Maximum Bending Moment at Distance x from End A Calculator

✖Load per unit length is the distributed load which is spread over a surface or line.ⓘ Load per unit length [w]			+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%
✖Length of shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+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.ⓘ Maximum Bending Moment at Distance x from End A [M_b]

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Formula

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Maximum Bending Moment at Distance x from End A

Formula

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

Example

`"3.75N*m"=("3"*("5m")^2)/2-("3"*"4500mm"*"5m")/2`

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Maximum Bending Moment at Distance x from End A Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
M_b = (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.
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.
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.

STEP 1: Convert Input(s) to Base Unit

Load per unit length: 3 --> No Conversion Required
Distance of small section of shaft from end A: 5 Meter --> 5 Meter No Conversion Required
Length of Shaft: 4500 Millimeter --> 4.5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_b = (w*x^2)/2-(w*L_shaft*x)/2 --> (3*5^2)/2-(3*4.5*5)/2

Evaluating ... ...

M_b = 3.75

STEP 3: Convert Result to Output's Unit

3.75 Newton Meter --> No Conversion Required

FINAL ANSWER

3.75 Newton Meter <-- Bending Moment

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft » Maximum Bending Moment at Distance x from End A

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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 Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Static Deflection at Distance x from End A

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

Natural Frequency due to Uniformly Distributed Load

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

Circular Frequency due to Uniformly Distributed Load

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

Maximum Bending Moment at Distance x from End A

Go 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

Length of Shaft given Circular Frequency

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

Uniformly Distributed Load Unit Length given Circular Frequency

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

Moment of Inertia of Shaft given Circular Frequency

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

Length of Shaft given Natural Frequency

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

Uniformly Distributed Load Unit Length given Natural Frequency

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

Moment of Inertia of Shaft given Natural Frequency

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

Length of Shaft given Static Deflection

Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)

Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

Go Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load

Go Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)

Uniformly Distributed Load Unit Length given Static Deflection

Go Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)

Circular Frequency given Static Deflection

Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

Natural Frequency given Static Deflection

Go Frequency = 0.5615/(sqrt(Static Deflection))

Static Deflection using Natural Frequency

Go Static Deflection = (0.5615/Frequency)^2

Maximum Bending Moment at Distance x from End A Formula

What is meant by bending moment?

A bending moment (BM) is a measure of the bending effect that can occur when an external force (or moment) is applied to a structural element. This concept is important in structural engineering as it is can be used to calculate where, and how much bending may occur when forces are applied.

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

Maximum Bending Moment at Distance x from End A calculator 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 calculate the Bending Moment, The Maximum bending moment at distance x from end A 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 Maximum Bending Moment at Distance x from End A using this online calculator? To use this online calculator 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. Here is how the Maximum Bending Moment at Distance x from End A calculation can be explained with given input values -> -0.33375 = (3*5^2)/2-(3*4.5*5)/2.

FAQ

What is Maximum Bending Moment at Distance x from End A?

The Maximum bending moment at distance x from end A 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*x^2)/2-(w*L_shaft*x)/2 or 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. Load per unit length is the distributed load which is spread over a surface or line, Distance of small section of shaft from end A is a numerical measurement of how far apart objects or points are & Length of shaft is the distance between two ends of shaft.

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

The Maximum bending moment at distance x from end A 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*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 Maximum Bending Moment at Distance x from End A, you need Load per unit length (w), Distance of small section of shaft from end A (x) & Length of Shaft (L_shaft). With our tool, you need to enter the respective value for Load per unit length, Distance of small section of shaft from end A & Length of Shaft 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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