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\ ^-in strands conforming to ASTM A 416 as shown in Fig. 2. Curbs are provided by 6- by 12 -in timbers held in place with ^-in bolts 18 in long.

No double bents were used in the bridge.

Both the cast-in-place caps and the columns were designed using /'o=: 3,500 psi. The indicated average 28-day concrete cylinder strength for the columns ranged from 4,900 to 6,300 psi. All the reinforced concrete columns were spliced at about the ground line. The reinforcing above the ground consists of eight No. 8 bars with a No. 4 spiral pitched at 2J^ in. Below the ground the reinforcing consists of eight No. 10 bars with No. 4 spiral at 6 in. All reinforcement conforms to ASTM A 305.

The design live load was Cooper E 65 and 33 percent impact. The impact equation used was:

7 = 35 ~

500

as suggested in AREA Proceedings, Vol. 67, page 400.

The design assumptions used for longitudinal force resulting from the starting and stopping of trains were based on:

a. Force due to braking: One half of 15 percent of the live load without impact on only 6 spans or 198 ft of trestle and longitudinal force transmitted to 7 bents.

b. Force due to traction: One half of 25 percent of the weight on the driving wheels, without impact, transmitted equally to 2 bents.

Five-inch SR-4 strain gages were appUed 20 ft 6 in below the caps, or about 6 in above ground line on the center columns of alternate bents, as shown on Fig. 1 and on test bents 8, 9 and 10 as shown on the same figure. All gages were placed on the north and south faces of the columns. Gages were also placed on the bottom, 1 ft 6 in south of the center of the beams of span 9.

The rail on the bridge was Colorado Sec. 903, 1915, OH, laid in 33-ft lengths with four-bolt angle bars. Since the rail joints on this bridge were staggered approximately one-half rail length it was necessary, before the test began, to provide squared joints at each abutment by sawing the rail opposite two existing joints and installing angle bars and bolts. The rail gages were placed approximately 2 ft beyond these squared joints, as shown (see Fig. 1). The 1-in SR-4 gages were placed on the neutral axis to record longi- tudinal, axial strains. The saw cuts left rail gaps of only about Y^ in and it was neces- sary to open these to about J^ in with a joint spreader. The two existing joints were also spread to a gap of % in.

All joint-bar bolts on the bridge (and those in the squared joints) were individually checked by railroad section men before the test began to make certain all were tight. For those runs conducted with loose joints, only the squared joints were loosened (the others on the bridge were left tight). The joints were disassembled and the angle bars and rail surfaces were cleaned. The fishing surfaces were greased and the joints reas- sembled. The bolts were tightened only enough to keep the angle bars in p>osition and the rails in line.

Longitudinal Forces in a Concrete Trestle 4J^

To measure the longitudinal movement of bent 8, a linear extensometer was used. The fixed end was fastened to a timber trestle immediately adjacent to the concrete trestle and the other end was connected to the concrete cap.

The response from all the strain gages was ampliiied and recorded by two 12- channel oscillographs on photographic paper. A detailed description of the o.scillographs and their auxiliary units is given in the AREA Proceedings, Vol. 46, page 201, 1945, and a description of the SR-4 wire resistance strain gages with the necessary equipment is given in the Proceedings, Vol. 52, page 152, 1951.

D. TEST TRAIN

The test train consisted of two 4-axle diesel locomotives and four loaded hopper cars. It had a total length of 277 ft 10 in and a total weight of 1,269.6 kips. One loco- motive had axle loads of 62.4 kips and the other, 61.9 kips. The axle loads of the cars ranged from 47.2 to 50.1 kips. It was assumed that the total locomotive and car weights were distributed equally to each axle. The axle loads and spacings are shown in Table 1.

The Cooper equivalent of the two-unit locomotive in bending on the test span is E 32.3 and for the cars (cars 1 and 2 combined), E 42.9.

E. TEST RESULTS

The bents and span were instrumented as shown on Fig. 1. The investigation was conducted in several series because of the various studies involved and the limitations of the recording equipment. These series were Braking, Traction and Normal Running of the test train over the bridge. In general, each series was conducted as follows:

Braking (a) Braking to a stop at various positions on the bridge; (b) braking across the bridge and stopping beyond it.

Traction Starting from various positions on the bridge and accelerating off the bridge.

Each of the above was conducted with: (a) Tight rail joints at each abutment; (b) Loosened joints at each abutment.

Simultaneous recordings were obtained to determine: (a) Bending strains at ground line in bents throughout length of bridge; (b) vertical distribution of bending strains in a single column; (c) bending strains in columns and axial strains in the rails at the abutments.

Normal Running (a) Constant speed, static runs (5 mph or less) across the test span; (b) constant speed, dynamic runs, at various speeds to 30 mph across the test span.

The above runs were made to determine: (a) Flexural strains in the beams; (b) compressive strains in the columns of the two supporting bents.

1. Typical Oscillograms for Braking and Traction

The data were recorded on oscillograms and typical traces are presented for:

(a) Braking to a stop on the bridge with tight rail joints. Fig. 4.

(b) Braking to a stop on the bridge with loosened rail joints at the abutments, Fig. 5.

(c) Traction or starting from a stopped position on the bridge with tight rail joints. Fig. 6.

(d) Traction with loosened rail joints. Fig. 7.

42 Longitudinal Forces in a Concrete Trestle

On Fig. 4 are shown the elevation of the bridge and symbols for SR-4 strain gages located near the ground line on bents 2, 4, 6, 8, 12, 14, 16 and 18. A light trace activated by a wheel trip is shown below the Elevation. The position of this wheel trip was on the center line of bent 13. Offsets to this trace indicated that 8 wheels passed over the trip before the train stopped. Below this are shown 15 traces responding to SR-4 gages. On the left hand side the bent number is shown corresponding to each of the traces.

Since the test train stopped at bent 10, the braking stress ahead of the train for bents 2, 4, 6 and 8 can be seen. For the other bents, however, the effect of the direct vertical stress is combined with the braking stress, and the latter was determined by reading the peak value and the value for direct stress. Also shown is the position of the first axle of the train when the brakes were applied as well as the position where vertical load began for each bent. For this run, the greatest braking stress of 273 psi occurred at bent 12 where a compression stress of 288 psi and a tensile stress of 258 were recorded.

On Fig. 5 are shown data similar to Fig. 4 except that the rail joints were loosened at the abutments. For this run, No. 24, the greatest braking stress occurred at bent 14, where a compression stress of 327 psi and a tensile stress of 278 psi were recorded.

After the train stopped the entire structure rebounded and vibrated longitudinally at a frequency of about 2.8 cps, as shown by the traces to the left of the point at which maximum braking stress occurred.

The oscillogram traces showing the effect of traction forces on the bridge are much less definitive than those for braking. Whereas the traces under braking attained a peak value at the instant of stopping, no such definite peak was apparent on the traces during traction runs. Every effort was made to develop a "hard start" by applying full power with the brakes set and then releasing them, but the transmission of power to the rails was not sudden (as in the case of braking) but gradual, and the maximum effect on the structure was not noted until the train had moved forward some distance. It was neces- sary, therefore, in determining the traction stresses, to compare the oscillogram traces under a normal slow-speed run of the train with a run under full traction. Fig. 6 shows such a comparison. The traces are shown in pairs: 1, 1-S; 2, 2-S; etc. The 1 trace repre- sents stress during traction, and the 1-S trace is for a regular slow-speed run. Com- paring the two traces and reading the maximum differences furnished the data for traction bending stresses.

Also on Fig. 6 are shown the elevation of the bridge and the initial starting posi- tion, as well as the position where maximum traction was read. At the left-hand side are the bent and trace position of the gages. The largest traction effect is shown for bent 8 where trace 6 indicates a tension stress of 117 psi and trace 7 a compressive stress of 158 psi for an average bending stress of 138 psi. This occurred during the condition of tight rail joints.

Fig. 7 shows typical traces with loosened joints, and is similar to Fig. 6. Under this condition for bent 8, traces 7 and 8, respectively, show a tensile stress of 124 psi and a compressive stress of 132 psi for an average bending stress of 128 psi.

2. Braking to a Stop on the Bridge

A total of 19 runs in which the test train came to a stop on the bridge was made and the results appear on Figs. 8 to 14, incl. Nine of the runs were recorded when the rail joints were tight and the others when the rail joints were loosened.

Each figure shows the elevation of the bridge and the stopped position of the test train for that particular run. The ordinate lines denote bent position, while the open

Longitudinal Forces in a Concrete Trestle 4^

circles denote the magnitude of the bending stress in psi for the bent. The exlremc right- and left-hand ordinates show the recorded axial force in the rails and these are plotted as closed circles showing the corresponding rail stresses in psi.

It can be seen that the curve described by the plotted points of these figures is somewhat parabolic in shape. The maximum values are shown to be under the train in its stopped position, with lower values toward the ends of the bridge. It should be noted, however, that the entire bridge is affected by the applied longitudinal force and that unloaded bents as well as those which receive vertical loads from the train are con- tributing to the resistance to this force. Furthermore, for the condition with tight rail joints, the rails at each end of the bridge resist longitudinal force regardless of where the train stopped on the bridge. It is apparent that higher bent stress occurred when the rail joints were loosened than when they were tight.

The maximum bending stress with the rail joints tight occurred during run 14 which appears in the middle chart on Fig. 8; its value is 280 psi. During run 24, with loose rail joints, the train stopped at nearly the same location and the maximum bend- ing stress was 295 psi. In general, all of the recorded values for this run are significantly higher than for run 14, due to loosened rail joints at the ends of the bridge.

The effect on rail stress of loosening the rail joints is apparent by comparing the recorded rail stress of Figs. 8, 9 and 10 with those on Figs. 11, 12, 13 and 14. At the south end of the bridge with tight joints the recorded stresses varied from 640 to a max- imum of 1,700 psi. After these joints were loosened the stresses varied from zero to a maximum of only 300 psi. At the north end of the bridge, there was a similar reduction. In the case of tight joints the recorded stresses varied from 130 to a maximum of 2,420 psi., and after loosening the variation was 220 to a maximum of 650 psi. It is apparent that the joints at the north end of the bridge were not completely unrestrained with respect to their ability to carry axial forces. The recorded values shown are the average of both rails, but the east rail (which had the sawed rail) still carried some force, whereas the west rail (which had the original joint) carried none. The southward move- ment of the bridge under braking force opened the joints at the north end and closed them at the south end. Apparently, this movement was more than the north joints on the east rail could accommodate and the holes in the rail came into bearing with the bolts. There may also have been some frictional resistance through the angle bars. Obvi- ously, there was some apprehension about operating with loose joints and it was, of course, important to maintain safe conditions, particularly since the north approach was on a curve that ended at the loosened joints. Thus, these joints in their loosened condi- tion were probably tighter than those at the south end.

On Table 2 are shown the recorded braking strains converted to force in kips. On the left hand side of the table are the individual bent numbers with the run numbers across the top. The table is separated into "Tight Joint Bars" and "Loosened Joint Bars."

The bent forces in Table 2 were derived from the recorded and interpolated values by assuming that the horizontal braking force due to stopping on the bridge acted at the top of the bent and that the bent was a cantilever fixed below the ground line. The section modulus, S, for one column at the lower gage location is 1,786 inl Using the recorded stress, free, at this gage location, the horizontal force, F, applied at a distance, d, from the gage location, was then determined as follows:

P __ 3iJ free.

d

44 Longitudinal Forces in a Concrete Trestle

It should be noted that the recorded values are actually strains and to convert them to stresses an assumption regarding the concrete modulus of elasticity was made. For an assumed concrete modulus of 5,000,000 psi the force conversion factor is:

F _ 3 X 1,786 X 5,000,000 XIO^^ _ 101.4 e

264

where e is the recorded strain in microinches per inch. For the case of a concrete modulus of 4,000,000 psi the braking force conversion factor is:

F = 81.2e

Values shown in Table 2 are given for two moduli because of the range of the strength of the concrete used in these columns. Maximum bent forces occurred during runs 14 and 24 and are shown to be 5.5 kips and 5.9 kips, respectively.

The rail forces in both rails at the north and south abutment were determined by adding the rail stresses together. For example, during run IS, the stress in each rail at the south end of the bridge was 980 and 1,000 psi. Since the area of the rail is 8.75 sq in and assuming this stress is spread over the total area, the total compressive force transmitted by the rails at the south end was (980 + 1,000) X 8.75 = 17,300 lb. At this same instant, tensile stresses induced in the rail at the north end of the bridge were + 1,680 and + 1,680 psi. The total tensile force transmitted by the rails at the north end was (1680+ 1680) X 8.75 = 29,400 lb. The total longitudinal force carried by the rails was, thus, 46,700 lbs or 46.7 kips for this particular run, and that is the value tabulated under run 15 in Table 2 for rail force.

To compare the values of Table 2 with respect to tight and loose joint bars, it is necessary to use runs where the stopped train positions were approximately the same. Such comparisons can be made using runs 14 and 24, 15 and 21, 12 and 25, 10 and 20. These are as follows:

Braking Force Kips

Run Number

To

tal Bent

Total Rail

14

62.8

55.8

Tight 15

65.5

46.6

Rail Joints 12

58.1

36.8

10

52.2

37.6

Average

59.6

44.2

Run Number

Total Bent

Total Rail

24

76.4

10.8

Loosened 21

73.9

7.8

Rail Joints 25

65.8

6.0

20

Ave

rage

51.0 66.8

9.8 8.4

From the above, it can be seen that the effect of loosening the rail joints was to increase the load to the bents by a total of 7.2 kips. Since the reduction in load to the rails was 35.8 kips, it seems reasonable to assume that the balance of the load, or about 28 kips, went directly to the abutments.

Table 2 also shows values of longitudinal force calculated from recorded accelera- tions. These were derived from the relationship, F ,= nm. The mass, m, is known from the scale weights furnished for the entire train. The acceleration, a, was taken from the oscillograms. As explained earlier, each wheel in passing over a wheel trip on the rail marked the record in the form of an offset to a trace. Since the oscillogram also has

Longitudinal Forces in a Concrete Trestle 45

timinji lines and the distance between wheels is known it is possible to calculate the velocity of the train at various instances. The rate of change of the velocity between two points is the average acceleration between those points. At the instant the train stopped, the velocity is zero, so the acceleration just before stopping can be determined and this was used to calculate the longitudinal forces shown in Table 2. These forces are the greatest that could be determined from the oscillograms, but may not be the absolute maximum.

From Table 2 it can be seen that the longitudinal force calculated from recorded accelerations exceeds the sum of the bent forces and the rail forces, indicating that the abutment backwall also shares in the resistance to the longitudinal force. Furthermore, it should be noted that the maximum calculated longitudinal force of 158 kips is about 12 percent of the total train weight. With tight rail joints the percentage range of total longitudinal braking force resisted by the bents was 41 to 56 percent, by the rails 20 to 46 percent and by the backwalls apparently S to 30 percent.

The longitudinal movement of the cap on bent 8 was measured during 20 runs of braking to a stop on the bridge. These values are shown in Table 4, and it can be seen that the maximum movement with the rail joints tight was 0.212 in and with the rail joints loosened, 0.231 in.

3. Vertical Distribution of Braking Stresses in Columns

A series of 23 runs of the test train comprises this study. The effect of braking to a stop at or near two bents instrumented with SR-4 strain gages near the top, the third points and near the ground line was measured and the individual run data are plotted on Figs. 15 to 25. Figs. 15, 16 and 17 indicate the results for bent 8 when the rail joints were tight; and Figs. 18 and 19 show the effect when the rail joints were loosened. Figs. 20 and 21 indicate the results for bent 10 with tight rail joints, while Figs. 22 through 24 indicate the results with loosened rail joints. Fig. 25 shows the results during two runs when the test train made emergency stops.

As can be seen in each of the figures, there was an increase in recorded stress from the cap to the ground line, and the general shape of the stress curve represents the moment curve of a cantilever beam. (This observation has been reported in previous ER reports*.) It can be seen that there is no point of contraflexure above the ground, and that the bents are free to rotate at their tops but are fixed below the ground line. Two sets of values are shown for the stress at the ground-line gages. The open circles are the actual recorded values. The vertical column bars were lap-spliced at this location and the moment of inertia is about 10 percent greater here than for the balance of the column. The open squares, then, indicate the stress that probably would have been recorded had the columns not been spliced.

If no forces other than the longitudinal force acted on this column above the ground line, it would be expected that the plot of recorded stress at the various levels would describe a straight line. It is apparent, however, that they do not and that there must be some resisting moment at the top of the column. This could be developed by the weight of the deck preventing complete freedom of rotation.

It is interesting to note that at the lower gages the magnitude of stress in each of the columns comprising bent 8 are approximately equal, indicating that the individual columns in the bent resist the longitudinal forces together.

* ER-61, Field Investigation of Prestre.ssed Concrete Beams and Piles on the Western Pacihc Railroad, September 1965: and ER-48, Field Investigation of Two Concrete Bridges on Seaboard Air Line Railroad, .\ugust 1964.

46 Longitudinal Forces in a Concrete Trestle

4. Maximum Recorded Direct and Bending Stresses in Columns During Braking Across and Stopping Beyond the Bridge

In addition to braking to a stop on the bridge, several runs of the test train were made while crossing the bridge with the brakes applied. This information is plotted on Figs. 26 and 27 as open squares for the locomotive and as closed squares for the cars. A few runs were also made as normal runs without any brake application. These data are plotted with open and closed circles.

It can be seen from Fig. 26 that the maximum direct stress in the columns was not appreciably affected by braking across the bridge and that the stresses under braking and normal running were approximately the same in the various bents. The greatest stress was recorded in bent 14 and was 235 psi.; however, the majority of all values was about ISO psi.

Fig. 27 shows that the maximum bending stresses were highest during the braking runs. These bending stresses are the combination of bending due to eccentricity of the vertical loads and bending due to longitudinal force. It can be seen that the combined bending stresses are about twice the normal bending and that for these runs the column bending stresses (at the ground line) are approximately equal for vertical loads and longitudinal loads. The maximum recorded bending stresses occurred on bent 12 and were 135 psi under cars and 142 psi under locomotives.

5. Starting On the Bridge and Accelerating Off the Bridge

A total of seventeen runs which started from a stopped position at different loco- tions on the bridge was made; the data for tight rail joints appear in Figs. 28 and 29 and for loosened joints the information is in Figs. 30, 31 and 32. On each figure are an elevation of the bridge and the starting position of the train, as well as the position of .the train when maximum traction stresses were recorded for that particular run. The vertical lines denote bent position, while the open circles denote the traction stresses in psi for the bent. At the extreme right and left are the rail stresses indicated by closed circles.

The traction forces, while applied opposite in direction to the braking forces, were transmitted to the structure in much the same manner. Maximum values are shown to be on those bents under the locomotive and decrease towards the ends of the bridge. Higher stresses are produced when the rail joints are loose but no stresses were as high as those under braking runs.

It can be noted on Fig. 28 that the positions of the train for traction readings made during runs 13 and 14 were nearly identical. This position is close to that for runs 23 and 24 on Fig. 30 where it can be seen that higher traction stresses occurred with loosened rail joints and, in general, when the test train was in the central portion in the span after accelerating about 65 ft. The maximum bending stress was 110 psi with light rail joints and 140 psi with loose joints.

On Table 3 are shown the traction values that were recorded at the ground line of the various bents and converted to force in kips at the top of the cap. The bent forces due to traction were calculated essentially in the same manner as previously outlined for braking, the difference being that the horizontal force due to starting from a stopped position is opposite in direction. On the right-hand side of the table are the individual bent numbers with the run numbers, for the column headings. As is the case for Table 2 for braking forces, Table 3 is divided into "Tight Joint Bars" and "Loosened Joint Bars." Although not every bent was instrumented, values for the other bents are inter- polated. For all the recorded readings, care was taken not to include any bending from

Longitudinal Forces in a Concrete Trestle 47

vertical loads. Maximum values are shown to be 2.5 kips with tight rail joints and 2.8 kips with loosened joints. The rail-force data were determined similarly, as presented in Table 2, except that tensile stressess occurred at the south end and compressive stresses occurred at the north end.

Comparing runs with similar train positions, the following is obtained:

Traction Force Kips Run Number Total Bent Total Rail

14 20.3

19.4

Tight 11 13.1

11.2

Rail Joints 15 17.3

20.5

12 19.0

18.2

Average 17.4

17.3

Run Number Total Bent

Total Rail

23 24.5

4.4

Loosened 24 30.7

6.3

Rail Joints 16 19.8

7.0

21 27.1

4.9

.Average 25.5

5.6

From the above, it can be seen that by loosening the rail joints, the load to the bents was increased and to the rails correspondingly decreased. It is also apparent that the total load to the bents and to the rails under traction runs is considerably less than that under braking runs.

Table 3 also shows values of longitudinal forces calculated from recorded accelera- tions. These were derived in a similar manner as for the braking runs. The train posi- tion for the maximum acceleration was not as definite as for braking, and it was found that the maximum acceleration was developed at some distance from the starting point. It can be seen that this force also exceeds the sum of the bent forces and rail forces. The maximum longitudinal force resulting from traction of the locomotives was 76 kips, which was 15 percent of the weight on the drivers.

The longitudinal movement of the cap on bent 8 was measured during 16 runs of starting on the bridge and accelerating off. These values are shown in Table 4, and it can be seen that the maximum movement with the rail joints tight was 0.070 in and with the joints loosened, 0.107 in.

6. Vertical Distribution of Traction Stresses in Columns

A series of 19 runs of the test train was made to determine the distribution of trac- tion bending stress along the length of a column in bents 8 and 10. Gages were located near the cap, at the third points and near the ground line. The individual run data are plotted on Figs. 33 to 40 incl., for each of the two bents and for tight and loosened rail joints. The distances shown give the loca'ion of the test train when the maximum traction stresses were recorded for that run.

In general, the vertical distribution of stresses under traction runs is similar to that under braking, except that the bending is in the opposite direction. The magnitudes of the traction stresses are also less than for I) raking. The cantilever action of the bent is demonstrated as well as the equal distribution of stresses to each of the three columns in a bent. The maximum column bending stresses due to traction were 162 psi for run 47 (Fig. 33) when the rail joints were tight and 168 psi for run 35 (Fig. 39) when loosened. The corresponding bent forces to produce these stresses were 3.4 kips and 3.5 kips, respectively.

48 , Longitudinal Forces in a Concrete Trestle

7. Static Stresses in Prestressed Concrete Beams under Normal Running

In addition to the investigation on the columns under braking and traction, a series of runs was made to determine the flexural strains of span 9 for a range of speeds from S mph to a maximum of 30 mph. Gages were positioned 1 ft 6 in south of the center line of the span on the bottom of the beams, as shown in Fig. 1.

The recorded and calculated static strains are shown in Table 5. The recorded values shown are the averages for the two bottom gages on each beam for runs 10 mph and slower.

The calculated static strain is based on the assumptions that the axle loads of the test locomotive are concentrated, transversely distributed equally to each of the four beams. It was also assumed that the section was uncracked. The concrete 28-day strength was not available, but for conversion purposes in this report j'r was assumed to be 6,000 psi and Ec = 5,000,000 psi.

The stress factor or the ratio of the recorded strains to the calculated strains is shown in columns 7 through 9. It can be seen that the values are close to unity and therefore the correlation between the recorded and calculated values is good, with regard to the assumptions made. The stress factors ranged from 0.83 to 0.94.

The distribution of load to each beam as a percentage of the total load is shown in Fig. 41. It is apparent that the combination of the transverse post-tensioning rods and the shear keys is effective in the transverse distribution of the live load.

8. Maximum Recorded Strains in Prestressed Concrete Beams Under Normal Running (Without Braking or Traction)

The maximum flexural live-load-plus-impact strains recorded at the bottom of each beam are shown in Fig. 42. These values are the averages of the two bottom SR-4 gages of each beam.

Type of Loading Locomotive

Strain micro injin 96

Stress

psi

480

61 S

Speed mph

IS

IS

Remarks Beam 2

Car

123

Beam 4

As can be seen, the maximum flexural tensile stress for the locomotive is 480 psi compared to the calculated stress of 500 psi plus an impact factor of ii percent or 665 psi.

Since the precompression of the bottom fibers was about 1,775 psi and the tensile stress of 615 psi represents a relief of the precompression, it is apparent that the stresses produced by the test train were not sufficient to overcome this precompression and develop a resultant tensile stress.

The recorded strains for the cars were higher than for the locomotive as would be expected, since the Cooper equivalent for the cars was 33 percent more than that for the locomotive. As shown on the charts of Fig. 42, the transverse distribution for the regular speed runs up to 30 mph for the test train indicated equal distribution to the beams.

9. Vertical Distribution of Recorded Static Direct and Bending Stresses in Columns Under Normal Running (Without Braking or Traction)

The individual static-run data showing vertical distribution of direct and bending stresses for bents 8 and 9 are shown in Figs. 43 and 44, respectively. On the left of each figure is shown the elevation of the bent, with symbols indicating the position of

Longitudinal Forces in a Concrete Trestle 49

the SR-4 strain gages. The plots show the individual static direct and bending stress for slow-speed runs, 10 mph and under. In general, the direct stresses for both the locomo- tive and the cars were the same over the length of the column. The majority were in the vicinity of 125 to 150 psi., although one value of 170 psi was recorded. It can be noted that higher bending stresses occurred at the top level of gages for bents 8 and o. This bending is the result of the eccentricity of the live-load reactions, or having one span on the bent loaded more than the other. Whereas, under the action of braking and traction, the maximum bending stresses occurred at the ground line, under vertical loads the maximum occurred near the cap. The maximum recorded bending stress was 131 psi.

10. Vertical Distribution of Maximum Direct and Bending Stresses in Columns Under Normal Running (Without Braking or Traction)

On Fig. 45 is plotted the vertical distribution of the direct stresses for a range of speeds from 5 to 30 mph which were recorded on bents 8 and 9. Generally, the distri- bution of direct stress was in the vicinity of 125 to 150 psi for each level of the column. Although on bent 8, 6 ft above the ground line, a high direct stress of 195 psi occurring under the car at a speed of 20 mph can be noted. M this same speed the locomotive developed 190 psi.

The vertical distribution along the center column at four levels of bents 8 and 9 for the bending stress is plotted on Fig. 46. In most cases, the solid circles denoting car bending stresses were higher than those stresses for locomotives, which are shown as open circles. In general, at the top level of the piles the greatest values of bending stresses occurred. As can be seen in the upper left-hand plot, a high stress of 140 psi for the cars and a stress of 95 psi for the locomotive can be noted. At the lower two levels (i.e., 6 ft above ground line and at ground line) the recorded values are less.

On Figs. 43 to 46, incl., it should be kept in mind that the column section at the ground-line gages due to the lapped reinforcement is greater than at the other sections, and the recorded stresses were about 10 percent less than if no splice had been made.

11. Comparison of Specified Longitudinal Forces with those Developed by the Test Train

The current AREA specifications for reinforced concrete trestles recommend a live load equivalent to Cooper E 72, and with respect to longitudinal force:

"The longitudinal force resulting from the stopping and starting of trains shall be either the force due to braking, equivalent to 15 percent of the total live load without impact; or the force due to traction, equivalent to 25 percent of the weight on the driving wheels on the span without impact, whichever is the greater.

"For trestles not exceeding 200 ft in length, having longitudinal continuity by fric- tional resistance and having no open rail joints, the entire longitudinal force may be considered carried to the embankments at the end of the trestle. For trestles exceeding 200 ft having continuity of members, no open rail joints and double bents, one-hall the specified longitudinal force shall be distributed to the bents in proportion to their relative stiffnesses."

This trestle does not qualify for the one-half reduction given above since no double bents were used in the 660-ft total length, and to comply with the specification the full longitudinal force should be applied.

The E 72 pier reaction for two 33 -ft spans is 335.6 kips. For braking, 15 percent of this reaction is 50.2 kips and should be applied at the top of the cap. The E 72 pier reaction for 4 drivers on the 2 spans is 310.0 kips and for traction, 25 percent of this reaction is 77,6 kips, also to be applied to the top of cap.

50 Longitudinal Forces in a Concrete Trestle

The Santa Fe engineers recognized that the full AREA longitudinal force would not be transmitted to these bents and for the design of this trestle used the following:

For braking: The E 65 live load on six spans, or 198 ft of trestle, would be effec- tive for a braking force. The longitudinal force would be one-half of 15 percent of this live load distributed equally to 7 bents. The total live load for 198 ft= 1,500 kips, and the braking force is 1500X3^X0.15 3=113 kips. This distributed to seven bents is 113/7:= 16.1 kii>s per bent.

For traction: The E 65 live load on each span would have four drivers effective for the tractive effort. The longitudinal force would be one-half of 25 percent of this live load distributed equally to the two supporting bents. The total live load per span = 260 kips, and the traction force is 260 X '5^ X 0.25 = 32.5 kips. This distributed to two bents is 32.5/2 = 16.3 kips per bent. Thus, the railroad design for bending of the columns was based on a force at the cap of 16.3 kips.

The maximum bent reaction of the test train is 158.5 kips. The calculated braking force to a bent is 0.15 X 158.5 = 23.8 kips.

With tight rail joints the maximum bent force corresponding to recorded stress was 5.5 kips and with loosened bars, 5.9 kips. These values are 23 percent and 25 percent, respectively, of the calculated force.

The maximum bent reaction of the test locomotive is 158.0 kips. The calculated traction force to a bent is 0.25 X 158.0=39.5 kips.

With tight rail joints the maximum bent force corresponding to recorded stresses was 3.4 kips and with loosened bars, 3.5 kips. These values are 9 percent of the calcu- lated force.

It is therefore apparent that the bent forces actually developed in this structure are even less than the railroad's assumptions and far less than the AREA specification recommendation.

F. CONCLUSIONS

On the basis of tests on this structure it may be concluded that:

1. The maximum longitudinal bent force measured was from braking and was 23 percent of the force computed on the basis of 15 percent of the test train bent reaction.

2. With tight rail joints the percentage range of total longitudinal braking force resisted by the bents was 41 to 56 percent, by the rails, 20 to 46 percent, and by the backwalls apparently was 5 to 30 percent.

3. That portion of the longitudinal braking force transmitted to the bent was resisted by all bents of the bridge, acting as cantilevers, including those which carried no vertical live load. The distribution of longitudinal force was not uniform throughout the length of the bridge, but was highest for bents under the test train and gradually decreased with increase in distance from the test train. Loosening the rail joints at the ends of the bridge increased the longi- tudinal force resisted by the bents.

4. The maximum longitudinal force resulting from braking was 158 kips, which was 12 percent of the weight of the train.

5. The maximum longitudinal force rsulting from traction of the locomotives was 76 kips, which was 15 percent of the weight on drivers.

6. Bending stresses were recorded in the columns due to eccentricity of the ver- tical loads. These stresses were lower than those resulting from longitudinal

Long itudinal Forces in a Concrete Trestle

51

forces. Also, bending stresses due to eccentricity were highest near the tops of the bents, while the stresses due to longitudinal forces were highest near the ground line.

7. For the test span, the arrangement of transverse tie rods and the shear keys used was effective in producing a very nearly uniform distribution of the live load to each of the box beams comprising the span.

8. For the test span, the ratio of recorded to calculated strains due to bending ranged from 0.83 to 0.94.

(The tables and figures referred to in this report begin on page 52)

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