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Transverse point load given maximum bending moment for strut Formula

GoTransverse point load for strut with axial and transverse point load at center Formula

GoTransverse point load given maximum deflection 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

Wp = \frac{M}{(\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}}}))}

Wp - Greatest Safe Load?M - Maximum Bending Moment In Column?I - Moment of Inertia Column?ε_column - Modulus of Elasticity Column?P_compressive - Column Compressive load?l_column - Column Length?

Transverse point load given maximum bending moment for strut Example

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Here is how the Transverse point load given maximum bending moment for strut equation looks like with Values.

Here is how the Transverse point load given maximum bending moment for strut equation looks like with Units.

Here is how the Transverse point load given maximum bending moment for strut equation looks like.

36.4344 = \frac{16}{(\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}}}))}

36.4344kN = \frac{16N*m}{(\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}}}))}

36.4344 = \frac{16}{(\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}}}))}

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Transverse point load given maximum bending moment for strut Solution

Follow our step by step solution on how to calculate Transverse point load given maximum bending moment for strut?

FIRST Step Consider the formula

Wp = \frac{M}{(\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}}}))}

Next Step Substitute values of Variables

∴

Wp = \frac{16N*m}{(\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}}}))}

Next Step Convert Units

∴

Wp = \frac{16N*m}{(\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}}}))}

Next Step Prepare to Evaluate

∴

Wp = \frac{16}{(\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}}}))}

Next Step Evaluate

∴

Wp = 36434.3568330503N

Next Step Convert to Output's Unit

∴

Wp = 36.4343568330503kN

LAST Step Rounding Answer

∴

Wp = 36.4344kN

Transverse point load given maximum bending moment 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: Wp

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Greatest Safe Load

Maximum Bending Moment In Column

Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment.

Symbol: M

Measurement: Moment of ForceUnit: N*m

Note: Value can be positive or negative.

Formulas to find Maximum Bending Moment In Column

Moment of Inertia Column

Moment of Inertia Column is the measure of the resistance of a body 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 Column

Modulus of Elasticity Column

Modulus of Elasticity Column 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

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 can be positive or negative.

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 can be positive or negative.

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

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

Go Transverse point load given maximum deflection for strut

Wp = \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})}

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) - (Wp \cdot \frac{x}{2})

Go Compressive axial load for strut with axial and transverse point load at center

P compressive = - \frac{M b + (Wp \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 + (Wp \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}{Wp}

How to Evaluate Transverse point load given maximum bending moment for strut?

Transverse point load given maximum bending moment for strut evaluator uses Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))) to evaluate the Greatest Safe Load, Transverse point load given maximum bending moment for strut formula is defined as a measure of the maximum load that can be applied to a strut subjected to compressive axial thrust and a transverse point load at the centre, taking into account the strut's properties and dimensions. Greatest Safe Load is denoted by Wp symbol.

How to evaluate Transverse point load given maximum bending moment for strut using this online evaluator? To use this online evaluator for Transverse point load given maximum bending moment for strut, enter Maximum Bending Moment In Column (M), Moment of Inertia Column (I), Modulus of Elasticity Column (ε_column), Column Compressive load (P_compressive) & Column Length (l_column) and hit the calculate button.

FAQs on Transverse point load given maximum bending moment for strut

What is the formula to find Transverse point load given maximum bending moment for strut?

The formula of Transverse point load given maximum bending moment for strut is expressed as Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))). Here is an example- 0.036434 = 16/(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))).

How to calculate Transverse point load given maximum bending moment for strut?

With Maximum Bending Moment In Column (M), Moment of Inertia Column (I), Modulus of Elasticity Column (ε_column), Column Compressive load (P_compressive) & Column Length (l_column) we can find Transverse point load given maximum bending moment for strut using the formula - Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))). This formula also uses Tangent, Square Root Function 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=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)))

Can the Transverse point load given maximum bending moment for strut be negative?

Yes, the Transverse point load given maximum bending moment for strut, measured in Force can be negative.

Which unit is used to measure Transverse point load given maximum bending moment for strut?

Transverse point load given maximum bending moment 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 bending moment for strut can be measured.

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Transverse point load given maximum bending moment for strut Formula

​GoTransverse point load for strut with axial and transverse point load at center Formula

​GoTransverse point load given maximum deflection for strut Formula

Transverse point load given maximum bending moment for strut Example

Transverse point load given maximum bending moment for strut Solution

Transverse point load given maximum bending moment 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 bending moment for strut?

FAQs on Transverse point load given maximum bending moment for strut

Variable Name

GoTransverse point load for strut with axial and transverse point load at center Formula

GoTransverse point load given maximum deflection for strut Formula