Experimental Investigation of Precast, Prestressed Inverted- Tee Girders with Large Web Openings

Experimental Investigation of Precast, Prestressed Inverted- Tee Girders with Large Web Openings James M. Thompson, Ph.D. Assistant Professor Department of Civil Engineering Ohio University Athens, Ohio A precast, prestressed concrete girder with large web openings allows building service systems (mechanical, electrical, communications, and plumbing) to cross the girder line within the member s depth, reducing a building s floor-to-floor height and the overall height of the structure. These height reductions have the potential to improve the competitiveness of total precast concrete structures versus other types of building systems. The experimental program reported in this paper tested three fullscale inverted-tee (IT) girders with large web openings (ITO girders) to failure to evaluate the openings effect on girder behavior. The load-deflection response of the ITO girders up to peak load was similar to that of a control girder without openings. The ITO girders reached their design loads but failed at lower loads than predicted and at values approximately 20% less than the failure load for the control girder. The ITO girders failed in a brittle manner due to diagonal cracking above the opening closest to the support. The test girders were designed using available recommendations in the existing literature. Testing in this experimental program demonstrated that available recommendations in the literature inadequately predict failure loads for ITO girders. Stephen Pessiki, Ph.D. Professor and Chair Department of Civil and Environmental Engineering Lehigh University Bethlehem, Pa. A typical precast, prestressed concrete, gravity-load-resisting floor system frequently used for parking structures employs double-tee (DT) beams, inverted-tee (IT) girders, and bearing walls or columns. Figure 1 shows a plan view of a typical interior bay using this structural system. This system has many attributes that make it attractive for constructing multistory buildings with a regular rectangular plan. Precast, prestressed concrete components are able to span long distances, reducing the number of pieces required for construction and resulting in rapid building-frame erection. Longer spans also provide large column-free spaces for greater flexibility in interior ar- PCI JOURNAL

girder depth is not required to offset the web openings, their inclusion reduces the overall floor system depth and, consequently, the building s overall height for a fixed number of stories. Figure 2 shows regularly spaced openings along the girder s length, which would stanrangements. Fabrication of the precast concrete components occurs at a precasting plant away from the building site, which improves quality control and allows site work and foundation construction to occur simultaneously with component fabrication. Despite the advantages of the precast concrete building system described previously, it is not widely used for occupied buildings. This is partly because occupied buildings (residential, commercial, educational, and office buildings) require many different types of building service systems (mechanical, electrical, communications, and plumbing) that must be routed below the IT girders wherever the services cross the girder line. This increases the floor system depth (depth between the ceiling of the story below and the floor of the story above), and a large floor system depth increases the building s overall height and volume for a fixed number of stories. An increased building height and volume increase the required area of exterior architectural finishes, the demand on building services and the length of their runs through the building, the size of foundation elements, and the costs associated with these items. An increased area of exterior finishes and an increased length for building services both contribute to an increase in the total building weight. In jurisdictions where building height limits exist, a large floor system depth reduces the number of stories that fit within the limit, making this precast concrete building system less competitive. Finally, in seismic regions, a taller, heavier building increases the demand on the lateral-load-resisting system and its respective cost. An IT girder with multiple web openings for service systems (ITO girder) has the potential to make a precast, prestressed concrete, gravity-load-resisting floor system more suitable for occupied buildings. Figure 2 shows cross sections through a typical interior bay with an ITO girder replacing an IT girder. The figure also shows an isometric rendering of a portion of the ITO girder. Web openings in the ITO girder allow the building s service systems to pass through the girder, eliminating the extra depth normally required for services. If an increase in the November December 2006 30 ft - 0 in. 28 ft - 6 in. 18IT36 Column (typ.) Fig. 1. Typical interior bay for an office building using conventional double-tee/ inverted-tee system. Note: 1 in. = 25.4 mm; 1 ft = 0.3048 m. 2 in. CIP topping slab Ceiling 44 ft - 0 in. 42 ft - 6 in. 10DT24+2 10DT24+2 10DT24+2 Double tee beam (DT) (typ.) ITO girder Column DT beam HVAC ITO girder 2 in. CIP topping slab DT beam Column 18IT36 dardize production and eliminate the need to coordinate individual openings with specific service systems. Multiple large web openings in an ITO girder have the potential to alter its behavior (compared with an IT girder) in several ways. These include Structural depth Floor system depth Corbel Fig. 2. Sections through conventional system with prototype inverted-tee girder with multiple web openings for service systems (ITO girder), ITO girder isometric. Note: CIP = cast-in-place; HVAC = heating/ventilating/air-conditioning; 1 in. = 25.4 mm.

2 in. CIP topping slab DT beam 2 in. CIP topping slab DT beam changing the distribution of internal forces on the cross section, the magnitude and distribution of concrete stresses, the cracking load and crack patterns (location, type, extent, and width), the load-deflection response, the peak load, and the failure mechanism and failure load. Understanding these changes is the first step in devising a method to design a safe and serviceable ITO girder. This paper presents and evaluates the results of an experimental program in which three full-scale ITO girders were tested to failure to assess the openings effects on the behavior of the girders. Coupling the ITO girder with DT beams with web openings, as the Duotek system proposed (reviewed in Pessiki et al. 1 ), creates a more versatile, lighter precast concrete floor system. Savage et al. showed that placing multiple openings in the webs of DT beams is feasible. 2 If openings can be provided in an IT girder, a revised and potentially more competitive precast concrete building system is possible. Stub girder Stub girder DT beam DT beam Fig. 3. Stub girder in plan and elevation, solid section and opening section. Note: CIP = cast-in-place; DT = double tee; 1 in. = 25.4 mm. Background This research began with an investigation of the precast concrete stub girder in Fig. 3, 3 which Pessiki et al. developed, based on a steel stub girder by Colaco. 4,5 Figure 3 shows the stub girder in plan and elevation and shows cross sections through a stub and between stubs. The stub girder resists construction loads with its bottom ledge alone and relies on composite action with the topping slab to resist the superimposed live and dead loads. Building services can pass through the spaces between the stubs rather than beneath the girder, which reduces the total floor system depth. Preliminary calculations showed that for unshored construction, the stub girder required a deep bottom flange (ledge) to support the construction loads before the slab reached its full strength and the system could act compositely. A structural (and floor system) depth approximately equal to the original system s depth resulted from the deep bottom flange, negating the efficiency gained by allowing the services to pass between the stubs. In a discussion of alternatives for the stub girder, engineers at High Concrete Structures Inc. (HCSI) suggested incorporating a precast concrete top flange across the stubs. This would allow the girder to support construction loads without the shoring that would typically be required of a shallower bottom flange. HCSI said a precast concrete top flange did not greatly increase fabrication difficulty or cost and that any increase in fabrication cost would still be less than the shoring cost. These discussions led to the prototype ITO girder shown in Fig. 2. It incorporates openings that are large enough to pass building services through and a precast concrete compression flange that supports construction loads. However, a girder with web openings is simpler to construct than a stub girder with a precast concrete top flange because the top flange of a girder is cast monolithically with the element, eliminating shear transfer and other composite construction issues. Complete details of the work presented in this paper are available in Thompson and Thompson and Pessiki. 3,6,7 Literature Review Neither ACI 318 nor the PCI Design Handbook directly addresses the design of prestressed concrete beams with large web openings. 8,9 ACI 318 notes, in Section R11.1.1.1, that web openings can reduce a member s shear strength and refers the designer to three publications for additional guidance. 10 12 While the American Concrete Institute (ACI) has not yet codified the design of reinforced and prestressed concrete members with large web openings, a significant amount of research on the subject is available beyond that listed in ACI 318. Most of the existing literature explains the behavior of a beam with web openings by comparing it to a Vierendeel truss. This research also follows that approach and calls it frame behavior. The frame behavior approach treats the portions of the girder above and below the opening, called chords, PCI JOURNAL

This research program started with the development of a prototype ITO girder based on the recommendations in Barney et al. and the applicable ACI 318 sections. 11 The cross section studied by Barney et al., a single tee, is different from an inverted-tee cross section. However, this research program started with the recommendations in Reference 11 because of their general and somewhat simplified approach to the design of a prestressed concrete beam with openings. The design recommendations in the paper include several elements, which this paper collectively calls the initial design model (IDM). Following are the recommendations: Restrictions on the applicability of the results of the research; Prescriptive requirements for opening placement, opening size, and distance between openings; Prescriptive requirements for transverse reinforcement at the abutments; An analytical procedure to determine the chord forces; and Recommendations on the applicable ACI 318 sections to design the chords for combined axial force, shear force, and moment. This research program allows openings within the prestressing strand development length. A desire to proas beams rigidly supported at the opening s edges (abutments). This approach assumes that the chords deform in double curvature with an inflection point at their midpoint and resist axial force, shear force, and moment. At a section through the opening s midpoint, statics and an assumption on the shear force distribution between the chords allow calculation of the chord forces. Once these forces have been determined, the chords are designed using standard approaches. Relevant findings common to the surveyed research are: 2,11,13,14 Reinforced and prestressed concrete beams can accommodate large web openings without sacrificing strength or serviceability; Web openings must be outside the strand development length for prestressed concrete members; An inflection point in the chord exists approximately at the opening s midpoint; and Cracking in the tension chord (the bottom chord for simply supported members) causes the shear force to redistribute from the bottom chord to the top chord. The critical issue, on which researchers have different opinions, is how to apportion the shear force between the chords at an opening. Ragan and Warwaruk tested pretensioned singletee beams and recommended dividing the shear force between the chords proportional to their areas. 13 Barney et al. also tested pretensioned single-tee beams and recommended dividing the shear force proportional to the chords flexural stiffnesses. 11 When the bottom chord is in compression, these stiffnesses simplify to the gross moments of inertia. If the bottom chord is in tension, Barney et al. recommended varying the shear force each chord resists, 11 depending on the magnitude of the bottom chord tension and the respective amount of anticipated cracking. Abdalla and Kennedy tested post-tensioned concrete beams with rectangular, I, and tee sections and recommended a ratio for the shear force distribution that includes both the chords areas and their moments of inertia. 14 November December 2006 2 in. Av + Ash A + s A v Ash A' s Fig. 4. Standard inverted-tee girder for the typical interior bay. Note: 1 in. = 25.4 mm. Prototype ITO Girder Av + A sh A v + A sh A v + A sh A v + Ash (4) #7 cont. (4) @ 12 in. o.c. (4) @ 12 in. o.c. A v+ A sh A sl A ps A ps (4) #4 cont. A l (typ. top and botom) (2) strands (6) strands (8) strands 9 in. 12 in. 24 in. 24 in. 2 sp. @ 8 in. = 16 in. (typ. each end) (typ.) 2 sp. @ 12 in. = 36 in. (typ. at interior load points) 11 5 / 8 in. A sl (typ.) vide regularly spaced openings along the girder s entire span, and the large cross-sectional dimensions of the girder s bottom chord, make this a reasonable choice. To provide a practical context for the prototype ITO girder s design, the authors selected a typical interior bay (Fig. 1), typical design loads, and typical material properties for an office building. The selected DT beam and IT girder spans maximize the efficiency of this precast concrete building system. The uniformly distributed service load is 200 psf (9.6 kpa), consisting of a 120 psf (5.8 kpa) dead load and an 80 psf (3.8 kpa) live load. These loads result in a 20 kip (90 kn) service load and a 30 kip (130 kn) factored load at each DT beam stem. The selected design concrete strength is 5 ksi (35 MPa), the mild reinforcement yield strength is 60 ksi (410 MPa), and the prestressing strand is 1 / 2 -in.-diameter (13 mm) special 270 ksi (1.9 GPa) low-relaxation strand. Designing a standard IT girder for strength and serviceability requirements is the first step recommended by Barney et al. in designing a girder with web openings. 11 Figure 4 shows the resulting IT girder elevation and cross sections and identifies the different types of reinforcement. In the cross section, the filled circles are prestressing strands and the open circles are mild steel reinforcement. Sixteen prestressing strands provide the flexural rein- A l 8 in. 18 in. 8 in. 34 in.

3 ft-0 in. 2 ft-6 in. 2 ft-6 in. 2 ft-6 in. 2 ft-6 in. 2 ft-6 in. 2 ft-6 in. 2 ft-6 in. 2 ft-6 in. 2 ft-6 in. 3 ft-0 in. Ash Aab Asl Avt A vb (4) #8 cont. A' s (4) #8 cont. A v+ Ash Asl A (1) #4 cont, l (1) strand (9) strands ps (9) strands A vt #4 @ 4 in. o.c. #4 @ 6 in. o.c. A vb Aab Ash Aab Avb Aab Ash Aab Asl Fig. 5. Prototype inverted-tee girder with multiple web openings for service systems (ITO girder) elevation and sections. Note: 1 in. = 25.4 mm; 1 ft = 0.3048 m. forcement A ps, four No. 7 (22M) bars provide the reinforcement for the tension stresses at transfer A s, and two No. 4 (13M) bars and two strands provide the ledge longitudinal reinforcement A l. The full-depth, closed-loop, No. 4 (13M) stirrups provide the shear reinforcement A v and the load point hanger reinforcement A sh, and the closed-loop, No. 4 (13M) stirrups in the ledge provide the ledge flexural reinforcement A sl. Figure 5 shows the prototype ITO girder in elevation with the opening dimensions. The openings are regularly spaced along the girder s length between the DT beam stem locations. The openings are tall enough to pass secondary heating/ventilating/airconditioning (HVAC) ducts through, and their bottoms are located at the ledge upper face for simplicity. The resulting chord proportions satisfy the length-todepth ratios prescribed in Barney et al. 11 The openings lengths are such to provide solid regions between the openings (posts) that satisfy the width-to-height A sl Typical solid section 28 ft-6 in. Aps Aab 1 2 3 2 1 A vt #4 @ 4 in. o.c. #4 @ 6 in. o.c. A vb 8 in. Al A s Typical abutment section Section through opening 1 Section through openings 2, 3 2 ft-10 in. A' s 1 ft-6 in. 8 in. A ab A ps ratio prescribed in Barney et al. 11 With the openings dimensions specified, the chord forces are determined as described previously. The bottom chord is in compression at openings 1 and 2 when subjected to the factored load, so the shear force divides between the chords proportional to their gross moments of inertia. Opening 3 has no shear force across it for symmetric loading, so the chords resist only axial load. Because unbalanced loading causes a shear force across opening 3, live load on half of the span was also considered as a load case. The chord moments at each opening caused by the shear forces (secondary moments) are equal and opposite at each end of the opening. The equal and opposite secondary moments in the chords result in tension at the chords upper support side and the lower span side faces. With the chord forces determined from factored loads, the chords at openings 1 and 2 were designed for the combined effects of axial force, shear force, and moment, and the required A l 1 ft-2 in. 10 in. 11.625 in. was reinforcement specified. At opening 3, symmetric loading governed the chords design, so the top chord was designed as a column (compression member) and the bottom chord was designed as a tension member. Figure 5 shows the resulting girder in elevation and identifies the different types of required reinforcement at various crosssection locations. The prestressed reinforcement in the bottom of the section (A ps in Fig. 5) is in two layers to provide the secondary moment tension reinforcement at the openings support side. This change requires adding two additional strands (compared with the initial design) to satisfy the midspan flexural strength requirements for the IT girder. The top chord reinforcement (A s in Fig. 5) supplies the secondary moment tension reinforcement at both sides and both faces of the top chord. It also provides the tension reinforcement required at transfer at the member s ends and the compression reinforcement at opening 3, which resists only compression for symmetric loading. The transverse reinforcement (abutment reinforcement) at the sides of each opening (A ab in Fig. 5) is closed loop stirrups sized to resist the factored shear force at the opening. The abutment reinforcement area is 2.8 in. 2 (1810 mm 2 ), 1.6 in. 2 (1030 mm 2 ), and 0.8 in. 2 (520 mm 2 ) at openings 1, 2, and 3, respectively. In the top and bottom chords, the stirrups (A vt and A vb in Fig. 5) provide the chords shear strength. In the top chord at all three openings, the minimum area and maximum spacing of shear reinforcement controls the stirrups design. At opening 3, for symmetric loading, this also satisfies the requirements for column ties. The bottom chord at opening 1 requires additional stirrups for strength, as the figure shows, while at openings 2 and 3, the minimum shear reinforcement area governs. The reinforcement in Fig. 5 labeled A sh, A sl, and A l attaches the ledge to the web per the PCI Design Handbook Section 4.5. The ITO girder design modifies the hanger and ledge flexural reinforcement arrangement from the PCI Design Handbook recommendations because the space between the openings is too short to distribute the 6 PCI JOURNAL

reinforcement as recommended. Instead, the reinforcement at the load points follows the distribution suggested by the Canadian Precast/Prestressed Concrete Institute s (CPCI) Design Manual, 15 which uses a strut-and-tie model approach for distributing this reinforcement. Consistent with the CPCI Design Manual recommendations, the hanger reinforcement is separate from the shear reinforcement. Reinforcement other than the required amount provided by the hanger reinforcement and the abutment reinforcement satisfies the shear reinforcement requirements in the solid sections between the openings. At the girder s ends, the shear reinforcement is separate and distinguishable. The end bearing reinforcement is the standard detail used by HCSI, so Fig. 5 does not show this reinforcement. The required prestressing force and estimated prestress losses were based on an analysis of a solid cross section. The selected prestressing force gives a concrete tensile stress of 6 f c at the extreme fiber in the precompressed tensile zone. Experimental Program The objective of the experimental program was to understand how an IT girder with openings responds to applied loads. Three full-scale ITO girders (S1, S2, and S3) were loaded to failure. The behavior of an identical longitudinally reinforced, full-scale IT girder (S4) and the ACI 318 strength and serviceability criteria serve as benchmarks when evaluating the behavior of the ITO girders. Comparison with the IT girder assesses the openings influence on load-deflection response, cracking, failure load, failure mode, and the distribution of forces on the cross section. Comparison with the ACI 318 criteria assesses the ITO girder s ability to satisfy building code requirements. Test Specimens Figure 6 shows the four test specimens, which use the parameters of the typical bay in the representative office building and have the same dimensions and longitudinal reinforcement November December 2006 S1 S2 S3 S4 Fig. 6. Test specimens. as the prototype ITO girder. The test specimens have three openings instead of five to reduce the instrumentation requirements. For symmetric loading, this provides a good indication of the prototype ITO girder s behavior. The test specimens solid section contains supplemental reinforcement to ensure that the failure occurs within the test region. The three ITO test specimens use different transverse reinforcement arrangements between the openings and in the top chord to investigate the reinforcement requirements in these areas. Figure 5 shows the prototype ITO girder, which has closely spaced transverse reinforcement in the top chords and a band of transverse reinforcement at the openings edges, as prescribed by Barney et al. 11 Figure 6 shows that specimen S1 has the same transverse reinforcement as the prototype ITO girder in both areas. The figure also shows that specimen S2 has alternative transverse reinforcement between the openings and specimen S3 has an increased top-chord transverse reinforcement spacing compared with the prototype ITO girder. In specimen S2, the sum of the total required transverse reinforcement between the openings from A sh, A ab, and A v is spread uniformly between the openings. This variation in abutment reinforcement allows investigation of the necessity of the prescriptive requirement for reinforcement beside the openings, as in Barney et al. 11 Specimen S3 has an increased top chord transverse reinforce- ment spacing compared with that in the prototype ITO girder. This variation allows the investigation of whether the ACI 318 requirements for maximum shear reinforcement spacing are applicable to the ITO girder s top chord. For specimens S1 and S2, like the prototype ITO girder, the maximum spacing limit for flexural members, d/2, applies to the transverse reinforcement. For specimen S3, the spacing limit for column ties (the least dimension of the compression member) was applied to the transverse reinforcement in an effort to reduce the amount of top chord reinforcement in this member. The transverse reinforcement in the top chord of specimen S3 still provides the minimum area of shear reinforcement required by ACI 318, but at a greater spacing than what is allowed for flexural members. Test Setup Figure 7 shows the test setup. Eight hydraulic jacks load the test specimens, Fig. 7. Test setup.

LS-6 LS-5 LS-4 LS-24 LS-23 LS-22 LS-29 LS-9 LS-8 LS-7 LS-20 LS-19 LS-18 LS-10 LS-26 LS-30 XS-2 XS-12 XS-16 XS-17 XS-28 XS-27 XS-15 XS-21 XS-3 XS-1 XS-11 XS-14 XS-13 XS-25 D-45 D-44 D-43 D-42 D-41 D-40 D-39 D-38 D-37 D-36 D-35 D-34 D-33 G-56 G-55 G-54 G-53 G-52 G-51 G-52 G-51 G-50 G-49 G-64 G-63 G-62 G-61 G-60 G-59 Fig. 8. Test specimen instrumentation. four on each side of the web, at the interior DT beam stem locations in the typical bay. The jacks apply load to the ledge s top surface through steel plates resting on bearing pads that have an area that is equal to that of a DT beam stem. Steel frames with bearing pads support the test specimens at each end. The bearing pads have an area equal to that provided by a typical column corbel. The test specimens are loaded at four interior DT beam stem locations, as opposed to the six locations in the typical bay (for reasons of economy). The two loadings closest to the supports were omitted during testing because the DT beam stem centerline nearest the support in the prototype building is 11 in. (279 mm) from the face of the support. It is likely that shear transfers this load directly to the support and that it will have little influence on the test specimens behavior. In a comparison of the two scenarios (with four or six loading points), the shear force and moment diagrams are similar, the shear force across the openings is the same, and the difference in the shear force to moment ratio is small. Instrumentation Figure 8 shows the instruments locations and designations on specimen S1. Instrumentation on the other three specimens is similar. Each designation refers to a different type of instrument or a different function of the instrument. Data from the instruments were recorded with a computer-based data acquisition system. The LS-xx and XS-xx instruments shown in Fig. 8 are electrical resistance strain gauges. The LS-xx gauges measure longitudinal reinforcement strains and are mounted on short lengths of No. 4 (13M) bars that are tied into the reinforcement cage. Specimen S4 uses only the two midspan gauges. The XS-xx gauges measure transverse reinforcement strains and are bonded directly to the stirrups. The instruments designated D-xx in Fig. 8 are linear variable displacement transducers (LVDTs) that measure the top and bottom surface deflections. These measurements provide data for plotting the deflected shape and comparing the ITO girders deflections to each other and to the IT girder. The LVDTs are located approximately 1.5 in. (38.1 mm) away from each opening s edges along the span, and their location and designation are the same for all test specimens. The instruments designated G-xx in Fig. 8 are linear potentiometers that measure crack opening displacements. These instruments provide both qualitative and quantitative information on crack widths; they signal the formation of cracks and allow a comparison with the different transverse reinforcement arrangements in the specimens. The potentiometers are placed at the same longitudinal locations as the LVDTs for all ITO specimens, and their designations are the same as well. Only the four instruments located at the loading points were used on specimen S4. Two rods that transfer load from the hydraulic jacks to the top surface of the specimen s ledge have a full-straingauge bridge mounted on them and serve as load cells. One rod was located at the load point nearest the support on the solid side and the other at the midspan load point on the solid side. For PCI JOURNAL

all tests, the readings from the two rods were in close agreement and their average provides the applied load Q. Test Procedure The test specimens were loaded in a quasi-static manner, and the time from the test s start to the peak load was approximately one hour. No attempt was made to regulate or monitor the rate of applied load versus time. Loading was stopped at various points during testing to take photographs and sketch cracks. Once a girder reached its peak load, further pumping of hydraulic fluid caused additional displacement at a reduced value of resistance. The test ended when the girder collapsed. Before starting to load each test specimen, the data acquisition software read and stored an initial value from every instrument, which was then subtracted from all subsequent readings. This procedure caused the recorded values of strain and displacement to be functions of the applied load only, excluding effects from the member s self-weight and the prestressing force. The concrete compressive strength and the mild steel reinforcement yield strength were evaluated as part of the experimental program. The 28-day concrete strength was 8.2 ksi (57 MPa), and the mild steel reinforcement had a yield strength of approximately 64 ksi (440 MPa) for the No. 4 (13M) bars and 68 ksi (470 MPa) for the No. 8 (25M) bars. The prestressing strand s material properties were not evaluated. Finite Element Analysis Using solid elements, threedimensional elastic finite element (FE) analyses of the test specimens were conducted to determine the elastic shear-force distribution for comparison with the IDM prediction. Because the IDM did not indicate shear force redistribution due to cracking, an elastic analysis was adequate and consistent for comparison. Figure 9 shows an isometric of the FE model. The overall FE model geometry, support conditions, and loading are the same as for the test specimens. November December 2006 Fig. 9. Isometric of inverted-tee girder with multiple web openings for service systems (ITO girder) finite element model. Applied load (kip) 80 60 40 20 Midspan cracking: 68 kip Factored load δ = 0.46 in. 9 8 Service load δ = 0.27 in. 5 1 34 The model s cross-sectional geometry represents the test specimens gross section. The model consists of eightnode solid elements with an aspect ratio that is never greater than two. The material properties required for the analysis are the concrete density, 150 lb/ft 3 (2400 kg/m 3 ), and modulus of elasticity, 5450 ksi (38 GPa). The model applies the prestressing force as an external equivalent load and introduces it linearly at the model s ends over the first 24 in. (610 mm) Y 9 Z 11 4 14 X 12 10, 11 Fig. 10. Specimen S1: load versus midspan deflection, cracks at peak load. Note: 1 in. = 25.4 mm; 1 kip = 4.448 kn. 8 13 15 3 15 1 10 15 1 2 3 5 15 14 12 13 9 15 12 12 0 0.0 0.5 1.0 1.5 Midspan deflection (in.) 14 86 kip Peak δ = 1.27 in. to approximate the transfer length assumed for the prestressing strand. The elastic FE model shows that for this cross section, the shear forces do not divide in proportion to the chords gross moments of inertia. The FE analysis predicts that the top chord resists 34% of the shear force compared with the 25% predicted by the IDM. The FE model also provides longitudinal and vertical normal stress distributions, which are compared with the experimentally observed cracks.

Fig. 11. Specimen S2: opening 1 at peak load. Results This section presents the experimental results with accompanying discussions. All three ITO girders exhibited similar behavior, so the discussions use data from different test specimens to represent the behavior of all of the test specimens. The only exception to these similarities is in specimen S3, where an unconsolidated region at midspan modified its load-deflection response. In the figures and tables in the following discussion, the load is the sum of the force applied by two jacks at one load point, one on each side of the web. The total load that a test specimen resisted is four times this value because the test specimens had four load points. Deflection is measured downward at the selected point due to the applied load, so it does not include upward camber Applied load (kip) 100 80 60 40 20 0 S1, S2, S4 S3 L/480 S2 S1 S3 Service load Fig. 12. Specimen S2: opening 1 at test s end. or downward self-weight deflection. Bearing pad compression is subtracted from the measured deflection values. Measured strains are due to the applied load only, so they do not include the effects of prestressing forces and the girder s self-weight. Overall Behavior Figures 10, 11, and 12 describe the ITO girders overall behavior. Figure 10 shows specimen S1 s midspan loaddeflection response with an inset sketch of specimen S1 showing the cracks present at the peak load. The numbered tick marks on the plot show the load at which the corresponding crack on the inset figure was visually observed during the test. Figure 11 shows the cracking at opening 1 for specimen S2 just after the peak load was applied, and S1: 86 kip S2: 84 kip S3: 77 kip Factored load S4: 108 kip 0 1 2 3 Midspan deflection (in.) Fig. 13. Load-deflection response and peak load comparison between an invertedtee (IT) girder and IT girders with multiple web openings for service systems (ITO girders). Note: 1 in. = 25.4 mm; 1 kip = 4.448 kn. S4 D-33 Fig. 12 shows the cracking at opening 1 for specimen S2 at the test s end. The ITO girder s overall midspan load-deflection response is bilinear. The initial linear range extends from the test s start to approximately the service load (40 kip [180 kn]). Between the service load and approximately 68 kip (300 kn), additional cracking at the openings edges, widening of the existing cracks, and midspan cracking gradually reduces the girder s stiffness. From 68 kip (300 kn) to the peak load, the girder s response is, again, linear. Each girder s midspan deflection is small throughout the test. It measures L/1260 at the service load, L/740 at the factored load, and L/270 at the peak load. Deflection beyond the service load is not a typical design criterion, but these values show that the girder s accumulated deflection remains small up to its peak load. Small, well-contained, diagonal, vertical, and horizontal cracks occur throughout the loading range. The majority of them occur at the openings edges and between openings 1 and 2. At the service load, the maximum measured crack width was 0.010 in. (0.25 mm) at the support side in the web at opening 1 (cracks 1 and 11 on Fig. 10). The number and size of the cracks at the service load suggest that the concrete stresses at this load level are acceptable. The ITO girder reached its loadcarrying capacity when a diagonal crack occurred in the top chord at opening 1 (Peak in Fig. 10). This crack, along with a drop in the load, occurred suddenly. Beyond the peak load, the load returned almost to the peak value as the deflection continued to increase. Additional cracks then formed in the top chord, as Fig. 11 shows, accompanied by the sharper load decrease shown in Fig. 10. At this point, the girder continued to deflect with decreasing load, with additional cracks forming in the bottom chord at opening 1. When the final load decrease occurred, the test ended. At the test s end, the bottom chord eventually failed due to a combination of flexure and shear force, as evidenced by the concrete crushing above the vertical crack and the diagonal crack that reached the concrete crushing zone (Fig. 12). 10 PCI JOURNAL

Load-Deflection Response The openings have a minimal effect on the ITO girder s load-deflection response as shown in the comparison between the ITO girders and the IT girder in Fig. 13. Up to the service load, the specimens responses are nearly indistinguishable on the graph. Beyond the service load, additional cracking at the openings reduces the ITO girders stiffness further, compared with the IT girder, but their load-deflection response is still very close to that of the IT girder s. After midspan cracking occurs, the slopes of the ITO girders load-deflection response curves are approximately equal to that of the IT girder. This similarity continues up to the ITO girders peak load. The ITO girders larger deflections compared with those of the IT girder are due to an additional component of deflection across the openings, as shown in the deflected shape comparison in Fig. 14. As cracking at the openings corners occurs, the additional deflection becomes more pronounced. This additional deflection across the openings is consistent with the frame behavior assumption and consequent double curvature of the chords across the openings. The figure also shows that between the openings, the relative deflection of the same two points is approximately the same among the ITO girders and the IT girder, as evidenced by the parallel lines in the deflected shapes. The ITO girders total load deflection at service load easily satisfies the ACI 318 live-load deflection limit as shown by the L/480 line in Fig. 13. The girders deflections are smaller than would have been predicted in design because the actual concrete compressive strength was greater than the design value. This increases the elastic modulus and decreases the measured deflections. With 5 ksi (35 MPa) concrete, the deflections would be approximately 26% larger but would still comfortably satisfy the ACI 318 criterion. An ITO girder with regular openings along its span would have a larger midspan deflection because of the additional two openings, but the deflection increase is not substantial. To estimate the additional deflection, the difference Top surface D-45 D-44 D-43 D-42 D-41 D-40 D-39 Opening 1 Opening 2 Opening 3 S1 Bottom surface S1 S2 D-38 D-37 D-36 D-35 D-34 D-33 S2 5.0 34.5 67.5 94.5 127.5 154.5 187.5 Distance from girder end (in.) Fig. 14. Service load deflected shape comparison between inverted-tee (IT) girders and IT girders with multiple web openings for service systems (ITO girders). Note: 1 in. = 25.4 mm. between the ITO and the IT girders service load deflections could be added to the ITO girder s deflection. This would result in a midspan service load deflection of 0.30 in. (7.6 mm) for the ITO girder, compared with the 0.27 in. (6.9 mm) measured deflection. This is an increase of 10% but still well below the allowable live load deflection of 0.7 in. (18 mm). This excellent load-deflection response results from setting the prestressing force such that the tension in the midspan bottom fibers at the service load does not exceed 6 f c. This limit delays cracking at midspan and is also likely to delay cracking in the bottom chord of the openings, which maintains the ITO girder s initial stiffness at higher loads. Because the patched concrete at midspan in specimen S3 was applied after the prestressing force was transferred, it was not prestressed, and specimen S3 s deflection is still within the allowable range. This observation, consistent with the increased tensile stress limit in the current ACI 318 (7.5 f c ), 16 suggests that the 6 f c limitation could potentially be increased. The amount and location of abutment reinforcement does not affect an ITO girder s deflection as shown by the similar responses of specimens S1 and S2. A comparison of the effects of the S4 S4 amount and placement of the top chord transverse reinforcement on the girders load-deflection responses is not possible because of the nonprestressed region in S3. However, it is unlikely that this reinforcement variation has any influence. In summary, multiple web openings do not significantly affect an ITO girder s load-deflection response. The openings effect on the ITO girder s deflection is observable as an additional deflection across the openings. An ITO girder s midspan deflection easily satisfies the ACI 318 live-load deflection limits. 8 Crack Patterns 0.3 in. 0.3 in. The ITO girders have vertical cracks in the chords at the openings edges, horizontal and diagonal cracks in the webs beside the openings, and vertical cracks in the bottom chords at midspan (Fig. 15). The vertical cracks in the chords at the edges of openings 1 and 2 (locations 4, 8, 13, 14, and 15 in Fig. 15) are consistent with the frame behavior assumption. These cracks occur in regions where the frame behavior assumption and the elastic FE model predict tension stresses from the secondary chord moments. The horizontal and diagonal cracks in the webs beside the November December 2006 11

11 4 Peak 1 3 15 10 5 15 9 14 8 15 14 12 13 9 15 12 12 Fig. 15. Peak load cracking comparison between inverted-tee (IT) girders and IT girders with multiple web openings for service systems (ITO girders). openings (locations 1, 3, 5, 11, and 15 in Fig. 15) result from large concrete tensile stresses in these areas. These cracks are consistent with the large concrete tensile stresses in the vertical and horizontal directions at the openings that the elastic FE analysis predicts. The FE analysis also shows the vertical normal stresses confined to a very narrow band next to the openings. All the girders, ITO and IT, exhibit Load (kip) 100 80 60 40 20 Compression gauge S3 S4 Service load Midspan cracking S1 S2 the similar vertical midspan cracking shown in Fig. 15, at approximately the same load, as shown in Fig. 13. Additional cracks occur in the ITO girders compared with the IT girder because they have more stirrups in the midspan region and cracking usually initiates at a stirrup. In specimen S2, the cracks at the support side of opening 1 (locations 1 and 11 in Fig. 15) opened much wider Tension gauge Factored load Compression (S3's tension gauge did not function) Tension 0-0.002-0.001 0.000 0.001 0.002 0.003 Strain (in./in.) Fig. 16. Midspan strain comparison between inverted-tee (IT) girders and IT girders with multiple web openings for service systems (ITO girders). Note: 1 in. = 25.4 mm; 1 kip = 4.448 kn. S2 S1 S4 than those in specimens S1 and S3 at comparable loads. This experimental observation, coupled with the elastic FE results, reveals that providing abutment reinforcement in a narrow band beside the opening is preferable. The ITO girders crack patterns show that the openings alter the distribution of internal forces, with the vertical cracks in the chords supporting the frame behavior assumption. The horizontal and diagonal cracks are likely due to stress concentrations at the openings corners. The similar midspan cracking in the ITO and IT girders suggests similar behavior in this area for both girder types. The elastic FE analysis and the experimental results both support placing the abutment reinforcement in a narrow band beside the ITO-girder openings. Failure Load, Mode, and Location While the capacity of all three ITO girders exceeded the factored design load, the openings in these specimens reduced their peak loads and changed the failure modes and the failure locations. The openings also affect the ITO girders ductility beyond the peak load compared with the IT girder. The IT girder reached a peak load of 108 kip (480 kn), at which point flexure caused concrete crushing and reinforcement 12 PCI JOURNAL

yielding at midspan. The post-peak response is ductile, as Fig. 13 shows, until a shear crack penetrates the flexural compression zone. As previously noted, the ITO girders all reached their peak loads when a diagonal crack occurred in their top chords at opening 1. The diagonal crack occurred suddenly and in a brittle fashion, as shown by the sharp load decrease in Fig. 13. Specimens S1 and S2 reached a peak load of approximately 85 kip (380 kn), and specimen S3 reached a peak load of 77 kip (340 kn). The similar failure loads between specimens S1 and S2 show that the abutment reinforcement differences did not significantly affect the distribution of forces or the failure load. This observation suggests that providing stirrups at each side of each opening sized for the full shear force at the opening is not necessary for this cross section. The reduced amount of transverse top chord reinforcement in specimen S3 likely caused its failure at a lesser load than that of specimens S1 and S2. The lesser amount of transverse reinforcement reduces the steel contribution to the chord s shear strength. In addition, at the lower peak load of specimen S3, the moment at the opening is less than that for specimens S1 and S2, which reduces the axial force in the specimen and the concrete contribution to the specimen s shear strength. The IDM did not correctly predict the failure load and mode observed in the ITO girders in the experimental program. The predicted failure load for all three ITO girders was 77 kip (340 kn), and the predicted failure mode was combined shear force and axial force in the bottom chord at opening 2. The failure mode and load were predicted from the chord forces at the factored load, 60 kip (270 kn), which affects the chords predicted shear strength and axial/flexural capacity. The predicted failure load for the observed failure mode, a top chord shear force and axial force failure at opening 1, was 176 kip (780 kn) for specimen S3 and 294 kip (1.3 MN) for specimens S1 and S2, based on chord forces of 60 kip (270 kn) and the supplied reinforcement. If the predicted chord forces and the estimated strengths are correct for all possible failure modes, the top chord at Load (kip) Load (kip) 70 60 50 40 30 20 10 9 Fig. 17. Top chord longitudinal strains. Note: 1 in. = 25.4 mm; 1 kip = 4.448 kn. opening 1 does not control the girder s failure, the predicted failure load is 77 kip (343 kn), and the specimen fails at the bottom chord in opening 2 due to combined shear and axial force. In summary, the ITO girders failed at lower loads than the IT girder did, and not in the failure mode predicted from the IDM. However, all three ITO girders exceeded the factored load, which shows that an ITO girder can be designed for the necessary strength. Two problems exist with the current design procedure for an ITO girder. First, the failure mechanism of an ITO girder is not predictable with the current design approach. Second, both the observed and predicted failure modes of ITO girders are brittle, compared with an IT girder s ductile failure mode. Address- 4 8 5 7 S2: Opening 1 6 5 4 9.5" 8" 8" CL 10 0-0.0005-0.0003-0.0001 0.0001 0.0003 0.0005 Strain (in./in.) 70 60 50 40 30 20 10 22 23 20 24 19 S2: Opening 2 242322 9.5" 8" 8" 201918 ing both aspects with a revised design procedure is required. Longitudinal Strains: Midspan Figure 16, which compares the midspan strains between the ITO girders and the IT girder, shows that the ITO girders midspan strains are similar to that of the IT girder. The similarity in the strains, coupled with the similar midspan crack pattern and cracking load, suggests that the midspan opening acts like a cracked flexural section, not like a frame section, when subjected to symmetric loading. These observations suggest that for symmetric loading, the midspan opening may be designed to fail as a cracked flexural section, rather 9 R = 0.001 6 CL 0 26-0.0006-0.0005-0.0004-0.0003-0.0002-0.0001 0.0000 Strain (in./in.) 18 8 7 R = 0.0006 November December 2006 13

Load (kip) Load (kip) 80 60 40 20 Fig. 18. Specimen S3: opening 1 abutment reinforcement strains. Note: 1 in. = 25.4 mm; 1 kip = 4.448 kn. XS-12 XS-1 0 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 Strain (in./in.) R = 0.0031 80 XS-16 XS-3 60 40 20 0 Factored load Service load Service load Factored load XS-12 XS-1 R = 0.0041 Inner gauges Outer gauges XS-16 XS-3 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 Strain (in./in.) than designing the chords as tension and compression members (with the attendant reduced resistance factors for compression design). This provides the ITO girder with a more ductile, predictable, and desirable failure mode, and potentially more strength, comparable to that of the IT girder. This alleviates the second problem noted in the previous section. However, it does not solve the first problem. To design for a midspan flexural failure, the chord failure modes must be such that they do not fail before the midspan fails in flexure. To achieve this, the chord forces and failure mechanisms have to be known with greater certainty than the observed experimental results provide. In addition, while symmetric loading causes the critical shear force and moment for an IT girder, nonsymmetric live load is more likely to be a critical design consideration for an ITO girder. Longitudinal Strains: Chords Figure 17 shows the top chord longitudinal strains from specimen S2 at openings 1 and 2. The recorded strains have intermittent symbols identified in the inset figure. The straight lines in the figure with a symbol only at the end are the predicted strains from the elastic FE model. The strain gauges record longitudinal strains, so assuming the chords behave as frame members with combined axial force, shear force, and moment, the gauges responses are a combina- tion of axial strain and bending strain. While the chords are uncracked and the materials are within their linear (elastic) ranges, mechanics predicts that the load-strain plots will be straight lines in a fan-shaped pattern. The load-strain response of the gauges nearest the inflection point should be in the middle of the fan because the strains are primarily axial. At the gauges away from the inflection point, the secondary moments tension and compression forces decrease or increase the compression force compared with the values measured by the gauges at the inflection point. This results in the six load-strain responses forming a fan-shaped pattern. The longitudinal strain pattern also indicates the inflection point location in the chord. In Fig. 17, the longitudinal strains patterns are consistent with the chords behaving as frame members. This is observable at both openings 1 and 2 for all the gauges at low loads. As cracking occurs, the cross section at the gauge changes and the strains no longer increase linearly at the cracked sections. The strains at both openings show this response, particularly gauges 6, 7, and 9 at opening 1 and gauge 18 at opening 2. In Fig. 15, gauge 6 is in the location where the cracks labeled 4 occurred. No vertical cracks near gauge 7 were observed, but apparently the cross section changed at approximately 40 kip (180 kn). At both openings, the strains show that the inflection point is not at the openings midpoints. At opening 1, the strains initially (at loads less than 20 kip [90 kn]) indicate that the inflection point is approximately at the location of gauges 5 and 8, or approximately 1.5 in. (38 mm) to the span side of the opening s midpoint. The strains in gauges 5 and 8 are approximately equal, and the observation that the compression at gauge 6 decreases more rapidly than at gauge 7 supports this observation. This inflection point location satisfies the assumptions for the approximate analysis of a Vierendeel truss. As cracking occurs, the compression strain in gauge 5 begins decreasing more rapidly than in gauge 8, possibly indicating that the inflection point has moved more toward the span side. At opening 2, the strains indicate 14 PCI JOURNAL