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Transverse Point Load given Maximum Deflection for Strut Formula

GoTransverse Point Load for Strut with Axial and Transverse Point Load at Center Formula

GoTransverse Point Load given Maximum Bending Moment for Strut Formula

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

W p = \frac{δ}{((\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})}

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

Transverse Point Load given Maximum Deflection for Strut Example

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Here is how the Transverse Point Load given Maximum Deflection for Strut equation looks like with Values.

Here is how the Transverse Point Load given Maximum Deflection for Strut equation looks like with Units.

Here is how the Transverse Point Load given Maximum Deflection for Strut equation looks like.

-0.0045 = \frac{12}{((\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})}

-0.0045kN = \frac{12mm}{((\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})}

-0.0045 = \frac{12}{((\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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Transverse Point Load given Maximum Deflection for Strut Solution

Follow our step by step solution on how to calculate Transverse Point Load given Maximum Deflection for Strut?

FIRST Step Consider the formula

W p = \frac{δ}{((\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

∴

W p = \frac{12mm}{((\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

∴

W p = \frac{0.012m}{((\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

∴

W p = \frac{0.012}{((\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

∴

W p = -4.46785258866468N

Next Step Convert to Output's Unit

∴

W p = -0.00446785258866468kN

LAST Step Rounding Answer

∴

W p = -0.0045kN

Transverse Point Load given Maximum Deflection for Strut Formula Elements

Variables

Functions

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

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

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 Greatest Safe Load

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 Transverse Point Load given Maximum Bending Moment for Strut

W p = \frac{M max}{(\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}}}))}

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 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}

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 Transverse Point Load given Maximum Deflection for Strut?

Transverse Point Load given Maximum Deflection for Strut evaluator uses Greatest Safe Load = Deflection at Column Section/((((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 Greatest Safe Load, The Transverse Point Load given Maximum Deflection for Strut formula is defined as a measure of the load applied perpendicularly to the axis of a strut at its midpoint, considering the maximum deflection of the strut under compressive axial thrust and a transverse point load, providing insights into the strut's behavior under combined loading conditions. Greatest Safe Load is denoted by W_p symbol.

How to evaluate Transverse Point Load given Maximum Deflection for Strut using this online evaluator? To use this online evaluator for Transverse Point Load given Maximum Deflection for Strut, enter Deflection at Column Section (δ), 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 Transverse Point Load given Maximum Deflection for Strut

What is the formula to find Transverse Point Load given Maximum Deflection for Strut?

The formula of Transverse Point Load given Maximum Deflection for Strut is expressed as Greatest Safe Load = Deflection at Column Section/((((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- -4.5E-6 = 0.012/((((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400)))))-(5/(4*400))).

How to calculate Transverse Point Load given Maximum Deflection for Strut?

With Deflection at Column Section (δ), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Compressive Load (P_compressive) & Column Length (l_column) we can find Transverse Point Load given Maximum Deflection for Strut using the formula - Greatest Safe Load = Deflection at Column Section/((((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 Greatest Safe Load?

Here are the different ways to Calculate Greatest Safe Load-

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

Can the Transverse Point Load given Maximum Deflection for Strut be negative?

No, the Transverse Point Load given Maximum Deflection for Strut, measured in Force cannot be negative.

Which unit is used to measure Transverse Point Load given Maximum Deflection for Strut?

Transverse Point Load given Maximum Deflection for Strut is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Transverse Point Load given Maximum Deflection for Strut can be measured.

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Transverse Point Load given Maximum Deflection for Strut Formula

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

​GoTransverse Point Load given Maximum Bending Moment for Strut Formula

Transverse Point Load given Maximum Deflection for Strut Example

Transverse Point Load given Maximum Deflection for Strut Solution

Transverse Point Load given Maximum Deflection for Strut Formula Elements

Other Formulas to find Greatest Safe Load

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

How to Evaluate Transverse Point Load given Maximum Deflection for Strut?

FAQs on Transverse Point Load given Maximum Deflection for Strut

Variable Name

GoTransverse Point Load for Strut with Axial and Transverse Point Load at Center Formula

GoTransverse Point Load given Maximum Bending Moment for Strut Formula