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Maximum Bending Moment at Distance x from End A Formula

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Bending Moment is the rotational force that causes deformation in a beam during natural frequency of free transverse vibrations, affecting its stiffness and stability. Check FAQs

M b = \frac{w \cdot x^{2}}{2} - \frac{w \cdot L shaft \cdot x}{2}

M_b - Bending Moment?w - Load per unit length?x - Distance of Small Section of Shaft from End A?L_shaft - Length of Shaft?

Maximum Bending Moment at Distance x from End A Example

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Here is how the Maximum Bending Moment at Distance x from End A equation looks like with Values.

Here is how the Maximum Bending Moment at Distance x from End A equation looks like with Units.

Here is how the Maximum Bending Moment at Distance x from End A equation looks like.

11.25 = \frac{3 \cdot 5^{2}}{2} - \frac{3 \cdot 3.5 \cdot 5}{2}

11.25N*m = \frac{3 \cdot {5m}^{2}}{2} - \frac{3 \cdot 3.5m \cdot 5m}{2}

11.25 = \frac{3 \cdot 5^{2}}{2} - \frac{3 \cdot 3.5 \cdot 5}{2}

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Maximum Bending Moment at Distance x from End A Solution

Follow our step by step solution on how to calculate Maximum Bending Moment at Distance x from End A?

FIRST Step Consider the formula

M b = \frac{w \cdot x^{2}}{2} - \frac{w \cdot L shaft \cdot x}{2}

Next Step Substitute values of Variables

∴

M b = \frac{3 \cdot {5m}^{2}}{2} - \frac{3 \cdot 3.5m \cdot 5m}{2}

Next Step Prepare to Evaluate

∴

M b = \frac{3 \cdot 5^{2}}{2} - \frac{3 \cdot 3.5 \cdot 5}{2}

LAST Step Evaluate

∴

M b = 11.25N*m

Maximum Bending Moment at Distance x from End A Formula Elements

Variables

Bending Moment

Bending Moment is the rotational force that causes deformation in a beam during natural frequency of free transverse vibrations, affecting its stiffness and stability.

Symbol: M_b

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Bending Moment

Load per unit length

Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit length

Distance of Small Section of Shaft from End A

Distance of small section of shaft from end A is the length of a small section of shaft measured from end A in free transverse vibrations.

Symbol: x

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance of Small Section of Shaft from End A

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

Go Circular Frequency given Static Deflection

ω n = 2 \cdot π \cdot \frac{0.5615}{\sqrt{δ}}

Go Natural Frequency given Static Deflection

f = \frac{0.5615}{\sqrt{δ}}

Go Uniformly Distributed Load Unit Length given Static Deflection

w = \frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot {L shaft}^{4}}

Go Length of Shaft given Static Deflection

L shaft = {(\frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot w})}^{\frac{1}{4}}

How to Evaluate Maximum Bending Moment at Distance x from End A?

Maximum Bending Moment at Distance x from End A evaluator uses Bending Moment = (Load per unit length*Distance of Small Section of Shaft from End A^2)/2-(Load per unit length*Length of Shaft*Distance of Small Section of Shaft from End A)/2 to evaluate the Bending Moment, Maximum Bending Moment at Distance x from End A formula is defined as a measure of the maximum bending stress that occurs at a specific point along a shaft, typically in a mechanical system, due to external loads or forces, providing critical information for structural integrity and design considerations. Bending Moment is denoted by M_b symbol.

How to evaluate Maximum Bending Moment at Distance x from End A using this online evaluator? To use this online evaluator for Maximum Bending Moment at Distance x from End A, enter Load per unit length (w), Distance of Small Section of Shaft from End A (x) & Length of Shaft (L_shaft) and hit the calculate button.

FAQs on Maximum Bending Moment at Distance x from End A

What is the formula to find Maximum Bending Moment at Distance x from End A?

The formula of Maximum Bending Moment at Distance x from End A is expressed as Bending Moment = (Load per unit length*Distance of Small Section of Shaft from End A^2)/2-(Load per unit length*Length of Shaft*Distance of Small Section of Shaft from End A)/2. Here is an example- 11.25 = (3*5^2)/2-(3*3.5*5)/2.

How to calculate Maximum Bending Moment at Distance x from End A?

With Load per unit length (w), Distance of Small Section of Shaft from End A (x) & Length of Shaft (L_shaft) we can find Maximum Bending Moment at Distance x from End A using the formula - Bending Moment = (Load per unit length*Distance of Small Section of Shaft from End A^2)/2-(Load per unit length*Length of Shaft*Distance of Small Section of Shaft from End A)/2.

Can the Maximum Bending Moment at Distance x from End A be negative?

No, the Maximum Bending Moment at Distance x from End A, measured in Moment of Force cannot be negative.

Which unit is used to measure Maximum Bending Moment at Distance x from End A?

Maximum Bending Moment at Distance x from End A 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 at Distance x from End A can be measured.

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Maximum Bending Moment at Distance x from End A Formula

Maximum Bending Moment at Distance x from End A Example

Maximum Bending Moment at Distance x from End A Solution

Maximum Bending Moment at Distance x from End A Formula Elements

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

How to Evaluate Maximum Bending Moment at Distance x from End A?

FAQs on Maximum Bending Moment at Distance x from End A

Variable Name