Bending Moment on Rail Calculator

✖Vertical Load on Member here specifies the vertical load acting on the member.ⓘ Vertical Load on Member [L_Vertical]			+10% -10%
✖Distance from Load here refers to the distance from the vertical load to the point considered.ⓘ Distance from Load [x]			+10% -10%
✖Characteristic length specifies the length of the rail which is defined as ratio of stiffness and track modulus.ⓘ Characteristic Length [l]			+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 on Rail [M]

⎘ Copy

👎

Formula

✖

Bending Moment on Rail

Formula

`"M" = 0.25*"L"_{"Vertical"}*exp(-"x"/"l")*(sin("x"/"l")-cos("x"/"l"))`

Example

`"1.575269N*m"=0.25*"49kN"*exp(-"2.2m"/"2.1m")*(sin("2.2m"/"2.1m")-cos("2.2m"/"2.1m"))`

Calculator

LaTeX

Reset

👍

Download Railway Track and Track Stresses Formulas PDF PDF Image

Bending Moment on Rail Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
M = 0.25*L_Vertical*exp(-x/l)*(sin(x/l)-cos(x/l))
This formula uses 3 Functions, 4 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., exp(Number)

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.
Vertical Load on Member - (Measured in Kilonewton) - Vertical Load on Member here specifies the vertical load acting on the member.
Distance from Load - (Measured in Meter) - Distance from Load here refers to the distance from the vertical load to the point considered.
Characteristic Length - (Measured in Meter) - Characteristic length specifies the length of the rail which is defined as ratio of stiffness and track modulus.

STEP 1: Convert Input(s) to Base Unit

Vertical Load on Member: 49 Kilonewton --> 49 Kilonewton No Conversion Required
Distance from Load: 2.2 Meter --> 2.2 Meter No Conversion Required
Characteristic Length: 2.1 Meter --> 2.1 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = 0.25*L_Vertical*exp(-x/l)*(sin(x/l)-cos(x/l)) --> 0.25*49*exp(-2.2/2.1)*(sin(2.2/2.1)-cos(2.2/2.1))

Evaluating ... ...

M = 1.57526903256187

STEP 3: Convert Result to Output's Unit

1.57526903256187 Newton Meter --> No Conversion Required

FINAL ANSWER

1.57526903256187 ≈ 1.575269 Newton Meter <-- Bending Moment

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Transportation Engineering » Railway Engineering » Railway Track and Track Stresses » Vertical Loads » Bending Moment on Rail

Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has verified this Calculator and 700+ more calculators!

< 7 Vertical Loads Calculators

Isolated Vertical Load given Moment

Go Vertical Load on Member = Bending Moment/(0.25*exp(-Distance from Load/Characteristic Length)*(sin(Distance from Load/Characteristic Length)-cos(Distance from Load/Characteristic Length)))

Bending Moment on Rail

Go 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))

Static Wheel Load given Dynamic Load

Go Static Load = Dynamic Overload-0.1188*Speed of Train*sqrt(Unsuspended Mass)

Dynamic Overload at Joints

Go Dynamic Overload = Static Load+0.1188*Speed of Train*sqrt(Unsuspended Mass)

Mass per Wheel given Dynamic Load

Go Unsuspended Mass = ((Dynamic Overload-Static Load)/(0.1188*Speed of Train))^2

Stress in Rail Head

Go Bending Stress = Bending Moment/Section Modulus in Compression

Stress in Rail Foot

Go Bending Stress = Bending Moment/Section Modulus in Tension

Bending Moment on Rail Formula

What are the objectives of station planning?

In planning any station the following objectives need to be kept very much in mind:
• Attractiveness in appearance.
• Free movement of passengers.
• Safe evacuation in emergency.
• Access for the disabled.
• Access for emergency services.
• Safe accumulation and dispersal of crowds.
• Reliable operation of train service.
• Resilience to failure.
• Cost-effective investment.

How to Calculate Bending Moment on Rail?

Bending Moment on Rail calculator 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 calculate 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 calculate Bending Moment on Rail using this online calculator? To use this online calculator for Bending Moment on Rail, enter Vertical Load on Member (L_Vertical), Distance from Load (x) & Characteristic Length (l) and hit the calculate button. Here is how the Bending Moment on Rail calculation can be explained with given input values -> 1.575269 = 0.25*49000*exp(-2.2/2.1)*(sin(2.2/2.1)-cos(2.2/2.1)).

FAQ

What is Bending Moment on Rail?

The Bending Moment on Rail is defined when the vertical loads acting on the rail creates flexural or bending stresses on rails and is represented as M = 0.25*L_Vertical*exp(-x/l)*(sin(x/l)-cos(x/l)) or 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)). Vertical Load on Member here specifies the vertical load acting on the member, Distance from Load here refers to the distance from the vertical load to the point considered & Characteristic length specifies the length of the rail which is defined as ratio of stiffness and track modulus.

How to calculate Bending Moment on Rail?

The Bending Moment on Rail is defined when the vertical loads acting on the rail creates flexural or bending stresses on rails is calculated using 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 calculate Bending Moment on Rail, you need Vertical Load on Member (L_Vertical), Distance from Load (x) & Characteristic Length (l). With our tool, you need to enter the respective value for Vertical Load on Member, Distance from Load & Characteristic Length and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search