Stirrups were fabricated from mild steel No. 3 reinforcing bars having a yield strength of 50,000 psi. They were U-shaped in the stem of the beam and placed throughout the span length spaced 1 ft apart. The stirrups looped under the prestressing tendon extended up to the midheight of the flange and out 6 in horizontally on both sides.

The tendon in the monolithic beam was located 6.1 in below the center of gravity for the Tee section and the prestress force was 45,000 lb. The location of the tendon in the split-beam was 8.7 in below the center of gravity of its composite Tee section and the prestress force was 27,000 lb. The essential difference here is that the location of the tendon and the prestress for the monolithic beam is determined from the properties of the full Tee section while, due to the nature of the construction of the split-beam [2], the location of the tendon and the prestress is determined by the prop

same for both the monolithic beam and the sp The stress condition (c) results from the com of (a) and (b).

The concrete used in the first 12 specim composed of Type III portland cement, silice and pea gravel. This concrete was mixed in the tory in a turbine-type mixer of 12 cu yd Concrete for the subsequent beams was obtain a local ready-mix company using the same n except for the coarse aggregate which was a M No. 7 crushed lime stone (size No. 8, ASTM C The mix proportions were varied around a des for 5000 psi concrete which was 1:3.2:2.6 by of cement, sand, and gravel. The water conten from 6 to 11 gal per sack of cement (94 lb). T crete strengths at the time of beam testing an in table 1. These strengths represent the averag determined from compressive tests of three 6-1 control cylinders.

2.3. Prestressing Steel

Two types of steel were used as prestressing t The stress-strain curves for the steels are sh figure 5. For the post-tensioned beams, high s heat-treated, stress-relieved bars were used. tests of these bars indicated a stress-strain relat that is essentially linear up to a stress of 108,0 and an initial tangent modulus of approximate x 106 psi. The yield strength of the steel was 1 psi as determined by the 0.2 percent offset n The tensile strength was 190,000 psi. The prest tendons for the pretensioned beams were 7-wire of high strength steel. Tensile tests of the showed a linear stress-strain relationship up to a

erties of the tensile element of the composite tee section.

Figure 4 shows the idealized stress conditions for both types of beams for two stages of loading. The stress conditions (a) show that for the monolithic beam the stress block tapers from the maximum value at the bottom fiber to zero at the top fiber of the beam. The stress block for the split-beam, for this stage, tapers from the maximum value at the bottom fiber to zero at the neutral axis of the composite section. This difference in the stress blocks reflects the same proportional difference in the required prestressing force for the two types of beams. The value of applied load that will cause zero stress in the bottom fiber is represented by the stress condition (b) and is the

STRESS, ksi

180

160

BAR

FIGURE 5. Stress-strain curves for prestressing steel tend

162,000 psi. The tangent modulus s 28.1 x 106 psi. The yield strength percent offset and was 221,000 psi. ngth of the strands, as could be beams, was not determined precisely he strands fractured in the grips in owever, indications from the tensile tests suggest that the manufacturers psi is valid.

Test Procedure

tested as soon as the desired conn the compressive element were of the beams at the time of testing 16 days. The specimens were tested qual loads applied at the quarter , load increments of 2000 lb were the range of cracking where increwere used. After the application of ent, the deflection of the beam, the orcing tendon for unbonded beams, concrete surface, and the extent of orded. The time required for these om 3 to 5 min and the time for the from 60 to 90 min. For the preelectrical resistance gages were ual wires of the strands for strain wever, readings from these gages g loads were erratic in all cases and

t Results and Analysis

1.1. Notations

n prestressing tensile steel nge of Tee section

b of Tee section

m extreme compressive fiber to the force

strength of concrete at time of test ess in the bottom extreme fiber of tion

ss in the top extreme fiber of the

I prestress after losses

stressing steel at ultimate load

d point stress of prestressing steel average compressive stress to maxessive stress

termining position of internal come (fig. 12)

pressive strength of concrete in inder strength

1 extreme fiber in compression to

at ultimate load (fig. 12)

im moment at ultimate load

of prestressing steel

Values of observed and computed characteristics of the beams are given in Table 1. The first order grouping of the specimens is by method of prestressing and attachment of tendons. There are three classifications: (1) post-tensioned, unbonded; (2) post-tensioned, grouted; and (3) pretensioned, bonded. The two beams with grouted tendons, SG-1 and SG-2, experienced bond failures beyond the cracking loads. Since there are no appreciable differences in the performance of beams with bonded and unbonded tendons prior to the onset of cracking, these beams were classed as unbonded for the purpose of comparison.

The beams in this investigation fall into one of five different steel ratio (p) groups. However, test results show that a better ordering of groups can be made in terms of a moment index, Asfsyd. All beams, except SU-11, SU-14, and SG-2, failed after the yield. strength of the reinforcement had been reached. Beams SU-11 and SU-14 had 1900 psi and 2000 psi concretes in the compressive zones, respectively, and failed by compression of concrete with the reinforcement in the elastic range. Beam SG-2 failed by interface separation in the shear span.

The performances of the beams are compared in terms of load-deflection characteristics, ultimate strengths, and crack patterns. The moment index Asfsyd shows a direct correlation with both the loaddeflection relationship and ultimate strength. However, the fact should not be overlooked that all beams in this study were of the same shape and size and were tested in the same manner.

1 Where bars were used, the area reported is the effective area in the threaded sections near the ends of the beam. 24, Computed depth of stress block at ultimate load using measured force in tendon, (T_/0.85 bf').

force to act at the level of the steel for equilibrium. In a prestressed beam the strains at the level of the steel are a function of the moment of inertia of the full transformed cross section up to the cracking load. Within this range of loading, the effect of large differences in steel areas on the straining rate at the level of the steel is relatively small. However, once the beam has cracked, the amount of strain in the steel for a given increment of loading will vary inversely with the tendon area.

Typical load-deflection relationships for post-tensioned beams with unbonded solid bar tendons are shown in figure 6 and for pretensioned beams with bonded strand tendons in figure 7. The three curves representing the post-tensioned beams in figure 6 clearly show the effect of the moment index (Asfsyd) on the performance of the beams. The same is true for the two curves representing the pretensioned beams in figure 7. The initial portion of the load deflection

for the two groups of beams. Typical crack patterns for the beams are shown in figure 9. For the posttensioned beams, a single crack first appeared at or very near midspan and was followed shortly, as loading proceeded, by the development of two or three additional cracks on both sides of the crack at midspan. In beams without stirrups, the midspan crack developed into a distinctive Y pattern with horizontal extensions just under the flange covering a large section of the constant moment zone. When stirrups were used in the post-tensioned beams, the horizontal extensions of the central crack were eliminated. Views of a post-tensioned and a pretensioned beam at ultimate load are presented in figures 10 and 11, respectively, to illustrate the difference in crack distributions and their effect on deflection. In all post-tensioned unbonded beams the central crack. dominated the failure mode causing the maximum compressive strain in the concrete, and consequently

curves in all cases was a straight line with practically the same slope, irrespective of the moment index. This portion of the curve reflects the response of the beam to loading prior to the onset of cracking. Subsequent to cracking, however, the curves are ordered in accordance with the moment index.

In figure 8 a basic difference is seen in the overall characteristics of the load-deflection curves between the post-tensioned and the pretensioned beam groups. The pretensioned beams (SB-1, SB-3) showed considerably more ductility in their response to loading than the post-tensioned group (SU-1, RU-2, SU-13). Distinctively different crack patterns were observed

the maximum curvature of the beam to concentrate at the midspan. For the pretensioned bonded beams, 10 to 12 equally spaced cracks developed in the constant moment zone. These cracks propagated and opened with equal magnitude as load increments were added and until failure occurred. This caused a more uniform and greater overall curvature in the pretensioned beams than for the post-tensioned ones.

4.3. Ultimate Strength

Final failure in flexure of a reinforced concrete beam may be initiated by excessive elongation of the reinforcement, in which case it is called tension failure,