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, 2011. All rights reserved. Unauthorized duplication of the material or presentation prohibited.

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.

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

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

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.

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.

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.

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.

STRESS AT RELEASE LRFD Table 5.9.4.1.2-1 limits tensile stresses in areas NOT in the precompressed tensile zone. With bonded steel: Without bonded steel:

STRESS AT RELEASE LRFD Table 5.9.4.1.2-1 also limits compressive stresses in the precompressed tensile zone. fc < 0.6fci’

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.

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

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

STRESS AT RELEASE Bottom @ Transfer Length

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.

CONTROLLING TOP TENSION Photos of Harped Strand

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.

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.

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.

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:

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

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.

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:

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:

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

STRESS AT RELEASE – Bottom @ Transfer Length

STRESS AT RELEASE – Top @ Harp Points Mg = 0.5(0.799k/ft)(35.5’)(119’-35.5’) = 1184 k-ft = 14210 k-in

STRESS AT RELEASE – Bottom @ Harp Points

STRESS AT RELEASE – Top @ Midspan Mg = 0.5(0.799k/ft)(59.5’)(119’-59.5’) = 1414 k-ft = 16970 k-in

STRESS AT RELEASE – Bottom @ Harp Points

STRESS AT RELEASE Distance from end of beam Top Stress ft ksi Bottom Stress fb ksi At Transfer Length 2.5’ +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

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.

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.

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.

SERVICE LEVEL STRESSES A quick reminder of unfactored moments:

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.

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

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

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

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

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

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

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

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.

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 = 0.596 lanes/beam Mfatigue = 1032 k-ft/lane(0.596 lanes/beam)(1.15)/1.2 Mfatigue = 589.5 k-ft = 7073 k-in

FATIGUE Fatigue uses a single truck, rear axles spaced at 30 ft. and no lane load. 3.6.1.4.1 Fatigue Truck uses 1 lane DF. 3.6.1.4.3b Remove Multiple Presence Factor 3.6.1.1.2

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