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Bending Moment at Some Distance from One End Calculator

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Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load General Shaft Shaft Subjected to a Number of Point Loads Uniformly Distributed Load Acting Over a Simply Supported Shaft

✖Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.ⓘ Load per unit length [w]			+10% -10%
✖Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%
✖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.ⓘ Distance of Small Section of Shaft from End A [x]			+10% -10%

✖Bending Moment is the rotational force that causes deformation in a beam during natural frequency of free transverse vibrations, affecting its stiffness and stability.ⓘ Bending Moment at Some Distance from One End [M_b]

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Bending Moment at Some Distance from One End Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
M_b = ((w*L_shaft^2)/12)+((w*x^2)/2)-((w*L_shaft*x)/2)
This formula uses 4 Variables

Variables Used

Bending Moment - (Measured in Newton Meter) - Bending Moment is the rotational force that causes deformation in a beam during natural frequency of free transverse vibrations, affecting its stiffness and stability.
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.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.
Distance of Small Section of Shaft from End A - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Load per unit length: 3 --> No Conversion Required
Length of Shaft: 3.5 Meter --> 3.5 Meter No Conversion Required
Distance of Small Section of Shaft from End A: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_b = ((w*L_shaft^2)/12)+((w*x^2)/2)-((w*L_shaft*x)/2) --> ((3*3.5^2)/12)+((3*5^2)/2)-((3*3.5*5)/2)

Evaluating ... ...

M_b = 14.3125

STEP 3: Convert Result to Output's Unit

14.3125 Newton Meter --> No Conversion Required

FINAL ANSWER

14.3125 Newton Meter <-- Bending Moment

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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Bending Moment at Some Distance from One End Formula

LaTeX Go

What is a Transverse Wave definition?

Transverse wave, motion in which all points on a wave oscillate along paths at right angles to the direction of the wave's advance. Surface ripples on water, seismic S (secondary) waves, and electromagnetic (e.g., radio and light) waves are examples of transverse waves.

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

Bending Moment at Some Distance from One End calculator 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 calculate 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 calculate Bending Moment at Some Distance from One End using this online calculator? To use this online calculator 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. Here is how the Bending Moment at Some Distance from One End calculation can be explained with given input values -> 14.3125 = ((3*3.5^2)/12)+((3*5^2)/2)-((3*3.5*5)/2).

FAQ

What is Bending Moment at Some Distance from One End?

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 and is represented as M_b = ((w*L_shaft^2)/12)+((w*x^2)/2)-((w*L_shaft*x)/2) or 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). Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations, Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft & 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.

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

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 is calculated using 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 calculate Bending Moment at Some Distance from One End, you need Load per unit length (w), Length of Shaft (L_shaft) & Distance of Small Section of Shaft from End A (x). With our tool, you need to enter the respective value for Load per unit length, Length of Shaft & Distance of Small Section of Shaft from End A and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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