Maximum Contact Shear Stress Calculator

✖Static Load is defined as the stationary load used for easy calculation of stress and moments.ⓘ Static Load [F_a]			+10% -10%
✖Radius of Wheel here specifies the radius of fully worn-out wheel.ⓘ Radius of Wheel [R_w]			+10% -10%

✖Contact shear stress is the shear stress at the contact point between wheel and rail.ⓘ Maximum Contact Shear Stress [F_s]

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Formula

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Maximum Contact Shear Stress

Formula

`"F"_{"s"} = 4.13*("F"_{"a"}/"R"_{"w"})^(1/2)`

Example

`"9.121644kgf/mm²"=4.13*("200tf"/"41mm")^(1/2)`

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Maximum Contact Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Contact Shear Stress = 4.13*(Static Load/Radius of Wheel)^(1/2)
F_s = 4.13*(F_a/R_w)^(1/2)
This formula uses 3 Variables

Variables Used

Contact Shear Stress - (Measured in Kilogram-Force per Square Millimeter) - Contact shear stress is the shear stress at the contact point between wheel and rail.
Static Load - (Measured in Ton-Force (Metric)) - Static Load is defined as the stationary load used for easy calculation of stress and moments.
Radius of Wheel - (Measured in Millimeter) - Radius of Wheel here specifies the radius of fully worn-out wheel.

STEP 1: Convert Input(s) to Base Unit

Static Load: 200 Ton-Force (Metric) --> 200 Ton-Force (Metric) No Conversion Required
Radius of Wheel: 41 Millimeter --> 41 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_s = 4.13*(F_a/R_w)^(1/2) --> 4.13*(200/41)^(1/2)

Evaluating ... ...

F_s = 9.12164405378232

STEP 3: Convert Result to Output's Unit

89452770.6600181 Pascal -->9.12164405378232 Kilogram-Force per Square Millimeter (Check conversion here)

FINAL ANSWER

9.12164405378232 ≈ 9.121644 Kilogram-Force per Square Millimeter <-- Contact Shear Stress

(Calculation completed in 00.004 seconds)

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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

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< 8 Lateral Forces Calculators

Section Modulus of Rail given Seat Load

Go Section Modulus = (Wheel Load*Sleeper Spacing)/(Characteristic Length of Rail*Seat Load)

Characteristic Length given Seat Load on Rail

Go Characteristic Length of Rail = Wheel Load*Sleeper Spacing/(Section Modulus*Seat Load)

Maximum Load on Rail Seat

Go Seat Load = Wheel Load*Sleeper Spacing/(Section Modulus*Characteristic Length of Rail)

Sleeper Spacing given Seat Load on Rail

Go Sleeper Spacing = Section Modulus*Characteristic Length of Rail*Seat Load/Wheel Load

Wheel Load given Seat Load

Go Wheel Load = Section Modulus*Characteristic Length of Rail*Seat Load/Sleeper Spacing

Maximum Contact Shear Stress

Go Contact Shear Stress = 4.13*(Static Load/Radius of Wheel)^(1/2)

Radius of Wheel given Shear Stress

Go Radius of Wheel = (4.13/Contact Shear Stress)^(2)*Static Load

Static Wheel Load given Shear Stress

Go Static Load = (Contact Shear Stress/4.13)^2*Radius of Wheel

Maximum Contact Shear Stress Formula

Contact Shear Stress = 4.13*(Static Load/Radius of Wheel)^(1/2)
F_s = 4.13*(F_a/R_w)^(1/2)

What are the Lateral Forces on rails?

The Lateral Force applied to the rail head produces a lateral deflection and twist in the rail. Lateral force causes the rail to bend horizontally and the resultant torque causes a huge twist in the rail as well as the bending of the head and foot of the rail. Lateral deflection of the rail is resisted by the friction between the rail and the sleeper, the resistance offered by the rubber pad and fastenings, as well as the ballast coming in contact with the rail.

How to Calculate Maximum Contact Shear Stress?

Maximum Contact Shear Stress calculator uses Contact Shear Stress = 4.13*(Static Load/Radius of Wheel)^(1/2) to calculate the Contact Shear Stress, The Maximum Contact Shear Stress is defined as the shear stress on the point of contact between the wheel and rail. The equation above is an empirical formula and the static load is in unit kg+1000kg for on-loading on curves. Contact Shear Stress is denoted by F_s symbol.

How to calculate Maximum Contact Shear Stress using this online calculator? To use this online calculator for Maximum Contact Shear Stress, enter Static Load (F_a) & Radius of Wheel (R_w) and hit the calculate button. Here is how the Maximum Contact Shear Stress calculation can be explained with given input values -> 9.3E-7 = 4.13*(1961329.99999986/0.041)^(1/2).

FAQ

What is Maximum Contact Shear Stress?

The Maximum Contact Shear Stress is defined as the shear stress on the point of contact between the wheel and rail. The equation above is an empirical formula and the static load is in unit kg+1000kg for on-loading on curves and is represented as F_s = 4.13*(F_a/R_w)^(1/2) or Contact Shear Stress = 4.13*(Static Load/Radius of Wheel)^(1/2). Static Load is defined as the stationary load used for easy calculation of stress and moments & Radius of Wheel here specifies the radius of fully worn-out wheel.

How to calculate Maximum Contact Shear Stress?

The Maximum Contact Shear Stress is defined as the shear stress on the point of contact between the wheel and rail. The equation above is an empirical formula and the static load is in unit kg+1000kg for on-loading on curves is calculated using Contact Shear Stress = 4.13*(Static Load/Radius of Wheel)^(1/2). To calculate Maximum Contact Shear Stress, you need Static Load (F_a) & Radius of Wheel (R_w). With our tool, you need to enter the respective value for Static Load & Radius of Wheel 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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