Load Rating of Permanent Bridges on U.S. Army Installations

Transcription

1 Tehnial Reprt SL-9- April 199 US Army Crps f Engineers Waterways Experiment Statin Lad Rating f Permanent Bridges n U.S. Army Installatins by James C. Ray, WES Terry R. Stantn, U.S. Army Center fr Publi Wrks Apprved Fr Publi Release; Distributin Is Unlimited DTIC QUALITY INSPECTED Sj Prepared fr U.S. Army Center fr Publi Wrks

2 The ntents f this reprt are nt t be used fr advertising, publiatin, r prmtinal purpses. Citatin f trade names des nt nstitute an ffiial endrsement r apprval f the use f suh mmerial prduts. The findings f this reprt are nt t be nstrued as an ffiial Department f the Army psitin, unless s designated by ther authrized duments. 0 PRINTED N RECYCLED PAPER

3 Tehnial Reprt SL-9- April 199 Lad Rating f Permanent Bridges n U.S. Army Installatins by James C. Ray U.S. Army Crps f Engineers Waterways Experiment Statin 909 Halls Ferry Rad Viksburg, MS Terry R. Stantn U.S. Army Center fr Publi Wrks Frt Belvir, VA Fina: reprt Apprved fr publi release; distributin is unlimited Prepared fr U.S. Army Center fr Publi Wrks Frt Belvir, VA

4 US Army Crps f Engineers Waterways Experiment Statin HEADQUARTERS summa ENTRANCE ENVnMCNTAL LABRATRY FR INFRMATIN NTACT; PUBLIC AFFAIRS FFICE U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATIN 909 HALLS FERRY RAD VICKSURG, MISSISSIPPI PHNE: (601) STRUCTURES LABRATRY «EAFfiESEfiVATI»!' J750II- Waterways Experiment Statin Catalging-in-Publiatin Data Ray, James C. Lad rating f permanent bridges n U.S. Army installatins / by James C. Ray, Terry R. Stantn ; prepared fr U.S. Army Center fr Publi Wrks. 14 p.: ill.; 2 m. (Tehnial reprt; SL-9-) Inludes bibligraphial referenes. 1. Military bridges Design and nstrutin. 2. Bridges Design and nstrutin. I. Stantn, Terry R. II. United States. Army. Crps f Engineers. II. U.S. Army Engineer Waterways Experiment Statin. III. Strutures Labratry (U.S. Army Engineer Waterways Experimentstatin) IV. US Army Center fr Publi Wrks. V. Title. VI. Series: Tehnial reprt (U.S. Army Engineer Waterways Experiment Statin); SL-9-. TA7 W4 n.sl-9-

5 Cntents Prefae Vll 1 Intrdutin, Bakgrund 1 bjetive ~ Spe 2 Lad Rating verview 2 2 Basi Cnepts 7 Bridge Terminlgy 7 Bridge Types and Lad Paths."!.'.'.'.".'.'.'.'.".'.'.".'.'.'."!.'.' General g Slab Bridges g Bx Culverts Multi-Girder Bridges ".'"."'" 9 Distributin Fatr 10 Tw-Girder r Truss Bridges n Railrad Bridges 12 Bridge Rating Guidelines and Criteria..."..". 1 Lad Effets 26 Dead and Sendary Lads 26 Live Lads 27 General 27 Civilian vehiular lads 27 Military vehiular lads 2 Speial military lads 29 Railrad lads 0 Maximum Live Lad Effets "..."". 1 General 1 Deks 1 Stringer r multi-girders 2 Flr beams Girders r trusses _ 111

6 Railrad bridges 4 Lad Effets n Cntinuus Spans 5 A Capaity and Safety Fatrs 72 Intrdutin 72 Allwable Stress Methd 7 Lad Fatr (Ultimate Strength) Methd 74 Lad and Resistane Fatr Rating (LRFR) Methd 74 Railrad Bridges 75 5 Summary 7 Basi Rating Predure 7 Military Lad Classifiatin (MLC) 7 Rating Examples 79 Referenes 0 Appendix A: Timber Bridge Example Al Appendix B: Steel Multi-Girder, Cnrete Dek Example Bl Appendix C: Truss Bridge Example Cl Appendix D: Cntinuus-Span Reinfred Cnrete Tee-Beam Example Dl SF29 List f Figures Figure 1. Basi design lads fr abridge 5 Figure 2. Lad psting signs resulting frm lad rating 6 Figure. Basi parts f a bridge 14 Figure 4. Superstruture elements 14 Figure 5. Slab bridges 15 Figure 6. Bx ulverts 15 Figure 7. General lad path fr a multi-girder bridge 16 Figure. Lngitudinal and transverse lad distributin 17 Figure 9. Timber stringer bridge 1 Figure 10. Steel multi-girder / nrete dek bridge 1 Figure 11. Cnrete tee-beam bridge 19 IV

7 Figure 12. Prestress / psttensin girder bridge 19 Figure 1. Cnrete bx girder bridge 20 Figure 14. Steel girder bridge 20 Figure 15. Truss bridge 21 Figure 16. Railrad bridges 21 Figure 17. Transverse lad distributin thrugh deks 22 Figure 1. General lad path fr a girder r truss bridge 2 Figure 19. General lad path fr an pen dek railrad bridge 24 Figure 20. General lad path fr ballast dek railrad bridges 25 Figure 21. Sendary lads n bridges 7 Figure 22. Civilian live lads (referene [1]) Figure 2. Military live lads (referene [4]) 9 Figure 2 (nt'd). Military live lads 40 Figure 24. Mment and shear urves fr HET verlaid nt standard MCL urves 41 Figure 25. Heavy Equipment Transprt System (HETS) 42 Figure 26. Mdel G515T-1500 general purpse army lmtive, 20 tns eah 4 Figure 27. Cmmn mmerial lmtive, Mdel SD40-2, 14 tns eah...44 Figure tn speial purpse flat ar; 1 tns with 2 Ml Al tanks 45 Figure 29. AMC amm bx ar, 10 tns eah 46 Figure 0. Cmparisn f E0 train t wrst-ase army trains 47 Figure 1. Equivalent E-ladings fr typial army trains, based n bending mment 4g Figure 2. Equivalent E-ladings fr typial army trains, based n endspan shear 49 Figure. Maximum dek ladings 50 Figure 4. Maximum stringer r multi-girder ladings 51 Figure 5. Vehile plaement fr maximum lad effets n elements 52 Figure 6. Maximum stringer r girder mments fr ivilian live lads (referene [1]) 5 Figure 7. Maximum stringer r girder shears fr live lads (referene [1]) 54 Figure 7 (nt'd). Maximum stringer r girder shears fr live lads 55 Figure. Maximum lngitudinal bending mments fr military live lads...56 Figure (nt'd). Maximum lngitudinal bending mments fr military live lads 57

8 Figure 9. Maximum endspan shears fr military live lads 5 Figure 9 (nt'd). Maximum endspan shears fr military live lads 59 Figure 40. Maximum flr beam ladings 60 Figure 41. Maximum flr beam ladings fr ivilian live lads (referene [1]) 61 Figure 41 (nt'd). Maximum flr beam ladings fr ivilian live lads 62 Figure 42. Maximum flr beam ladings fr military live lads (sure: WES derived) 6 Figure 42 (nt'd). Maximum flr beam ladings fr military live lads (sure: WES derived) 64 Figure 4. Maximum girder r truss ladings (shwn fr bending mment nly) 65 Figure 44. Calulatin f wheel lines per truss 66 Figure 45. Lad distributin in railrad bridges 67 Figure 46. Cmparisn f simple and ntinuus span bridges 6 Figure 47. Bridge deks are ften ntinuus in the transverse diretin 69 Figure 4. Mving lad analysis n ntinuus spans 70 Figure 49. Mving lad analysis by hand 71 Figure 50. Allwable stress mpared t lad fatr methd 76 Figure 51. Rating fatr equatin fr three different lad rating methds (vehiular bridges nly) 77 VI

9 Prefae The wrk reprted herein was spnsred by the U.S. Army Center fr Publi Wrks (USACPW), Frt Belvir, Virginia. Mr. Terry Stantn, USACPW, was bth Prgram Mnitr and Tehnial Mnitr. All wrk was arried ut by Mr. James C. Ray, Strutural Mehanis Divisin (SMD), Strutures Labratry (SL), U.S. Army Engineer Waterways Experiment Statin (WES) and Mr. Terry Stantn, USACPW. Reprt Preparatin was amplished by Ms. Jennifer Bennett, (WES). The wrk at WES was nduted under the general supervisin f Dr. Bryant Mather, Diretr. SL; Mr. Jhn Ehrgtt, Assistant Diretr; and Dr. Reed Msher, Chief SMD. At tb time f this reprt, the Diretr f WES was Dr. Rbert W. Whalin. The Cm lander was Cl. Brue K. Hward, EN. The ntents f this reprt are nt t be used fr advertising, publiatin, r prmtinal purpses. Citatin f trade names des nt nstitute an ffiial endrsement r apprval f the use f suh mmerial prduts. VII

10 1 Intrdutin Bakgrund It is widely knwn that the United States wns and maintains many bridges thrughut its highway system. Hwever, it may me as a surprise t mst that the Department f the Army wns and maintains ver 1500 bridges. These bridges are n U.S. military installatins thrughut the wrld and arry pedestrians, ivilian and military vehiles, and trains. Like the U.S. infrastruture, these bridges require ntinual inspetin, maintenane, and lad apaity assessment. The Amerian Assiatin f State Highway and Transprtatin ffiials (AASHT) has prvided numerus tehnial guidelines fr the inspetin, maintenane, and lad rating f bridges n the U.S. Highway system. The Amerian Railway Engineering Assiatin (AREA) prvides similar guidelines fr railrad bridges and the Army has tehnial manuals t address temprary theater-f-peratins bridges. Hwever, past experiene has shwn that these riteria are nt mpletely appliable t bridges n military installatins and that they prvide innsistent levels f safety. Table demnstrates that usage-wise installatin bridges fall smewhere between a nventinal highway r railrad bridge, and a temprary theater-fperatins bridge. Mst imprtantly, they have very different traffi vlumes and traffi types depending upn their latin and purpse n the installatin. Thse bridges that are in areas pen t the publi must arry the same ivilian ladings as nventinal highway bridges (althugh generally in muh lwer vlumes) and at the same time arry heavy and frequent ladings frm military wheeled and traked vehiles. Yet, thse bridges in training areas (i.e., nt pen t publi) typially arry nly military vehiles. Likewise, mst railrad bridges n installatins are ff f the mainline and must nly ammdate lighter and muh less frequent military trains entering and leaving the installatin. In summary, installatin bridges are widely varied in their usage levels and d nt fall easily under any nventinal lad rating guidelines. This variatin has prdued a wide dispersin f lad rating methds and levels f safety amng military installatins. Army Regulatin, AR420-72, prvides a greater unifrmity in the lad rating predures and pliies by stipulating speifi guidelines. These guidelines are based heavily upn thse set frth by the AASHT in Referenes [1] thrugh []. T aid in the adptin f these guidelines and t train Chapter 1 Intrdutin

11 installatin engineers wh might be inexperiened in bridge lad rating, the USACPW funded the SL-WES t develp a shrt urse entitled, "Lad Rating f Bridges n Military Installatins." Sine the urse began, the U.S. Army Crps f Engineers has als begun partiipating in the urse. This reprt prvides a summary f the material develped fr the urse and, at the same time, duments the lad rating methdlgy. bjetive The bjetive f this wrk was t prvide unifrmity in the predures and pliies fr determining the lad apaity f bridges n U.S. Army Installatins, and als t prvide a mmn referene fr this infrmatin. Spe It is regnized that many installatin engineers have very little experiene in bridge lad rating. Therefre, the first part f this reprt presents a general verview f bridges and rrespnding engineering nepts. The verview inludes basi bridge types, bridge elements, bridge ladings and ptimal lad plaement, lad paths thrugh bridges, lad distributin nepts, and lad rating guidelines and riteria. While it is prvided in the atual Lad Rating urse, a review f basi strutural mehanis is nt prvided herein sine these nepts are well dumented in the literature. The last part f this reprt presents detailed lad rating examples utilizing the methdlgy desribed herein. Lad Rating verview The sle purpse f bridge lad rating is t determine the allwable lad apaity f an in-servie bridge. Speifially: Hw big f a vehile (r train) an safely utilize the bridge? As shwn in Figure 1, bridges are riginally designed fr three basi lasses f lads: self-weight, knwn as "dead lad"; vehiular (r usage) lads, knwn as "live lads"; and "sendary lads", suh as wind, snw, et. Therefre, the required apaity f eah individual bridge element (i.e., the members making up the bridge as a whle) may be expressed as: Required Member Capaity = Dead + Live + Sendary Lads. (1) Fr lad rating purpses, a methd is needed fr evaluating the bridge's ability t arry speifi live lads, and fr evaluating whether there is a need t restrit traffi ladings n the bridge. Fr this, Equatin 1 an be wrked bakwards and slved fr the allwable live lad as: Allwable Live Lad = Member Capaity - Dead Lad - Sendary Lads. (2) Chapter 1 Intrdutin

12 Sendary lads are f a temprary and spradi nature, and it is unlikely that they will be present n the bridge at the same time as a wrst-ase live lad. Therefre, sendary lads an usually be negleted in a lad rating analysis and the prtin f the member apaity that was prvided fr these lads may nw be utilized t arry additinal live lad. Fr lad rating, the basi equatin thus bemes: Allwable Live Lad = Member Capaity - Dead Lad Effet. () Frm this equatin, the prtin f ttal member apaity available t arry live lad is the apaity remaining after the dead lad effet is arried. Allwable live lad is ften nveniently expressed in terms f a "Rating Fatr" (RF), whih is basially the rati f the expressin abve as fllws: _. _, Available Capaity Member Capaity - Dead Lad Effet Kr = = (4) Applied Live Lad Applied Live Lad Effet In mst ases, the member apaity and the dead lad effet (the numeratr) des nt hange. By simply adjusting the applied live lad effet (the denminatr), several vehiular ladings an be evaluated quikly t determine if any restritin is needed. Paragraph 6.5 f Referene [1] prvides the abve equatin in the fllwing generi frm: *F- - A ' D ; (5) A 2 L(l + I) K } where: C = Member Capaity D = Dead lad effet n the member L = Live lad effet n the member / = Impat fatr fr live lad Aj = Fatr fr dead lads A 2 = Fatr fr live lads Eah f these variables will be disussed in detail in the fllwing hapters. It is extremely imprtant t understand that a RF must be btained fr eah ritial bridge element, fr eah pssible mde f stress, and fr eah f the desired Rating and Psting vehiles. (These terms will be disussed in the fllwing hapters.) Fr example, refer t the bridge and rating summary shwn in Table 2. In this ase there are three different spans that must be evaluated. If just the superstrutures are nsidered fr the tw girder (apprah) spans, bth the dek and girders must be evaluated fr shear and bending fr eah f the vehiles. Fr the truss span, the dek, stringers, and flr beams must be evaluated fr shear and bending. Hwever, the truss elements need nly be evaluated fr tensin r mpressin. This example makes it easy t see why many sftware pakages are available t ndut these alulatins. But ne all RFs are btained, the element with the smallest RF bemes the "ntrlling element" and the verall bridge rating is based nly n its apaity. Fr many small r simple bridges (suh as thse n many Army installatins), ne this Chapter 1 Intrdutin

13 Cntrlling element is determined, fllw-n analyses need nly nsider that element. In Equatin 5 abve, a RF less than 1.0 means that the element r bridge annt arry the desired live lad and a restritin is required. A RF greater than, r equal t, 1.0 means that it is suffiient fr the desired live lad and n restritin is required. Fr example, in Table 2 the RF fr the bttm hrd in the truss span is 0.4 fr ne f the rating vehiles. This means that the bttm hrd f the truss is nly apable f arrying 40% fthat vehile's grss vehile weight (and that is what wuld be psted). Likewise, the girders in the 40-ft span have a bending RF f 1.10 fr ne f the rating vehiles. This RF means that the girders in this span are apable f arrying 110% fthat vehile's grss vehile weight. A typial ivilian psting sign is shwn in Figure 2a. This type f sign shuld nly be psted n the bridge if the RFs are less than 1.0 fr any f the psting vehiles. The allwable weights (in tns) shwn n these signs are btained by multiplying the ttal weight (in tns) f the rating r psting vehile by the ntrlling (i.e. lwest) RF as fllws: Allwable Weight = (RF)(Vehile Weight in tns) (6) Nte in Figure 2a that the allwable weight f the lnger truk is larger than that fr the shrter truks. This is mmn and lgial fr shrter span bridges, where the truks may be lnger than the bridge span. In that ase, the ttal lad f the lnger truk will never be mpletely n the bridge span at the same time; whereas, the ttal lad f the shrter truk an be mpletely n the span at ne time. Figure 2b shws typial military lad lass (MLC) psting signs. These signs are required n all bridges n military installatins that arry military traffi. The signs shw wheeled and traked, ne- and tw-way lassifiatins. The meaning f these terms and MLC alulatin will be disussed in the fllwing hapters. Table 1 Cmparisn f Bridges Servie Life Highway Bridges 50+ years Theater f peratins Bridges 1 t 5 years 50+ years Military Installatin Bridges Military Traffi Vlume Essentially ,000 per day per day Civilian Traffi Vlume >100,000 per day ,000 per day Vehile Speeds >65 mph 25 mph mph Train Types Cper E-0 Cper E-series Army speifi Fatigue Suseptibility High Lw Lw t Medium Guidelines Available AASHT TM5-12 Mixed Chapter 1 Intrdutin

14 I Span! 1 1 Span2 1 1 Span Span4 T Table 2 ±± M* U, J-L XL Example Bridge Rating Fatr Summary Bridge Element H20 Vehile HS 20 Vehile Type Vehile Type S2 Vehile Type - Vehile Girder Span Dek (bending) Dek (shear) Girders (bending) Girders (shear) Truss Span Dek (bending) Dek (shear) Stringers (bending) Stringers (shear) Flrbeams (bending) Flrbeams (shear) Tp rd Bttm rd Vertials Diagnals Cntrlling RF Vehile = Live Lad * ** ;; Transprt ; Snw«Figure 1. Basi design lads fr a bridge Chapter 1 Intrdutin

15 15T 16T 1T a. Civilian Psting Sign b. Military Lad Class Signs Figure 2. Lad psting signs resulting frm lad rating Chapter 1 Intrdutin

16 2 Basi Cnepts Bridge Terminlgy Bridges are mpsed f many different members, referred t as "elements." The mst basi elements f a bridge are the substruture, superstruture, and dek, as shwn in Figure. The substruture supprts the superstruture and dek, and nsists f the abutments and intermediate piers r pile bents. These elements are supprted n spread ftings r piles. Substruture elements are generally versized frm the lad-arrying standpint sine they must als withstand suh additinal fres as buyany, stream flw, debris and barge impat, and wind. As a result, they seldm ntrl (i.e., limit the live lad apaity) in a lad rating analysis and are thus nt disussed in detail herein. Hwever, if fr any reasn the substruture is suspet, it shuld be heked. This is nsistent with the remmendatins f Referene [1]. An exeptin t this rule is timber bent aps and piles, where ap shear r lateral-trsinal bukling f the expsed prtin f the piles may ntrl. These shuld always be heked. ne f the elements f the bridge superstruture will generally ntrl in a lad rating analysis. Typial superstruture elements and their prper terminlgy are shwn in Figure 4. They are usually nstruted frm timber, steel (either rlled stk r built-up plate) r nrete (either reinfred r prestressed). A "girder" is the largest superstruture element, always spans between substruture elements, and mst ften runs lngitudinally (i.e., parallel t the diretin f traffi). A "truss" an be used in plae f a girder and serves the same purpse. Trusses are basially an effiient methd f making a very deep girder. Like the bttm and tp flanges f the girder, the bttm and tp hrds f the truss at primarily t resist bending fres in the span. Likewise, the vertial and diagnal truss members at like the girder web t primarily resist shear fres. A "flr beam" always spans between either girders r trusses and mst ften runs transversely (i.e., perpendiular t the diretin f traffi). A "stringer" is generally the smallest superstruture element, always spans between flr beams, and mst ften runs lngitudinally. Figure 4 shws all f the elements nneted tgether at their ends. This is amplished with either blts, rivets (ld bridges nly), r welds. Althugh nt shwn, anther means f nnetin is t lay the members ver the tp f eah ther; i.e., stringers n tp f flr beams and flr beams n tp f girders. Chapter 2 Basi Cnepts

17 The superstruture elements supprt the dek, whih prvides the surfae ver whih the traffi travels. Deks are usually either timber (plank r laminated), steel grid, r nrete. They span either lngitudinally r transversely, depending upn the supprting superstruture nfiguratin. "verlays", usually f asphalt r nrete, are ften used n tp f deks t prvide misture prtetin and a wearing surfae. While nt strutural elements, they nstitute a signifiant added dead lad n the bridge and must be nsidered in the lad rating. The same is true fr suh appurtenanes (i.e., attahments) as railing, lighting, sidewalks, utilities, et. Bridge Types and Lad Paths General Bridges are generally desribed in terms f their superstruture type and the primary material mpsing the superstruture. The bridges in the fllwing paragraphs are desribed in this manner. Frm the analytial standpint, it is als imprtant t understand the manner in whih the bridge arries vehiular ladings frm the bridge dek dwn t its substruture. This is referred t as the bridge's "lad path" and will als be disussed fr eah bridge type in the fllwing paragraphs. Slab Bridges ne f the mst basi bridges is a slab bridge, as shwn in Figure 5. Unlike all ther bridge types, the dek f a slab bridge is the nly element mpsing the superstruture. As demnstrated in Figure 5, the lad path is very simple. The wheel ladings are arried thrugh the slab, in a lngitudinal diretin (parallel t traffi), diretly ut t the substruture supprts fr the slab bridge. Beause this type f bridge spans lngitudinally between its supprts, the main reinfring in a slab bridge als runs lngitudinally. Bx Culverts A bx ulvert (Figure 6) is basially an extensin f a slab bridge, where the tp slab (r rf) is made integral with its substruture supprts, whih nsist f the ulvert walls and flr. Sine they are integral, all f the elements at tgether as a frame t supprt the lads. As shwn in Figure 6, lads are distributed t the bx ulvert elements nly thrugh the surrunding sil. The degree t whih wheel lads are spread ut ver the tp slab depends primarily upn the amunt f sil ver. In additin t wheel ladings, eah f the ulvert elements must als supprt the ladings impsed by the surrunding bakfill. Chapter 2 Basi Cnepts

18 Multi-Girder Bridges Multi-Girder bridges are a very mmn mdern bridge type. Multiple girders span lngitudinally frm substruture- t substruture element. The girders may be timber, steel, r nrete (reinfred r prestressed). A dek, usually timber r reinfred nrete, spans transversely between the girders. The lad path fr these bridges is demnstrated in Figure 7. In this figure, typial multi-girder bridge has been separated int its separate elements. It an be seen that a vehile may be at any psitin n the bridge dek. Fr lad rating purpses, the vehile must be lated at the psitin n the dek (bth lngitudinally and transversely) t prdue the wrst-ase lading fr eah f the elements t be rated. Nte that the wrst-ase psitin fr the dek rating will nt be the wrst-ase psitin fr the girder rating. The psitins will als be different fr nsideratin f mment r shear effets. The exat manner in whih t plae lads in rder t maximize lad effets will be disussed in detail in Chapter. Referring t the end view f Figure, it an be seen that the dek serves t spread ut the wheel lads, effetively transmitting them ver and dwn t the girders. In the side view it an be seen that the dek als serves t distribute the wheel lad ut in a lngitudinal diretin. Hwever, this effet is generally ignred in lad ratings. The girders share in the lads t varying degrees, with ne arrying mre f the lad than the thers due t its lser prximity t the applied lads vary. This girder will be the "ntrlling girder"; i.e., the bridge will nly be as strng as the member with the mst lad r the weakest member. The exat amunt f lad that the ntrlling girder must arry is determined by a "distributin fatr", whih in the fllwing setin. A timber multi-girder bridge is demnstrated in Figure 9. This type is very mmn n many military installatins. A mre mmn name fr it is "timber stringer bridge." Hwever, in keeping with the terminlgy disussed abve, it shuld atually be referred t as a timber multi-girder bridge sine the superstruture beams span frm substruture t substruture. Lng bridges f this type, ver multiple pile bents, are als referred t as "timber trestles." The deks f these bridges are almst always nstruted frm transversely-laid timber and are very ften verlaid with sarifiial "treadways" t prvide a prtetive wearing surfae. A steel multi-girder bridge is shwn in Figure 10. While innsistent with the terminlgy used herein, this type is als ften referred t as a "steel stringer bridge." The dek types may f urse vary; but that shwn in Figure 10 is reinfred nrete and is the mst mmn fr steel multi-girder bridges. These deks at as ntinuus ne-way spans arss the tps f the girders. The upper steel flanges may r may nt be embedded int the nrete dek. If fully embedded, the flange is nsidered t be fully braed against lateral-trsinal bukling (disussed later). In additin, the nrete dek may be made t at mpsitely with the steel girders thrugh shear studs n tp f the girders, referred t as "mpsite nstrutin." The shear studs serve t transfer hrizntal shear stress, and thus lngitudinal bending stresses, between the girders and the dek, allwing them t bth share in arrying the superstruture lads. The extent t whih the mpsite setin shares in the superstruture lads will depend upn whether the girders were "unsupprted" r "supprted" during nstrutin f the bridge. The mst mmn methd f nstrutin is Chapter 2 Basi Cnepts

19 unsupprted, wherein the girders alne supprt their wn weight plus that f the wet dek nrete prir t uring f the dek nrete (i.e., befre the dek and girders effetively beme mpsite). In this ase, the mpsite setin is nsidered t nly arry live lads and any "superimpsed" dead lads suh as asphalt verlays, railing, and utilities. If it is desired t utilize the mpsite setin t arry all lads, then supprted nstrutin is used. In this methd, the girders are fully supprted alng their length during bridge nstrutin, keeping all stresses ut f the girders until full mpsite atin is ahieved. A nrete "tee-beam" r "tee-girder" bridge is shwn in Figure 11 and is similar t the steel girder bridge desribed abve, exept nrete beams (either nventinally reinfred r prestressed) are used in plae f the steel girders. Beause they are pured mnlithially with the dek, the nrete girders are effetively shaped like T's with the dek mprising the upper flange. The primary nventinal r prestressed reinfring will always run parallel t the diretin f the girder. A "prestressed girder bridge" is shwn in Figure 12. Prestressed girders are very effiient and beause tensile stresses are inherently lw in them, raking is pratially nnexistent, whih greatly imprves durability. These girders are almst always preast and are prestressed in ne f tw ways: pretensining r psttensining. With pretensining, the prestressing wires are tensined by jaking against the ends f the wires prir t nrete plaement. ne the nrete has ured, the ends f the wires are released frm the jaks and the tensile stresses are effetively transferred int the girder. With psttensining, the nrete is ast arund the untensined wires, whih are generally separated frm the nrete by duts. ne ured and in plae n the bridge, the prestress wires are tensined by jaking against the ends f the girders. ne the girders are plaed n their substruture supprt n the jbsite, the nrete dek is frmed and ast n tp f them. Mst ften, the girders have lps f reinfring prtruding ut their tp that at as shear studs t frm a mpsite dek. As with the mpsite steel girder bridge desribed abve, the mpsite atin may be fr live lad nly, depending upn whether supprted r unsupprted nstrutin was used. It is als mmn t make these girders ntinuus ver ne r mre supprts after plaement in the field. This an be amplished thrugh a variety f means, with the mst mmn being external psttensining at the girder ends r by making the dek ntinuus ver the supprts and prviding negative mment reinfring (usually nt prestressed) in the dek itself. A very effiient type f nrete girder bridge is the "nrete bx girder." These take many shapes and may be single- r multiple elled. Tw mmn shapes are shwn in Figure 1. These bridges behave in the same manner as the ther nrete girder bridges disussed abve. They may be nventinally reinfred r prestressed (pre- r psttensined). While they an be ast in plae, they are mst ften preast. Beause f their deep bx-like shape, they are very gd at resisting trsinal fres and are thus gd fr bridges in urves. Distributin Fatr The distributin fatr (DF) aunts fr the fat that vehile lads are spread ut transversely t all bridge members, whih share in arrying the lads 10 Chapter 2 Basi Cnepts

20 t varying degrees. This nept is demnstrated in Figure 14. This fatr is ne f the biggest variables in bridge analysis and greatly affets the results. As demnstrated in Figure 14, there are several fatrs that affet the degree f distributin t members. Dek stiffness, determined by its material type and thikness has a signifiant effet. A nn-stiff dek will essentially at like paper and will be ineffetive in spreading the lad well. A stiff dek will greatly spread the lad, meaning eah girder will arry a muh smaller perentage f lad; i.e., a small DF. The stiffness f the members supprting the dek (suh as stringers) als affets the DF. Stiff members will at like hard pints and attrat mre lad than a sfter member. Member spaing als has a signifiant effet n the DF. As members get farther apart, the wheel lads begin t appear mre like pint lads n simple spans. bviusly, tire and axle widths als ntribute t this effet. The number f traffi lanes is als a fatr. With tw lanes f traffi, tw wheel lads will effetively feed int the same stringer, whereas nly ne wheel lad wuld have ntributed if there were nly ne traffi lane. The abve disussin prvides the nept f DFs and the variables that affet them. Speifi values fr DFs are prvided in Referene [] in Table.2.1. A study f this table will reveal that the same fatrs as disussed abve are aunted fr in the table. These values are quite generi in their usage and are thus nservative. DFs signifiantly affet the results f analytial lad rating and thus their hie is very imprtant. If mre aurate and/r less nservative results are desired, a mre aurate DF may be btained thrugh - dimensinal analysis r lad testing f the bridge. Hwever, in mst ases, the DFs in Referene [] will prvide suffiient and nservative results. Use f DFs will be demnstrated in greater detail in Chapter. Tw-Girder r Truss Bridges As ppsed t the multi-girder bridges disussed abve, the bridge in Figure 15 nly has tw main girders spanning frm substruture t substruture. Beause these girders supprt the entire superstruture, they are usually very large. The girders are mst ften nstruted frm built-up plates, but may smetimes be large rlled shapes. They supprt the "flr system", whih is mpsed f flr beams and stringers. The flr system in turn supprts the dek. The bridge in Figure 15 is a "thrugh-girder" bridge in that vehiles atually drive between the girders. This is mst effiient when under-bridge learanes are restrited. When this is nt the ase, anther mmn methd is t plae the flr system and dek mpletely n tp f the deep girders. As previusly disussed, a truss bridge (Figure 16) wrks in the exat same manner as the girder bridge disussed abve. The lighter-weight truss allws fr spanning f larger gaps. As shwn in Figure 16, a truss is mpsed f tp and bttm hrds that are nneted tgether by vertial and diagnal members. These members supprt the flr system. Lateral braing is als prvided t keep the lngitudinal truss members parallel as they underg lateral fres frm wind. The general lad path fr a girder r truss bridge is shwn in Figure 17. With these bridges, the ladings are spread ut and transferred thrugh the dek int the stringers. The stringers span between and are supprted by the suessive flr beams. As a result, the flr beams nly reeive lads thrugh Chapter 2 Basi Cnepts 11

21 the end reatins f the stringers (i.e., their supprts). Flr beam ladings thus appear as a series f pint lads (at the spaing f the stringers) ver the length f the flr beam. Beause they are nly laded thrugh the stringers, wrst-ase flr beam ladings are btained by maximizing the stringer reatins. The exat manner in whih t plae lads in rder t maximize lad effets will be disussed in detail in Chapter. Flr beams are supprted at their ends by the lngitudinal girders r trusses. As a result, the girders r trusses nly reeive lads thrugh the supprt reatins f the flr beams and thus, wrst-ase ladings are prdued n these members by maximizing the supprt reatins n ne end f the flr beams. This is amplished by plaing the vehile lngitudinally n the bridge t prdue the wrst-ase bending mment r shear and transversely n the bridge t prdue the highest flr beam supprt reatins n the ntrlling girder r truss. The exat manner in whih t plae lads in rder t maximize lad effets will be disussed in detail in Chapter. Railrad Bridges Railrad bridges have the same superstruture types as the vehiular bridges desribed abve, exept f urse, their deks are different. As shwn in Figure 1, there are tw types f deks fr railrad bridges: "pen" r "ballast". With an pen dek, the rssties transfer the rail lads diretly int the superstruture. With a ballast dek, the rssties are supprted n regular railway ballast (rks), whih is ntained within the sme frm f "pan." With this type f bridge, the regular railway ballast is just ntinued arss the bridge. This makes fr easy trak maintenane, but makes inspetin f the bridge superstruture very diffiult. The lad paths in railrad bridges are very similar t thse fr vehiular bridges, exept they are atually easier sine the lateral psitin f lads is always fixed due t the rails n whih the train must run. The lad path fr an pen dek railrad bridge is shwn in Figure 19. The rails spread the wheel ladings ut lngitudinally t the rssties, whih transfer diretly int the stringers. In mst ases, the stringers are entered r symmetrially plaed diretly beneath the rails s as t keep bending and shear stresses very lw in the rssties. Frm the stringers dwnward thrugh the bridge, the lad paths are the same as fr vehiular bridges. The lad path fr a ballast dek railrad bridge is demnstrated in Figure 20. The wheel lads are spread ut lngitudinally thrugh the rails t the rssties, whih are supprted by the deep ballast. The ballast serves t spread the lads ut unifrmly dwn t the supprting dek and superstruture elements. Speifi distributin fatrs and wrst-ase lading methds fr these bridge types will be disussed in detail in Chapter. 12 Chapter 2 Basi Cnepts

22 Bridge Rating Guidelines and Criteria As previusly disussed, there are numerus guidelines and riteria fr the lad rating f bridges. Fr military installatins, speifi dtrine fr this purpse is fund in Army Regulatin , entitled, "Surfaed Areas, Railrad Traks, Bridges, Dams and Assiated Appurtenanes." This regulatin shuld always be the starting pint fr any lad rating analysis. It will prvide the neessary referenes t fllw. Fr vehiular bridges, the AR stipulates the use f the analytial riteria set frth by the Amerian Assiatin f State Highway and Transprtatin ffiials, speifially, that in the "Manual fr Cnditin Evaluatin f Bridges" [1]. This manual ntains the mst reent and state-fthe-art riteria fr highway bridges and has thus als been adpted fr military installatins. Fr steel and nrete vehiular bridges, the AR remmends the use f the reently develped "Lad and Resistane Fatr Rating" (LRFR) methd, as ppsed t the mre familiar "Allwable Stress" methd r "Ultimate Strength" methd (disussed in Chapter 4). Guidelines fr the LRFR methd are prvided in the AASHT manual entitled, "Guide Speifiatins fr Strength Evaluatin f Existing Steel and Cnrete Bridges" [2]. This methd has nt yet been applied t timber bridges, and thus the nventinal Allwable Stress methd must still used fr them. Referenes [1] and [2] prvide nly a limited amunt f detailed analytial riteria. Fr detailed riteria, these referenes refer the user t the AASHT design manual entitled, "Standard Speifiatins fr Highway Bridges" []. Speifi vehiular live ladings t be used with the abve riteria must be fund in tw different latins: Referene [1] speifies the ivilian vehiular ladings and Referene [4] speifies the military wheeled and traked vehiular ladings. It is very imprtant t emphasize that nly the vehiular lading in Referene [4] shuld be used. The analytial riteria in this referene are intended fr temprary bridges and thus have redued safety margins that are nt appliable t permanent bridges n military installatins. Fr railrad bridges, bth analytial riteria and train ladings me frm the Amerian Railway Engineering Assiatin (AREA) manual entitled, "Manual fr Railway Engineering" [5]. Muh f its analytial riteria are very similar t that fr vehiular bridges as disussed abve. Speifi adaptatin f the Referene [5] ladings t Army trains will be disussed in Chapter. All f the abve-mentined referenes were adpted/mdified frm industryspeifi riteria suh as Referenes [6] thrugh []. While nt speifially required fr the lad rating predures disussed herein, they an prvide greater insight t the rigins f the riteria in Referenes [1] thrugh [4]. Chapter 2 Basi Cnepts 1

23 Dek Superstruture CT~ Railing Figure. Basi parts f a bridge Stringer (Spans between S\<? flr beams) /.s, Flr Beam (Spans between girders) Girder (Spans substruture t substruture) Figure 4. Superstruture elements 14 Chapter 2 Basi Cnepts

24 Figure 5. Slab bridges Bx Culverts MM MM Figure 6. Bx Culverts Chapter 2 Basi Cnepts 15

25 5 > «- -IC 'S E Ji I X a. E > XI 1 i Jl 1 j <0 a> (0 > E T S. * (ft 'S s g XI u a>»i a) XI IB 5 5 -H h -I I- H H 0 T 0 "E D) i E C CL " t T5 2 ü = «a» -I TJ i r^ 0 i_ a> 16 Chapter 2 Basi Cnepts

26 V I (A k 1- ^ 0 f L. t a kt w 0) 0) ) <** * «*J (0 M tf) «1 0) E a> ** 2 ** a> E L. (A C re U i. > (A a> JC a> Q. I- (0 2 E -5 s ««0 = S u. ** > t = = 5; a) +* a- 2 S n C Q. ^ Urn <5 i re -g a> Z. ~ v> > E E E 5» w re = "5 2 S &» m J2 /> ) i. re i_ >. ~ «^ u. S u. w I» i X! 0 > t C " TJ ^1- "05 e a> Li_ Chapter 2 Basi Cnepts 17

27 Figure 9. Timber stringer bridge ^^^^H HHH Kwä 1 Cmpsite verlay SL^SH ^^E pi* lap I -Nn-Cmpsite and Embedded "Girders" run parallel t traffi and span between substrutures (piers r abutments) End View Figure 10. Steel multi-girder / nrete dek bridge 1 Chapter 2 Basi Cnepts

28 ft n Flanges Webs 4^ " Reinfring fr Tee Beam verlay Dek V - Primary Dek Reinfring Figure 11. Cnrete tee-beam bridge fl ; verlay \ Dek : k^ J-J k^ r S^ > ^ > ^ p-j Prgressed " i "-Pst-tensind Figure 12. Prestress / psttensin girder bridge Chapter 2 Basi Cnepts 19

29 ^r-^-^r^-^/^ ^SF I I F ^1 Figure 1. Cnrete bx girder bridge Figure 14. Steel girder bridge 20 Chapter 2 Basi Cnepts

30 Figure 15. Truss bridge I I Flr Beam a. pen Dek Girders r Trusses Girders Ballast Dek Figure 16. Railrad bridges Chapter 2 Basi Cnepts 21

31 T sz D5 g "t x> D 0 i > : T 22 Chapter 2 Basi Cnepts

32 - -H -H- 0) ÖS * en +-K - -H a. u 0) Q a> ) (0 10 E (0 a ffi < <0 0),_ t "E» 5 0 a V) -h 0 0 > UJ (0 a. T C EZ0 -I- a> LL Chapter 2 Basi Cnepts 2

33 -a k_ ' T C Q. C i_. Q. T i I I 24 Chapter 2 Basi Cnepts

34 J2 a a>. re i_ I- S > 0) w C/ T5 U a> a a 5 I I- I h I I- I I* 0 T 0 T "ü 0 Q. T " i 0 0 d 0 0 Chapter 2 Basi Cnepts 25

35 Lad Effets Dead and Sendary Lads Bridge ladings may be brken int three basi ategries: dead lads, sendary lads, and live lads. The dead lad f a bridge is the weight f the struture itself. Eah element f the bridge must supprt its wn weight plus the weight f any elements that it supprts. The weights f all appurtenanes, suh as railings, utilities, urbs, et., are ften signifiant and must als be inluded as dead lad. Fr railrad bridges, the weights f the railings, rssties, ballast, and ther rail-speifi items must als be inluded. Sendary lads ver a wide variety and basially enmpass all sures f stress ther than dead lads and thse frm vehiular live lads. The main sures f sendary lads are demnstrated in Figure 21. Referring t this figure, expansin/ntratin fres result frm temperature hanges and agerelated shrinkage and reep within the bridge elements. If members are prperly detailed and bearings are prperly designed and maintained, these fres shuld nt develp. Wind lads n bth the struture and passing vehiles may be a signifiant sure f lateral lading. Buyany, stream flw, and ie/barge impat fres affet mainly the substruture elements. Braking/tratin fres frm vehiles an prdue lngitudinal fres in the bridge, while lateral entrifugal fres an result frm vehiles traversing a urved bridge. Snw lads and earthquake lads are als nsidered sendary lads. While sendary lads have a signifiant impat n the design f bridges, they are nsidered intermittent lads and thus are generally nt nsidered in lad rating analyses n vehiular bridges, as per Referene [1]. Referene 5 des nt differentiate between design lads and rating lads fr railrad bridges. Therefre, unlike vehiular bridges, sendary lads must be nsidered fr these bridges. Speifially, sendary railrad ladings inlude entrifugal fres frm trains in urves, wind n the train and bridge, nsing f the lmtive (i.e., lateral steerage fres against the rails), and inreased impat frm steam lmtives. The speifi referenes fr these ladings are summarized in Table Chapter Lad Effets

36 Table 2. Sendary lads fr railrads Artile # in Referene 5 Lading 1 Timber Cnrete Steel Chap. 7 Chap. Chap. 15 Dead Lad frm trak, ties, ballast, et (b) Centrifugal fre (e) Wind n struture (h) Wind n Train (i) Nsing f lmtive NA NA Impat NA Referene 5 stipulates the use f these ladings fr rating as well as design. Hwever, their imprtane will be bridge and lale dependent. Thus, apply at the disretin f the engineer. 2. Artile , Referene 5, stipulates: Beause f the limited duratin f these lads, lateral fres frm wind and nsing need nt be nsidered with stringers. Thus, these fres are nly appliable t rails and lateral braing.. Nte that this is the nly hapter that differentiates between rating and design lads. Live Lads General Live lads nsist f the mving transient traffi n the bridge, inluding ars, truks, trains, and pedestrians. Sine there are untless varieties f live lad traffi n any bridge, generi representative ladings are defined fr whih the bridge an be designed and lad rated. Bridges n military installatins will be expsed t fur basi live lad types: ivilian vehiles (ars and truks); military vehiles (wheeled and traked); trains, and pedestrians. The generi vehiles defined t represent these ladings are presented in the fllwing paragraphs. While they must be inspeted fr safety and integrity, pedestrian bridges d nt require lad rating and are thus nt disussed herein. Civilian vehiular lads Civilian vehiular lads inlude ars and truks. bviusly, truk traffi will prdue muh heavier lads than ars, and thus truks are nsidered the ntrlling lads fr analysis. There are untless types, sizes, and weights f truks n the rads tday, and bviusly a bridge annt be analyzed fr eah ne f the speifi truks expeted t use the bridge. Therefre, Referene 1 prvides the generi truks shwn in Figure 22 fr use in bridge "rating" and "psting." Bridges must be bth rated and psted. The distintin between rating and psting is disussed in the fllwing paragraphs. A bridge is rated in rder t diretly mpare its existing lad apaity t its riginal design apaity, and thus btain an indiatin f its urrent state f deteriratin. T btain a diret mparisn, the vehiles fr whih the bridge was riginally designed must als be used in the lad rating analysis. The mst Chapter Lad Effets 27

37 mmn rating truk shwn in Figure 22a is referred t as the HS20. It is the same as that used fr the design f U.S. and many freign bridges. In additin, a lad rating using the HS20 truk is required fr input t the Natinal Bridge Inventry (NBI), whih is nw a requirement fr all installatin bridges within the U.S. The HS truk in Figure 22a was riginally derived in It is a hypthetial vehile intended t represent the heaviest truk lading n highway bridges. The axle ladings (in kips) and spaings (in feet) are shwn in Figure 22a. Fr the HS20, the spaing f the additinal axle varies between 14- and 0 feet in rder t maximize the lad effet n the bridge (disussed in a later setin). The effets frm the single HS20 lading must als be mpared t the "lane lading" shwn in Figure 22a. The lane lading represents the effet f multiple HS20 truks n a span at ne time and generally will nt ntrl fr span lengths less than 150 feet. The psting vehiles shwn in Figure 22b are used t atually determine the lad limit that will be psted n the bridge. Rating vehiles are generally nt used fr this purpse. The psting vehiles are referred t as Type, Type -S2, and Type -, and are intended t mre realistially represent the atual truks using the bridge. Many states have derived their wn psting vehiles, referred t as "State Legal Lads." If an installatin bridge is within a state that has its wn legal lads, they shuld be used alng with r in lieu f the psting vehiles shwn in Figure 22b. Based n the abve desriptins, bridges with ivilian traffi shuld be lad rated fr at least fur different truks: the HS20 fr rating and NBI reprting purpses, and the three "Type" truks (r equivalent state legal lads) fr psting purpses. The maximum live lad effets frm these vehiles will be disussed in the fllwing setin and their use demnstrated in the lad rating examples f the appendies. Military vehiular lads Military vehiles are quite different frm ivilian vehiles. They inlude bth wheeled (i.e., rubber tired) truks and traked vehiles suh as tanks. Beause bridges n military installatins must ften arry high vlumes f these vehiles, the Military Lad Classifiatin (MLC) must be determined in additin t the ivilian lad ratings disussed abve. The MLC desribes the maximum type and size f military vehile that may safely use the bridge. As with ivilian vehiles, the hypthetial military vehiles shwn in Figure 2(Referene [4]) have been defined arding t a Standard NAT Agreement (STANAG). They were develped t represent all military vehiles used by the partiipating NAT untries. All real vehiles are related t the hypthetial vehiles thrugh an analytial press (nt disussed herein) invlving the mparisn f the bending mments and shears prdued by the atual vehile n varius span lengths t thse prdued by the hypthetial vehiles. The real vehile's MLC is plaarded n its frnt grill in a speifi latin. The allwable MLC is als psted n all bridges that must arry military traffi. A speifi vehile may rss all bridges that have higher psted MLCs than itself. The hypthetial vehiles in Figure 2 are gruped arding t their "Class" (Clumn 1). Fr eah Class, there is an assiated hypthetial wheeled and 2 Chapter Lad Effets

38 traked vehile. Fr traked vehiles, the Class diretly relates t its ttal weight (in tns). Fr wheeled vehiles, the Class is nt exatly the same as the weight, but represents a wheeled vehile that prdues a similar lad effet (i.e., span mment r shear) t that f the same Class traked vehile. Speifi axle ladings (in tns) and spaings fr these vehiles are shwn in Clumns 2 and f Figure 2. The maximum lad t be expeted fr any axle n the vehile is shwn in Clumn 4. The maximum live lad effets frm these vehiles will be disussed in the fllwing setin and their use demnstrated in the lad rating examples f the appendies. Speial military lads In reent years, it has been fund that sme f the newer and larger vehiles in the U.S. inventry are nt well represented by the hypthetial vehiles shwn in Figure 2. While MLCs have been applied t these vehiles, their lad effets (i.e., span bending mment and shear) nly rrespnd t thse frm the speified hypthetial vehile fr spans within a very narrw range. The Heavy Equipment Transprt (HET) System, used fr hauling the Ml tank ver rads, is a speifi and ne f the mst extreme examples f this prblem. The HET has an assigned MLC f 95. As fr all military vehiles, this was determined by alulating the bending mments prdued by the HET and verlaying these values nt the standard mment and shear urves frm the hypthetial vehiles, as demnstrated in Figure 24. The highest Class t whih the HET urve rrespnds is Class 95 (linearly interplated between the Class 90 and 100 urves) at span lengths f 200 feet and greater. The HET has therefre been assigned MLC 95. Hwever, the HET mment urve nly rrespnds t this large f an MLC fr spans greater than 200 feet. Fr shrter spans, whih are muh mre mmn n military installatins, it rrespnds t nsiderably smaller Classes. As an example, the bending mment atually prdued by the HET n a 0- ft span rrespnds t that prdued by a Class 70 vehile n the same span length (Refer t Figure 24). Therefre, if the stated MLC f 95 is used indisriminately fr the HET (as is ften dne), a bridge with a 0-ft span will be designed and/r rated fr the bending mment fr a Class 95 hypthetial vehile, whih frm Figure 24 is apprximately 740 ft-kips. Hwever, in atuality, the HET nly prdues a bending mment f apprximately 560 ftkips, whih rrespnds t an MLC f 70. This effet has been demnstrated in Figure 25, whih shws the equivalent MLC fr the HET n varius span lengths. The reasn fr the disrepany an be understd when the HET and Class 95 hypthetial vehiles are mpared as in Figure 25. Althugh they bth have similar ttal weights (115.7 tns fr the laded HET mpared t 110 tns fr the Class 95), the HET is feet lnger and has fur mre axles ver its length. Additinally, the ladings n eah axle are lwer. As a result f these differenes, the HET ladings are better spread ut ver shrt spans. nly spans greater in length than feet (the length f the HET) will see all f the HET lading at ne time; i.e., the HET will nt mpletely fit n spans shrter than this. Chapter Lad Effets 29

39 T address the abve disrepany in a lad rating fr the HET, the Equivalent MLC hart in Figure 25 shuld be used. Fr the span length under nsideratin, determine the equivalent MLC fr the HET n that span length. Use the atual mment and shear values fr that MLC. This press will be demnstrated in the lad rating examples in the Appendies. As an als be seen in Figure 25, the HET has eight wheels arss its trailer axles as ppsed t fur n the hypthetial vehiles. The additinal wheels shuld serve t better distribute the trailer ladings ut transversely t a bridge's lngitudinal lad arrying members (suh as stringers and girders); i.e., the perentage f ttal lad t eah member, as represented by Distributin Fatrs, shuld be less. Researh is underway t develp mre aurate and generi DFs fr the HET. But until these results are btained, If the standard DFs frm Referene prve t be t nservative, mre detailed -dimensinal analyses (suh as with finite elements) r atual lad tests may be nduted t speifially address the lad effet f the vehile n the speifi bridge. Railrad lads In rder t understand the requirements fr Army rail lines, it is imprtant t first understand thse fr the mmerial rail lines as fllws: Cmmerial rail lines must supprt high vlumes f heavy freight traffi n a daily basis. Fr these lines, Referene [5] stipulates that their bridges shuld be designed t arry the ladings frm the generi (hypthetial) Cper "E" series f lading, with the heaviest being that frm the E0 lading. The E0 lading was develped lng ag when steam trains were muh heavier than the diesel trains f tday. T aunt fr this, Referene [5] stipulates that "bridges shall be rated fr the Cper series f lading r fr the maximum train that the speifi bridge must arry. Fr purpses f reprting, these trains shall be nverted t equivalent E- ladings." Speifi trains are nverted t equivalent E-ladings by mparing the lad effets (i.e., applied shear and mment) frm the speifi train t that fr the E0 as fllws:., it, T,. Lad effet frm atual train / >. Equivalent E - Lading = (0), (7) Lad effet frm E0 train where the term "lad effet" may be either applied shear r bending mment. The new Army Regulatin, AR states that the abve lading methdlgy shuld als be used fr Army railrad bridges. The heaviest and mst typial lmtives and rail ars utilizing Army railrads are depited in Figures 26 thrugh 29. There axle ladings are mpared t the E0 lading in Figure 0 and it an be seen that their axle ladings are signifiantly lwer than thse frm the E0. The midspan bending mments and endspan shears prdued by these trains n varius span lengths are prvided in Figures 1a and 2a, respetively. Additinally, these values have been nverted using Equatin 7 t Equivalent E-ladings and pltted in Figures lb and 2b. 0 Chapter Lad Effets

40 Maximum Live Lad Effets General Frm basi strength f materials, it is knwn that fr a pint lad n a beam, maximum bending mment urs when the lad is at the midspan and the maximum shear will ur when the lad is at r near the end f the span. The same general prinipals are applied in the appliatin f vehiular live ladings t bridge elements. Exept, the prblem bemes smewhat mre mpliated with multiple lads suh as frm a series f truk axles. Vehiular live ladings and the manners in whih their lads are transmitted thrugh the bridge, frm the wheel ntat pints dwn t the substruture, were demnstrated previusly. Eah live lading must be plaed n the bridge in rder t maximize the lad effet (mment and shear) in eah f the elements nsidered in the analysis. This latin will be different fr eah element type. bviusly, the vehile latin t prdue maximum bending mment in a transverse flr beam will be different frm that fr a lngitudinal girder. Referene [] (Artile.2) prvides speifi guidane fr the lading f all elements. A summary fr the mst mmn bridge elements is in the fllwing paragraphs. Deks The maximum lading latins fr bridge deks are demnstrated in Figure. The stringers supprt the dek. Alng the length f the bridge (i.e., lngitudinally), the dek essentially has an infinite span length mpared t its transverse span between stringers r girders. Thus, its strength in the lngitudinal diretin is negleted and the dek is nsidered t nly span transversely between the supprting stringers r girders. Therefre, the lngitudinal latin f the live lad is irrelevant fr deks. The lateral latin f the wheel line (i.e., half the axle lad) is the imprtant parameter. Referring t the end view f Figure, it an be seen that fr nrmally spaed stringers (spaing less than axle width), the dek is nsidered laded by a single pint lad, whih is atually ne wheel f the live lad. Therefre, the maximum bending mment in a dek span is prdued by plaing the maximum wheel lad at the enter f the lngest span between stringers r girders. Sine the dek spans multiple girders, whih are the dek's supprts, the dek is essentially a ntinuus span beam arss its supprts and shuld be nsidered as suh in alulating the resulting bending mment. The ntinuus beam diagrams in Referene [6] prvide an exellent aid fr this purpse. Fr simpliity in these alulatins, the mment-reduing effet f the wheel lad at the ther end f the axle n the same ntinuus span is ften nservatively negleted. The maximum shear is prdued n a dek span by plaing the wheel lad at the supprt. Therefre, the resulting shear will be equal t the applied wheel lad. Fr ivilian lads, btain the maximum wheel lads frm the rating and psting vehiles in Figure 22 by dividing the axle lads by 2. Fr military lads, use the maximum axle lads f lumn 4, Figure 2. Nte that the axle lads in Chapter Lad Effets 1

41 Figure 2 are in tns. Thus, the wheel lad (i.e. ne-half the axle lad) in kips will equal t the axle lad in tns. Stringers r multi-girders The maximum lading latins fr lngitudinally-spanning stringers r multi-girders are demnstrated in Figure 4. These elements supprt the dek and thus all lads me thrugh the dek. As with any simple beam, the maximum bending mment will be prdued in a simply-supprted stringer r girder when the live lad is near the midspan. Beause multiple pint ladings f different magnitudes are invlved, the maximum mment will nt be at exatly midspan. A general rule in this ase is that the maximum mment will ur under the heaviest axle when that axle is the same distane frm the midspan as the truk's enter f gravity, as demnstrated in Figure 5). These maximum values may be determined analytially with simple beam thery. Hwever, these values have been pre-alulated and are prvided in Figures 6 and 7 fr ivilian ladings [1], and Figures and 9 fr military ladings [4]. Nte arefully that the military lading values are fr axle ladings, as ppsed t wheel lines fr the ivilian ladings. A wheel line lading represents ne side f the vehile nly, and is thus ne-half f an axle lading. Referring t the "End View" f Figure 4, it an be seen that the live lad effets are shared amng individual stringers beause the dek serves t disperse, r distribute the lading utward t all stringers, t varying degrees. Cneptually, the effet n an individual stringer is maximized by plaing a wheel line lad diretly ver that stringer. Aunting fr this lad distributin analytially an be quite mplex. Frtunately, alulatinal aids have been prvided in Table.2.1 f Referene [] in the frm f Distributin Fatrs (DFs), whih were previusly disussed in Chapter 2 f this reprt. The apprpriate DF (depending upn dek and stringer type, and stringer spaing) shuld be multiplied by the maximum bending mment. The resulting value represents the maximum mment that a single stringer shuld experiene. Figure 4 als demnstrates that the maximum endspan shear will ur when the truk's heaviest axle is at the supprt and will equal t the supprt reatin. These values are easily alulated by hand using nventinal stati beam analysis tehniques, but an als be determined frm the equatins shwn in Figure 7[1]. These equatins an als be used fr alulating the maximum shears at any pint, x, n the span. Nte that there are span length limits utside f whih these equatins are nt valid. Fr spans utside f these limits, slutins must be alulated by hand. Maximum endspan shears frm military ladings are prvided in Figure 9. Nte arefully that these values are fr axle ladings (as ppsed t wheel lines) and the units are in tns. Distributin f shear ladings is different than fr bending mment. Beause stringers will be very stiff near their supprts, very little distributin f shear ladings near the supprts will ur. Hwever, shear ladings ut frm the supprts will be distributed similar t that fr mment. Artile f Referene prvides speifi guidane fr the distributin f shear ladings. 2 Chapter Lad Effets

42 Flr beams The maximum lading latins fr flr beams are demnstrated in Figure 40. A flr beam ats as a simple beam t supprt the stringers, whih in turn supprt the dek. Therefre, the flr beam an nly reeive lads frm the supprt reatins f the stringers. Referring t the "Side View" f Figure 40, it an be seen that the live lad must be plaed s as t maximize the stringer supprt reatins. These reatins is an be maximized analytially, muh by trial and errr, r thrugh the aid f the pre-alulated tables in Figure 41 fr ivilian lads, and Figure 42 fr military lads. These maximum reatins are used fr alulatin f bth bending mment and shear in the flr beam. Referring t the "End View" f Figure 40, the maximum bending mment will ur when the axle lads are as lse t the enter f the flr beam as pssible. The fllwing equatin (Referene [1]) may be used, alng with the maximum reatins disussed abve t alulate the maximum flr beam bending mment: (L-) 2 R M = -, fr ne-lane lading; and () ( 2 25^1 M = I L R, fr tw-lane radways; (9) where: M = Mment in transverse beam, R = Maximum reatin (Tabular value frm Figures 41 and 42), L = Span f transverse beam, in feet. Maximum shear will ur when the axle is as lse t the edge as pssible. The axle lad distane frm the edge f the bridge is limited by Referene [1] t 2.0 feet between the wheel enterline and the inside urb. The fllwing equatin frm Referene [1] may be used, alng with the maximum reatins frm Figures 41 r 42 t alulate the maximum flr beam shear: ( W-9\ V = I 1 + IR, fr ne-lane lading; and (10) f W-l&V V = \l + - I R, fr tw-lane lading; (11) where: W= Width f radway, in feet; C = Length f flrbeam between supprts, in feet. Girders r trusses The maximum lading latins fr girders r trusses are demnstrated in Figure 4. As previusly disussed, girders and trusses are similar in the way that they reeive and arry lads. They supprt the flr system, whih is mpsed f the dek, stringers, and flr beams. Therefre, all lading is Chapter Lad Effets

43 transmitted t girders r trusses thrugh the supprt reatins f the flr beams. Hwever, in the lngitudinal diretin (refer t the "Side View" f Figure 4), it is simpler t neglet this effet and nsider the live lad diretly supprted by the girder r truss. Sine these members span lngitudinally between substruture elements the same as the girders f a multi-girder bridge, the maximum bending mments and shears will be prdued in the same manner. Therefre, fr girders, the maximum live lad mments and shears will be taken frm Figures 6 thrugh 9. Fr trusses, the maximum axial lads in eah truss member an be fund frm the Appendies f Referene 1. As demnstrated in the "Side View" f Figure 4, the girders r trusses will share t varying degrees in aring the ttal live lad effet, depending upn the lateral psitin f the live lad n the dek. The nly way that they wuld share equally in arrying the live lad wuld be if vehile drve exatly alng the enterline f the bridge. This will rarely, if ever be the ase. Cneptually, the wrst-ase lading will be prdued in a single girder r truss (i.e., n ne side f the bridge) by plaing the live lad as lse t the edge f the bridge as pssible. Referene [1] prvides a generi equatin t represent the maximum perentage f live lad fr a single girder r truss. This value is referred t as "wheel lines per truss" r "distributin fatr" (DF) and shuld be multiplied by the maximum lad effets as desribed abve. The generi equatin is as fllws: ( W-9\ Wheel lines per truss = 1 H 1, fr ne-lane lading and (12) f W-IS] Wheel lines per truss = I 1 + j, fr tw-lane lading. (1) This equatin is fr a vehile latin f 2.0 feet between the wheel enterline and the inside urb. If ther limiting senaris must be nsidered, the equatin an be easily derived by summing mments abut ne f the girders r trusses as demnstrated in Figure 44. ne alulated, the DF shuld be multiplied by the maximum bending mments r shears as disussed abve. Railrad bridges Sine railrad bridges have essentially the same strutural makeup as vehiular bridges, the lad effets will be maximized in the same way als; i.e., plae lads near midspan fr maximum bending mment and at r near the supprts fr maximum shear. Laterally, railrad bridges are muh easier t nsider sine the lateral psitin f trains is maintained by the rails. Beause f this fat, lngitudinal lad-arrying members (stringers r multiple girders) are plaed symmetrially beneath the rail latins. Referene [5] prvides speifi guidane fr the distributin f train ladings. This guidane is summarized as fllws: Fr timber bridge members: Crss-tie size and stringer arrangement beneath the rails will usually be suh that the trak lads will be equally distributed (laterally) t all stringers. If fr sme reasn, this situatin is suspet, Referene [5] prvides an apprximate analysis predure fr stringer distributin. Fr 4 Chapter Lad Effets

44 Ballast Dek Bridges, the live lad is assumed distributed laterally ver a width equal t the length f the tie plus twie the depth f ballast belw the base f the tie, as demnstrated in Figure 45a. Alng the length f a stringer, eah axle lading is assumed t be spread ut ver three ties. This is nly true if the remmended maximum lear spae between ties des nt exeed inhes fr pen Dek Bridges and 24 inhes fr Ballast Dek Bridges. Fr Cnrete bridge members: Axle lads are t be distributed lngitudinally ver feet plus the depth f ballast under the tie, plus twie the effetive depth f slab; but nt t exeed the axle spaing (Refer t Figure 45b). Laterally, the live lad frm a single trak ver ballasted dek is assumed t have unifrm distributin ver a width equal t the length f trak tie plus the depth f ballast belw the bttm f the tie, unless limited by the extent f the struture (Refer t Figure 45). Fr Steel bridge members: Where tw r mre lngitudinal beams per rail are prperly diaphramed and symmetrially spaed beneath the rail, they are assumed t share equally in arrying the lad. Fr pen Dek Bridges, axle lads are assumed t be distributed equally alng the length f the beam (i.e., lngitudinally) thrugh all ties r fratins theref within a distane f 4 feet, but nt t exeed ties (Figure 45d). Fr ballasted dek bridges, eah axle lad is t be distribute lngitudinally ver feet plus the minimum depth between the bttm f the tie and tp f the beam; but nt t exeed 5 feet r the minimum axle spaing (Figure 45 e). Lad Effets n Cntinuus Spans All f the previus disussins f maximum lad effets have been nly fr simple span bridge members. Hwever, bridge members an als be ntinuus ver their supprts fr tw r mre spans; i.e., ntinuus span. A ntinuusspan multi-girder bridge is mpared t a similar simple-span bridge in Figure 46. Cntinuus spans serve t spread ut and share applied lads with adjaent spans, thereby reduing the verall effet f the lads at any ne latin; i.e., shear, mment, and defletin. Figure 47 demnstrates that bridge deks, supprted by the main superstruture members, are ften ntinuus span. While nt as easy as simple-span beam analysis, alulatin f lad effets n ntinuus span beams is fairly rutine fr statially-applied lads, suh as dead lad. Cnventinal strutural analysis tehniques, suh as the Mment Distributin and Slpe Defletin methds, may be perfrmed by hand with reasnable ease fr these prblems. Many pre-alulated slutins als exist fr mmn stati lad and span mbinatins [6]. Hwever, the prblem bemes mre diffiult with ntinuus span bridge members sine they must arry mving lads (i.e., live lads). Figure 4 demnstrates that lading effets at any latin n the span will vary with eah psitin f the live lad n the span. Fr example, the psitin f the truk that wuld prdue the maximum mment at the middle f span 1 will be mpletely different than that fr the maximum negative mment at supprt A. The same nventinal strutural analysis tehniques as mentined abve an als be used fr a mving lad analysis. Multiple slutins fr a mving pint lad an be used t generate influene lines, whih lead t maximum shear Chapter Lad Effets 5

45 and mment envelpes fr the span nfiguratin. This press is demnstrated in Figure 49 fr a simple span beam. While the same type f slutin an be ahieved fr any ntinuus span mbinatin, it will be very tedius and time nsuming. Cmputerized slutins t these prblems are highly remmended. Many prgrams already exist fr this purpse and may be purhased at reasnable pries. 6 Chapter Lad Effets

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54 C * 5= 0 Q. t_ Q. ' a. ü. Chapter Lad Effets 45

55 CJ W X E CN ) 46 Chapter Lad Effets

56 i i 10!" :r*~ k»- 5 U) C a t k»- ; in ISZ9 w~ C ID in in M9Z9 u» - in n > u a. in *- I9Z9 Ö) I. *- u. k.»~ Ü...»- in ra in ** u. IZ'W W09 in MZS in en t Z9 ZW»- in IZ9»-: 10 in en MZS 5IS-Z9 Ü 1«; in >- ; in D) ^ m 9'Z9 a a in )f0 m»-; UJ in 10 M9Z9 t. m e in T" 10 ai»~ «* ; r- WP9 0fr in in T- in Ü) t in en in in»-»>~»>- Z9 5IZS MZS ZS 10 M0 In (0 11 "5 k i UJ SJ.U M0 Jffr (0 (0 LU in in in m in in SI m~\ **'»- 1 0) a «s 1929 m M9'Z9 I9Z9 M929 9Z9 Speial Purpse Flat Ca (1 Tns) C 0 C ) > < ( a 1 S H s < y\ip9 t en T- iri in e iri 1ZW Z"W ZW < 1 'i g u ] en in en ^ *~ ^ W M9Z9 irw 1009 u Q 2 y> F 0) 1- S- X t a < a) H LL in >i 1 * IT 11 1 T C 2 ä! > < in 1- ' E 0 (0 5 "t L. LU t a. E d 0 L- Chapter Lad Effets 47

57 (A Ö). gg (0 2 C S fl> ärä ff 5 0) x: 1 1 i r ^"^ *. * ^"^ X "* --** \ N > ^ ra ) - - x n u. «5 ^\. J \ \ ' a>» Jf \ s^^^ \ -^ ''' 140 Bx -axle ü -» 7 << t E FRSM AMC Train Tw Tande S ) _l ra a w "5 a) C E 2.E^S a < s- Ssl E " W S-5 C u- a CB < a ü N. \^'^ \ VS, e n n ^"^ «- \^ ^ Tn«Cars sengl 140 Bx axl * E i- 00(D-*0C Bujpei- luaieajnbg xx^ ^%.-. \.^ ^ \^V-\ S* \s. > \ tt 0 ^%- E S } \Y! '! i 11 1 i i a> a a _j ra a. en C a> E E T5 C.Q C T 0 0 C 5* E C t a. _>» 05 C TJ I HI > HI (sd!>)-y) 1UUJ0N Bujpuag I 05 4 Chapter Lad Effets

58 & = 2 tu *- T5 'S «5 a.«bhc > i-ili "- S UJ 5 e u n u. in * E Tn xcars leeng»x? m 7 f \ \ / ' / L V A \ E> \ ' : t E / ne»ri- / \ f 0 ; i ' S * i / u. «11- I ]/ i y4 ^' / \ / 0) 09 w C 0) _l (0 a (0 l "D a W 0 (0 0) (0 e ~ «It (0 (- ^ E is Ill ** t S Q. Sil J- u. s ü / '-""" -/" '/. ^ \. ^^** l t Butpe-]- juaieambg \ \ \ \ n \\ Tn M1 Fla (Cars e Engines V \- \ \ X X \ \ *? \ % \ E> E all* t E = \ \ \ FRSM AMC Train Tw Tande Cper E! >!! 11 :! i 11 / ^ Nl 5 (0 Q, «in C ^ W C _1 J= (/) Q. t» -a C X! 05 C " >N E " "a. a tn D) 111 > UJ (sdj> ) jeaqs ueds PU Chapter Lad Effets 49

59 H! flj C a»; ). :' D. Q. 0) (A CL HI : 01 : t : <D l"e jz) n >> 0 z~ =. T H! S <D Q. S s S T fl % (A C (0» 0. (D E tu E 2 m «ll ) t- Q ) x> E X 0 I 50 Chapter Lad Effets

60 IHi <N Q. h-ii a.ts (0 _J 0. HI! I (5 IIH; i 4S T( * t -n a <» & _n J - r a g 5 r*-: ~ t: r - S-2 * t < > fh SS«gS" J S. Z ~ < w 5.E T T C7 T (0 a> E 0 'i *» E ) *; (0 0) LL Chapter Lad Effets 51

61 0 E 0 0 C w (0 E E x r E 0 E 0 Q. 0 0 > in 0 i 52 Chapter Lad Effets

62 Apply Distributin Fatr frm Table.2.1 f Referene 0 Ü 0 a in 0 > r "> ' 0 E 0 7 ") t- 0 n E ( Chapter Lad Effets 5

63 APPENDIX A FRMULAE FR MAXIMUM SHEAR AT ANY PINT N SPAN (N Impat Induted) (Simple Spans nly) Type Lad L-X L Use fr Girder Lengths HS Under 42' Frmula fr Maximum Shear (1) 6(X-4.67) L Minimum L-X X ' t 120- HS Under 42* V V ~ KX-9.) L 270C-4.6T) L * t 120'* H t 5'* H t 5** V 27(X-9) L (X-2.} L (X-2.) L 0 14 (1) All values based n standard trak ladings. * Truk lading des nt gvern shear beynd the lengths speified. Use lane lading. (Dimensins Measured in Feet) V - Shear t Leftfpint "P"in kips per wheel line. Figure 7. Maximum stringer r girder shears fr live lads (referene [1]) 54 Chapter Lad Effets

64 APPENDIX M FRMULAE FR MAXIMUM SHEAR AT ANY PINT N SPAN {N Impat Inluded) (Simple Spaas nly) Type Lad L-X L Use fr Girder Lengths HS Under 42' Frmula fr Maximum Shear (1) 60C-4.67) v L Minimum L-X X 't 120'«HS Under 42" V v 60C-9) L 27(X-4.67) L ' t 120'* H t 5'* 1 H t 5'«V " V V 270C-9) L (X-2.) L (X-2.) L 0 14 (1) All values based n standard trak ladings. Trak lading des nt gvern shear beynd the lengths speified Use lane lading. HfillM L-X X L [Dimensins Measured m Feet) V - Shear t Left f pint "P" in kips per wheel line. Figure 7 (nt'd). Maximum stringer r girder shears fr live lads (referene [1] Chapter Lad Effets 55

65 56 Chapter Lad Effets

66 )? I" «0 g 5 > * <0 10 t «>" 1 I <D" «0 10 a S (A J > «a u e 0 "0. > ID «i E ir> E 5 > g 15 "5> w (0 10 SSB 0 a 00 I 0> If) 10 I 0 5 s n a > T a 1 a 5 E x <0 Ü e T Chapter Lad Effets 57

67 u H- (0 => (0 z a a a I a V u 2 H «I 91 JC B «_i n a 0 0) «r ID in t in tn "9 f». * in s d g d t rv g d s «0 s rv IV d H S IV s hi tn «i rv rv in s iv i» 9 v S tv" g s Iv in T- T- 0» 00 IA «0 - i s tn t* s «0 ID s I 00 tt s i I rv v - t in i t i fv s t I ft in tri tri in I s > v? > d v 04 j i d a s i 1 I I s d I s > d * is d Iv s s Ö s d» d d d d 9 i i? tft J 9 9 IK d Ö S rv d <0 I u> Ö 0> s i s in 10 0> a tri s tri in a tri * rv d 9 in Ö i d I ö I» i 9 iv d Si si!5 5 9 si i IV S fv 1 si fv N «0 d I i 9 d # t i t ss tri "W S t u> rv tn t d tri < m. en m t tv d d «t d in * i > Ö Ö >-' i tn t d 5? 5? x n m d t d S tri <* I 9 I» tn 9 5 IV IV 9 S M t i t in fv s R 9 9 tn m 9 9 S 9 g 9 5 In 9 -er s 9' t in i I m «0 I i ft «n tn tn»v 5 fv i2 m rv S S S 9 IÖ rv i rv i t 5 9 Si s 9 n IV 9 fv 9 9 d s i S 9 S t tn " in j IV t 5? «> Ö d i <0 d 9 d rv IV t d in IV i 5 ff S d i s t 9 9 fv > tri «r 9 S»n 9 S 9 tn r in 9? i a s 1» i g? S' Ch S fv S I rv t rv IV tn rv 9 9» fv IV <Q i 9 9» t fv rv > in Cf si g r^. > f^. m IV fv d m rv * s g tn g g n v d 9 i fv 5 m tn «tri tn > m 9. tv* iri tri 5 tn m > tn in IV tn s If tn i rv g g i rv m t»v tn i in g 9 r» * tri S m»v v tri g s g $ d tri ) i 0» > s g tri m 5 k i fv" S J i fv fv 9 tri 5» Cl * fv g. d t v tn IV g IV i d «9 i «= 5 H- 5 t- 5 r- 5 H 5 H 5-5 V- s K 5 t- 5 H : f- S 1-5 H? r- 5 h 5 H "* 00 <M T- <* in SSBI0 ) 9 tri i fv S? m 9 i S J < rv 9 en tri > - tn IV *v 9 g fn. t (0 S i tn S tn rv i v d fv. tn > fv tn i tn d in g 9 fv in in m rv 6 i in t a <D > f> : w f- > I 1 11} J= II) t Q.»_ a a a) E 2 E > X 2 jr ) is I <D s J 5 Chapter Lad Effets

68 w <n => *- Ifl M-l 0> *» z as a «r w > at 9 s * S (0 a W 0) in T- T- T- 10 T" T" T" T* r- s 00 *v" t iv iv *v" iv* (0 ß t' s Iv" "0" iv u> in t r«' Si tri tn «I iv s s tv ri s t t t t in t s 0 t 2 > t* s ri S a <*> s 5 / t 5 ri ri s i s «1 si s ' e i 5 IV i S S fv»v t ' 5 s S 5 u> 5? S S S s 5 ^1 S N 5 t 5j 1» 5 i 5 t t 5 ri 5 s i «en 5 s CNI 5 S «5 t 5 fv 5 ' 10" i S i IV t s s S" 5> 5 «0 vi 5 ri > i 5 i tri t tn t «5 ri. s s u> d <D t t «0 in s tri 5 5 in «0 5r i ' eft in Iv t 5> s t u> eft iv «1 m t ifl ri i IV > a* a> Si Iv «0 IV ' rv t «q ' 5 00 ri C4 g ri s «' Si s? ) tv s t rv a» in 0* iv ft in «6 S 2 0) ai Iv" >i 10 IM t «in IV t 0> Iv IV IV in 5 t 5 m 'M» Iv 1*» 00 t 5 in u> fv t 5 IV. "C> > > 5 5 SI id s S 0 i ' ti m «0. S ri iri. ) s. 5 s IV 5 in 5» en s K fv' S en 10 «ti ' S S a S ' S. 5 s 5 s 5 «fv in ' t» s ß ß t S 5 2 ß ei ' i Iv 1^ fv *v S <n 5 ri «0 I R tn > " > en > S ri in tn i S K in in» 5 in en «0 fv 5 > «0 ri iv t S. m i 5 4 tri d Iv fv IV «v " ß ri fv ß i en S 55 ß " t ß S' 5 IV* > * l». Iv 5 fv > e» 0» fv S > ß' R ß i»v fv fv tn fv m fv t iv ft 5 5 ß N tn S as ß fv i 5 f*. ß ri. S ' 5 ri rr ri i i R t fv S m fv* R" ai m 5 > in en i en in ri >» in e «0 Iv in s \i en R S S fv Si a 5 I ri t S t ß 5 fv IV v" <n 1 5» in R t V * S tri i» t " iv s m d i V iv rv ft «*»- s t- 5 H * H S *-! h s K? t- S H s h- 5 i- I- 5 H 5 t- s r- 5 H * T 10 SSJ0 N 0) T- 10 a > en t_ «u xz s: 0 > 1 CL tn -a i-»- E E CIS t r a T > *-* T) C 0 IB Ü r 5 i 5 ) Chapter Lad Effets 59

69 ' m HI H H n C "ös (A Q. Hi 5= Dl i C r-e : Q. Q. II) H! <0 => b S2? Ü H -H * I? E M 5 'S ) Sir s sf * m >- J E * i_ C T < H H H; H H 12 > w n w 0. ; d> = f _g> q=? I r Ö) ts QQ V) ) TJ E <D E X ( Chapter Lad Effets

70 APPENTUX M STRINGER LIVE LAD REACTINS N TRANSVERSE FLR BEAMS & CAPS (INTERMEDIATE TRANSVERSE BEAMS) (Simple Span nly) STRINGER SPAN FEET UVE LAD REACTINS (R) IN KIPS PER WHEEL LINE N IMPACT NE LANE LADING " 2L TW LANE RADWAY VER 1 FEET -M <L.,^) R NE LANE LADING - (l+ ^) WHEEL LINESmtUSS: TW LANE LADING «(]+ 2tl?\2 Where: M R - L «W. C Mment in Transverse Beam Reatin (Tabular Value) Span f Transverse Beam Width f Radway Spaing, Ctr t Cfir f Trusses AD values based n standard truk lading»based n 9 ft. Jane width. a. Intermediate beams Figure 41. Maximum flr beam ladings fr ivilian live lads (referene [1]) Chapter Lad Effets 61

71 STRINGER SPAN FEET APPENDIX AS STRINGER LIVE LAD REACTINS N TRANSVERSE FLR BEAMS & CAPS (END TRANSVERSE BEAMS) (Simple Span nly) LIVE LAD REACTINS (R) IN KIPS PER WHEEL LINE N IMPACT TYPEFLADE KG TYPE TYPE -S2 TYPE - H-15 HS AU values based n standard trak ladings. b. End beams Figure 41 (nt'd). Maximum flr beam ladings fr ivilian live lads 62 Chapter Lad Effets

72 ;? IF (sdpi) M 'uipeay aun JIBJI -XB /\ C P *! P ' T > L_ 0) in > w T U m t l_ H (0 a> > in D5 (sdpi) y 'ujjeay un speji -xew I. l E E x C = a) Chapter Lad Effets 6

73 0 E re a n D > 111 in hi S C/J '^" (0 m JC T> > " <a U) > (D (D x: r 5 I. "E w ) x> E 0 5= E E x 05 2 C Ü (sdpi) a 'uijeay aun l»ai M '«W C5 64 Chapter Lad Effets

74 ' >w H ' w / :-: : : : : :-: :-: / : : : : / : : : : ' ;?> / :-.-: : / : : : : / :<< : "w. 75 "5 ' ' : : / :-: : : / : : : : : : : : / : : : : / : : : ' ' <: > / : : : : H / : :-:-: E (0 ' ' >>: 0) ' ' <<<.n 1 ' '-YA- 1 q= ' :I / : :. : t ' / :-C 1 im F Q., T ' ><> 0 ' <<< :->: : S 0, H / : : : : d 1 / : : : : * : : : : ' w / : : : : P <U I / : : : : 1 ' -<<y / : >: : '?>y ' ::":":" ' <<> ' '<<y ' +<y ' ' : >: / Xw ' ' <>: ; / :< : / : : :%; H >v j E E C 0 n «S ' ) 12 (A C n (0 ) T E x g> Chapter Lad Effets 65

75 1.2 \ r 2' P 6' P R L ^ 1 ' 1 1 i i 1 _ 16.5'C. t C. f trusses end view i R EM^ =0=P( )-/? Ä (16.5) R x =.SSP R L =2P-.SSP = U2P=* Max. Therefre, DF = 1.12 fr wheel line lads r 0.56 fr axle lads Figure 44. Calulatin f wheel lines per truss 66 Chapter Lad Effets

76 ID T D C _ n X 0 in = Chapter Lad Effets 67

77 0 C C a. U-^ D. w 'i_ Q. E "" 0 k_ D) Li. 6 Chapter Lad Effets