Isolated Vertical Load given Moment Calculator

✖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 [M]			+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%

✖Vertical Load on Member here specifies the vertical load acting on the member.ⓘ Isolated Vertical Load given Moment [L_Vertical]

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Isolated Vertical Load given Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
L_Vertical = M/(0.25*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

Vertical Load on Member - (Measured in Kilonewton) - Vertical Load on Member here specifies the vertical load acting on the member.
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.
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

Bending Moment: 1.38 Newton Meter --> 1.38 Newton Meter 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

L_Vertical = M/(0.25*exp(-x/l)*(sin(x/l)-cos(x/l))) --> 1.38/(0.25*exp(-2.2/2.1)*(sin(2.2/2.1)-cos(2.2/2.1)))

Evaluating ... ...

L_Vertical = 42.926000957455

STEP 3: Convert Result to Output's Unit

42926.000957455 Newton -->42.926000957455 Kilonewton (Check conversion here)

FINAL ANSWER

42.926000957455 ≈ 42.926 Kilonewton <-- Vertical Load on Member

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Coorg Institute of Technology (CIT), Coorg

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< Vertical Loads Calculators

Isolated Vertical Load given Moment

LaTeX 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

LaTeX 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))

Stress in Rail Head

LaTeX Go Bending Stress = Bending Moment/Section Modulus in Compression

Stress in Rail Foot

LaTeX Go Bending Stress = Bending Moment/Section Modulus in Tension

Isolated Vertical Load given Moment Formula

LaTeX Go

where will be the bending moments maximum?

According to equation, the bending moment is zero at points where x = pi/4, 3pi/4 and maximum at x= 0, pi/2, 3pi/2 etc.
The general theory of bending of rails is based on the assumption that the rail is
a long bar continuously supported by an elastic foundation.

How to Calculate Isolated Vertical Load given Moment?

Isolated Vertical Load given Moment calculator uses 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))) to calculate the Vertical Load on Member, Isolated Vertical Load given Moment is defined as vertical load which caused bending or flexural stress on rail. theory of stresses in rails takes into account elastic nature of supports. Vertical Load on Member is denoted by L_Vertical symbol.

How to calculate Isolated Vertical Load given Moment using this online calculator? To use this online calculator for Isolated Vertical Load given Moment, enter Bending Moment (M), Distance from Load (x) & Characteristic Length (l) and hit the calculate button. Here is how the Isolated Vertical Load given Moment calculation can be explained with given input values -> 0.042926 = 1.38/(0.25*exp(-2.2/2.1)*(sin(2.2/2.1)-cos(2.2/2.1))).

FAQ

What is Isolated Vertical Load given Moment?

Isolated Vertical Load given Moment is defined as vertical load which caused bending or flexural stress on rail. theory of stresses in rails takes into account elastic nature of supports and is represented as L_Vertical = M/(0.25*exp(-x/l)*(sin(x/l)-cos(x/l))) or 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))). 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, 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 Isolated Vertical Load given Moment?

Isolated Vertical Load given Moment is defined as vertical load which caused bending or flexural stress on rail. theory of stresses in rails takes into account elastic nature of supports is calculated using 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))). To calculate Isolated Vertical Load given Moment, you need Bending Moment (M), Distance from Load (x) & Characteristic Length (l). With our tool, you need to enter the respective value for Bending Moment, 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.

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