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Bending Moment at Some Distance from One End 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 {L shaft}^{2}}{12}) + (\frac{w \cdot x^{2}}{2}) - (\frac{w \cdot L shaft \cdot x}{2})

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

Bending Moment at Some Distance from One End Example

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Here is how the Bending Moment at Some Distance from One End equation looks like with Values.

Here is how the Bending Moment at Some Distance from One End equation looks like with Units.

Here is how the Bending Moment at Some Distance from One End equation looks like.

14.3125 = (\frac{3 \cdot {3.5}^{2}}{12}) + (\frac{3 \cdot 5^{2}}{2}) - (\frac{3 \cdot 3.5 \cdot 5}{2})

14.3125N*m = (\frac{3 \cdot {3.5m}^{2}}{12}) + (\frac{3 \cdot {5m}^{2}}{2}) - (\frac{3 \cdot 3.5m \cdot 5m}{2})

14.3125 = (\frac{3 \cdot {3.5}^{2}}{12}) + (\frac{3 \cdot 5^{2}}{2}) - (\frac{3 \cdot 3.5 \cdot 5}{2})

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Bending Moment at Some Distance from One End Solution

Follow our step by step solution on how to calculate Bending Moment at Some Distance from One End?

FIRST Step Consider the formula

M b = (\frac{w \cdot {L shaft}^{2}}{12}) + (\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 {3.5m}^{2}}{12}) + (\frac{3 \cdot {5m}^{2}}{2}) - (\frac{3 \cdot 3.5m \cdot 5m}{2})

Next Step Prepare to Evaluate

∴

M b = (\frac{3 \cdot {3.5}^{2}}{12}) + (\frac{3 \cdot 5^{2}}{2}) - (\frac{3 \cdot 3.5 \cdot 5}{2})

LAST Step Evaluate

∴

M b = 14.3125N*m

Bending Moment at Some Distance from One End 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

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

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

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

Go Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

ω n = \frac{2 \cdot π \cdot 0.571}{\sqrt{δ}}

Go Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

δ = {(\frac{0.571}{f})}^{2}

Go Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

f = \frac{0.571}{\sqrt{δ}}

Go M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

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

How to Evaluate Bending Moment at Some Distance from One End?

Bending Moment at Some Distance from One End evaluator uses Bending Moment = ((Load per unit length*Length of Shaft^2)/12)+((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, Bending Moment at Some Distance from One End formula is defined as a measure of the turning force around a pivot point or fulcrum, resulting from the external forces acting upon a beam or shaft, which is essential in structural analysis and design to ensure the stability and safety of the system. Bending Moment is denoted by M_b symbol.

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

FAQs on Bending Moment at Some Distance from One End

What is the formula to find Bending Moment at Some Distance from One End?

The formula of Bending Moment at Some Distance from One End is expressed as Bending Moment = ((Load per unit length*Length of Shaft^2)/12)+((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- 14.3125 = ((3*3.5^2)/12)+((3*5^2)/2)-((3*3.5*5)/2).

How to calculate Bending Moment at Some Distance from One End?

With Load per unit length (w), Length of Shaft (L_shaft) & Distance of Small Section of Shaft from End A (x) we can find Bending Moment at Some Distance from One End using the formula - Bending Moment = ((Load per unit length*Length of Shaft^2)/12)+((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 Bending Moment at Some Distance from One End be negative?

No, the Bending Moment at Some Distance from One End, measured in Moment of Force cannot be negative.

Which unit is used to measure Bending Moment at Some Distance from One End?

Bending Moment at Some Distance from One End 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 Bending Moment at Some Distance from One End can be measured.

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Bending Moment at Some Distance from One End Formula

Bending Moment at Some Distance from One End Example

Bending Moment at Some Distance from One End Solution

Bending Moment at Some Distance from One End Formula Elements

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

How to Evaluate Bending Moment at Some Distance from One End?

FAQs on Bending Moment at Some Distance from One End

Variable Name