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Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Formula

GoMaximum Bending Moment given Max Deflection for Strut Subjected to Uniformly Distributed Load Formula

GoMaximum Bending Moment given Max Stress for Strut Subjected to Uniformly Distributed Load Formula

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Maximum Bending Moment In Column is the highest amount of bending force that a column experiences due to applied loads, either axial or eccentric. Check FAQs

M = - q f \cdot (ε column \cdot \frac{I}{P axial}) \cdot ((\sec ((\frac{l column}{2}) \cdot (\frac{P axial}{ε column \cdot I}))) - 1)

M - Maximum Bending Moment In Column?q_f - Load Intensity?ε_column - Modulus of Elasticity of Column?I - Moment of Inertia?P_axial - Axial Thrust?l_column - Column Length?

Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Example

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Here is how the Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load equation looks like with Values.

Here is how the Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load equation looks like with Units.

Here is how the Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load equation looks like.

-3.3351 = - 0.005 \cdot (10.56 \cdot \frac{5600}{1500}) \cdot ((\sec ((\frac{5000}{2}) \cdot (\frac{1500}{10.56 \cdot 5600}))) - 1)

-3.3351N*m = - 0.005MPa \cdot (10.56MPa \cdot \frac{5600cm⁴}{1500N}) \cdot ((\sec ((\frac{5000mm}{2}) \cdot (\frac{1500N}{10.56MPa \cdot 5600cm⁴}))) - 1)

-3.3351 = - 0.005 \cdot (10.56 \cdot \frac{5600}{1500}) \cdot ((\sec ((\frac{5000}{2}) \cdot (\frac{1500}{10.56 \cdot 5600}))) - 1)

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Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load?

FIRST Step Consider the formula

M = - q f \cdot (ε column \cdot \frac{I}{P axial}) \cdot ((\sec ((\frac{l column}{2}) \cdot (\frac{P axial}{ε column \cdot I}))) - 1)

Next Step Substitute values of Variables

∴

M = - 0.005MPa \cdot (10.56MPa \cdot \frac{5600cm⁴}{1500N}) \cdot ((\sec ((\frac{5000mm}{2}) \cdot (\frac{1500N}{10.56MPa \cdot 5600cm⁴}))) - 1)

Next Step Convert Units

∴

M = - 5000Pa \cdot (1.1E+7Pa \cdot \frac{5.6E-5m⁴}{1500N}) \cdot ((\sec ((\frac{5m}{2}) \cdot (\frac{1500N}{1.1E+7Pa \cdot 5.6E-5m⁴}))) - 1)

Next Step Prepare to Evaluate

∴

M = - 5000 \cdot (1.1E+7 \cdot \frac{5.6E-5}{1500}) \cdot ((\sec ((\frac{5}{2}) \cdot (\frac{1500}{1.1E+7 \cdot 5.6E-5}))) - 1)

Next Step Evaluate

∴

M = -3.33509071134627N*m

LAST Step Rounding Answer

∴

M = -3.3351N*m

Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Formula Elements

Variables

Functions

Maximum Bending Moment In Column

Maximum Bending Moment In Column is the highest amount of bending force that a column experiences due to applied loads, either axial or eccentric.

Symbol: M

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment In Column

Load Intensity

Load Intensity is the distribution of load over a certain area or length of a structural element.

Symbol: q_f

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Load Intensity

Modulus of Elasticity of Column

Modulus of Elasticity of Column is a quantity that measures column'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 of Column

Moment of Inertia

Moment of Inertia 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

Axial Thrust

Axial Thrust is the force exerted along the axis of a shaft in mechanical systems. It occurs when there is an imbalance of forces that acts in the direction parallel to the axis of rotation.

Symbol: P_axial

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Axial Thrust

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

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

Other Formulas to find Maximum Bending Moment In Column

Go Maximum Bending Moment given Max Deflection for Strut Subjected to Uniformly Distributed Load

M = - (P axial \cdot C) - (q f \cdot \frac{{l column}^{2}}{8})

Go Maximum Bending Moment given Max Stress for Strut Subjected to Uniformly Distributed Load

M = (σb max - (\frac{P axial}{A sectional})) \cdot \frac{I}{c}

Go Maximum Bending Moment given Elastic Modulus for Strut subjected to Uniformly Distributed Load

M = (σb max - (\frac{P axial}{A sectional})) \cdot ε column

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Uniformly Distributed Load category

Go Bending Moment at Section for Strut subjected to Compressive Axial and Uniformly Distributed Load

M b = - (P axial \cdot δ) + (q f \cdot ((\frac{x^{2}}{2}) - (l column \cdot \frac{x}{2})))

Go Axial Thrust for Strut Subjected to Compressive Axial and Uniformly Distributed Load

P axial = \frac{- M b + (q f \cdot ((\frac{x^{2}}{2}) - (l column \cdot \frac{x}{2})))}{δ}

Go Deflection at Section for Strut Subjected to Compressive Axial and Uniformly Distributed Load

δ = \frac{- M b + (q f \cdot ((\frac{x^{2}}{2}) - (l column \cdot \frac{x}{2})))}{P axial}

Go Load Intensity for Strut Subjected to Compressive Axial and Uniformly Distributed Load

q f = \frac{M b + (P axial \cdot δ)}{(\frac{x^{2}}{2}) - (l column \cdot \frac{x}{2})}

How to Evaluate Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load?

Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load evaluator uses Maximum Bending Moment In Column = -Load Intensity*(Modulus of Elasticity of Column*Moment of Inertia/Axial Thrust)*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity of Column*Moment of Inertia))))-1) to evaluate the Maximum Bending Moment In Column, The Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load formula is defined as the maximum turning force that occurs in a strut when it is subjected to both compressive axial force and a transverse uniformly distributed load, which can cause the strut to bend and potentially fail. Maximum Bending Moment In Column is denoted by M symbol.

How to evaluate Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load using this online evaluator? To use this online evaluator for Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load, enter Load Intensity (q_f), Modulus of Elasticity of Column (ε_column), Moment of Inertia (I), Axial Thrust (P_axial) & Column Length (l_column) and hit the calculate button.

FAQs on Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load

What is the formula to find Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load?

The formula of Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load is expressed as Maximum Bending Moment In Column = -Load Intensity*(Modulus of Elasticity of Column*Moment of Inertia/Axial Thrust)*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity of Column*Moment of Inertia))))-1). Here is an example- -3.335091 = -5000*(10560000*5.6E-05/1500)*((sec((5/2)*(1500/(10560000*5.6E-05))))-1).

How to calculate Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load?

With Load Intensity (q_f), Modulus of Elasticity of Column (ε_column), Moment of Inertia (I), Axial Thrust (P_axial) & Column Length (l_column) we can find Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load using the formula - Maximum Bending Moment In Column = -Load Intensity*(Modulus of Elasticity of Column*Moment of Inertia/Axial Thrust)*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity of Column*Moment of Inertia))))-1). This formula also uses Secant (sec) 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=-(Axial Thrust*Maximum Initial Deflection)-(Load Intensity*(Column Length^2)/8)
Maximum Bending Moment In Column=(Maximum Bending Stress-(Axial Thrust/Cross Sectional Area))*Moment of Inertia/(Distance from Neutral Axis to Extreme Point)
Maximum Bending Moment In Column=(Maximum Bending Stress-(Axial Thrust/Cross Sectional Area))*Modulus of Elasticity of Column

Can the Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load be negative?

No, the Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load, measured in Moment of Force cannot be negative.

Which unit is used to measure Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load?

Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load 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 Subjected to Compressive Axial and Uniformly Distributed Load can be measured.

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Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Formula

​GoMaximum Bending Moment given Max Deflection for Strut Subjected to Uniformly Distributed Load Formula

​GoMaximum Bending Moment given Max Stress for Strut Subjected to Uniformly Distributed Load Formula

Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Example

Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Solution

Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Formula Elements

Other Formulas to find Maximum Bending Moment In Column

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Uniformly Distributed Load category

How to Evaluate Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load?

FAQs on Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load

Variable Name

GoMaximum Bending Moment given Max Deflection for Strut Subjected to Uniformly Distributed Load Formula

GoMaximum Bending Moment given Max Stress for Strut Subjected to Uniformly Distributed Load Formula