METHODOLOGY FOR THE SELECTION OF SECOND HAND (RELAY) RAIL

Transcription

1 METHODOLOGY FOR THE SELECTION OF SECOND HAND (RELAY) RAIL The G-Index and Wear Rates. Written By Michael R. Garcia, P.E. Chief, Rail Engineering Bureau of Railroads Room 302 Illinois Department of Transportation 2300 South Dirksen Parkway Springfield, IL Bus: (217) Fax: (217)

2 ABSTRACT The railroad industry has long known the importance of cascading rail in an effort to maximize its resources. Railroad engineering departments knew what relay rail sections would work with what traffic configurations (speed and load) from experience and practice. Unfortunately, this ability to know has never been published in a practical way for the short line and light density community to use. The following paper establishes a methodology for the selection of a second hand (SH) or relay rail section taking into account speed, tonnage and loading criteria and is based on the same procedure used for the selection of new rail. This process also takes into consideration the available railhead steel. A new index, known as the G-Index or Girder Strength Index, is introduced in this paper ranks SH rail s resistance to bending to the requirements of the user. This allows the user to compare SH rail sections to each other for purposes of economic selection. The second part of the paper deals with known traffic density and recommended SH rail selection to provide for sufficient head wear until the next scheduled rail relay. Key Words: rail selection, railhead wear, G-Index, relay rail, second hand rail

3 METHODOLOGY FOR THE SELECTION OF SECOND HAND (RELAY) RAIL The G-Index and Wear Rates. The railroad industry has long known the importance of cascading rail in an effort to maximize its resources. Railroad engineering departments knew what relay rail sections would work with what traffic configurations (speed and load) from experience and practice. Unfortunately, this ability to know has never been published in a practical way for the shortline and light density community to use. This paper establishes a methodology for the selection of a second hand (SH) or relay rail section, taking into account speed, tonnage and loading criteria and is based on the same procedure used for the selection of new rail. The process also takes into consideration the available railhead steel. New Rail Selection, Deflection and Bending Moment. When determining new rail selection, the American Railway Engineering and Maintenance-of-Way Association s (AREMA) Manual (AREMA Manual for Railway Engineering, , EQ 12), Professor William Hay s text (Railroad Engineering, 2 nd Edition, page 250, equation 15.19), and the Talbot reports (Stresses In Railroad Track, page 1008, section 48) all use the same basic following equation: dyn dyn σ M allow = max ( 1) Z req

4 Equation 1 shows that the allowable dynamic rail stress (σ) equals the maximum dynamic rail bending moment (M) divided by the required rail section modulus (Z) about the base. This equation provides a rail section that will meet conditions and not get bent to a point where the steel in the rail yields. If Equation 1 is taken another step further by solving for the required section modulus about the base (Z), and the maximum dynamic rail bending moment (M) is replaced with its own defining equation (AREMA Manual for Railway Engineering, EQ 11 & EQ 9), a revised Equation 2 is produced as follows: P v 100d Z req = 4 k 4E I req 1 4 (2) dyn σallow Z = Section Modulus of Rail about the Base (required) P = Wheel Load (lbs.) k = Modulus of rail support (psi) v = Dominant Train Speed (mph) d = Wheel Diameter (in.) E = Young s Modulus of Elasticity for Rail Steel (30,000,000 psi) I = Moment of Inertia of Rail about Horizontal Centroidal Axis (required) σ = Rail Stress (allowable dynamic)

5 By taking Equation 2 and solving for it in terms of Z (section modulus) and I (moment of inertia), a completely new form of this equation is devised. Z req 1 4 I req v E P d = = G dyn 1 4 Index k σ allow (3) This arrangement produces an Equation 3 in which all rail dimensional unknowns are on the left side and all other track & train characteristics and constants are on the right. Thus, each side of this new equation defines a needed condition. The number generated from either side will hereinafter be referred to as the G-Index or Girder Strength Index. G-Index - Track & Train With this new equation, the G-Index can be determined for various track & train loading conditions (right side of Equation 3). Results of this are shown in Table 1 which is based on a wheel diameter (d) of 36 and an allowable stress (σ) of 25,000 psi (Railroad Engineering, 2 nd Edition, page 258). For ease of G-Index selection, Table 1 is graphed for the 100, 110 & 125-ton car loading in the following Figure 1.

6 TABLE 1, G-Index for Track & Train p = 26,250 lbs. (70-ton car) V k = 1,000 psi k = 3,000 psi k = 6,000 psi k = 11,000 psi 60 mph mph mph mph p = 32,875 lbs. (100-ton car) V k = 1,000 psi k = 3,000 psi k = 6,000 psi k = 11,000 psi 60 mph mph mph mph p = 35,750 lbs. (110-ton car) V k = 1,000 psi k = 3,000 psi k = 6,000 psi k = 11,000 psi 60 mph mph mph mph p = 39,375 lbs. (125-ton car) V k = 1,000 psi k = 3,000 psi k = 6,000 psi k = 11,000 psi 60 mph mph mph mph

7 Rail Support Modulus (k) Versus G-Index [allowable rail stress 25,000 psi & 36" wheel diameter] 12,000 10,000 8,000 k (psi) 6,000 4,000 2, G-Index 60 mph 125tn 40 mph 125tn 25 mph 125tn 10 mph 125tn 60 mph 110tn 40 mph 110tn 25 mph 110tn 10 mph 110tn 60 mph 100tn 40 mph 100tn 25 mph 100tn 10 mph 100tn Figure 1, Graph of k versus G-Index Notice that as speed and loading increase so does the G-Index or the need for increased girder strength, but as rail support (k) increases the need for increased girder strength is reduced. It should be noted that a value for k of less than 2,000 psi is considered poor (soft) track, whereas a value for k of greater than 10,000 psi is considered stiff (hard) track. Both of these conditions defeat the beam on elastic foundation theory of track support from which the equations are based.

8 G-Index Original Rail Profile (New) Alternatively a G-Index can easily be calculated for rail in its original profile (new), by dividing Section Modulus (Z) by the one-fourth power of Moment of Inertia (I) (left side of Equation 3). These values can be found in the AREMA manual or from most rail charts. TABLE 2, Section Modulus, Moment and G-Index for New Rail Design Rail Moment Section G-Index Section of Inertia (I) Modulus(Z) AREA 140 RE AREA AREA AREA AREA AREA AREA NYC 12722/ AREA AREA AREA AREA AREA AREA NYC AREA ARA-A ARA-B ARA-A ARA-B ASCE ASCE 8040/8004/ ASCE Table 2 shows these values and the calculated G-Index values for various rail sections in their original profile. By comparing track & train G-Index requirements (from Table 1) with a rail section whose G-Index (from Table 2) is equal to or greater than the track & train G-index needed, a new rail section can be quickly selected which fulfills speed, loading, and track condition requirements.

9 Second Hand (Relay) Rail Selection If the head of the rail remained constant the G-Index of the rail would never change; but as we all know this is not the case. Railhead wear is constantly occurring under traffic and is reducing the G-Index. So, while we may have had a perfect match when 100-ton cars were the norm and we had minor headwear on our rail, we are now faced with 110- ton cars (286,000 lbs.) and worn rail. How do we choose the right rail section for our next relay project if we can t afford new rail? G-Index Second Hand (Relay) Rail This process of determining a girder strength or G-Index can also be applied to SH rail provided that Z and I is calculated for the worn rail profile. Loss in cross sectional head area affects both Z and I. Figure 1 illustrates various top and combined side wear conditions for 115# rail: 1/8 wear, 3/16 wear, and 1/4 wear. These wear conditions, in addition to 3/8 wear (for heavier sections) are used as divisions for determining the Z, I, and G-Index for various AREMA rail sections and a few non-arema sections. While no rail has headwear which is uniform as shown in Figure 2, the actual G-Index will always be greater than calculated because the calculated value is based on the loss of all the steel within that wear condition. If any part of the loss exceeds that wear condition (total gage wear exceeds 1/8, but top wear is only 1/16 for example) it is dropped to the next lower wear condition (3/16 wear).

10 New /16" 1/8" 10.5% Head Loss 3/32" 3/16" 16.3% Head Loss 1/8" 1/4" 21.9% Head Loss Figure 2, 115RE Rail Head Wear Profiles

11 Table 3 provides the calculated G-Index for SH rail sections with the wear conditions as described previously (copies of the calculations for Z and I of relay rail would exceed the space requirements of this paper and can be obtained by contacting the author). TABLE 3, G-Index for Second Hand (Relay) Rail Rail G-Index G-Index G-Index G-Index G-Index Section New 1/8 wear 3/16 wear 1/4 wear 3/8 wear 140 RE / /8004/ Ranking New Rail and SH Rail Now that the Girder Strength Index is known for both new and relay rail, a chart can be arranged for comparison by G-Index value which is shown as Table 4. Comparisons of relay rail sections can now be made with ease using the same criteria AREMA recommends for new rail selection. Knowing track conditions, maximum speed and loading requirements a track & train G-Index can be matched with a relay or new rail section G-Index.

12 TABLE 4, G-Index for New & Second Hand (Relay) Rail by Descending Value Top/ Top/ Top/ Design Section G-Index Side Design Section G-Index Side Design Section G-Index Side Wear Wear Wear AREA New AREA /8 AREA New AREA 140 RE 9.15 New AREA /4 AREA /8 AREA /8 AREA /4 AREA /16 AREA New AREA /8 AREA /4 AREA /16 NYC /8 AREA New AREA 140 RE /8 AREA /16 ARA-A New AREA New AREA /8 AREA /8 AREA /4 AREA /8 ARA-A /8 AREA 140 RE /16 AREA /4 AREA /16 AREA /8 AREA XL ARA-A /16 NYC New AREA New AREA / AREA 140 RE /4 AREA /8 ARA-A /4 AREA /8 AREA /16 NYC New AREA /16 AREA New NYC /8 AREA /8 AREA /4 NYC /16 AREA New AREA /8 NYC /4 AREA /4 AREA New ARA-B New AREA /16 AREA New ARA-B /8 NYC /8 AREA /16 ARA-A New AREA New AREA /8 ARA-B /16 NYC /16 AREA New ARA-A / AREA /4 AREA /4 ARA-B /4 AREA 140 RE /8 AREA /8 ARA-A /16 AREA /8 AREA /16 ARA-B New AREA /8 AREA /8 ARA-B /8 NYC /4 AREA /16 ARA-B / AREA /8 AREA /4 ASCE New AREA /16 AREA /16 ASCE /8 AREA New AREA /4 ASCE /16 AREA /16 AREA /4 Wear Rates, Traffic Density, And Available HeadWear. Although a relay rail section could be selected based only on speed, track condition and loading, it is advisable that one other element be considered before a reasonable selection can be made; namely, the longevity of the rail to be installed, which is a function of traffic density and alignment, both of which will affect the rate of cross sectional wear to the relay rail head. While wear rates differ in curves and tangents, and on grades and flat, Professor Hay s Text suggests an overall wear rate of 0.1

13 square inches per 100 MGT (Railroad Engineering, 2 nd Edition, pages 533 and 534). Using this as a guide, a table is produced (Table 5) with the various rail head loss profiles (example as shown in Figure 2). TABLE 5, Estimated Available Rail Wear in MGT Existing Rail Head Wear Design Section 1/8 3/16 1/4 3/8 AREA 140 RE 1,274 1, AREA ,253 1, AREA , AREA , AREA , AREA , AREA , NYC , AREA AREA AREA AREA AREA AREA NYC AREA ARA-A ARA-B ARA-A ARA-B ASCE ASCE ASCE This table will provide the user with the information needed for estimated available rail wear for various relay rail sections and traffic densities. Table 5 uses a 25% loss in railhead wear as the maximum limit for usable rail weight of 126# and less and a 35% limit for 127# and heavier. Example Of A SH Rail Section Selection With the previous information known, a method for the selection of a relay rail section now exists. Let s set up an example for its use. Say that Short Line XYZ & Western currently has a rail section with 1/4 maximum top and combined side wear with

14 a fair crosstie, ballast and subgrade condition. The average annual traffic density (AATD) is roughly 4 MGT and the maximum speed is 25 mph with 100-ton cars as the normal traffic. As can be seen from Table 1 or Figure 1, the G-Index needed for the existing track & train conditions, using a k value of 3,000 psi, is Alternatively, SH rail with 1/4 wear has a G-Index of 6.53 (from Table 3). Therefore the existing rail is not being over stressed beyond its allowable limit until the k value deteriorates below approximately 2,000 psi. Let us suppose that XYZ & Western wants to accept 110-ton cars and must maintain its speed of 25 mph. A rail, crosstie, ballast and surface program is proposed. Rail support k value will be increased to 5,000. To determine the needed rail section, we refer to Figure 1 (or the equations), 110 ton, 25 mph, and 5,000 psi for k produce a G- Index of 5.5. Thus, the existing will not be overstressed in its new support condition. However, two other issues must be addressed: one, if the track is left to deteriorate as in the first condition, will the stresses in the rail be exceeded; and, two, is there sufficient steel in the rail head to last until the next scheduled upgrade? First, the track condition only needs to drop to a k of 2,500 to exceed allowable rail stresses. If we use a lower limit of 2,000 psi for k, a new SH rail section should be considered. If XYZ has any desire to increase speed or allow 125-ton cars, this should be factored into our selection. Looking again at Table 1 we notice that 40 mph with 110-ton cars or 25 mph with 125-ton cars produce a G-Index of about 7.70 at the lower limit of k equals 2,000 psi. From Table 4 we see that this condition is met with 119# rail with 3/16 wear or any rail section with a G-Index greater than 7.70.

15 Second, with respect to AATD, as can be seen in Table 5, it is recommended that the head and combined side wear not exceed 3/16 for sections less than 127#. This will allow a 50-year wear period at current traffic and average wear rate (50 years times 4 MGT/year equals 200MGT). Now it is a matter of economics ($/LF) and rail section reliability, as to which of the possible sections are selected. Conclusions This methodology of G-Index and rail wear provides an academic way to select a SH rail section which will satisfy the users track and train needs. By using the same method adhered to for selection and design of new rail, theory for all rail selection remains constant. This method does not, however, take into account the actual rail pedigree (for example, control cooled or not), internal defects, metallurgy, etc. or historical reliability of the rail section. This is left up to the user. The proposed procedure merely gives the user the knowledge as to whether the geometric dimensions of the rail section with known head/gage wear will meet or exceed the needs of the user.