AASHTO LRFD Pedestrian Bridge Design Example Half-Through Truss Bridge ith Tu!ular "em!ers #eneral $ote%s&' - Use the AASHTO LRFD Guide Specifications for Pedestrian Bridges (Draft - ! !"# - Artic$e Artic$e 1&%' Pedestrian +ridges sha$$ +e designed for a unifor) pedestrian $oading of not $ess than 5! psf& 3)pact is not inc$uded in the pedestrian $oading& - Artic$e Artic$e %&&%' ini)u) )eta$ thic*ness o f c$osed structura$ tu+ing )e)+ers sha$$ +e %, inch& ./a$uate the +ridge for the fo$$o0ing $i)it states per Artic$e 1&2 Strength 3 Strength 333 Ser/ice 3 Fatigue 444
AASHTO LRFD #uide Spe(ifi(ation Pedestrian Bridge Design Example Half-Through Truss Bridge ith Tu!ular "em!ers )LL*STRAT)+E E,A"PLE OF E. PRO+)S)O$S OF #*)DE SPE/)F)/AT)O$S Load and Resistance Factor Design #E$ERAL )$FOR"AT)O$ Spe(ifi(ations *sed' - AASHTO LRFD Bridge Design Specifications, 2008 (AASHTO LRFD) - AASHTO Standard Specificationsfor Str#ct#ra% S#pports for Hig!a" Signs, L#$inaires and Traffic Traffic Signa%s, 2008 (AASHTO (AASHTO Signs) - LRFD ide Specifications for 'edestrian Bridges (Specification)
#eometr0' Span 6 Dec* 0idth< 0 dec* 6 7L-7L trusses 6 A8!!< Gr& B< F= 6
2
ft&
%! %!&8
ft& ft&
9
* si
TR*SS "E"BERS' All Stru(tural Tu!ing Top and Botto) 7hords' Section' Section' 9 : 1 : 8,%9; structura structura$$ tu+ing A 6 06
&5" %9&59
in p$f
.nd Posts' Section' Section' 9 : 1 : 8,%9; structura structura$$ tu+ing A 6 &5" in 06 %9&59 p$f >ertica$ Posts' Section' Section' 8 : 1 : 8,%9; structura structura$$ tu+ing A 6 06 3: 6 3c 6
&19 %&"1
in p$f
%1&
in
Diagona$s' Section' Section' : 1 : %,; structura$ structura$ tu+ing tu+ing A 6 1&!5 in 06 %!&8% p$f
FLOORBEA"S' Section' 3: 6 3+ 6 S: 6 Spacing 6
?":%! 1!&"
in
2&"%
in1
9
ft& at each pane$ point
DEAD LOAD' ?eight of each truss 6
9!
p$f per truss
Assu)ed dec* $oading 6
8
psf
?eight of dec* @ f$oor f$oor s=ste) 6 8 psf : %!&8! ft& , 6 %1 p$f per truss Tota$ dead $oad 6 9! p$f %1 p$f 6 %5 p$f
Use
!!
p$f
(Specification< Artic$e 1&%#
PEDESTR)A$ L)+E LOAD' "A)$ "E"BERS' Trusses
- The dec* area )a= +e used to co)pute design pedestrian $i/e $oad for a$$ )ain )e)+e r co)ponents (truss )e)+ers#& The dec* area is the non-Cero inf$uence surface for a$$ such co)ponents& co)ponents& - Use 5! psf 0ithout i)pact& Li/e $oad per truss 6 pedestrian $oading : dec* 0idth , 6 5! psf : %!&! ft& , 6 8! p$f
SE/O$DAR. "E"BERS' De(12 Stringers2 Floor!eams - Use 5! psf 0ithout i)pact&
+EH)/LE LOAD'
(Specification< Artic$e 1&#
- >ehicu$ar access is not pre/ented += fi:ed ph=sica$ )ethods< therefore< the pedestrian +ridge shou$d +e designed for an occassiona$ sing$e )aintenance /ehic$e $oad& - Use Ta+$e Ta+$e 1&-% for ini)u) A:$e Loads and Spacings& - The /ehicu$ar $oad sha$$ not +e p$aced in co)+ination 0ith 0ith the pedestrian $oad& 7onsideration of i)pact is not inc$uded 0ith this /ehicu$ar $oading& Use the fo$$o0ing /ehic$e for a c$ear dec* 0idth +et0een 2 ft& and %! ft& Front a:$e 6 Rear a:$e 6 A:$e spacing 6 ?hee$ spacing 6
"
* *
% 9
ft& ft&
ote' For this e:a)p$e< the pedestrian $oad contro$s for the truss design ho0e/er< the /ehic$e $oad 0i$$ contro$ for the f$oor s=ste) design&
3)$D LOAD' - Assu)e %!! )ph design 0ind&
(Specification< Artic$e 1&#
- Use 0ind $oad as specified in the AASHTO the AASHTO Signs< Signs< Artic$es 1&" and 1&5& - eg$ect 0ind $oad on the $i/e $oad /ehic$e& - The design $ife sha$$ +e ta*en as 8! =ears for the purpose of ca$cu$ating the 0ind $oading&
Hori4ontal 3ind Loading - App$= the design horiConta$ 0ind pressure on the truss co)ponents& PC 6 design 0ind pressure on superstructure using AASHTO AASHTO Signs< .E& 1-% or Ta+$e Ta+$e 1-2< psf 6 !&!!89CG> 3r 7d (AASHTO Signs< .E& 1-%# 0here' C 6 height and e:posure factor fro) AASHTO Signs< .E& 71-% or Ta+$e 1-8 6 %&!! %&!! (con (conse ser/ r/at ati/ i/e$ e$= = ta* ta*en en fro) fro) Ta+$e a+$e 1-8 for for a hei heigh ghtt of of 1& 1&" " ft& ft# G 6 gust effec effectt factor factor 6 %&% ()ini)u)# > 6 +asic 0ind /e$ocit= /e$ocit= 6 %!! )ph 3r 6 0ind i)portance factor fro) AASHTO Signs< Ta+$e Ta+$e 1- 6 %&!! 7d 6 0ind drag coefficient fro) AASHTO Signs< Ta+$e 1-9 6 &!! PC 6
8"&
psf
(A$ternati/e$=< (A$ternati/e$=< AASHTO Signs< Ta+$e 1-2 )a= +e used 0ith a 7d /a$ue of &! app$ied#
Proected /ertica$ area per $inear foot' 7hords' 1 in&, % : 9 ft& , 9 ft& >ertica$s' 1 in&, % : &28 ft& $ong , 9 ft& Diagona$s' 1 in& : 2&"% ft& $ong , 9 ft& Tota$ per Truss' Dec* Stringers'
%!; , %
!&8! !&! !&11 %&!1
SF,ft& SF,ft& SF,ft& SF,ft&
!&"1
SF,ft&
?SH 6 tota$ horiConta$ 0ind on superstructure< p$f 6 ( trusses : %&!1 SF,ft& !&"1 SF,ft : 8"& psf 6 %95 p$f ote' The fu$$ $atera$ 0ind $oads )ust +e resisted += the entire superstructure& Appropriate portions of the design 0ind $oads )ust a$so +e distri+uted to the truss top chord for design $atera$ forces on the truss /ertica$s&
+erti(al 3ind Loading - App$= a /ertica$ pressure of !&!! *sf o/er the fu$$ dec* 0idth concurrent$= 0ith the horiConta$ $oading& This $oading sha$$ +e app$ied at the 0ind0ard Euarter point of the dec* 0idth& ?S> 6 /ertica$ 0ind $oad on the fu$$ proected area of the superstructure app$ied at the 0ind0ard Euarter point< p$f 6 P/I0dec* 0here' P/ 6 /ertica$ 0ind $oading on superstructure< *sf 6 !&!! *sf 0dec* 6 tota$ dec* 0idth< ft& 6 %!&! ft& Therefore< ?S> 6 !&!! *sf : %!!! : %!&!! ft& 6 !! p$f >ertica$ >ertica$ $oad on $ee0ard truss 6 !! p$f : (2&8 ft& (!&8 in& &8 in , %# , %!&8! ft& 6 %2&9 p$f >ertica$ >ertica$ $oad on 0ind0ard truss 6 !! p$f : (&8 ft& (!&8 in& &8 in , %# , %!&8! ft& 6 8& p$f (up$ift#
TOTAL +ERT)/AL LOADS PER TR*SS'
(Specification< Artic$e 1&2#
D.AD LOAD (D7%D7#' L3>. LOAD (Pedestrian< PL#' ?3D (O/erturning< ?S#'
!! 8! %"
p$f p$f p$f
Load Factors (AASHTO LRFD Ta+$e 1&&%-%# Li)it State St r 3 Str 333 S er 3
D7% @ D7
PL
?S
%&8 %&8 %&!!
%&28 ! %&!!
! %&! !&1!
STR.GTH 3 L33T STAT. ( gD7%D7I(D7%D7# gPLIPL# 6
%
p$f
STR.GTH 333 L33T STAT. ( gD7%D7I(D7%D7# g?SI?S># 6
82
p$f
S.R>37. 3 L33T STAT. (gD7%D7I(D7%D7# gPLIPL g?SI?S># 6
95
p$f
TR*SS "E"BER DES)#$ LOADS' Pane$ point $oad $oad fro) contro$$ing contro$$ing $oad co)+& 6 %&!1" *$f : 9&! ft& pane$ 6 9&1 *,pane$ a:i)u) Truss e)+er A:ia$ Loads (fro) separate truss ana$=sis#' 7h 7hord (U!8-U!9# %1&82 * (co)pression# .nd Post (U!!-L!!# 1&2 * (co)pression# Diagona$ (U!!-L!%# 81&8 * (tension# >ertica$ (U!%-L!%# "&! * (co)pression#
TR*SS TOP /HORD LATERAL S*PPORT'
(Specification< Artic$e 2&%#
- Assu)e the truss /ertica$s are adeEuate to resist the $atera$ force per Specification< Artic$e 2&%&% (ust /erif= assu)ption see section tit$ed ;LAT.RAL FOR7. TO B. R.S3ST.D BJ >.RT37ALS;# - Latera$ support is pro/ided += a trans/erse U-fra)e consisting of the f$oor+ea) and truss /ertica$s& Deter)ine the design effecti/e $ength factor< < for the indi/idua$ top chord )e)+ers supported + et0een the truss /ertica$s u sing Specification< Ta+$e 2&%&-%& 7o)pute 7L,Pc for use in the Ta+$e& Ta+$e& 0here' 76 6
P,D &5%2
*,in&
(fro) a separate D ana$=sis#
L 6 un+raced $ength of the chord in co)pression (i&e& $ength +et0een pane$ points#< in& 6 2 in& Pc 6 desired critica$ +uc*$ing $oad (i&e& factored co)pressi/e force# )u$tip$ied += %&11< * (Specification< Artic$e 2&%&# 6 %2"&52"% * 7L,Pc 6
%&%2
n 6 nu)+er of pane$s pane$s 6
%
Therefore< %, 6 6
!&9"" %&8
(Specification< += interpo$ation of Ta+$e 2&%&-%#
TOP 7HORD 7OPR.SS3>. R.S3STA7.'
(AASHTO LRFD< Artic$e 9&5&#
7hec* the s$enderness ratio against the $i)iting /a$ue& For )ain )e)+ers' For +racing )e)+ers'
L,r £ %! L,r £ %!
Section' Section' 9 : 1 : 8,%9; Structura Structura$$ Tu+e Tu+e A 6
&5"
in
r : 6 radius of g=ration a+out the :-a:is< in& 6 &!9 in& r = 6 radius of g=ration a+out the =-a:is< in& 6 %&%" in& 6
%&8
L6
2
in&
L,r : 6 (%&8 : 2 in , &!9 in& 6 8!&" K
%!
O
L,r = 6 (%&!! : 2 in , %&%" in& 6 9%&! K
%!
O
Pr 6 factored resistance of co)ponents in co)pression< * 6 fcPn
(AASHTO LRFD< .E& 9&5&&%-%#
0here' fc 6 resistance factor for co)pressi/e per AASHTO LRFD< Artic$e Artic$e 9&8& & 6 !&5 Pn 6 no)ina$ co)pressi/e resistance per AASHTO LRFD< Artic$e 9&5&< * Deter)ine the no)ina$ co)pressi/e resistance< Pn 3f l £ &8< then' Pn 6 !&99lF= As
(AASHTO LRFD< .E& 9&5&&%-%#
3f l &8< then' Pn 6
!&"" !&""F F= A s
l
(AASHTO LRFD< .E& 9&5&&%-#
F l 6 HL = rs . 6
(AASHTO LRFD< .E& 9&5&&%-1#
!&9!
0here' As 6 gross cross-sectiona$ area< in 6
&5"
in
F= 6 specified )ini)u) =ie$d strength< *si 6 9 *si . 6 )odu$us )odu$us of e$asticit= e$asticit=<< *si 6 5
9%
Therefore< the top chord factored resistance is' Pn 6 !&99!&9! : 9 *si : &5" in 6 %2" * fcPn 6
%9! *
Pchord 6 %1&82 *
LATERAL FOR/E TO BE RES)STED B. +ERT)/ALS'
O
(Specification< Artic$e 2&%&%#
Hf 6 )ini)u) $atera$ force< * 6 !&!%,IPa/g 0here' 6
%&8
Pa/g 6 a/erage design co)pressi/e force in adacent chord )e)+ers< * 6 %1&82 * >erif= $i)it !&!% , %&8 6
!&!!2
!&!!1
O
Therefore< Hf 6 !&!% , %&8 : %1&82 * 6 !&51 * App$= Hf as the $atera$ force at the top of the Truss >ertica$s& >ertica$s& App$= Hf concurrent$= 0ith other pri)ar= forces in the >ertica$s >ertica$s (co)+ined co)pression p$us +ending ana$=sis#& ana$=sis#& 3nc$ude $atera$ 0ind forces for AASHTO LRFD Load 7o)+ination Strength 333& Length of /ertica$ 6
8&!
in&
Latera$ o)ent in >ertica$ due to 7 6 !&51 * : 8&! in& 6 8!&!! *-in&
E$D POSTS'
(Specification< Artic$e 2&%&%#
- App$= the $atera$ force< 7< at the top end of post and design as a canti$e/er co)+ined 0ith a:ia$ $oad& The $atera$ force< 7< is ta*en as %&!N of the end post a:ia$ $oad& Late Latera ra$$ Forc Force' e' 7 6 !&!% !&!% : 1& 1&2 2 * 6
!&1 !&1 *
ote' A$$ other truss )e)+ers are are ana$=Ced using con/entiona$ )ethods )ethods per AASHTO AASHTO LRFD&
DEFLE/T)O$'
(Specification< Artic$e 8#
a:i a:i)u )u) ) ped pedes estr tria ian n LL LL Def$ Def$ec ecti tion on 6 %,8 %,8!! !! of the the spa span n $en $engt gth h6 Fro) Truss Ana$=sis< LL Def$ection (0 LL 6 !&8! *,ft# 6 %&! in&
+)BRAT)O$S'
2&! 2&!! ! ft& ft& : % % , 8!! 8!! 6 K L,8!!
%&21 %&21 in& in&
O
(Specification< Artic$e 9#
+erti(al +erti(al Dire(tion - .sti)ate the funda)enta$ freEuenc= in the /ertica$ direction< f< += appro:i)ating the truss as a si)p$= supported unifor) +ea)' - The funda)enta$ freEuenc= in a ertica% )ode )ode 0ithout consideration of $i/e $oad shou$d +e greater than 1&! HC to a/oid the first har)onic& f 6 !&%"ISMRT(g , DDL#
0here' g 6 acce$eration due to gra/it=< gra/it=< ft,s 6 1& ft,s DDL 6 )a:i)u) /ertica$ def$ection of the truss due to the dead $oad< ft& !&! ft& = (fro) a separate ana$=sis 0ith 0 6 !&! *$f per truss#
f 6 !&%" !&%"IS ISMR MRT( T(1 1& & , !&! !&! ## 6
&"8 &"8 HC 1&! 1&! HC )ini )ini)u )u) ) desi desira ra+$ +$e< e< O
For i$$ustration purposes< assu)e higher har)onics har)onics (second< third< etc are a concern& The +ridge shou$d +e proportioned such that the fo$$o0ing criteria is satisfied' f ³ &"9 $n (%"! , ?# ?# 0here' fu$$ 0eight of the supported structure inc$uding dea d $oad and an a $$o0ance for ? 6 actua$ pedestrian $i/e $oad< * 6 trusses trusses : !&! *$f *$f : 2&!! 2&!! ft& 6 "&" * (Dead Load On$=# &"9 &"9 $n (%" (%"! ! , "&" "&"!# !# 6
8& & HC HC
f 6 &"8 HC is not greater than 8& HC< inc$ude a portion of the pedestrian $i/e $oad&
Assu)e so)e pedestrian $i/e $oad contri+ution and re-e/a$uate re-e/a$uate the e:pression' ? 6 DL %!NLL %!NLL 6 "&" "&" !&%! !&%! : : (!&8! *$f : 2&!! 2&!! ft ft 6
18&" *
&"9 $n (%"! , 18&"# 6
&"8 HC
&99 HC
K
f6
O
Lateral Dire(tion - .sti)ate the funda)enta$ freEuenc= in the $atera$ direction< f $at< += appro:i)ating the truss as a si)p$= supported unifor) +ea) rotated 5! degrees' - The funda)enta$ freEuenc= in a %atera% )ode 0ithout consideration of $i/e $oad shou$d +e greater than %&1 HC to a/oid the first har)onic& Assu)e the $atera$ 0ind 0ind +racing is 1 : 1 : %,; structura$ structura$ tu+ing&
f 6 !&%"ISMRT(g , DDLLat#
0here' g 6 acce$eration due to gra/it=< gra/it=< ft,s 6
1&
ft,s
DDLLat 6 )a:i)u) $atera$ def$ection of the truss due to the dead $oad< ft& !&!" ft& (fro) a separate ana$=sis# =
f 6 !&%" !&%"IS ISMR MRT( T(1 1& & , !&!" !&!" ## 6
1&8 1&8 HC %&1 %&1 HC )ini )ini)u )u) ) desi desira ra+$ +$e< e< O
FAT)#*E' (Specification< Artic$e 1&8# Use AASHTO Signs< Artic$e %%&2&1 AASHTO Signs< Signs< Artic$e Artic$e %%&2& %%&2& - ot used as it is assu)ed that that the Pedestrian Bridge is not o/er a high0a= P? 6 8& 7d 3F 7d 6 0ind drag coefficient per AASHTO Signs< Ta+$e 1-9 6 &!! 3 6 0ind i)portance factor per AASHTO Signs< Ta+$e Ta+$e 1- 6 %&!! F
P? 6
%!&
psf
?SH 6 tota$ horiConta$ 0ind on superstructure< p$f 6 ( trusses : %&!1 SF,ft& !&"1 SF,ft SF,ft : %!& psf 6 1% p$f
FAT)#*E 7ontd' FAT)#*E 7ontd' a:i)u) e)+er Force' Botto) 7hord< e)+er L!8-L!9 6
8&9
*ips
(fro) a separate Ana$=sis#
f 6 Stress Range 6 (8&9 *ips , &5" in# 6 Q(f #
%&%
in (AASHTO LRFD .E& 9&9&%&&-%#
£ (F#n
0here' Q6 f 6
%&!
(Specification< Artic$e 1&2#
%&%
*si (Specification< Artic$e &%#
(F#n 6 (F# TH 0here (F#n 6
%9
*si
(%&!#(%&%#
£
%9
%&%
K
%9
(7ategor= B -+ase )eta$# (AASHTO Signs< Ta+$e %%-1#
O
?e$ded e)+er connections and Fracture Toughness ReEuire)ents are outside the $i)its of this Pedestrian Bridge design e:a)p$e& The= 0i$$ +e the responsi+i$it= of the designer& designer&