Railway Track Stresses

Track Stresses

Dynamic Augment (speed effect)

• for N.G

Space factor 

Where, V = Speed in km/hr.

μ = Track modulus in kg/cm/cm.

• For B.G & M.G

Speed factor 

Speed factor 

Hammer Blow Effect

Hammer blow 

Where, M = Net over weight in kg.

R = Crank pin diameter in m.

N = Number of revolution of wheel per sec.

θ = Crank angle.

Stream Effect

The vertical component of pressure of steam acting on piston is given in F.P.S units.

Where, L = Length of connecting rod in inches.

D = Diameter of piston in inches.

H = Height of cross head above the centre line of driving wheels in inches.

θ = Crank angle.

Inertia of Reciprocating Forces

Where, F_v = The vertical component of the accelerating force in the connecting rod (F_v) at crank

M = Mass of reciprocating parts

L = Length of connecting rod.

N = Number of revolution rod.

H = Height of cross head above the center line of driving wheel in inches.

θ = Crank angle.

Method of calculating longitudinal bending stress in rail

•  Where, x_i = Distance from the load to the point of contra flexure of the rail in cm.

I = Vertical moment of inertia of rail section in cm⁴

μ =Track modulus in kg/cm/cm.

• 
•  Where, M₀ = The bending moment in tone-cm-immediately under an isolated load P tone on one rail.

f_comp = The consequent compressive stress in the rail head under the load P in tone per square cm.

f_tension = The consequent tensile stress in the rail foot, under the load P, in tone per square cm.

D = Deflection of track in cm.

P = Load in on one rail in tones.

z_comp = Section modulus of rail in compression (cm³)

z_tension = Section modulus of rail in tension (cm³).

Rail wheel contact stresses

The maximum contact shear stress which occur in the transverse direction at right angle to the rail is,

 Where, T_max = Maximum shear stress in kg/mm².

Q = Static wheel load in kg. (p), increased for on-loading on curve. This on-loading is taken as 1 ton (1000kg)

Q = (P+100) kg.

R = Wheel radius in mm (fully worn condition).

Formation pressure

 Where, P_max = Maximum formation pressure

S = Sleeper spacing

D = Depth of ballast under sleeper

L = Effective length of sleeper under one rail seat.

= 76 cm for BG & 63 cm for MG.

μ = Track modulus (only track modulus in elastic range is considered)

I = Moment of inertia of worn rail along horizontal axis.

E = Modulus of elasticity of rail steel.

Track deterioration and Maintainability of Track

TD=P³(1+3S²)

Where, TD = Track deterioration factor

P = Nominal wheel load

TD∞P³