Draft
12.3CaseStudy: Walnut LaneBridge 209
12.3.3 Loads
26 Theselfweight of thebeamisq 0 = 1: 72 k/ft.
27 Theconcrete(density=.15 k=ft
3
) roadhasa thicknessof 0.45feet.Thus fora 44 foot width,thetotalloadover onesinglebeamis
qr;tot=
1
13
(44)ft(0:45)ft(0:15)k=ft
3
= 0: 23 k/ft (12.20)28 Similarlyforthesidewalkswhich are9.25feetwideand0.6feetthick:
qs;tot=
1
13
(2)(9:25)ft(0:60)ft(0:15)k=ft
3
= 0: 13 k/ft (12.21)We note thatthe weight can be evenlyspreadoverthe 13 beams beacauseof the lateral
diaphragms.
29 Thetotaldeadloadis
qDL= 0:23 + 0:13 = 0: 36 k/ft (12.22)
30 Thelive loadis createdby thetrac,andis estimatedto be 94psf,thusover a widthof
62.5feetthisgives a uniformlive loadof
wLL=
1
13
(0:094)k=f t
2
(62:5)ft= 0: 45 k/ft (12.23)31 Finally, thecombineddeadandlive loadper beamis
wDL+LL= 0:36 + 0:45 = 0: 81 k/ft (12.24)
12.3.4 FlexuralStresses
- Prestressingforce,Pionly
f 1 =
Pi
Ac
1
ec 1
r
2
(12.25-a)
=
(2 10
6
)1 ; 354
1
(31:8)(39:5)
943 :
= 490 :psi (12.25-b)
f 2 =
Pi
Ac
1 +
ec 2
r
2
(12.25-c)
=
(2 10
6
)1 ; 354
1 +
(31:8)(39:5)
943 :
= 3 ; 445 :psi (12.25-d)
- Piandtheselfweight of thebeamM 0 (which hasto be accontedforthemoment the
beamcambersdueto prestressing)
M 0 =
(1:72)(160)
2
8
= 5; 504 k.ft (12.26)
The
exuralstresseswillthus be equalto:
f
w 0
1 ; 2
=
M 0
S 1 ; 2
=
(5; 50 :4)(12;000)
943 :
= 2 ; 043 psi (12.27)