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

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

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Maximum Initial Deflection is the greatest amount of displacement or bending that occurs in a mechanical structure or component when a load is first applied. Check FAQs

C = (q f \cdot (ε column \cdot \frac{I}{{P axial}^{2}}) \cdot ((\sec ((\frac{l column}{2}) \cdot (\frac{P axial}{ε column \cdot I}))) - 1)) - (q f \cdot \frac{{l column}^{2}}{8 \cdot P axial})

C - Maximum Initial Deflection?q_f - Load Intensity?ε_column - Modulus of Elasticity of Column?I - Moment of Inertia?P_axial - Axial Thrust?l_column - Column Length?

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

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

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

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

-10414.4433 = (0.005 \cdot (10.56 \cdot \frac{5600}{1500^{2}}) \cdot ((\sec ((\frac{5000}{2}) \cdot (\frac{1500}{10.56 \cdot 5600}))) - 1)) - (0.005 \cdot \frac{5000^{2}}{8 \cdot 1500})

-10414.4433mm = (0.005MPa \cdot (10.56MPa \cdot \frac{5600cm⁴}{{1500N}^{2}}) \cdot ((\sec ((\frac{5000mm}{2}) \cdot (\frac{1500N}{10.56MPa \cdot 5600cm⁴}))) - 1)) - (0.005MPa \cdot \frac{{5000mm}^{2}}{8 \cdot 1500N})

-10414.4433 = (0.005 \cdot (10.56 \cdot \frac{5600}{1500^{2}}) \cdot ((\sec ((\frac{5000}{2}) \cdot (\frac{1500}{10.56 \cdot 5600}))) - 1)) - (0.005 \cdot \frac{5000^{2}}{8 \cdot 1500})

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

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

FIRST Step Consider the formula

C = (q f \cdot (ε column \cdot \frac{I}{{P axial}^{2}}) \cdot ((\sec ((\frac{l column}{2}) \cdot (\frac{P axial}{ε column \cdot I}))) - 1)) - (q f \cdot \frac{{l column}^{2}}{8 \cdot P axial})

Next Step Substitute values of Variables

∴

C = (0.005MPa \cdot (10.56MPa \cdot \frac{5600cm⁴}{{1500N}^{2}}) \cdot ((\sec ((\frac{5000mm}{2}) \cdot (\frac{1500N}{10.56MPa \cdot 5600cm⁴}))) - 1)) - (0.005MPa \cdot \frac{{5000mm}^{2}}{8 \cdot 1500N})

Next Step Convert Units

∴

C = (5000Pa \cdot (1.1E+7Pa \cdot \frac{5.6E-5m⁴}{{1500N}^{2}}) \cdot ((\sec ((\frac{5m}{2}) \cdot (\frac{1500N}{1.1E+7Pa \cdot 5.6E-5m⁴}))) - 1)) - (5000Pa \cdot \frac{{5m}^{2}}{8 \cdot 1500N})

Next Step Prepare to Evaluate

∴

C = (5000 \cdot (1.1E+7 \cdot \frac{5.6E-5}{1500^{2}}) \cdot ((\sec ((\frac{5}{2}) \cdot (\frac{1500}{1.1E+7 \cdot 5.6E-5}))) - 1)) - (5000 \cdot \frac{5^{2}}{8 \cdot 1500})

Next Step Evaluate

∴

C = -10.4144432728591m

Next Step Convert to Output's Unit

∴

C = -10414.4432728591mm

LAST Step Rounding Answer

∴

C = -10414.4433mm

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

Variables

Functions

Maximum Initial Deflection

Maximum Initial Deflection is the greatest amount of displacement or bending that occurs in a mechanical structure or component when a load is first applied.

Symbol: C

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Maximum Initial Deflection

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 Initial Deflection

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

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

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 Deflection for Strut Subjected to Compressive Axial and Uniformly Distributed Load?

Maximum Deflection for Strut Subjected to Compressive Axial and Uniformly Distributed Load evaluator uses Maximum Initial Deflection = (Load Intensity*(Modulus of Elasticity of Column*Moment of Inertia/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity of Column*Moment of Inertia))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust)) to evaluate the Maximum Initial Deflection, The Maximum Deflection for Strut Subjected to Compressive Axial and Uniformly Distributed Load formula is defined as the maximum displacement of a strut under the simultaneous action of compressive axial force and uniformly distributed transverse load, providing a critical measure of the strut's stability and structural integrity. Maximum Initial Deflection is denoted by C symbol.

How to evaluate Maximum Deflection for Strut Subjected to Compressive Axial and Uniformly Distributed Load using this online evaluator? To use this online evaluator for Maximum Deflection 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 Deflection for Strut Subjected to Compressive Axial and Uniformly Distributed Load

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

The formula of Maximum Deflection for Strut Subjected to Compressive Axial and Uniformly Distributed Load is expressed as Maximum Initial Deflection = (Load Intensity*(Modulus of Elasticity of Column*Moment of Inertia/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity of Column*Moment of Inertia))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust)). Here is an example- -10414443.272859 = (5000*(10560000*5.6E-05/(1500^2))*((sec((5/2)*(1500/(10560000*5.6E-05))))-1))-(5000*(5^2)/(8*1500)).

How to calculate Maximum Deflection 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 Deflection for Strut Subjected to Compressive Axial and Uniformly Distributed Load using the formula - Maximum Initial Deflection = (Load Intensity*(Modulus of Elasticity of Column*Moment of Inertia/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity of Column*Moment of Inertia))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust)). This formula also uses Secant (sec) function(s).

What are the other ways to Calculate Maximum Initial Deflection?

Here are the different ways to Calculate Maximum Initial Deflection-

Maximum Initial Deflection=(-Maximum Bending Moment In Column-(Load Intensity*(Column Length^2)/8))/(Axial Thrust)

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

No, the Maximum Deflection for Strut Subjected to Compressive Axial and Uniformly Distributed Load, measured in Length cannot be negative.

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

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

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

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

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

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

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

Other Formulas to find Maximum Initial Deflection

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

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

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

Variable Name

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