrt{\frac{P compressive}{I \cdot \frac{ε column}{P compressive}}}))) - (\frac{l column}{4 \cdot P compressive}))

Next Step Substitute values of Variables

∴

δ = 0.1kN \cdot (((\frac{\sqrt{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}}{2 \cdot 0.4kN}) \cdot \tan ((\frac{5000mm}{2}) \cdot (\sqrt{\frac{0.4kN}{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}}))) - (\frac{5000mm}{4 \cdot 0.4kN}))

Next Step Convert Units

∴

δ = 100N \cdot (((\frac{\sqrt{5.6E-5m⁴ \cdot \frac{1.1E+7Pa}{400N}}}{2 \cdot 400N}) \cdot \tan ((\frac{5m}{2}) \cdot (\sqrt{\frac{400N}{5.6E-5m⁴ \cdot \frac{1.1E+7Pa}{400N}}}))) - (\frac{5m}{4 \cdot 400N}))

Next Step Prepare to Evaluate

∴

δ = 100 \cdot (((\frac{\sqrt{5.6E-5 \cdot \frac{1.1E+7}{400}}}{2 \cdot 400}) \cdot \tan ((\frac{5}{2}) \cdot (\sqrt{\frac{400}{5.6E-5 \cdot \frac{1.1E+7}{400}}}))) - (\frac{5}{4 \cdot 400}))

Next Step Evaluate

∴

δ = -0.268585405669941m

Next Step Convert to Output's Unit

∴

δ = -268.585405669941mm

LAST Step Rounding Answer

∴

δ = -268.5854mm

Maximum Deflection for Strut with Axial and Transverse Point Load at Center Formula Elements

Variables

Functions

Deflection at Column Section

Deflection at Column Section is the lateral displacement at the section of the column.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection at Column Section

Greatest Safe Load

Greatest Safe Load is the maximum safe point load allowable at the center of the beam.

Symbol: W_p

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Greatest Safe Load

Moment of Inertia in Column

Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis.

Symbol: I

Measurement: Second Moment of AreaUnit: cm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia in Column

Modulus of Elasticity

Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

Symbol: ε_column

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Column Compressive Load

Column Compressive Load is the load applied to a column that is compressive in nature.

Symbol: P_compressive

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Column Compressive Load

Column Length

Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l_column

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Deflection at Column Section

Go Deflection at Section for Strut with Axial and Transverse Point Load at Center

δ = P compressive - \frac{M b + (W p \cdot \frac{x}{2})}{P compressive}

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre category

Go Bending Moment at Section for Strut with Axial and Transverse Point Load at Center

M b = - (P compressive \cdot δ) - (W p \cdot \frac{x}{2})

Go Compressive Axial Load for Strut with Axial and Transverse Point Load at Center

P compressive = - \frac{M b + (W p \cdot \frac{x}{2})}{δ}

Go Transverse Point Load for Strut with Axial and Transverse Point Load at Center

W p = (- M b - (P compressive \cdot δ)) \cdot \frac{2}{x}

Go Distance of Deflection from end A for Strut with Axial and Transverse Point Load at Center

x = (- M b - (P compressive \cdot δ)) \cdot \frac{2}{W p}

How to Evaluate Maximum Deflection for Strut with Axial and Transverse Point Load at Center?

Maximum Deflection for Strut with Axial and Transverse Point Load at Center evaluator uses Deflection at Column Section = Greatest Safe Load*((((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load)))))-(Column Length/(4*Column Compressive Load))) to evaluate the Deflection at Column Section, The Maximum Deflection for Strut with Axial and Transverse Point Load at Center formula is defined as the maximum displacement of a strut subjected to both compressive axial thrust and a transverse point load at its center, which affects its stability and structural integrity. Deflection at Column Section is denoted by δ symbol.

How to evaluate Maximum Deflection for Strut with Axial and Transverse Point Load at Center using this online evaluator? To use this online evaluator for Maximum Deflection for Strut with Axial and Transverse Point Load at Center, enter Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Compressive Load (P_compressive) & Column Length (l_column) and hit the calculate button.

FAQs on Maximum Deflection for Strut with Axial and Transverse Point Load at Center

What is the formula to find Maximum Deflection for Strut with Axial and Transverse Point Load at Center?

The formula of Maximum Deflection for Strut with Axial and Transverse Point Load at Center is expressed as Deflection at Column Section = Greatest Safe Load*((((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load)))))-(Column Length/(4*Column Compressive Load))). Here is an example- -268585.40567 = 100*((((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400)))))-(5/(4*400))).

How to calculate Maximum Deflection for Strut with Axial and Transverse Point Load at Center?

With Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Compressive Load (P_compressive) & Column Length (l_column) we can find Maximum Deflection for Strut with Axial and Transverse Point Load at Center using the formula - Deflection at Column Section = Greatest Safe Load*((((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load)))))-(Column Length/(4*Column Compressive Load))). This formula also uses Tangent (tan), Square Root (sqrt) function(s).

What are the other ways to Calculate Deflection at Column Section?

Here are the different ways to Calculate Deflection at Column Section-

Deflection at Column Section=Column Compressive Load-(Bending Moment in Column+(Greatest Safe Load*Distance of Deflection from end A/2))/(Column Compressive Load)

Can the Maximum Deflection for Strut with Axial and Transverse Point Load at Center be negative?

No, the Maximum Deflection for Strut with Axial and Transverse Point Load at Center, measured in Length cannot be negative.

Which unit is used to measure Maximum Deflection for Strut with Axial and Transverse Point Load at Center?

Maximum Deflection for Strut with Axial and Transverse Point Load at Center is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Maximum Deflection for Strut with Axial and Transverse Point Load at Center can be measured.

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Maximum Deflection for Strut with Axial and Transverse Point Load at Center Formula

​GoDeflection at Section for Strut with Axial and Transverse Point Load at Center Formula

Maximum Deflection for Strut with Axial and Transverse Point Load at Center Example

Maximum Deflection for Strut with Axial and Transverse Point Load at Center Solution

Maximum Deflection for Strut with Axial and Transverse Point Load at Center Formula Elements

Other Formulas to find Deflection at Column Section

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre category

How to Evaluate Maximum Deflection for Strut with Axial and Transverse Point Load at Center?

FAQs on Maximum Deflection for Strut with Axial and Transverse Point Load at Center

Variable Name

GoDeflection at Section for Strut with Axial and Transverse Point Load at Center Formula