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

GoMaximum Bending Moment if Maximum Bending Stress is given for Strut with Axial and Point Load Formula

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Maximum Bending Moment In Column is the highest moment of force that causes the column to bend or deform under applied loads. Check FAQs

M max = 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}}})))

M_max - Maximum Bending Moment In Column?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 Bending Moment for Strut with Axial and Transverse Point Load at Center Example

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

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

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

0.0439 = 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}}})))

0.0439N*m = 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}}})))

0.0439 = 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}}})))

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

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

FIRST Step Consider the formula

M max = 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}}})))

Next Step Substitute values of Variables

∴

M max = 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}}})))

Next Step Convert Units

∴

M max = 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}}})))

Next Step Prepare to Evaluate

∴

M max = 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}}})))

Next Step Evaluate

∴

M max = 0.0439145943300586N*m

LAST Step Rounding Answer

∴

M max = 0.0439N*m

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

Variables

Functions

Maximum Bending Moment In Column

Maximum Bending Moment In Column is the highest moment of force that causes the column to bend or deform under applied loads.

Symbol: M_max

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment In Column

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 Maximum Bending Moment In Column

Go Maximum Bending Moment if Maximum Bending Stress is given for Strut with Axial and Point Load

M max = σb max \cdot \frac{A sectional \cdot (k^{2})}{c}

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 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}

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

Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center evaluator uses Maximum Bending Moment In Column = 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))))) to evaluate the Maximum Bending Moment In Column, The Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center formula is defined as a measure of the maximum bending stress that occurs in a strut when it is subjected to both compressive axial thrust and a transverse point load at its center, providing critical information for structural engineers to design safe and stable structures. Maximum Bending Moment In Column is denoted by M_max symbol.

How to evaluate Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center using this online evaluator? To use this online evaluator for Maximum Bending Moment 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 Bending Moment for Strut with Axial and Transverse Point Load at Center

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

The formula of Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center is expressed as Maximum Bending Moment In Column = 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))))). Here is an example- 0.043915 = 100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))).

How to calculate Maximum Bending Moment 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 Bending Moment for Strut with Axial and Transverse Point Load at Center using the formula - Maximum Bending Moment In Column = 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))))). This formula also uses Tangent (tan), Square Root (sqrt) function(s).

What are the other ways to Calculate Maximum Bending Moment In Column?

Here are the different ways to Calculate Maximum Bending Moment In Column-

Maximum Bending Moment In Column=Maximum Bending Stress*(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))/(Distance from Neutral Axis to Extreme Point)

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

No, the Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center, measured in Moment of Force cannot be negative.

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

Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center is usually measured using the Newton Meter[N*m] for Moment of Force. Kilonewton Meter[N*m], Millinewton Meter[N*m], Micronewton Meter[N*m] are the few other units in which Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center can be measured.

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

​GoMaximum Bending Moment if Maximum Bending Stress is given for Strut with Axial and Point Load Formula

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

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

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

Other Formulas to find Maximum Bending Moment In Column

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

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

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

Variable Name

GoMaximum Bending Moment if Maximum Bending Stress is given for Strut with Axial and Point Load Formula