p = Dynamic wheel load (static load + 1% per MPH over 5 MPH)
= Modulus of elasticity of rail steel (30 x 10 6 psi)
= Moment of Inertia of rail (65.6 in 4 for 115RE)
= Track modulus of elasticity
AREMA recommended limit of deflection is 0.25”
Y 0 = p (64 3 ) ¼
27.
Maximum Rail Bending Moment (M 0 ) M 0 = p 64 ¼
28.
Maximum Rail Bending Stress C = distance in inches from the base of rail to its neutral axis AREMA recommended maximum = 25,000 psi Rail steel yield point = 70,000 psi M 0 C S =
29.
Ballast Pressure Under Centerline of Tie (P C ) P a = uniformly distributed pressure over the tie face h = depth below bottom of tie in inches P c of 20 psi is AREMA suggested value for firm subgrade soil. P C = 16.8 P a h 1.25
30.
Unit Pressure (P a ) Transmitted from Bottom of Tie to Ballast (psi) P = wheel load (lbs) 2P = Total tie load L = Tie length in inches b = Tie width in inches 2/3 = factor for 2 load bearing thirds of tie P a should not exceed 65 psi for wood ties 85 psi for concrete ties P a = 2P 2/3 bL 3P bL =
31.
Rail Stress from Temperature Change 115RE rail Area = 11.2465 sq.in. Moment of Inertia about neutral axis = 65.9 Yield Strength 70,000 psi min. Modulus of elasticity “E” 30x10 6 psi To determine tensile force for temperature change. Rail changes 0.0000065 of its length per degree. F S = unit stress . 0000065 t = S 30,000,000
32.
Rail Stress from Temperature Change For 70 F change Total Restraining Force F = 70x195 x 11.2465 F = 153,515 lbs Yield Point of 115 # Rail 70,000 x 1102465 = 787,255 lbs Insulated Joints tested to 600,000 lbs For 1 F change S = 30,000,000 x 0.0000065x1 = 195 psi
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