1. EXAMPLE 9.3 – Part III PCI Bridge Design Manual
2011/12 Edition
EXAMPLE 9.3 – Part III 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. TRANSFER AND DEVELOPMENT LENGTH
Stress is transferred from the steel to the concrete through bond.
TRANSFER LENGTH is the bonded length needed to develop service level stresses in the steel, fpe.
DEVELOPMENT LENGTH is the bonded length needed to develop the maximum stress in the steel, fps.

3. TRANSFER AND DEVELOPMENT LENGTH
This diagram illustrates transfer and development length.
Transfer length is 60 bar diameters.

4. TRANSFER AND DEVELOPMENT LENGTH
fps = stress in the steel at the strength limit state
fpe = stress in the steel at the service limit state after all losses
db = bar (strand) diameter

5. TRANSFER AND DEVELOPMENT LENGTH
is a factor
= 1.0 for prestressed panels, piles or pretensioned members < 24 inched deep
= 1.6 for pretensioned members > 24 inches deep.
Transfer length will be needed for release and service level stresses calculations. Development length will be calculated later.

6. STRESS AT RELEASE
Stresses due to loads are usually linear or parabolic as a function of length.
Stresses from straight strands are constant over the length.
At the ends, tensile stresses can develop on top.
LRFD does not allow this cracking.

7. STRESS AT RELEASE
This situation is most critical at the time when prestressing forces are first applied.
At this time, the prestressing force is highest, the concrete is weaker and only beam DL is applied.

8. STRESS AT RELEASE Definition: Precompressed tensile zone:
The side of the beam precompressed by the prestressing, but which may eventually have tensile stresses due to applied loads.
In this figure, the precompressed tensile zone is the BOTTOM.

9. STRESS AT RELEASE
LRFD Table limits tensile stresses in areas NOT in the precompressed tensile zone.
With bonded steel:
Without bonded steel:

10. STRESS AT RELEASE
LRFD Table also limits compressive stresses in the precompressed tensile zone.
fc < 0.6fci’

11. STRESS AT RELEASE Transfer Length = 60db = 60(0.5”) = 30” = 2.5’
Self weight moment at transfer length:
This calculation uses the overall length of 119’ as it is assumed the beam cambers up on release and sits on its ends.

12. STRESS AT RELEASE Top @ Transfer Length
The stress calculation requires Pi. This is the same Pi as for elastic shortening, ES.
The loss due to ES was found to be approx. 9%.
Pi = 44 strand(0.153in2/strand)(0.91)(202.5ksi)
Pi = 1241 kips

13. STRESS AT RELEASE Top @ Transfer Length
Limit assumes bonded reinforcement
Tensile stress is negative (-).

14. STRESS AT RELEASE Bottom @ Transfer Length

15. CONTROLLING TOP TENSION
Debond strand
Some strands are coated with plastic so they don’t bond.
This reduces top tension by reducing P at the end of the beam.
Harp Strand
Strand is deflected or HARPED.
Changes “e”.
This example harps strand.

16. CONTROLLING TOP TENSION
Photos of Harped Strand

17. CONTROLLING TOP TENSION
Harping strands: Number of harped strand is determined by trial and error. Harp 12 strands as shown. Harp at 0.3L. The harp point is arbitrary and chosen by the engineer.

18. CONTROLLING TOP TENSION
The harp point, chosen by the engineer (usually by state standard, experience or trial and error), is 35 ft. 6 inches from the end of the beam.

19. CONTROLLING TOP TENSION
To calculate stresses, the value of “e” is needed. To calculate e, the location of the centroids of the various strand groups are needed.

20. CONTROLLING TOP TENSION
Find the centroid of the harped strands from the top at the end of the beam:
Find the centroid of the harped strands from the bottom at the harp point:

21. CONTROLLING TOP TENSION
Distance from the bottom of the beam to the centroid of the non-harped strands

22. CONTROLLING TOP TENSION
When calculating the stress due to prestressing, the horizontal force in harped stands is Pcos, but the cos is approximately 1, so horizonatl force in the harped strands is taken as P.

23. CONTROLLING TOP TENSION
At the transfer length (2.5’ from the end), the distance from the top of the beam to the centroid of the harped strand is:

24. CONTROLLING TOP TENSION
At the transfer length, the distance from the centroid of all the strands to the bottom of the beam and the eccentricity are:

25. STRESS AT RELEASE – Top @ Transfer Length
Limit is compressive because stress is now compressive!!!

26. STRESS AT RELEASE – Bottom @ Transfer Length

27. STRESS AT RELEASE – Top @ Harp Points
Mg = 0.5(0.799k/ft)(35.5’)(119’-35.5’) = 1184 k-ft = k-in

28. STRESS AT RELEASE – Bottom @ Harp Points

29. STRESS AT RELEASE – Top @ Midspan
Mg = 0.5(0.799k/ft)(59.5’)(119’-59.5’) = 1414 k-ft = k-in

30. STRESS AT RELEASE – Bottom @ Harp Points

31. STRESS AT RELEASE Distance from end of beam Top Stress ft ksi
Bottom Stress
fb ksi
At Transfer Length ’
+0.334
+2.946
At Harp Points 35.5’
+0.062
+3.226
At Midspan 59.5’
+0.242
+3.041
All stresses compressive. Limit = 0.6fc’=3.30 ksi

32. STRESS AT RELEASE
This graph shows the stress at the bottom of the beam (pre-compressed tensile zone) along the entire length.
It compares straight strands to harped.

33. STRESS AT RELEASE
This graph shows the top stress and compared straight and harped strand. Note that compression is (+) and tension is (-). Harping eliminates tensile stress at release.

34. SERVICE LEVEL STRESSES
Unlike reinforced concrete, prestressed concrete is checked under service stresses.
Service I applies to the compression side of the beam and to the slab.
Slab stress almost never controls
Tension in the precompressed tensile zone is governed by Service III.

35. SERVICE LEVEL STRESSES
A quick reminder of unfactored moments:

36. SERVICE LEVEL STRESSES
Only the prestressed beam is subject to service level stresses.
The NEGATIVE moment area is a REINFORCED member, so it is NOT subject to service load checks.
Only the positive moment areas need be checked.
Midspan is critical.

37. SERVICE LOAD STRESS – Bottom of Girder Midspan – All Loads (Service III)
A quick reminder:

38. SERVICE LOAD STRESS – Bottom of Girder Midspan – All Loads (Service III)

39. SERVICE LOAD STRESS – Top of Girder Midspan – Permanent Loads (Service I)

40. SERVICE LOAD STRESS – Top of Girder Midspan – All Loads (Service I)

41. SERVICE LOAD STRESS – Top of Slab Midspan – Permanent Loads (Service I)

42. SERVICE LOAD STRESS – Top of Slab Midspan – All Loads (Service I)

43. SUMMARY OF SERVICE LOAD STRESSES
Top of Deck (ksi)
Service I
Top of Beam (ksi)
Bottom
(ksi)
Serv.III
Permanent Loads
All
Loads
At Midspan
+0.035
+0.407
+2.05
+2.36
-0.343
Allowable
+1.800
+2.400
+3.150
+4.200
-0.504

45. Service Load Graph If the bottom stress is COMPRESSIVE, use Service I.
The total service moments are 0 at about 13 feet from the center of bearing on each end. The negative moment area, from center of bearing to 13 feet on each end should be considered as reinforced, not prestressed.

46. FATIGUE Maximum moment for fatigue truck, one lane: 1032 k-ft.
No lane load.
Divide by Multiple Presence Factor of 1.2.
IM = 15% DFone lane = lanes/beam
Mfatigue = 1032 k-ft/lane(0.596 lanes/beam)(1.15)/1.2
Mfatigue = k-ft = 7073 k-in

47. FATIGUE
Fatigue uses a single truck, rear axles spaced at 30 ft. and no lane load.
Fatigue Truck uses 1 lane DF. b
Remove Multiple Presence Factor

48. FATIGUE
Fatigue stress + ½ the stress at top of girder due to prestressing and permanent load: