BRI DGE RAILS FOR MESSINA STRAIT BRIDGE
Final Report to Professor Allessandro Ronzo and Professor G. D. Gilardini l'Administratore Delegate Stretto Di Messina, Sp. A. via Verdinois, nr. 6 00158 Roma, Italy Telex 612545 ITAlST Phone 039-06-844-8532
by T. J. Hirsch, Professor & Research Engineer and C. E. Buth, Assoc. Professor & Research Engineer Civil Engineering Department Texas Transportation Institute The Texas A&M University System College Station, Texas 77843 through Texas A&M Research Foundation
Project RF 7067
September 1986 TABLE OF CONTENTS Page SUMMARY lV
METRIC-ENGLISH CONVERSION FACTORS v INTRODUCTION vi
IMPACT CONDITIONS, IMPACT FORCES AND GEOMETRICS 6 ANALYSIS PROCEDURES 11
EXTERNAL BRIDGE RAIL 15 INTERNAL BRIDGE RAIL 20
CONNECTIONS 24
Rail Splices 24 Rail to Post Connections 24 Post Base Plate 26
SELECTION OF POST SHAPE 31 MATERIALS 33
Aluminum Rail Elements 33 Steel Posts 33 Rail-to-Post Brackets 34 Post Mounting Bolts 34 REFERENCES 35
APPENDIX A - COMPUTER ANALYSIS WITH BARRIER VII PROGRAM 38 APPENDIX B - ANALYSIS AND DESIGN COMPUTATIONS IN SUPPORT OF FIGURES 5, 6, 9, 10, 11, 12 and 16 59
i i LIST OF FIGURES Page Figure 1. Typical Des i gn Trucks •••....•••.•..•.....•...•.••••... 3
Figure 2. Proposed External Bridge Rail 4
Figure 3. Proposed Internal Bridge Rail 5 Figure 4. Bridge Rail Design Truck ...... 7
Figure 5. Comparison of Vehicle Impa~t Forces to Total Vehicle Weight-Theory and Test Results-Stiff Rails ..•.•••.•.•• 8 Figure 6. Comparison of Required Barrier Height to Vehicle Center of Gravity-Theory and Test Results ..•....••••.. 10 Figure 7. Typical Failure Mechanisms for Bridge Rails •••.••••••. 12
Figure 8. Possible Failure Modes for Metal Rails •...... ••••...• ~ 13 Figure 9. Alternate External Rail Design No.3 ..••...••...•...•. 16 Figure 10. Load Capacity Analysis of Alternate External Rail Design No.3 •••..••..•••••••...••....•••••.•....• 17 Figure 11. Alternate Internal Rail Design No.3 ...... •....•••••• 22 Figure 12. Load Capacity Analysis of Alternate Internal Rail Design No.3 .....•••.•••..•...... •••••....••••• 23 Figure 13. Typical Tube Rail Splice Detail ..•....•...•••.•...••.. 25 Figure 14. Typi ca 1 Ra i 1 to Pos t Connector .....••..•..•..•....••.• 27 Figure 15. Example Toggle Bolt from AASHTO Hardware Standards •.•. 28 Figure 16. Typical Post Base Plate Details ••....•...••...•.•..... 29 Figure 17. Post Selection - Post Aerodynamics .....•••..•..•.••... 32
LIST OF TABLES
Table 1. Comparison of Bridge Rail Designs with Various Span Lengths ...... •...... 13
iii SUMMARY This report presents an External and an Internal Bridge Rail Design for use on the Messina Strait Bridge. The External Bridge Rail is 89.5 in. (2273 mm) high and is designed to restrain and redirect a 30.7 metric ton (67,500 lb) tank truck at 80 km/hr (50 mph) and 20° angle. This External Rail is constructed of three 11 in. (280 mm) diameter aluminum tubes supported by 12 in. (305 mm) deep s tee 1 wi de fl ange pos ts spaced 8 ft-8 in. (2642 mm) center to center. This External Rail weighs 109 lb/ft (162 kg/m) which is considerably less than early preliminary designs (185 lb/ft or 276 kg/m). The Internal Bridge Rail is 62 in. (1575 mm) high and is designed to restrain and redirect a van-type. truck at the same weight, speed and impact angle as above. This Internal Rail is constructed of two 12 in. (305 mm) diameter aluminum tubes supported by 12 in. (305 mm) deep steel posts as above. The Internal Bridge Rail weigh,s 82 lb/ft (122 kg/m) which is considerably less than early preliminary designs (165 lb/ft or 246 kg/m). The two bridge rails were analyzed and designed by an ultimate strength and plastic failure mechanism procedure. For this procedure to be valid, ductile material and good connections of structural elements are required. These special requirements are presented in the report.
iv METRIC - ENGLISH CONVERSION FACTORS
MASS 1 lbm = 0.4535924 kg FORCE 1 lb = 4.4482219 N (Newtons) 1 kip = 1000 lb = 4.4482219 kN LENGTH 1 in. = 2.54 cm = 25.4 mm 1 ft = 0.3048 m 1 mile = 1609.344 m = 1.609344 km STRESS - FORCE/AREA 1 psi = 6.895K N/m2 - 6895 Pascals 1 ksi = 6.895 N/mm 2 SPEED 1 mph = 0.44704 m/sec = 1.609344 km/hr 1 fps = 0.3048 m/sec DERIVED UNITS 1 lb/ft = 1.488164 kg/m
v INTRODUCTION In June 1986 the Texas Transportation Institute began making analytical evaluations of several proposed bridge rail designs for use on the Messina Strait Bridge. The bridge rail requirements were set forth in the January 30, 1986 letter from G. D. Gilardini of Stretto Di Messina, Sp. A., to T. J. Hirsch. The bridge rail should be minimum weight and maximum ultimate strength. The bridge rail should be of high strength aluminum or steel. The design vehicle should be a 50 metric ton truck traveling 80 km/hr and impacting at 20° angle (110,000 lb truck at 49.7 mph). Some typical design trucks are shown by Figure 1. Stretto Di Messina proposed an external bridge rail as shown by Figure 2 and internal bridge rail as shown by Figure 3. Both rails used a New Jersey type steel safety shape in the lower 550 mm (22 in.). A preliminary progress report was submitted to Stretto Di Messina on July 17, 1986. This report pointed out that the proposed design vehicle for the Messina Strait Bridge will produce an impact force of about 1557 kN (350 kips) which is considerably larger than the 890 kN (200 kips) impact force now used in the USA (80,000 lb truck impacting at 50 mph and 15° angle). Stretto Di Messina therefore reduced the design impact force to 1000 kN (225 kips) whi ch is equ iva 1ent to a 30.7 metri c ton truck impacting at 80 km/hr and 20° (67,500 lb truck, 50 mph and 20°). The analytical evaluation of the proposed external bridge rail (Figure 2) indicated its strength to be 560 kN (126 kips) if made of aluminum with a yield strength of 240 N/mm2 (35 ksi). The total weight of this proposed rail was 185 lb/ft (275 kg/m). Since the lower 550 mm New Jersey type steel safety- shape contributes noth i ng towa rd the streng th of th is ra i 1, it was recommended that it be deleted. This steel safety shape weighs about 186 kg/m (125 1b/ft) so a considerable saving in weight and costs results from deleting this with no sacrifice in strength of rail. In addition, recent research such as
Reference 26 II Rollover Caused by Concrete Safety Shaped Barri er, Task A Report ll would indicate the expensive, heavy New Jersey Safety Shape is not desirable for the Messina Strait Bridge.
2 +- i .,'o ~-
.,o ,.., - 1900 P 45 t 1.Hb t (max) I ~--+ Vma~ =118 Km
12 10 10 6 99fKIPS) 8500
I ----+-- .. • Vmox=118Km '1000 I ~ i 1 J 1 ! 10 110 ~ A 8 6 105.6 [KIPS) 9510 tI
I I ~ I :H = 1700 ~(moxJ
I Vmax:: lOb " l7 94.6 (KIPS) Figure 1. Typical Design Trucks. 3 RAILS & N.J. STEEL GUilE RAL & WIND REDUCTION ELEMENTS PROPOSED FOR STRAIT OF MESSINA BRIDGE ULTIMATE CAPACrtv 40 mt Tonn. 125 Ib/ft o o o (\I o o ,..CD Figure 2. Proposed External Bridge Rail. 4 TOTAL WEIGHT: 165 Ib/tt 200 8Ib/tt--- . 32 Ib/tt o o .,..(\I 125 Ib/ft . _. -'-,______...• -AC:------~ ... _- DOUBLE B.B. a N.J. STEEL BARRIER (PROPOSED FOR INTERNAL EDGES) STRArr OF MESSINA BRIDGE Figure 3. Proposed Internal Bridge Rail. 5 IMPACT CONDITIONS, IMPACT FORCES AND GEOMETRICS In our preliminary progress report, the 48 metric ton (105.6 kip) tank truck shown on Figure 1 was scaled up to 50 metric tons (110 kips) for our design vehicle. The center of gravity of this vehicle was 2000 mm (79 in.). Figure 4 shows how this 110 kip truck compares with the 80 kip design truck typical of the USA. Using these typical trucks as design vehicles, the theoretical procedures presented in references 1 and 2 were used to compute (see Appendix B) the design impact forces shown on Figure 5. Figur~ 5 shows the 50 ms average impact force for various weight vehicles at various speeds and angles of impact. The heavy truck bridge rails constructed and tested to date in the USA were designed for an 80 kip truck (Figure 4) impacting at 50 mph (80 km/hr) and 15° angle or a 200 kip (890 kN) average 50 ms impact force. The Federal Highway Administration (FHWA) has proposed that we increase the impact speed to 55 mph (88 km/hr). This would produce an impact force of 245 kips (1090 kN) as shown on Figure 5. The proposed Italian design truck, 110 kips, impacting at 50 mph (80 km/hr) and 20° would produce an impact force of 350 kips (1557 kN). These impact forces were di scussed wi th engi neers of Stretto Di Messina and a compromise design impact force of 1000 kN (225 kips) was agreed upon. This impact force would be equivalent to the following: (1) 30.7 metric ton (67.5 kip) truck impacting at 80 km/hr (50 mph) and 20° angle or, (2) 32.7 metric ton (72 kip) truck impacting at 88 km/hr (55 mph) and 15° angle, or 6 15 ft --.-__ -+ e.g. Trailer 13 ft 68 in. to 78 in. USA 71 in. to 7fj in. ITALY 12.5 ft 27.5 ft USA 3 ft .I. 14 ft .I. 30 ft USA 80 kip 10 kips + 35 kips + 35 kips ""'-J ITALY 110 kip 14 kips + 46 kips + 50 kips MESSINA 67.5 kip 8.6 kips 28.2 kips 30.7 kips r-- ~ I' ------I I I I I e.g. Tra tor 8ft -$ I I I I I .---,,. 1 I ______..J ITALY AL: 14.1 ft ~ ,. - "' , USA AL: 14.2 ft 5.8 ft ,. - 20 ft Figure 4. Bridge Rail Design Truck. 400 /" /// 350 ~ ~ 350k~ /" ITALY /" 300 / 4500 Ib 9000 Ib SCHOOL ~ INTERCITY TRUCKS .. /e D > CAR VAN BUS BUS ... • "d • / " "'(1)" 250 C! ... ,,/ -..:0- "" (l)G: A.Q ~a "" Ii 200 ~ ...... / ...u"'· /' /"" __ I\. ~ ;;::uu .up __ ,.- ...... Wo ---- ~.- Oil. II.!:!: --,.- -- -- OJ 0(1).-'- ~ ~c, _ _ 1""- -- ..:z -§ '" ~Q - ....-::zo4B\l-- A.O 150 /B • ! ~~ 0_ ./ __ ~,,~~ _o-f"i!fo~ &o~ ...W I ~ 0 -g~ ~o 0""-'" --'1-'&- ..- i • ....- _ ....- _0",.;t)Ot(\9 ~ -- .....- W • A > ~~I..;. ~ c~ ... ~. -- I· 100 •• ___ ...... ~~1-. fO~ ".,. LEGEND ,.- 060 mph-15 deg THEORY ------. • 60 mph-15 deg TEST RESULTS 50 060 mph-25 deg THEORY • 60 mph-25 deg TEST RESULTS A50 mph-15 deg TEST RESULTS OLV ______~~ ______~ ______~ ______~~ ______~ ______~ ____~~~ ______~ ______~ ______~ ______~ o 10 20 30 40 50 60 70 80 90 100 110 TOTAL VEHICLE WEIGHT - KIPS Figure 5. Comparison of Vehicle Impact Forces to Total Vehicle Weight-Theory and Test Results-Stiff Rails. (3) 40 metric ton (88 kip) truck impacting at 80 km/hr (50 mph) and 15° angle. The initial design truck had a center of gravity of 2000 mm (79 in.), and it was agreed that this could be reduced to 1800 mm (71 in.). Using this center of gravity height, 1800 mm (71 in.), and the formulas presented in references 1 and 2, we get a maximum Glat = 3.31 gls and an effective barrier height of (1420 mm) 56 in. as shown in Figure 6 (see Appendix B). These design values were arrived at considering that Stretto Di Messina can control the weight and speed of trucks using the bridge. 9 90 in. t T TANK TRUCK RAILS 78 in. to 90 in. 70 60 B B EFFECTIVE HEIGHT 56 in.- B B 0 w ------~- :r: u V AN TRUCK RAILS 50 in. to 54 in. ! 50 I I I I- :r: I CJ BB B B .... iii 40 :r: ------BUS RAILS 38 in. to 42 in. - -- I w Figure 6. Comparison of Required Barrier Height to Vehicle "Center of Gravity-Theory and Test Results. ANALYSIS PROCEDURES Ultimate strength and plastic failure mechanism analysis procedures were used in this study (see reference 5). In this procedure, plastic hinges are assumed to develop at points of maximum bending moment. At failure, a sufficient number of hinges are developed to form a mechanism. No factor of safety is used in this analysis. The critical failure mechanism will barely resist the design impact force of 1000 kN (225 kips) in this case. When impacted by the design force the rail is expected to yield and deform permanently. Our margin of safety is in the inertia of the barrier and in the ductil ity and toughness of the aluminum and steel materials used. In order for a structure to behave as assumed, materials with adequate ductility must be used. Materials considered in this study have adequate ductility to meet this requirement. Also, joints must be designed to resist the full bending moment strength of the member being joined. This means that joints in the rail elements and the connection between the post and deck must resist bending. Joints or splices in the rail elements should be at quarter points in the span when they occur. It is not necessary for the connection between the rail elements and post to resist bending moment, however the rail elements should be continuous across this connection. Failure mechanisms for one, two and three spans are illustrated in Figure 7. -Mechanisms involving more spans are also possible. For the failure mechanisms considered, the rail elements function as beams as shown in Figure 8. The failure load for each rail element is expressed by: w= w£ = 8 Mp/(L - £/2) 11 Figure 7. Typical Failure Mechanisms for Bridge Rails. 12 L r-·L 1 M Mp Mp M ===I====~I=====P~l~ I f II ~f::j:~===p :::::::::::=:1======wl (A) Single Span Failure Mode LWI.t j (8) Two Span Failure Mode IE------.-.-----L' ..... - Mp " Mp ~ wl./ ~ (C) Three Span Failure Mode Mp =, plastic momeht tapacity of rail Pp = ultimat~ load capacity of a single post wl= total ultimate vehicle impact load - . aMp w~ = L - (,(/2) = W Figure 8. Possible Failure Modes for Metal Rails. 13 where: W is total applied load, kips Mp is plastic bending moment capacity of rail, ft-kip L is total span length of failure mechanism, ft ~ is length over which applied load is distributed, ft For one span the shear force, V, in each rail element at the ends of the mechanism is W/2. For a mechanism involving only one span, the total load carri ed by the ra i 1i ng sys tem wou 1d be the number of ra i 1 elements multiplied by the total load for each rail element. It would be possible for a one-span mechanism to occur if each ~ost were capable of supporting a load equal or greater than one-half the total load for all rail elements for a one-span mechanism. If the post is weaker than this, the mechanism that wi 11 deve lop wi 11 i nvo 1ve more than one span. I f such a mechani sm occu rred, the total load ca rri ed by the ra i 1 sys tern wou 1d be the 10ad carried by each rail element as a beam mechanism plus the load carried by each post that is located within the mechanism (not including posts at each end of the mechanism). 14 EXTERNAL BRIDGE RAIL Figure 9 shows our proposed alternate External Rail design number 3 (number 1 is shown by Figure 2 and number 2 was presented in the preliminary report of July 1986). This design consists of three aluminum tubes 11 in. 0.0. x 5/16 in. wall thickness structural aluminum with yield strength of 35 ks i (245 N/mm2). These three tubes along wi th the s tee 1 wide flange posts W 12 x 50 spaced at 8 ft-8 in. center to center (2642 mm) provide the design strength of 225 kips (1000 kN). The steel posts are of yield strength 50 ksi (345 N/mm2). The lower 6 in. 0.0. x 5/16 in. wall thickness aluminum tube is a rub-rail to prevent automobile tires from snagging the posts (see Appendix B for supporting computations). Figure 10 summarizes the load capacity analysis of this External Bridge_Rail. The three span failure mechanism is the critical mechanism which produces a load capacity of 237 kips (1054 kN).With this mechanism two posts within the 26 ft (7.9 m) span will develop plastic hinges. The 8 ft-8 in. (2642 mm) post spacing was chosen since the floor beams of the bridge appear to be at this spacing. The steel post can be attached to these floor beams to develop these plastic moment strength (see Appendix B). This External Bridge Rail weighs about 109 lb/ft (172 kg/m) whereas the one shown by Figure 2 weighs about 185 lb/ft (276 kg/m). Table 1 compares three External Bridge Rails designed with three different span 1engths or pas t spac i ngs. Wi th the 5 ft (1500 mm) pas t spacing the rail sizes and weight decreases but the number and weight of pas t per 1ength of bri dge increases. The net resu 1ts in an increase in the total weight of bridge rail, 123 lb/ft (183 kg/m) in this case. For 15 WEIGHT OF RAIL PER FOOT OF BRIO'GE Aluminum Tubes 44.8 lb/ft Post 43.2 lb/ft r~i see 11 aneous 2l.0lb/ft TOTAL 109.0 lb/ft ALUMINUM TUBES 11 In. 0.0. x 6/1 e In. wall F = 35 ks i y = 245 N/mm2 .E ~- W 12x.60 STEEL POST Fy = 50 ksi 2 = 345 N/nrn at 8 ft-8 in. spacing "E (2642 mm spacir.g) E 0 C') ~ ~ ....,C\I E E .5 C\I ..,. C\I co . ..,. ....,~ .6 (Q It) 1/2.ln. STIFFNERS ' e -·1-1f.4 In. diameter A325 BOLTS Fu = 120 ksi = 827 N/mm2 Figure 9. Alternate External Rail Design No.3. 16 500 400 I , STRENGTH OF FAILURE MECHANISM en e: -I \ \ 3 Alum. Tubes 11 in. 0.0. x 5/16 in. wall ~ ...... I ...... 300 ...... :c ...... ac , ...... ' I&. 0 ...... >- ~ ...... ' t: ...... I CJ ...... 237 kips - ,...... -.....J C 200 CRITICAL MECHANISM A...... C .,.. f>0 ...... 3 Span 26 Feet CJ ~\'l. ,...... 5 ca ,...... 0 51 c ... ,...... Of' 0.... t\G1~ ee.c'(\ 100 S1"~ (; \C.\\ls - 6 A• No. Spans 1 2 3 4 o -'------~------~ o 83 17~ 28~ 343 LENGTH OF FAILURE MECHANISM - FEET Figure 10. Load Capacity Analysis of Alternate External Rail Design No.3. Table 1. Comparison of Bridge Rail Designs with Various Span Lengths. Type Rail Span Alum. Tubes Steel Load Weight Failure Post Spacing No. x Di am. x Post Capaci ty lb./ft Mechanism thickness kips External 5.0 ft 3-8 in. x 5/16 in. W12x45 229 123 3 span - 15 ft External 8.67 ft 3-11 in. x 5/16 in. W12x50 237 109 3 span - 26 ft I External 10.0 ft 3-11 in. x 1/2 in. W12x58 227 112 2 span - 20 ft Internal 5.0 ft 2-10 in. x 5/16 in. W12x35 238 84 3 span - 15 ft Internal 8.67 ft 2-12 in. x 3/8 in. W12x40 240 82 3 span - 26 ft Internal 10.0 ft 2-11 in. x 1/2 in. W12X50 236 93 2 span - 20 ft CX> the 10 ft (3 m) post spacing, the size and weight of the rail increases but the net weight of post per length of bridge decreases. Note also the length of failure mechanism reduced to 2 spans or 20 ft (6 m). Remember the External Bridge Rail posts are about 7.5 ft (2.3 m) high. The o~timum rail span or post spacing might be about 7.5 ft (2.3 m) in this case. The 84 in. (2130 mm) height of the top rail was chosen so that it would engage the outer edge of large diameter tank trucks to prevent them from rolling over during redirection or impact. The center ra i 1 at 56 in. (1422 mm) hei ght was se 1ected so that it will engage the floor system of most" van-type trucks. The lower structural rail at 28 in. (711 mm) height will engage the 42 in. (1067 mm) diameter bus and truck tires. The tires and axles are hard points and transmit a significant amount of impact force into the bridge rail system. The lower rub-rail is to prevent small passenger car tires from snagging on the posts. 19 INTERNAL BRIDGE RAIL Figure 11 shows our alternate Internal Bridge Rail design number 3 (number 1 is shown by Figure 3 and number 2 would have been a modification from preliminary report of July 1986). This design consists of two 12 in. 0.0. x 3/8 in. wall thickness aluminum tubes with yield strength of 35 ksi (245 N/mm2). These two tubes have the same strength as the three tubes used on the External Rail. These two tubes along with the steel wide fl ange pos ts W12x40 spaced at 8 ft-8 in center to center (2642 mm) provides the design strength of 225 kips (1000 kN). The steel posts are of yield strength 50 ksi (345 N/mm2). The lower 6 in. 0.0. x 5/16 in. wall thickness aluminum tube is a rub-rail to prevent automobile tires from snagging the posts. Figure 12 summarizes the Load Capacity Analysis ·of this Internal Bridge Rail. The three-span failure mechanism is the critical mechanism which produces a load capacity of 240 kips (1068 kN). With this mechanism two posts within the 26 ft (7.9 m) span will develop plastic hinges. This Internal Bridge Rail weighs about 82 lb/ft (122 kg/m) whereas the one shown on Figure 3 weighs about 165 lb/ft (246 kg/m). Table 1 compares three Internal Bridge Rail designs with three different spans. The 8 ft-8 in. (2642 mm) span seems to be a good one. The 56 in. (1422 mm) height of the top rail was chosen because it would engage the floor systems of most van-type trucks. The lower structural rail at 28 in. (711 mm) height will engage the 42 in. (1067 mm) diameter bus and truck tires. The tires and axles are hard points and transmit a significant amount of impact force into the bridge rail system. One fi na 1 poi nt is that the I nterna 1 Bri dge Ra i 1 appearance and geometry is compatible with the lower two thirds of the External Bridge 20 Rail. Messina Strait engineers may want to select the same diameter tubes for both the Internal and External Rails. For example, use three 12 in. 0.0. x 1/4 in. wall aluminum tubes for the External Rail instead of the three 11 in. 0.0. x 5/16 in. wall tubes. If this is done, all rails will be 12 in. in diameter and the splices and post-rail connections could be the same. This should reduce fabrication costs. 21 WEIGHT OF RAIL PER FOOT OF BRIDGE Aluminum Tubes 38.8 1b/ft Post 25.0 1b/ft ~-1i see 11 aneou s 18.2 1b/ft TOTAL 82.0 1b/ft ALUMINUM TUBES 12 In. 0.0. x 3/8 In. wall F = 35 ksi y = 245 N/mm2 W 12x40 STEEL POST .5. F = 50 ksi 2 ,... co y = 345 N/mm E C\I E at 8 ft-8 in. spacing C\I (2642 mm spaci:lg) C\I ~ ~ ,...... E . E .s .5 6 In. 0.0. x 5/16 In. <0 ~ <0 &0 ~ ~ ...... -.s c C\I ~ FLOOR BEAMS - 1/2 In. STIFFNERS Spaced- 8 ft-8 In. (2642 mm) 6 - 1-1/8 In. diameter A325 BOLTS Fu = 120 ksi = 827 N/mm 2 Figure 11. Alternate Internal Rail Design No.3. 22 500 400 t- \ r- STRENGTH OF FAILURE MECHANISM ·2 Alum. Tubes 12 in. 0.0. x 3/8 il. wall U) !!: ~ • ...... ::! ...... C 300 ...... a:: ...... LI. .... 0 ...... >- ~ .... "" !:: ...... (.) ...... f-v ,Ar...... 240 kips w C 200 A. ,0 ...... CRITICAL MECHANISM c 'l. "#-...... (.) ~"\ ...... :'(5 3 Span 26 Feet Q ...... Of~05 c ...... ~G1" e&c~ 0 ... S1"e S ~\9& 100 60 • No. Spans 1 2 3 4 o ~'------~------~------~------~ o 8.7 17.3 28.0 34.7 LENGTH OF FAILURE MECHANISM - FEET Figure 12. Load Capacity Analysis of Alternate Internal Rail Design No.3. CONNECTIONS Rail Splices Structura 1 a 1umi num tubi ng used for the ra i 1 elements shou 1d be as long as possible to minimize the number of splices that must be provided. Such splices can also accommodate thermal expansion and contraction. Splices, made in rail elements, should be adequate to develop the full plastic bending moment capacity of the rail element. For the designs considered here it is not necessary to develop significant tensile axial strength. Sp 1 ices may be made in the proposed ra i 1 elements by inserting a smaller diameter round tube sleeve inside the main rail elements. The plastic section modulus of the sp~ice tube should be equal to or greater than that of the rail elements. Splices should be located at quarter points between post spans. Figure 13 shows a typical tube rail splice. The outside diameter (0.0.) of the sleeve spl ice tube should be about 1/4 in. (6 min) smaller than the inside diameter (1.0.) of the main rail tube. The sleeve splice tube should extend at least two diameters into the main tube. Rail to Post Connections Rail elements must be continuous across posts so that the full plastic bending moment can be developed in the rail elements at the posts. Connections between rail elements and posts need only hold the rail in place and transfer lateral forces in the posts. The primary lateral force is directed outward and places the connections in compression. In addition, an inward (tension) lateral force of about the same magnitude wi 11 occur just beyond each end of a loaded area as a resul t of the deflected shape of the continuous rail elements. This force will place 24 STEEL POST W 12x50 II I 1-1/4 in. Joint II .... 2 It _II..... 2 It II -I --II -, F ------=- =- ======- === - ~ --=- =- =- ==- ==- -==- - ~-, I ' II I I 1 I ::.: ~ =-L_-_-_--=--=-=-- ::: = =--=-____-_--=--=-J N U1 II 1 12 in. fD PIN (Driving Fit) II II ALUMINUM TUBE 11 in. 0.0. x 5/16 in. wall ALUMINUM SPLICE TUBE 10 in. 0.0. x 7/16 in. wall 4 ft-1 1/4 in. long EXTERNAL RAIL Figure 13. Typical Tube Rail Splice Detail. the connection in tension. For the External and Internal Rails shown by Figures 9 and 11, the post compression force is about 65 kips (289 kN) and tension force is about 56 kips (249 kN). The post forces are divided in three rails for the External Rail and divided into two rails for the Internal Rail. A cast or welded connector similar to the concept shown in Fi gure 14 is recommended. The connector wou 1d be bo 1ted to the pos t flange with standard structural bolts. The rail element would be bolted to the connector with two toggle bolts similar to those shown in Figure 15. Post Base Plate Figure 16 shows a typical post base plate and its full bending moment connection to a floor beam. The 12 in. wide flange steel post should be welded to the base plate with fillet welds to develop the full plastic moment capaci ty of the pos t. The we 1d meta 1 shou 1d be equal or better than the pos t yi e 1d strength of 50 ks i (345 N/mm2). The 3/8 in. and 5/8 in. fillet welds shown would develop the moment capacity of the W12x50 steel post. The base plate is bolted to the floor beam flange with six high strength ASTM A325 bolts which have an ultimate tensile strength of 120 ksi (827 N/mm2). The bolt pattern shown will develop the full plastic moment of the post in both directions (outward and inward). These bolts should be tightened by the "turn of the nut" method or by torque wrenches or other means to achieve 70% of their ultimate strength in pretension. The floor beams of the bridge should be reinforced with web stiffners as shown to prevent local buckling of the web. The size of the base plate and anchor bolts for the two posts shown on Figures 9 and 11 are as follows: 26 Rail Force Post Force ... II1II( Ultimate Rail Force =60 kips (267 kN) compression from Barrier VII =47 kips (209 kN) tension Figure 14. Typical Rail to Post Connector. 27 VI +>- SPECIFICATIONS Toggles shall conform to A.S.T.M., A570, Grade D or better; toggle bolt to A.S.T.MfA3S4, Grade BD; hex nul to A.S.T.M. A563, Grade D; rivet to A.S.T.M. A276, Type 304 Condition B. Plain washers shall be made of steel and shall meet the dimensional requirements of A.N.S.I. B27.2 Type A Plain Washers. Spring lock washers 5/16 X 1-1/16 Pan Head Small shall meet the requirements of A.N.S.I. B27.1. 1/2-13 UNC-2A Steel components shall be cadmium plated to A.S.T.M. A165, Type as, or better. Required minimum tensile load shall equal 9000 pounds when in open position and tested through a 1" ¢ hole. Dimensional tolerances not shown or implied are intended to be those consistent with the proper functioning of the part, including its appearance, and accepted manufacturing practices. INTENDED USE 9/161.0_.1-3/80.0 .• 7/64 Thk. N Type A, Plain Washer 0:> This toggle bolt is used to connect 5" 00 tubular rails in bridge designs BRI (Aluminum) Type A, BR2A (Aluminum) Type A, BR2 (Aluminum) Type A, and BR3A (Aluminum) Type A. 1/2" Spring 1/2"·13 Heavy Hex Nut TOGGLE BOLT ASSEMBLY 1/2" TOGGLE BOLT HM-TF-13 F- 25·73 STANDARD Figure 15. Example Toggle Bolt from AASHTO Hardware Standards. PLASTIC MOMENT 1~--12 In. WIDE FLANGE POST I 112 In. WEB STIFFNERS ~ FLOOR BEAM S ft-S in. c-c 2642 mm c-c 3/S In •. 5/8 In. 3/S In • .5 C\I 5/S In. .E .~ 0,.. (D Sin. 8 In. 2 in. 2 In. 20 In. BASE PLATE 1.5 In. x 10 In. x 20 In. for W 12x40 Post BOLTS 6 - 1-1/8 in. rzs A325 . BASE PLATE 1.75 In. x 10 in. x 20 In. forW12x50 Post BOLTS 6 - 1-114 in. f6 A325 . Figure 16. Typical Post Base Plate Details. 29 W12 x 40 Post Base Plate 1-1/2" x 10" x 20" Fy = 50 ksi (345 N/mm2) Bolts 6 - 1-1/811 ~ A325 Fu =120 ksi (827 N/mm2) W12 x 50 Post Base Plate 1-3/4" x 1011 x 20" Fy = 50 ksi (345 N/mm2) Bolts 6 - 1-1/4" ~ A325 Fu = 120 ksi (827 N/mm2) 30 SELECTION OF POST SHAPE A significant consideration in the design of bridge rail for the proposed structure is aerodynamics. Several cross sections for posts were considered. The post is subjected to bending loads, and a wide flange shape is very efficient for resisting bending. However, a wide flange shape has a relatively high wind drag coefficient. Other shapes such as square and round tubes have lower wind drag coefficients but are less efficient (strength-to-weight ratio) in resisting bending. For compa ri sons of va ri ou s pos t shapes, it is neces sa ry to cons i der the drag coeffi ci ent and wi dth of post . on ly because the vari ous pos t shapes would be the same length. The shapes considered are shown in Table 1. A wide flange post would.be 8 in. (0.67 ft) wide and have a drag coefficient of about 2.3. Multiplication of these factors gives a load factor of 0.67 x 2.3 = 1.54. For a square structural tube the width would be 10 in. (0.83 ft) and have a drag coefficient of 1.2. Multiplication of these factors gives a load factor of 0.83 x 1.2 = 1.00. Similar calculations for a 12 in. diameter round tube post would give a load factor of 0.80. If a wide flange were filled with foam or some other means of making it present a rectangular shape, its load factor would become 0.80, which is as low as the round tube of the same bendi ng strength. Thi slatter design is recommended since it also has the least weight. 31 8 in. W12x45 lb/ft f = 1.11 3 3 S = 58.1 in. Z = 64.7 in. 12 in. I = 350 in.4 Cd = 1.7 to 2.8 LOAD FACTOR Cd = 2.3 avq. Wt = 45 1b/ft 0.67 ft x 2.3 = 1.54 Effectiveness = 1.54 x 45 = 69.3 ST 10 x 10 x 1/2 f = 1. 125 10 in. 3 S = 54.2 in. Z = 61 in. 3 10 in. I = 271 in.4 Wt = 62.5 lb/ft Effectiveness = 62~5 LOAD FACTOR 0.83 ft x 1.2 = 1.00 12 in. diameter Tube 12 in. 0.0. x 1/2 In. wall f = 1.27 3 S = 50.95 in. 3 Z = 64.7 in. I = 300 in.4 A = 18.06 ; n. Cd = 1.1 to 0.5 ~Jt = 61.4 1b/ft LOAD FACTOR Cd = 0.8 avq. Effectiveness = 49.2 1 ft x 0.8 = 0.80 W12x45 8 in. with Foam Fill 12 in. Wt = 45 1b/ft MOST EFFECTIVE LOAD FACTOR 0.67 x 1.2 = 0.80 Figure 17. Post Section - Post Aerodynamics 32 MATERIALS Aluminum Rail Elements The specified yield strength for the tubular aluminum rail elements is 35 ksi. The material should also have sufficient ductility to withstand the deformations that will occur in regions of plastic hinges when a mechanism is developed. Material meeting the Aluminum Association (Washington, D.C.) designation 6061-T6 should be adequate. This material has a specified minimum yield strength of 35 ksi and an ultimate strength of about 38 to 42 ksi. The elongation in two inches is 17 percent. This is an aluminum alloy having the following nominal chemical composition: (Reference: Aluminum Association Specifications) Composition Percentage by Weight Copper 0.25 Silicon 0.6 Magnesium 1.0 Chromium 0.25 Aluminum 97.9 Steel Posts The steel wideflange posts have a specified yield strength of 50 ksi. Material meeting American Society for Testing and Materials specification A441 should be used •. This material has a specified minimum yield strength of 50 ksi and a minimum tensile, ultimate strength of 70 ksi. The elongation for this material is 18 percent. The posts should also possess adequate ductility to allow rotation in the plastic hinges that must form in the posts immediately above the base plates when a mechanism forms in the bridge rail. 33 Base plates should also be fabricated from material meeting specification A441 and should be welded to the posts using properly designed welds and welding procedures. Rail-to-Post Brackets It is anticipated that these brackets will be made of aluminum alloy and will be either fabricated from sheet and plate or will be cast. The Texas State Department of Highways and Public Transportation has had very good experience with a cast aluminum bridge rail post that is somewhat similar to the bracket proposed for the Messina Strait Bridge. The post is made of alloy A444- T4 in accordance wi th Ameri can Soci ety for Testi ng and Materials specification Bl08. A material such as this is recommended for the brackets connecting the rail members to the posts in the Messina Strait Bridge rails. Post Mounting Bolts Bolts used to connect the posts to the floor beam should be high strength structural steel bolts meeting American Society for Testing and Materials Specification A325. These bolts should be installed according to specifications using the turn-of-the-nut method to assure that adequate preload is achieved. 34 REFERENCES 1. Hirsch, T. J., "Longitudinal Barriers for Buses and Trucks," Transportation Research Record 1052, Symposium on Geometric Design for Large Trucks, Transportati on Research Board, Nati ona 1 Research Council, Washington, D.C., 1986, pp. 95-102. 2. Hirsch, T. J., "Longitudinal Barriers for Buses and Trucks, State of the Art, II Research Report 416-2F,. Texas Transportation Institute, College Station, Texas, February 1986. 3. Hirsch, T. J. and Arnold, A., IIBridge Rail to Restrain and Redirect 80,000 lb Trucks ,II Research Report 230-4F, Texas Transportation Institute, Texas A&M University, November 1981. 4. Hirsch, T. J. and Fairbanks, William L., "Bridge Rail to Restrain and Redirect 80,000 lb Tank Trucks,1I Research Report 911-1F, Texas Transportation Institute, Texas A&M University, February 1984. 5. Hirsch, T. J., "Analytical Evaluation of Texas Bridge Rails to Contain Buses and Trucks ," Research Report 230-2, Texas Transportation Institute, Texas A&M University, August 1978. 6. Hirsch, T. J., Fairbanks, W. L., and Buth, C. E., "Concrete Safety Shape with Metal Rail on Top to Redirect 80,000 lb Trucks,1I Research Report 416-1F, Texas Transportation Institute, Texas A&M University, December 1984. 7. Hirsch, T. J., "Bridge Rail to Restrain and Redirect Buses," Research Report 230-3, Texas Transportation Institute, Texas A&M University, . February 1981. 8. Michie, Jarvis D., "Recommended Procedures for the Safety Performance Eva 1ua t i on of Hi ghway Appurtenances, II NCHRP _ Report 230, Transportation Research Board, National Research Council, Washington, D.C., March 1981. 9. Noel, J. S., Buth, C. E., and Hirsch, T. J., "Loads on Bridge Railings," Transportation Research Record No. 796, 1981. 10. Hirsch, T. J., Panak, J. J., and Buth, C. E., "Tubular W-Beam Bridge Rail,1I Research Report 230-1, Texas Transportation Institute, Texas A&M University, October 1978. 11. Wiles, E. 0., Kimball, C. E., and Bronstad, M. E., "Evaluation of Concrete Safety Shapes by Crash Tests with Heavy Vehicles," Transportation Research Record 631, Transportation Research Board, 1977. 12. Kimball, C. E., Bronstad, M. E., and Michie, J. D., "Heavy-Vehicle Tests of Tubular Thrie-Beam Retrofit Bridge Railing," Transportation Research Record 796, Transportation Research Board, 1981. 35 13. Arnold, Althea and Hirsch, T. J., "Bridge Deck Designs for Railing Impacts ," Research Report 295-1F, Texas Transportation Institute, Texas A&M University, November 1983. 14. Hirsch, T. J. and Post, E. R., "Truck Tests on Texas Concrete Median Barrier," Research Report 146-7, Texas Transportation Institute, Texas A&M University, December 1972. 15. Olson, R. M., Post, E. R., and McFarland, W. F., "Tentative Service Requ i rements for Bri dge Ra i 1 Sys terns," NCHRP Report 86, Hi ghway Research Board, National Research Council, Washington, D.C., 1970. 16. Kimball, C. E., Bronstad, M. E., et al., "Development of a New Collapsing Ring Bridge Rail System," Report No. FHWA-RD-76-39, Federal Highway Administration, Washington, D.C., January 1976. 17. Bloom, J. A., Rudd, T. J., and Labra, J. J., "Establishment of Interim Guidelines for Bridge Rails Required to Contain Heavy Veh i c 1es , II Report No. FHWA-RD-7 5-45, Vo 1 • I , Report No. FHWA-RD-75-46, Vol. II, and Report No. FHWA-RD-75-47, Vol. III, Federal Highway Administration, Washington, D.C., November 1974. 18. Buth, C. E. and Campise, Wanda L., "Performance Limits of Longitudinal Barrier Systems," Vol. 1: Summary Report, FHWA Contract DTFH61-82-C-00051, Texas Transportation Institute, January 1985. 19. Bronstad, M. E., et al., IIDevelopment of Retrofit Railing for Through Truss Bri dges, II Transportati on Research Record 942, Transportati on Research Board, 1982. 20. Ivey, D. L. and Buth, C. E., "Barriers in Construction Zones ," Vol. 1: Summary Report;' Appendix A "Individual Test Reports," FHWA Contract No. DOT-FH-11-9458, Texas Transportation Institute, Texas A&M University, March 1984. 21. Standard Specifications for Highway Bridges, Thirteenth Edition, American Association of State Highway and Transportation Officials, Washington, D.C., 1983. 22. Ivey, D. L., Buth, C. E., Love, M. L., and Campise, W. L., liThe Response of Atypical Vehicles During Collisions with Concrete Median Barriers," Report on Task 5 of Contract DOT-FH-11-9458, Texas Transportation Institute, January 1985. 23. Davis, S., Baczynski, R., Garn, R., Bjork, T., IITest and Evaluation of Heavy Vehicle Barrier Concepts, II Technical Report on Contract DOT-FH-11-9115, Dynamic Science, Inc., July 1981. 24. Buth, C. E., Noel, J. S., Arnold, A. G., and Hirsch, T. J., "Safer Bridge Railings,1I Vol. 1, 2, and 3, FHWA Contract DOT-FH-11-9181, Texas Transportation Institute, December 1980. 36 25. Powell, G. H., "BARRIER VII: A Computer Program for Evaluation of Automobile Barrier Systems,1I Report No. FHWA-RD-73-51, Final Report, Dept. of Civil Engineering, University of California, Berkeley, April 1973. 26. Mak, King K., and Sicking, Dean L., "Rollover Caused by Concrete Safety Shaped Barri er, Task A Report, II TTl Report No. RF 7051 on Contract No. DTFH61-85-C-00129, Texas Transportation Institute, Texas A&M University, Feb. 1986. 27. Buth, C. E., Campise, Wanda L., and Marquis, Eugene L., IIDevelopment of A Hi gh-Performance Medi an Barr'; er, II Fi na 1 Report, Work Order Number 2, Contract DOT-FH-II-9485, Texas Transportation Institute, Texas A&M University, April 1983. 28. Buth, C. E., Hayes, G. G., and Dolf, Tim, "Test Report No.1, Aluminum Bridge Rail Systems," Texas Transportation Institute, Texas A&M University, Report prepared for The Aluminum Association Inc., Washington, D.C., Feb. 1980. 29. Buth, C. E., Hayes, G. G., and Dolf, Tim, "Test Report No.2, Aluminum Bridge Rail Systems," Texas Transportation Institute, Texas A&M University, Report prepared for The Aluminum Association, Inc., Washington, D.C., March 1980. 30. Arnold, Althea, and Buth, C. E., "Full-Scale Crash Test of Tru-Beam Aluminum Bridge Railing," Texas Transportation Institute, Texas A&M University, Report prepared for The Aluminum Association, Inc., Washington, D.C., June 1981. 31. Campise, Wanda L., and Suth, C. E., "Crashworthiness of Aluminum Tru-Beam Sri dge Ra i 1 i ng, II Fi na 1 Report on Project RF 4583, Contract DTFH61-81-P-30117, Texas Transportation Institute, Texas A&M University, Sept. 1982. 37 APPENDIX A COMPUTER ANALYSIS WITH BARRIER VII PROGRAM Messrs. Dean Sicking and Roger Bligh of TTl performed a BARRIER VII computer program analysis (reference 25) of a truck impact with the External Bridge Rail (Figure 9 and simulated as shown in Figure AI), and summari es of the resu 1ts are presented in Fi gures A2 through All and Tables Al through A6. TTl has used the BARRIER VII computer program to simulate numerous automobile and bus impacts with longitudinal barriers and found it to give good comparisons. The BARRIER VII program only has provi s ions for two ra i 1 s so the mi ddl e and lower a 1 umi num tubes are combined into one as shown on Figure AI. Impact was wi th the tractor of the Mess ina truck shown by Fi gure 4 with 8.6 kips on the front axle and 28.2 kips on the rear axle. The total weight of the tractor was 36.8 kips. Previous crash tests with tractor-tra i 1er trucks such as th is have shown the rear ax 1e of the tractor del ivers the major impact force to the bridge rail, and this BARRIER VII analysis confirms this. The rear axle of the trailer frequently does not even touch or impact the traffic rail. The truck tractor impacts the bridge rail at 50 mph (80 km/hr) and a 20° angle with the centroid of the tractor directed at Post No.4 as shown by Fi gure A3. The 1eft front of the tractor contacts the ra i 1 m; dway between Post No. 2 and 3. Before proceed; ng , the fo 11 ow; ng ; s a summa ry of s tee 1 pos t and "- aluminum rail strength properties: POST W12 x 50 Plastic Bending Moment Strength = FyZ = 3620 kip-in. (strong axis) 38 Plastic Deformation will occur about strong axis when the top post deflection > 0.6 in. Shear Yield Strength about x-x axis = 0.55 Fytd = 124.0 kips Plastic Bending Moment Strength = 1070 kip-in. (weak axis) ALUMINUM RAILS 11 in. 0.0. x 5/16 in. Wall Plastic Bending Moment Strength = Fy Z = 1211 - kip-in. Moment reduced 21 percent to allow for some local buckling and possible loss of shape because of aluminum Thus M = 956 kip-in. TOP RAIL P and M = 1912 kip-in. BOTTOM RAIL P I n Tables A3 and A4 you wi 11 note that the posts and ra i 1s yi e 1d when moments are within plus or minus 10 percent of these values. BARRIER VII program does this to assure numerical stability of the computer program. Figure A4 shows the tractor and bridge rai 1 0.08 sec after' impact. Since the transverse deflections of posts 2, 3, and 4 exceed 0.6 in., they have already yielded. Figures A5, A6 and A7 show the truck tractor after it loses contact with the rail and rotates from a heading of 12.2° to -4.2°. Figure A8 at 0.29 sec shows the rear tandem axles of the tractor impacting the rail and generating the maximum acceleration of 7.37 gls. At this time the aluminum rails have achieved a plastic moment at posts 3 and 4. From Table A5 one can see that the rear of the tractor actually impacts the rail at 0.25 sec. At 0.33 sec Figure A9 shows that the aluminum rail has achieved a plastic moment at Posts 2, 3, 4 and 5 and the design failure mechanism has formed (3 span, 2 posts). At 0.39 sec Figure AIO shows the design failure mechanism more clearly. Posts 3 and 4 are clearly yielding and the 39 aluminum rail has plastic moments at posts 2, 3, 4 and 5 as shown by Figures 7 and 8 of the main report. The 3-span failure mechanism which was found critical in the static design analysis is verified by the BARRIER VII dynamic analysis. Figure All shows the tractor leaving the bridge rail at about 0.44 sec and the post deflections shown are the final permanent deformations. Table Al is a summary of the post deformation at selected times. Table A2 is a summary of the post shear force at various times. Note there are both transverse and 1ongi tudi na 1 shear forces on the pas ts. This is because a coefficient of friction -of 0.3 was used between the tractor and the aluminum rails. The maximum post shear is 118.7 kips which is less than the post shear yield strength of 124 kips. Table A3 presents a summary of the post bending moments at selected times. The posts never yield about the weak axis. Note post 3 has yield moments about the strong axis of 3680 kip-in. and 3550 kip-in. which are within plus or minus 10 percent of the yield moment of 3620 kip-in. Table A4 presents a summary of the aluminum rail bending moments at selected times. Note the bottom rail is twice as strong as the top rail (Figure AI). The yield moments shown are also within plus or minus 10 percent of the rail plastic moment strength of 956 kip-in. (top rail) and 1912 kip-in. (bottom rail). Table A5 presents a summary of the truck tractor accelerations, speed, etc., at 10 ms i nterva 1s. The transverse acce 1erati on vector is perpendicular to the rail. Note the maximum 50 ms average acceleration is 6.25 g's. This would yield a maximum transverse force of 6.25 x 36.8 kips = 230 kips (50 ms average) which was used to design this bridge rail (Figures 5 and 10). 40 Table A6 presents a summary of the kinetic energy lost during the tractor-bri dge ra i 1 i mpac t. After the impact was over 0.44 sec, the tractor lost 39.6 percent of its initial kinetic energy. Of the total kinetic energy lost, 17.7 percent was absorbed by bending of the posts and rails, 5.3 percent by crushing of the truck tractor, and 77.0 percent due to friction losses between the tractor and rails and tire-pavement friction. Conclusions - The results of the BARRIER VII computer analysis of the EXTERNAL RAIL confirm the validity of the relatively simplified analysis and design procedures used to design the External and Internal Bridge Rails (Figures 9 and 11). This analysis indicates the maximum deflection of the top rail under the design i~pact will be about 17.9 in. This would indicate the maximum roll angle of the impacting truck would be about 12° (Figure A2) which is acceptable. The BARRIER VII analysis indicates the three span/two post failure mechanism found critical in our simplified static analysis and design procedure was correct. 41 ALUMINUM TUBE 11 In. 0.0. x 5/18 In. wall F = 35 ksi y = 245 N/mm2 .Ii co ~ W12x50 STEEL POST Fy = 50 ksi, 2 = 345 N/nm at 8 ft-G in. spacing ""E (2642 mfll spacir.g) E 0 C') .s ,.. co 2 AWM, TUBES COM BIN ED ~ ""E (\I ~ E .5 INTO oW E FIGURE Alo EXTERNAL BRIDGE RAIL AS SIMULATED BY BARRIER'VII. 42 11 In. 0.0. x 6/18 In. wall F = 35 ksi y = 245 N/rrm2 .Ii GO C\f W 2x50 STEEL POST = 50 ksi y = 345 N/ri-m2 at 8 ft-3 in. spacing """e (2642 nuil spacir.g) e I 0 .5 C") .I I ~ D~FLr;CTED posr ~ co ~ """E ('II ~ e .S ~ ('II ~ ... co ~ ~ .6 .5 CD ,..CD 10 oS 1/2 In. STIFFNERS e - 1-1/'·ln. diameter A325 BOLTS Fu = 120 ksi = 827 N/mm2 FIGURE A2. DEFLECTED EXTERNAL BRIDGE RAIL POST NO.3 • . (See Fi gure A) 43 POST NO, in. 700 - TRUCk WBGIIT· 67, Ski ps /HPACT SPEED" 50.0mp), [HPACT ANCL£ = 20.0 0 ~ ALUM. TUBE RAJLS --3 '--'I~·r--· W/2 )(50 STEEL POS T rooo - (TRACTOR OF T{f(Jcf, ~. '8 .. G KIPS F~. AXE L N 2.8.2 k IP~ REAR AX~ 36. B KIPS TOTA-L See Fi9' '+ -, ~ ~ ~ ~ 500 - ~ '< ~ s· V'I 20° -1 ACCn. v::crop; 1-:/;';NITUlE ~ 0·0/ ( 400 - 4-~O.o' H FIGURE A3. PLAN VIEW OF TRACTOR AND RAIL. (Time = 0.00 sec) 44 5 H DistaHc.e in .. 800 POST TIME = 0.08 SeC, NO, Lf- H~ 0.8 In, 700 -3 GOo rJ ~ 0:( n. I HEADING 4- " 17. -I # ~) I \ I VELOCITY VECTOR: HAGNlruDEc 47.0 '1!JJ, 4'" /5.0· 2- I-~ k- 500 T-t .":2. ~ If) 1 .-t 407 FIGURE A4. PLAN VIEW OF TRACTOR AND RAIL. (Time = 0.03 sec) 45 5 t-4 TIME = 0./2 SEC 800 - POST NO. _ - Lf- H 1,1 in. 700 - 3 I ~oo I I I I I - 2. k~ I 2.6/n 500 I I 1 400 FIGURE AS. PLAN VIEW OF TRACTOR AND RAIL. (Time = 0.12 sec) 46 H 900 POST tVO, TIME:: 0./8 s[.c. 5 H 300 - ,f- 1.1 in. ?OO - I I I I I , -- 3 .-t r-- 6,0 ;11. HEADING 4- I \ \ V£LOC I T'I V,ceroR; HA;f.JlrU[E: 45·3 mph I \ if.. -= /2.5 0 \ .. !-\ I "p I i ACCEL. VU r~i?: /.fA';I/ITUL.E" )":,, 0 I . r 4---3:";" I I k~6 i..,. I 500 .-l I I I FIGURE A6. PLAN VIE WOF TRACTOR AND RAIL (Time = 0.18 sec) 47 H 900 - TIME = 0.::"4 SEC. POS T NO. 5 H 800 r f 1 ,1 I, '.1 in. lOa I I ~ HEADING 4. = -4.2 • I I \ I I ECTOR.' Iv1I.GNITUDE = 71'Y)r~ \ VELOCITY, V 45. 4- -= /2.1 " -3 H l - G.Din, f- A~ I , .. --I I I I ACC£L. ,VEcro I I ! I I -1 I 2. H r'- 2. .61n, SuI) - I I FIGURE A7. PLAN VI EW OF TRACTOR AND RAIL. I (Time = 0.24 sec) 48 H 900 TIME = 0.29 SEC. _ POST NO, 5 H 800 - 700 - - 3 000 I I I t-~ 3 . 6 I"rt, 2. k__ .500 - I I FIGURE AS. PLAN VIEW OF TRACTOR AND RAIL. (Time = 0.29 sec) I 49 TIME = 0.33 SE:. 900 POST NO. 800 700 - - 3 "-.,~ GY) - I I I I I I~ 500 I I FIGURE Ago PLAN VIEW OF TRACTOR AND RAIL. (Time = 0.33 sec) I 50 H 900 - POST NOo 800 - 701) 3 H 17.8 i., .. 1<- ---- 5, 2 iV). So/) - I I FIGURE A10. PLAN VIEW OF TRACTOR AND RAIL. I (Time = 0.39 sec) 51 TIME:z J. {{ SEC. H 900 f'aST 800 - / vnOClTY VECTOR .. MA.;}//TUDE:: 39.:" m:..j1 / 4 . -/28' ' ACC£L. V€CTOR : N4G/I/,'''U[)£ = O'~l 4,='-105.5=' ~,_ 1'1,6 iS1, fj//(,'::.'cp DEFLECT/O:v" GOO I I _I I ? I '- r 5 . 2 ;». soC) FIGURE All. PLAN VIEW OF TRACTOR AND RAIL. (Time = 0.44 sec) 52 TABLE A1. SUMMARY OF POST DEFLECTION VS. TIME FROM BARRIER VII ANALYSIS OF EXTERNAL BRIDGE RAIL TOP POST DEFLECTION (in.) TIME (sec) POST 1 POST 2 POST 3 POST 4 POST 5 0.0 0.0 0.0 0.0 0.0 0.0 0.40 -0.02 0.13 0.22 -0.01 0.0 O.BO 0.06 2.79 6.51 0.79 -0. 11 O. 12 0.06 2.63 5.97 1.13 -0.03 0.16 0.06 2.63 5.97 1 • 13 -0.03 o.1B 0.06 2.63 5.97 1 • 13 -0.03 0.20 0.06 2.63 5.97 1 • 13 -0.03 0.24 0.06 2.63 5.97 1 • 13 -0.03 0.28 0.02 2.B5 6.B5 1 • 17 -0.06 0.29 -0.01 3.60 10.23 1.70 -0.13 0.32 O.OB 5.36* 16.B3 5.66 O.OB 0.33 0.07 5.34 17 .85* 6.09 0.09 0.36 0.09 5.25 17.77 7.39 O. 15 0.39 O. 10 5.20 - 17. 7B 9.31 0.29 0.40 0.10 5.20 17 .71 9.32* 0.31 0.44 0.09 5.22 17.6 8.85 0.52* No contact t = 0.12 to 0.24 sec. **Max. Top of Post Deflection 53 TABLE A2. SUMMARY OF POST SHEAR FORCE VS. TIME FROM BARRIER VII ANALYSIS OF EXTERNAL BRIDGE RAIL POST SHEAR FORCE - KIPS TIME POST 1 POST 2 POST 3 POST 4 POST 5 (sec) Long. Trans. Long. Trans. Long. -Trans. Long. Trans. Long. Trans. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.4 2.11 -6.17 5.26 37.6 5.33 67.4 1.76 -6.5 1.09 0.52 0.8 2.5 6.9 6.9 54.2 8.2 110.9 11.7 57.7 2.4 -22.6 0.12 -1. 12 8.4 2.43 22.0 -5.7 -46.6 3.3 36.5 -0.7 -9.3 0.16 -0.6 8.2 3.0 22.3 -5.2 -46.9 3.8 36.6 -0.2 -9.1 0.18 -0.24 8.2 3.3 22.3 -4.9 -46.9 4.2 36.6 0.2 -9.1 0.20 -0~3 8.2 3.3 22.3 -4.9 -46.9 4.1 36.6 0.1 -9.1 0.24 -0.2 8.2 3.3 22.3 -4.8 -46.9 4.2 36.6 0.2 -9.1 0.28 5.2 -0.5 10.1 62.7* 6.6 115.7 11.5 43.0 3.2 -13.1 0.29 11.0 -7.3 12.5 65.4 12.7 117.4 14.5 69.0 4.8 -29.0 0.32 9.2 12.9 10.3 34.2 15.2 118.7* 3.9 72.9 7.8 10.1 0.33 9.05 9.8 8.4 27.5 13.5 110.9 4.5 72.7 10.8 12.7 0.36 7.7 14.5 4.9 10.7 11.5 69.6 5.7 85.5 13.4 23.9 0.39 10.0 15.5 2.2 3.3 10.9 56.0 17.5 103.9 12.8 50.9 0.40 6.8 15.3 1.6 4.8 5.7 42.2 24.4 104.8* 13.2 53.4* 0.44 0.8 13.8 -5.6 10.4 -12.2 10.6 14.3 -38.4 4.9 51.0 No contact t = 0.12 - 0.24 sec *Max. Post Shear Transverse 54 TABLE A3. SUMMARY OF POST BENDING f'()MENT VS. TIME FROM BARRIER VII ANALYSIS OF EXTERNAL BRIDGE RAIL POST BENDING f'()MENT - KIP-IN. TIME POST 1 POST 2 POST 3 POST 4 POST 5 (sec) Weak Strong Weak Strong Weak Strong Weak Strong Weak Strong Axis Axis Axis Axis Axis Axis Axis Axis Axis Axis 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.4 70.8 -212.3 74.6 1516.8 73.0 2591.1 65.5 -155.7 58.6 -26.7 0,8 338.0 670.0 300.1 3016.0 214.2 3680.0* -22.0 3414.0* -32.0 -1258.0 0.12 98.0 723.0 58.0 1081.0 7.0 -2659.0 -150.0 2037.0 -149.0 -411.0 0.16 133.0 714.0 93.0 1094.0 42.0 -2679.0 -116.0 2043.0 -115.0 -404.0 0.18 155.0 713.0 115.0 1096.0 63.0 -2674.0 -94.0 2046.0 -94.0 -403.0 0.20 151.0 713.0 111.0 1096.0 60.0 -2674.0 -98.0 2046.0 -97.0 -403.0 0.24 156.0 713.0 116.0 1096.0 64.0 -2673.0 -93.0 2046.0 -93.0 -403.0 0.28 374.0 247.0 346.0 3327.0* 261.0 3550.0* 27.0 2571.0 13.0 -684.0 0.29 627.0 -138.0 588.0 3327 .0* 634.0 3550.0* 101.0 3579.0* 70.0 -1498.0 0.32 ' 488.0 983.0 389.0 2218.0 724.0 3550.0* 132.0 3440.0* -65.0 978.0 0.33 504.0 797.5 402.0 1972.0 625.0 3550.0* 272.0 3440.0* 44.0 1106.0 0.36 408.0 1060.0 316.0 894.0 533.0 2675.0 427.0 3440.0* 80.0 1840.0 0.39 346.0 1163.0 260.0 249.0 462.0 2724.0 652.0 3440.0* 67.0 3294.0 0.40 340.0 1155.0 249.0 312.0 461.0 1968.0 694.0 3341.0* 108.0 3315.0* 0.44 -29.0 1092.0 -139.0 541.0 85.0 477.0 393.0 -2247.0 -92.0 2908.0 No contact t = 0.12 - 0.24 sec *Yie1d Moment (For numerical stability, yield moment is ±10%.) 55 TABLE A4. SUMMARY OF ALUMINUM RAIL BENDING M)t-£NT VS. TIME FROM BARRIER VII ANALYSIS OF EXTERNAL BRIDGE RAIL ALUMINUM RAIL BENDING M)MENT - KIP-IN. POST POST POST POST POST POST TlfI£ 1 SPAN 1 2 SPAN 2 3 SPAN 3 4 SPAN 4 5 SPAN 5 6 (sec) Top Bottom Top Bottom Top Bottom Top Bottom Top Bottom Rail Rail Rail Rail Rail Rail Rail Rail Rail Rail 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.4 38.0 600.0 102.0 1468.0 102.0 729.0 77.0 124.0 21.0 28.0 0.8 497.0 1045.0 893.0* 1045.0 893.0* 1281.0 771.0 1281.0 27.0 113.0 0.12 488.0 764.0 535.0 764.0 535.0 935.0 408.0 935.0 155.0 15.0 0.16 490.0 765.0 534.0 765.0 534.0 933.0 408.0 933.0 154.0 17.0 0.18 490.0 765.0 534.0 765.0 534.0 933.0 408.0 933.0 154.0 17.0 0.20 490.0 765.0 534.0 765.0 534.0 933.0 408.0 933.0 154.0 17.0 0.24 490.0 765.0 534.0 765.0 534.0 933.0 408.0 933.0 154.0 17.0 0.28 489.0 1280.0 885.0* 1359.0 885.0* 1079.0 635.0 1079.0 119.0 7.4 0.29 730.0 1693.0 885.0* 1794.0* 885.0* 1820.0* 864.0* 1820.0* 183.0 -81.4 0.32 868.0* 1451.0 885.0* 1451.0 885.0* 1757.0* 834.0 1756.0* 836.0 706.0 0.33 854.0 1469.0 868.0* 1597.0 866.0* 1757.0* 861.0* 1756.0* 861.0* 797.0 0.36 831.0 1263.0 746.0 1838.0* 477.0 1838.0* 862.0 1756.0* 862.0* 1050.0 0.39 847.0 1270.0 623.0 1776.0* 880.0* 1776.0* 880.0* 1609.0 862.0* 1609.0 0.40 850.0 1286.0 614.0 1650.0 880.0* 1650.0 880.0* 1700.0 846.0 1700.0 0.44 857.0 1369.0 603.0 1369.0 566.0 1158.0 575.0 1626.0 575.0 1626.0 No contact t = 0.12 - 0.24 sec *Yield Mo~nt 56 TABLE A5. SUMMARY OF ACCELERATION AND VELOCITY DATA OF TRACTOR IN BARRIER VII ANALYSIS TIME AFTER ACCEL. VECTOR TRACTOR HEADING TRANSVERSE IMPACT VECTOR ANGLE VELOCITY ANGLE ACCEL. (sec) (gls) (deg) (mph) (deg) (gls) .25* 0.43 -97.8 45.67 12.0 .43 .26 0.94 -102.0 45.62 11 .8 .92 -;,... ~, .27 1.92 -104.4 45.50 11 .5 1.86 (7) t '\ 6.52t..~~ .28 6.82 -107.0 45.06 10.6 ,0 .29 7.37 -107.2 44.3 8.5 7.04 ~ ~... .30 6.06 -106.9 43.72 6.8 5.80 - (J .31 5.79 -106.9 43.22 5.3 5.54 -..) )C- ~ .32 6.67 -107.5 42.7 3.5 6 .36 ~ , £ .33 5.75 -108.0 42.2 1.8 5.47 .34 5.43 -108.7 41 .83 0.3 5.14 .35 5.65 -110.2 41.44 -1.3 5.30 .36 5.21 -111.7 41.0 -2.9 4.84 .37 5.68 -113.0 40.67 -4.4 5.23 .38 5.84 -113.4 40.3 -6.2 5.36 .39 5.71 -113.9 39.9 -7.9 5.22 .40 5.47 -113.3 39.6 -9.7 5.02 .41 4.41 -112.4 39.35 -11.2 4.08 .42 2.78 -111.5 39.21 -12.4 2.59 .43 O. 17 -105.7 39. 17 -12.8 • 16 .44 O. 16 -105.5 39.17 -12.8 • 15 *Rear Impact of Tractor Begins 57 TABLE A6. SUMMARY OF KINETIC ENERGY LOST DURING TRACTOR IMPACT - BARRIER VII ANALYSIS ENERGY BALANCE, TIME = .4400 SECS TYPE OF PERCENT OF PERCENT OF PERCENT OF ENERGY ORIGINAL AUTO KE ORIGINAL KE ENERGY LOSS Translational KE of Auto = 60.4 Rotational KE of Auto = .0 Barri er KE = .0 -" Elastic Energy in Members - Beams = .4 Posts = .0 ~ . 7.0 Barri er 17.7% Inelastic Work on Members Beams = 3. 1 Posts 3.5 = - Elastic Energy in Auto = .oL Inelastic Work on Auto = 2.0 I 2. 1 Tractor 5.3% I Damping Losses = • 1 .J Auto-Barrier Friction Loss = 26.7l·-~~ 30.5 Friction 77.0% Auto-Pavement Friction Loss = 3.8 _1 Sum of All Contributions = 100.0 39.6 Total 100.0% of Loss Energy Lost Original Kinetic Energy of Tractor = 3,036,806 1b-ft - 44 Sec. Kinetic Energy of Tractor = 1,834,3081b-ft Total Energy Lost in Collision = 1,202,4981b-ft Bridge Rail Absorbed 17.7% = 212,842 lb-ft Tractor Absorbed 5.3% = 63,7321b-ft Barrier and Pavement Friction 77.0% = 925,924 lb-ft 58 APP EN DI X II B " AN AL '(S/5 AND DE-51/,N COM PtJrATltJt.j 5 T1I£OR,( IMP,4C7 FORCE (s~e Fi~. I( ) 50mp~ =- 20 0 A1l8 Je. 0 G'fI+. "" (72,1 '+f/sec.. t . 5iY1 Z 20 ...... ""'''''www 2 www 2 J( 32,2 rVscz7.. [N. J tf siYJ20· - If f+ (1- cos ~~~ dTI 000 U"le~ _~o. ForGe MaJ<, = ,--51 1'ti''>" x._~9-!; If'S .. =\ 3~~m~ kips /1 .I~r 1I0,OOOlbTt'lJd Gee Fret 5)' ~-----l?t F,J' Lf- q+ '\-::\.o.---...... 'J_' -....- \ 50 'ttl Pr, 2 0 ~ ~.~.. ----- T~eoY'~ F~.:: 3,31 ~/5 )( 60 k,p' 5"Ol'llpn 20· = 19<6, b k IpS for 1l0,OOOlb Tii ':! 3 I 3} GIl '> '< tt.S- .~., i p5 0eh' '30,000 Ib Tn)c.~ =- 3,3J x .~7 "7 - 1\ -r" • 7:" I 2. 3 _ )) i F)':' )t' \ C, J ,'-:> ~0 ;i:) n:;.:!c -~====~§;. ~.~=-= ... -~.,,-.---- .. ~::====:::======-.:..:::.=... tvofc::; The 1,7Y ·U.:.:'f:f 1),;1; '/:.. ;.-L/ -fo C/(f.jvs/ ?heOY1 -to .f ~e CJ. 0 5 0 5 ec Cf V 1' ~)( fey- i ;,}J e wI q / 59 THEORY - EFFecTIVE HEIGHT OF RIJIL H = ~. G/.,f. C - 5/z. wwW tYJa>( , Gr I ~+ ««« "'''''''::1::1::1 000 8 50mph - 2.0 A n,Je. 0.ee: F[~~ G ) 60 I I SAMPLE BRIDGE RIJIL [)ESJ6N - EXTER.NlfL F/G~ cr POST $P,tCIN&, ~ ~ f+- ~i~ '= ~,6 7 If : 2b'f2 ~~ 3 Mt1iV} Reti/~ Lo~+(!d a+ ~lfll I 56" t:I~c/ cr'l/ AWM,7VJE 1/"O,D, b~ O,3}3" +hlGkut!-ss _ (3w,1I b~I1$"~) S:: 2 7. 2 {. ,~ . ~ -~ '" I, Z 7 5 :: 3'1-, I> 2 110\. ~ - -, 5p~Y\ W -::: ~!v1 e .. -=8'" r2 .. 1J - ! , - L - ~/?.. /04- - If-7 L-= :C(;, 67 oll1 e. rC(, I .. 10 If 1/ w =: <6 xl2.JI· GO .'nlp~ 20~ - !f~ "Jlte fA" I :, 5p~ Y1 ~::;. ~.)( )2,11 _L: "3' 2.') 312-- ~g> Lf5~Vl L:: ttJb)) TRY PosT .~, " .... Pp 61 Mee~aY)lsW1 L04 d C4 'fAIl C- j '-/- I-j MeGh • '. ,L oqd Cq pt:I(." of Rtti)s + Po!St ,=. ro-t., ) P05~ tA./ ------r--=~==~ RtI,~/s 173 ~-~ 3 Post _No.Ul COCOa)) MMM~ ~~~i 51 <=t If I P ~ , 2 9.2 Iff ' 2 $p~~ ~al·1.> 60r:: J\ '3 I %0 If 3 x 6 tt, b I L: 17,3~ - Po 5 + 6lf;')t.) 6lf;b~ 1<13, ? 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SPA N w = ~ x 1725" -- L = 208 I, zoe - 1Y8 3 5P4fV W '= ~"17 2';- - L. '& 3 12." 3/z-'fB Lt 5P41\1 ,w ~ ~)( '7 Z, ~ 37/rips l-= '+1 b II ttlb - 'f8 5/ee I PD.5 f I I . :S::J 1<5 i ' 57, 5 if!. " :: Z 6 75 /'4 - k 1/4 ---- ... --.--.-~-.. ~-~ .~-.------"-. Z. 65 I I - Mec ~a~f s YY\ Loac/ C4 peu;, dt-j Mec:...u. L04J ~P4t.4jl Rtfi ) s +- Pas f . To~1 POSTS (JtI L. Y IoUIoUW """"""«<=>=>=> 000 ",V""...... 0-0-0- "'''''''www . :~ IoU",W SPI}f\) 2)( 2lfb 2 x be xxx 1. litl/ Is If-92 III"'", 000 I/')~~ < _C""IC)o.r/'J CX)COCD:) 0 MMM~ L~ i.67' Posts 0 ~~~! - ~92 I),p, 13' ~/¥J~ It~i ~ 2 SP{fAJ 1<4i/$ 2)( ~6 -::: \72 ,~ b8 -: .. 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',...... '--...... ""--~ -'-'R_ 6A--SE PL4TE TftiCtNE55 Mp= 2 ~. 90t5 /) JP~ ( 2 i~J :.. 36 2. J~ - r11 ~ ...... w "'''' ... •••j:;:j Me K-r., ;. CCC ~ - - 362 7, 2,lI- 1'11,"3 .,,"''''...... - - , §§§ ~o )r S J .,,"'''':x::r::r: ~ 000 ~2~ _No.rn IDCD/;O'J MMM: ~~~i b t '-- : Z z.tJ.. l} i 1...... 7, z./f )( tt ~ 2./'10 /0 - Mp ::: Z V 71, <7 Ir JP$ l( 21 V1 -:: Z- 1: '::> Me.. ~ z. T7. 6 :;> 5.75 F;, So b ~ ~ s-; 7!J- t 'L :=-,f:..2!:7;( \j_ JD t-~~ /,5 II vse fa r tv J 2 x If 0 / / 69 27 in. to 32 in. 0 I a:- ~". ~~c:r BUS B &r::II a: 20 t-=------..,.!) ~~ I ~-<;. ~I ct TRUCK T .... m I I fOO I I I 'I I VAN &1 I 10 I eAR I :LTo TRll BUS I I TRUd< I ~G! : eG's I I eG's I I eG', I I .... , ... .. ,- • I I I I 17 1 in. I 0 1 I I I I I I I I o 10 20 30 40 50 60 70 80 90 VEHICLE CENTER OF GRAVITY HEIGHT (CG) - INCHES