Bending Moment at Some Distance from One End Calculator

✖Load per unit length is the distributed load which is spread over a surface or line.ⓘ Load per unit length [w]			+10% -10%
✖Length of shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%
✖Distance of small section of shaft from end A is a numerical measurement of how far apart objects or points are.ⓘ Distance of small section of shaft from end A [x]			+10% -10%

✖The Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment at Some Distance from One End [M_b]

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Formula

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Bending Moment at Some Distance from One End

Formula

`"M"_{"b"} = (("w"*"L"_{"shaft"}^2)/12)+(("w"*"x"^2)/2)-(("w"*"L"_{"shaft"}*"x")/2)`

Example

`"4.72875N*m"=(("3"*("4500mm")^2)/12)+(("3"*("0.05m")^2)/2)-(("3"*"4500mm"*"0.05m")/2)`

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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) - The Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.
Distance of small section of shaft from end A - (Measured in Meter) - Distance of small section of shaft from end A is a numerical measurement of how far apart objects or points are.

STEP 1: Convert Input(s) to Base Unit

Load per unit length: 3 --> No Conversion Required
Length of Shaft: 4500 Millimeter --> 4.5 Meter (Check conversion here)
Distance of small section of shaft from end A: 0.05 Meter --> 0.05 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*4.5^2)/12)+((3*0.05^2)/2)-((3*4.5*0.05)/2)

Evaluating ... ...

M_b = 4.72875

STEP 3: Convert Result to Output's Unit

4.72875 Newton Meter --> No Conversion Required

FINAL ANSWER

4.72875 Newton Meter <-- Bending Moment

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load » Bending Moment at Some Distance from One End

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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< 17 Natural Frequency of Free Transverse Vibrations of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

Static Deflection at Distance x from End A given Length of Shaft

Go Static deflection at distance x from end A = (Load per unit length/(24*Young's Modulus*Moment of inertia of shaft))*(Distance of small section of shaft from end A^4+(Length of Shaft*Distance of small section of shaft from end A)^2-2*Length of Shaft*Distance of small section of shaft from end A^3)

Bending Moment at Some Distance from One End

Go 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)

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load

Go Natural Circular Frequency = sqrt((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load

Go Frequency = 3.573*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Length of Shaft = ((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Natural Circular Frequency^2))^(1/4)

Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Load per unit length = ((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Natural Circular Frequency^2))

M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*Young's Modulus*Acceleration due to Gravity)

Length of Shaft given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Length of Shaft = 3.573^2*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Frequency^2))^(1/4)

Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

Go Load per unit length = (3.573^2)*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Frequency^2))

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

Go Moment of inertia of shaft = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity)

Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4)

Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load)

Go Load per unit length = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^4))

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

Go Moment of inertia of shaft = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft

Go Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)

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

Go Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))

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

Go Frequency = 0.571/(sqrt(Static Deflection))

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

Go Static Deflection = (0.571/Frequency)^2

Bending Moment at Some Distance from One End Formula

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, The Bending Moment at some Distance from One End formula is defined as a measure of the bending effect that can occur when an external force (or moment) is applied to a structural element. 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 -> 4.72875 = ((3*4.5^2)/12)+((3*0.05^2)/2)-((3*4.5*0.05)/2).

FAQ

What is Bending Moment at Some Distance from One End?

The Bending Moment at some Distance from One End formula is defined as a measure of the bending effect that can occur when an external force (or moment) is applied to a structural element 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 distributed load which is spread over a surface or line, Length of shaft is the distance between two ends of shaft & Distance of small section of shaft from end A is a numerical measurement of how far apart objects or points are.

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

The Bending Moment at some Distance from One End formula is defined as a measure of the bending effect that can occur when an external force (or moment) is applied to a structural element 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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