C. C. Fu, Ph.D., P.E.

Transcription

1 ENCE710 C. C. Fu, Ph.D., P.E. Shear Coectors Desig by AASHTO RFD (RFD Art ) I the egative flexure regios, shear coectors shall be rovided where the logitudial reiforcemet is cosidered to be a art of the comosite sectio. Otherwise, shear coectors eed ot be rovided i egative flexure regios, but additioal coectors shall be laced i the regio of the oits of ermaet load cotraflexure. A (1) Fatigue imit State f r sr AC (RFD Eq ) Z r Z V r (RFD Eq ) sr Z r α d d 2 /2; (RFD Eq ) where α log N (RFD Eq ) (2) Stregth imit State Q r φ Q (RFD Eq ) sc P (RFD Eq ) (a) Nomial Shear Force, Simle&cotiuous sas that are ocomosite for egative flexure: where P mi. P P + F P 2 2 (RFD Eq ) of F yw Dt w 0.85 f cbsts + F b t + F yt ft ft yc b t ( RFD Eq ) ( RFD Eq ) F P (RFD Eq ) R (For straight sas or segmets, F may be take equal to zero) Cotiuous sas that are comosite for egative flexure:

2 P where mi. P P T + F T T 2 2 (RFD Eq ) P P + P (RFD Eq ) of F yw Dt ( RFD Eq ) ( RFD Eq ) w + Fytb ftt ft + F 0.45 f b t c s s yc b t FT PT (RFD Eq ) R (b) Shear Resistace, Q Stud shear coector Q 0.5Asc Ec AscFu (RFD Eq ) Chael shear coector 0 (RFD Eq ) Q.3( t f t w ) c Ec

3 Desig Ste Desig Shear Coectors Sice the steel girder has bee desiged as a comosite sectio, shear coectors must be rovided at the iterface betwee the cocrete deck slab ad the steel sectio to resist the iterface shear. For cotiuous comosite bridges, shear coectors are ormally rovided throughout the legth of the bridge. I the egative flexure regio, sice the logitudial reiforcemet is cosidered to be a art of the comosite sectio, shear coectors must be rovided. Studs or chaels may be used as shear coectors. For this desig examle, stud shear coectors are beig used throughout the legth of the bridge. The shear coectors must ermit a thorough comactio of the cocrete to esure that their etire surfaces are i cotact with the cocrete. I additio, the shear coectors must be caable of resistig both horizotal ad vertical movemet betwee the cocrete ad the steel. S S a The followig figure shows the stud shear coector roortios, as well as the locatio of the stud head withi the cocrete deck. 8½" 3½" 7/8"φ 5" (Ty.) 14" 6" A B C Figure 5-1 Stud Shear Coectors Shear Coector Embedmet Flexure Regio A B C Positive 2.875" 3.125" 5.375" Itermediate 2.25" 3.75" 4.75" Negative Table 5-1 Shear Coector Embedmet 5-2

4 Shear Coector ayout It is commo to use several stud shear coectors er trasverse row alog the to flage of the girder. The umber of shear coectors er trasverse row will deed o the to flage width. Refer to S c for trasverse sacig requiremets. Shear Coector egth The stud shear coector legth is commoly set such that its head is located ear the middle of the deck slab. Refer to S d for shear coector embedmet requiremets. The ratio of the height to the diameter of a stud shear coector must ot be less tha 4.0. For this desig examle, the ratio is comuted based o the dimesios reseted i Figure 5-1, as follows: S a Height stud 6.0 i Diameter stud i Height stud 6.86 Diameter stud The itch of the shear coectors must be determied to satisfy the fatigue limit state as secified i S ad S , as alicable. The resultig umber of shear coectors must ot be less tha the umber required to satisfy the stregth limit states as secified i S S b The itch,, of the shear coectors must satisfy the followig equatio: Z r I V sr Q The arameters I ad Q are based o the short-term comosite sectio ad are determied usig the deck withi the effective flage width. 5-3

5 I the ositive flexure regio: 3 I i 4 (see Figure 5-1) (see Table 3-4) S b Q ( 8.0 i) ( i) 8 Q i 3 V sr V sr 34.97K i 0.75 ( K K) ( i) I the ositive flexure regio, the maximum fatigue live load shear rage is located at the abutmet. The factored value is comuted as follows: Z r α d 2 (see live load aalysis comuter ru) 5.5 d 2 2 N (see Desig Ste 3.14 at locatio of maximum ositive flexure) S S α log( N) α d α d i 5.5 d Therefore, Z r 2.11 K Z r I V sr Q i 5-4

6 I the egative flexure regio: 3 (see Figure 5-1) I the egative flexure regio, the arameters I ad Q may be determied usig the reiforcemet withi the effective flage width for egative momet, uless the cocrete slab is cosidered to be fully effective for egative momet i comutig the logitudial rage of stress, as ermitted i S For this desig examle, I ad Q are assumed to be comuted cosiderig the cocrete slab to be fully effective. I i 4 Q ( 8.0 i) ( i) 8 Q i 3 (see Table 3-5) i ( i) SC b V sr 0.75 ( 0.00 K K) V sr 34.90K (see Table 3-1 ad live load aalysis comuter ru) Z r α d 2 Z r 5.5 d K (see revious comutatio) S Z r I V sr Q i Therefore, based o the above itch comutatios to satisfy the fatigue limit state, use the followig itch throughout the etire girder legth: 10 i 5-5

7 Shear Coector Pitch The shear coector itch does ot ecessarily have to be the same throughout the etire legth of the girder. May girder desigs use a variable itch, ad this ca be ecoomically beeficial. However, for this desig examle, the required itch for fatigue does ot vary sigificatly over the legth of the bridge. Therefore, a costat shear coector itch of 10 iches will be used. I additio, the shear coectors must satisfy the followig itch requiremets: S b 24 i 6 d d i 6d 5.25 i For trasverse sacig, the shear coectors must be laced trasversely across the to flage of the steel sectio ad may be saced at regular or variable itervals. S c Stud shear coectors must ot be closer tha 4.0 stud diameters ceter-to-ceter trasverse to the logitudial axis of the suortig member. 4d 3.50 i Sacig trasverse 5.0 i (see Figure 5-1) I additio, the clear distace betwee the edge of the to flage ad the edge of the earest shear coector must ot be less tha 1.0 ich. Distace clear 14i 2 Distace clear 1.56i 5i d 2 (see Figure 5-1) The clear deth of cocrete cover over the tos of the shear coectors should ot be less tha 2.0 iches, ad shear coectors should eetrate at least 2.0 iches ito the deck. Based o the shear coector eetratio iformatio reseted i Table 5-1, both of these requiremets are satisfied. S d 5-6

8 For the stregth limit state, the factored resistace of the shear coectors,, is comuted as follows: S φ sc Q S a φ sc 0.85 S The omial shear resistace of oe stud shear coector embedded i a cocrete slab is comuted as follows: S c Q 0.5 A sc f' c E c A sc F u A sc f' c E c π d2 A sc 0.601i ksi (see Desig Ste 3.1) S ksi (see Desig Ste 3.3) S F u 60.0 ksi S K K Therefore, Q K φ sc Q Therefore, 30.65K The umber of shear coectors rovided betwee the sectio of maximum ositive momet ad each adjacet oit of 0.0 momet or betwee each adjacet oit of 0.0 momet ad the ceterlie of a iterior suort must ot be less tha the followig: S a The total horizotal shear force,, betwee the oit of maximum ositive momet ad each adjacet oit of 0.0 momet is equal to the lesser of the followig: 0.85 f' c b t s S b or F yw D t w + F yt b t t t + F yc b f t f 5-7

9 where f' c 4.0ksi (see Desig Ste 3.1) S b t s i (see Desig Ste 3.3) 8.0 i (see Desig Ste 3.1) F yw 50 ksi (see Desig Ste 3.1) STable D 54 i (see Desig Ste 3.18) t w 0.50 i (see Desig Ste 3.18) F yt 50 ksi (see Desig Ste 3.1) STable b t t t 14 i (see Desig Ste 3.18) i (see Desig Ste 3.18) F yc 50 ksi (see Desig Ste 3.1) STable b f t f 14 i (see Desig Ste 3.18) i (see Desig Ste 3.18) 0.85 f' c b t s 2802 K F yw D t w + F yt b t t t + F yc b f t f 2400 K Therefore, 2400 K Therefore, the umber of shear coectors rovided betwee the sectio of maximum ositive momet ad each adjacet oit of 0.0 momet must ot be less tha the followig: S a 78.3 The distace betwee the ed of the girder ad the locatio of maximum ositive momet is aroximately equal to: 48.0 ft (see Table 3-7) Similarly the distace betwee the sectio of the maximum ositive momet ad the oit of dead load cotraflexure is aroximately equal to: 83.6 ft 48.0 ft (see Table 3-7) 35.6 ft 5-8

10 Usig a itch of 10 iches, as reviously comuted for the fatigue limit state, ad usig the miimum legth comuted above, the umber of shear coectors rovided is as follows: 3 12 i ft 35.6 ft 10i For cotiuous sa comosite sectios, the total horizotal shear force,, betwee each adjacet oit of 0.0 momet ad the ceterlie of a iterior suort is equal to the followig: A r F yr where A r i 2 (see Desig Ste 3.3) S b F yr 60 ksi (see Desig Ste 3.1) A r F yr 766 K Therefore, the umber of shear coectors rovided betwee each adjacet oit of 0.0 momet ad the ceterlie of a iterior suort must ot be less tha the followig: S a 25.0 The distace betwee the oit of dead load cotraflexure ad the ceterlie of the iterior suort is aroximately equal to: 120 ft 83.6 ft (see Table 3-7) 36.4 ft Usig a itch of 10 iches, as reviously comuted for the fatigue limit state, the umber of shear coectors rovided is as follows: 3 12 i ft 10i

11 Therefore, usig a itch of 10 iches for each row, with three stud shear coectors er row, throughout the etire legth of the girder satisfies both the fatigue limit state requiremets of S ad S ad the stregth limit state requiremets of S Therefore, use a shear stud sacig as illustrated i the followig figure. Symmetrical about C Pier " 120'-0" (3 Stud Shear Coectors Per Row) C Bearig Abutmet C Pier Figure 5-2 Shear Coector Sacig Desig Ste Desig Bearig Stiffeers Bearig stiffeers are required to resist the bearig reactios ad other cocetrated loads, either i the fial state or durig costructio. S For late girders, bearig stiffeers are required to be laced o the webs at all bearig locatios ad at all locatios suortig cocetrated loads. Therefore, for this desig examle, bearig stiffeers are required at both abutmets ad at the ier. The followig desig of the abutmet bearig stiffeers illustrates the bearig stiffeer desig rocedure. The bearig stiffeers i this desig examle cosist of oe late welded to each side of the web. The coectios to the web will be desiged to trasmit the full bearig force due to factored loads ad is reseted i Desig Ste