1. EXAMPLE 9.2 – Part I PCI Bridge Design Manual
2011/12 Edition
EXAMPLE 9.2 – Part I PCI Bridge Design Manual
BULB “T” (BT-72)
THREE SPANS, COMPOSITE DECK
LRFD SPECIFICATIONS
Materials copyrighted by Precast/Prestressed Concrete Institute, All rights reserved. Unauthorized duplication of the material or presentation prohibited.

2. BRIDGE LAYOUT - Longitudinal
Continuous for Live Load

3. BRIDGE LAYOUT – Cross Section

4. DESIGN SPECIFICATIONS
LRFD – 5th Edition (2010)
HL-93 Truck Loading
No Skew
Composite Deck

5. DESIGN SPECIFICATIONS
Concrete:
fc’ = days
fci’ = 5.5 release
wc = kcf
Ecb = 33000w1.5 (fc’)0.5 (LRFD )
= 33000(0.150)1.5(7.0)0.5 = 5072 ksi
Prestressing Steel:
GR 270 (fpu = 270 ksi; fpy = 243 ksi)
½” strand (Ap = in2 / strand)
Ep = ksi

6. DESIGN SPECIFICATIONS
Mild Steel
GR 60 (fy = 60 ksi)
Es = ksi
Future Wearing Surface
2” thick
wws =0.150 kcf
Barriers
New Jersey type
0.300 k/ft

7. DESIGN SPECIFICATIONS
Deck
7.5” Structural thickness
0.5” wearing surface
Total thickness = 8”
fc’ = days
wc = kcf
Ecs = 33000w1.5 (fc’)0.5 (LRFD )
= 33000(0.150)1.5(4)0.5 = ksi
Note – LRFD uses kip, inch, foot units in formulae

8. CONTINUOUS FOR LL PRECAST BRIDGES
Precast beams are made in a factory and shipped to site. The beam is set on simple supports – beam carries self weight and prestressing force as a simple beam.

9. CONTINUOUS FOR LL PRECAST BRIDGES
The deck is formed and poured. Since the beams are NOT shored, the beams carry the deck load as simple beams.

10. CONTINUOUS FOR LL PRECAST BRIDGES
The deck is cast continuous over the piers. When the deck hardens, a continuous structure is formed. The negative moment connection is usually made with non-prestressed steel over the piers. Thus, the negative moment region is conventionally reinforced.

11. CONTINUOUS FOR LL PRECAST BRIDGES
Once the deck hardens and continuity is established, any superimposed dead load (asphalt surfaces, barriers, utilities) is carried by the beams as a continuous structure.
All live load is carried as a continuous structure.

12. CONTINUOUS FOR LL PRECAST BRIDGES
After the slab is poured, the beams will continue to creep and shrink; cambering up.
Temperature will also cause camber.
Positive moments will form causing cracking.

13. CONTINUOUS FOR LL PRECAST BRIDGES
A positive moment connection is required. The requirements for this will be discussed later. (LRFD )

14. CONTINUOUS FOR LL PRECAST BRIDGES
It is thought that creep and shrinkage will redistribute dead load, so some states design using simple spans for all dead load and assuming a continuous bridge for live load only.
Some states completely ignore the continuity and design as simple span for all loads.

15. DESIGN SPANS Beams: Overall Length Design Spans –Simple Span beam
110 ft. end spans
119 ft center span
Design Spans –Simple Span beam
109 ft. end spans
118 ft. center span
Design Spans – Continuous Beam
120 ft. center span

16. PROPERTIES OF BT-72
A = 767 in.2
h = 72 in.
I = in. 4
yb = in.
yt = in.
Sb = in. 3
St = in. 3
w = k/ft

17. PROPERTIES OF COMPOSITE BT-72
Ecs = 3834 ksi Ecb = 5072 ksi (prev. defined)
Modular ratio: n = Ecs /Ecb = 3834/5072 =
LRFD (NEW IN 2009):
The effective flange width is now the TRIBUTARY AREA:
bf = 144 inches

18. PROPERTIES OF COMPOSITE BT-72
Note: ½ inch haunch assumed.
Shaded area is transformed.

19. PROPERTIES OF COMPOSITE BT-72
Transformed Flange Width =
(Effective Flange Width)*n = 144(0.756)= in.
Transformed Flange Area = 108.9”(7.5”) = in2
Note: only 7.5” of deck thickness is structural.

20. PROPERTIES OF COMPOSITE BT-72
Haunch – assumed ½” over BT-72 flange width to account for differential camber in the beams.
Transformed Haunch Width = 0.756(42”) = in.
Transformed Haunch Area = 31.75”(0.5”) = in2

21. PROPERTIES OF COMPOSITE BT-72
Atr
in2 yb
in.
Ayb
in.3
A(ybc-yb)2
in.4 I
I+A(ybc-yb)
Beam
767.00
36.60
28072
325484
545894
871378
Haunch
15.87
72.25
1147
3601
Deck
816.8
76.25
62280
296420
3829
300249
Sum
1599.7
91500
ybc = 91500/ = in.
(distance to bottom of composite)

22. PROPERTIES OF COMPOSITE BT-72
Ac = 1599 in2
Ic = in4
hc = 80 in.
ybc = 91477/ = in.
(distance to bottom of composite)
ytc = 80 – = in.
(distance to top of composite)
ytg = 72 – = in.
(distance from composite neutral axis to top of beam)

23. PROPERTIES OF COMPOSITE BT-72
Composite Section Modulus to Bottom:
Sbc = Ic / ybc = /57.20 = in.3
Composite Section Modulus to Top of Composite:
Stc = Ic /nytc = /(0.756*22.8) = in.3
Note: 1/n converts stress in transformed concrete to stress in actual concrete.
Composite Section Modulus to Top of Beam:
Stg = Ic / ytg = /14.8 = in.3

24. DEAD LOADS - DC DC – Applied to precast only.
Beam self weight wg = kip/ft.
Slab weight – include ½” integral wearing surface.
ws = (8”/12”/ft)(12 ft.)(0.150 kcf) = 1.20 kip/ft
Haunch
wh = (0.5”/12)(42”/12)(0.150 kcf) = kip/ft

25. DEAD LOADS - DC
DC – Applied to composite section. To determine if the barrier weight and the future wearing surface can be equally distributed, the following must be met (LRFD ):
Width of deck constant OK
Number of beams > OK
Curvature < specified in OK straight
Cross section matches one given in LRFD Spec. table OK type “k”

26. k

27. DEAD LOADS - DC
The overhang of the roadway, from the outside of the web, de < 3.0 ft.
de = 3 ft OK
Def. of de changed in
2008 interim (LRFD ).

28. DEAD LOADS - DC DC – Applied to composite section
Barrier weight – 0.30 kip/ft
wb = 2 barriers (0.3 k/ft) / (4 beams) =
0.150 k/ft/beam
Diaphragm weight – assumed steel X braces. Weight ignored in this example. Typically, they weigh a few hundred pounds.

29. DEAD LOADS - DW DW – Future wearing surface and utilities.
Future wearing surface kcf
(2”/12)(0.150 kcf) = ksf
0.025 ksf (42’ roadway width) / 4 beams
= k/ft /beam

30. UNFACTORED DEAD LOADS
All loads are uniform. DL moments and shears on the precast can be found from:
Use overall length at initial (release) condition.
Center to center of bearing at deck placement.

31. UNFACTORED DEAD LOADS
The shears and moments due to the future wearing surface and the barrier weight are computed by considering the bridge as a continuous, three span structure.
The span lengths after continuity is established are center of support to center of pier for end spans and center of pier to center of pier for the middle span.
Shears and moments can be found using any analysis program or by a hand calculation.

32. Unfactored DL Moments
End Spans
Middle
Span

33. LIVE LOAD DISTRIBUTION FACTORS
To use distribution factors, the following must be met:
Width of deck constant OK
Number of beams > OK
Curvature < specified in OK straight
Cross section matches one given in LRFD Spec. table OK type “k”
de < 3 ft. OK 3 ft.
Beams parallel and approximately same stiffness. OK

34. LIVE LOAD DISTRIBUTION FACTORS - MOMENT
Number of design lanes = integer part of
42 ft. / (12 ft./lane) = 3 lanes
42 ft. is clear roadway width.
Interior Beams (Table b-1):

35. LIVE LOAD DISTRIBUTION FACTORS - MOMENT
To use these factors:
3.5’ < S < 16’ S = 12 ft. OK
4.5” < ts < 12” ts = 7.5 in. OK
20’ < L < 240’ L = 120 ft. OK
Nb > 4 beams Nb = 4 beams OK
Note: Although this is a 3 lane bridge, there is NO reduction to the LL for multiple presence. The distribution factors already account for multiple presence.

36. LIVE LOAD DISTRIBUTION FACTORS - MOMENT
eg = (7.5/2) = 39.65
= distance between centroids of beam and slab
A = area of non-composite beam
I = moment of inertia of non-composite beam

37. LIVE LOAD DISTRIBUTION FACTORS - MOMENT
Kg = (1.323)[ (39.65)2]
= in4

38. LIVE LOAD DISTRIBUTION FACTORS - MOMENT
S = 12 ft.
L = 120 ft.
Kg = in4
ts = 7.5”
DFM = lanes/beam

39. LIVE LOAD DISTRIBUTION FACTORS - MOMENT
S = 12 ft L = 120 ft Kg = in ts = 7.5”
DFM = lanes/beam
DFM = lanes/beam –two lanes CONTROLS

40. LIVE LOAD DISTRIBUTION FACTORS - SHEAR
Interior Beams:

41. LIVE LOAD DISTRIBUTION FACTORS - SHEAR
To use these factors:
3.5’ < S < 16’ S = 12 ft. OK
4.5” < ts < 12” ts = 7.5 in. OK
20’ < L < 240’ L = 120 ft. OK
Nb > 4 beams Nb = 4 beams OK
< Kg <
Kg = OK

42. LIVE LOAD DISTRIBUTION FACTORS - SHEAR
S = 12 ft.
DFV = lanes/beam two lane CONTROLS
DFV = lanes/beam one lane