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Bending Moment on Rail Formula

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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. Check FAQs

M = 0.25 \cdot L Vertical \cdot \exp (- \frac{x}{l}) \cdot (\sin (\frac{x}{l}) - \cos (\frac{x}{l}))

M - Bending Moment?L_Vertical - Vertical Load on Member?x - Distance from Load?l - Characteristic Length?

Bending Moment on Rail Example

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Here is how the Bending Moment on Rail equation looks like with Values.

Here is how the Bending Moment on Rail equation looks like with Units.

Here is how the Bending Moment on Rail equation looks like.

1.5753 = 0.25 \cdot 49 \cdot \exp (- \frac{2.2}{2.1}) \cdot (\sin (\frac{2.2}{2.1}) - \cos (\frac{2.2}{2.1}))

1.5753N*m = 0.25 \cdot 49kN \cdot \exp (- \frac{2.2m}{2.1m}) \cdot (\sin (\frac{2.2m}{2.1m}) - \cos (\frac{2.2m}{2.1m}))

1.5753 = 0.25 \cdot 49 \cdot \exp (- \frac{2.2}{2.1}) \cdot (\sin (\frac{2.2}{2.1}) - \cos (\frac{2.2}{2.1}))

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Bending Moment on Rail Solution

Follow our step by step solution on how to calculate Bending Moment on Rail?

FIRST Step Consider the formula

M = 0.25 \cdot L Vertical \cdot \exp (- \frac{x}{l}) \cdot (\sin (\frac{x}{l}) - \cos (\frac{x}{l}))

Next Step Substitute values of Variables

∴

M = 0.25 \cdot 49kN \cdot \exp (- \frac{2.2m}{2.1m}) \cdot (\sin (\frac{2.2m}{2.1m}) - \cos (\frac{2.2m}{2.1m}))

Next Step Prepare to Evaluate

∴

M = 0.25 \cdot 49 \cdot \exp (- \frac{2.2}{2.1}) \cdot (\sin (\frac{2.2}{2.1}) - \cos (\frac{2.2}{2.1}))

Next Step Evaluate

∴

M = 1.57526903256187N*m

LAST Step Rounding Answer

∴

M = 1.5753N*m

Bending Moment on Rail Formula Elements

Variables

Functions

Bending Moment

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.

Symbol: M

Measurement: Moment of ForceUnit: N*m

Note: Value can be positive or negative.

Formulas to find Bending Moment

Vertical Load on Member

Vertical Load on Member here specifies the vertical load acting on the member.

Symbol: L_Vertical

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Vertical Load on Member

Distance from Load

Distance from Load here refers to the distance from the vertical load to the point considered.

Symbol: x

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance from Load

Characteristic Length

Characteristic length specifies the length of the rail which is defined as ratio of stiffness and track modulus.

Symbol: l

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Characteristic Length

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other formulas in Vertical Loads category

Go Isolated Vertical Load given Moment

L Vertical = \frac{M}{0.25 \cdot \exp (- \frac{x}{l}) \cdot (\sin (\frac{x}{l}) - \cos (\frac{x}{l}))}

Go Stress in Rail Head

S h = \frac{M}{Z c}

Go Stress in Rail Foot

S h = \frac{M}{Z t}

Go Dynamic Overload at Joints

F = F a + 0.1188 \cdot V t \cdot \sqrt{w}

How to Evaluate Bending Moment on Rail?

Bending Moment on Rail evaluator uses Bending Moment = 0.25*Vertical Load on Member*exp(-Distance from Load/Characteristic Length)*(sin(Distance from Load/Characteristic Length)-cos(Distance from Load/Characteristic Length)) to evaluate the Bending Moment, The Bending Moment on Rail is defined when the vertical loads acting on the rail creates flexural or bending stresses on rails. Bending Moment is denoted by M symbol.

How to evaluate Bending Moment on Rail using this online evaluator? To use this online evaluator for Bending Moment on Rail, enter Vertical Load on Member (L_Vertical), Distance from Load (x) & Characteristic Length (l) and hit the calculate button.

FAQs on Bending Moment on Rail

What is the formula to find Bending Moment on Rail?

The formula of Bending Moment on Rail is expressed as Bending Moment = 0.25*Vertical Load on Member*exp(-Distance from Load/Characteristic Length)*(sin(Distance from Load/Characteristic Length)-cos(Distance from Load/Characteristic Length)). Here is an example- 1.575269 = 0.25*49000*exp(-2.2/2.1)*(sin(2.2/2.1)-cos(2.2/2.1)).

How to calculate Bending Moment on Rail?

With Vertical Load on Member (L_Vertical), Distance from Load (x) & Characteristic Length (l) we can find Bending Moment on Rail using the formula - Bending Moment = 0.25*Vertical Load on Member*exp(-Distance from Load/Characteristic Length)*(sin(Distance from Load/Characteristic Length)-cos(Distance from Load/Characteristic Length)). This formula also uses Sine (sin)Cosine (cos), Exponential Growth (exp) function(s).

Can the Bending Moment on Rail be negative?

Yes, the Bending Moment on Rail, measured in Moment of Force can be negative.

Which unit is used to measure Bending Moment on Rail?

Bending Moment on Rail 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 on Rail can be measured.

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Bending Moment on Rail Formula

Bending Moment on Rail Example

Bending Moment on Rail Solution

Bending Moment on Rail Formula Elements

Other formulas in Vertical Loads category

How to Evaluate Bending Moment on Rail?

FAQs on Bending Moment on Rail

Variable Name