Your Partner in Structural Concrete Design TN402_ULS_cracks_grouted_032211 STRENGTH EVALUATION OF A CRACKED SLAB REINFORCED WITH GROUTED TENDONS 1 Bijan O. Aalami 2 First draft: March 22, 2011 This Technical Note describes the evaluation of the observed cracks in the floor slab of Roya building with respect to its design-intended serviceability and safety requirements. The floor slab is reinforced with grouted post-tensioning tendons and non-prestressed reinforcement. BACKGROUND The ground floor of Roya building is constructed with a 300 mm post-tensioned slab, using grouted tendons. The slab is supported on interior columns and a perimeter wall extending along the entire length of one of the sides as shown in Fig. 1. FIGURE 1 THREE DIMENSIONAL VIEW OF THE SLAB Observation of the slab subsequent to the application of post-tensioning and removal of shoring revealed a pattern of crack formation as illustrated schematically in Fig. 2. 1 Copyright ADAPT Corporation 2011 2 Emeritus Professor, San Francisco State University; Principal, ADAPT Corporation, bijan@adaptsoft.cm support@adaptsoft.com www.adaptsoft.com ADAPT Corporation, Redwood City, California, USA, Tel: (650) 306-2400 Fax (650) 306 2401 ADAPT International Pvt. Ltd, Kolkata, India, Tel: 91 33 302 86580 Fax: 91 33 224 67281
FIGURE 2 SCHEMATIC VIEW OF CRACK PATTERN The observed cracks radiated from the perimeter wall toward the interior of the slab. The cracks were essentially normal to the perimeter wall. Several of the cracks were as wide as 2mm, and extended through the entire depth of the slab, indicating complete loss of precompression in the slab at the crack location. SCOPE OF EVALUATION The evaluation targets to determine whether the formation of the observed cracks leads to a compromise in the design-intended performance of the floor system. It considers the performance of the floor for both its in-service and strength limit states required by the building codes. CAUSE OF CRACKING AND ITS POSSIBLE IMPACT several factors can lead to crack formation in slabs. Properties of the concrete mix, such as watercement ratio, additives to concrete, curing, early stage loading are examples. In addition, restraint of supports to free shortening of a slab can also lead to slab cracking. The pattern of cracks shown in Fig. 2 suggests that, while other factors may have been contributory, the restraint of the long perimeter wall against free shortening of the slab has been the prominent cause of crack formation. In post-tensioned structures, restraint cracks rarely lead to design-significant loss of flexural stiffness and increased deflection, since cracks are generally few in number. As a result, sealing of cracks and verification of deflection through observation generally satisfies the intended in-service performance of the structure. Prestressing force diverted to the restraining supports, such as walls and columns can lead to a reduction in the safety margin of a floor system at strength limit (ULS). The mechanism of force diversion to the restraining supports, and its impact on the design capacity of a slab are outlined in ADAPT TN 224 The concepts outlined in TN224 arrive at several conclusions: 2
The magnitude of force in a prestressing tendon remains essentially unchanged. The restraint of supports reduces the loss of force in tendon due to elastic shortening and creep of the floor slab. The uplift force provided by post-tensioning tendons remains unchanged. Uplift is a function of the force in tendon and its profile. Cracking does not change the tendon shape, nor does it reduce the tendon force. Precompression in a slab will be lost by the amount the prestressing force is diverted to the restraining supports. The loss of precompression leads to a reduction in a slab s capacity to resist cracking. At strength limit state (safety), for grouted tendons the prestressing force available to resist the demand moment is the difference between the force in tendon when in service, and the force a tendon develops at the strength limit state. Thus, the fraction of tendon force that will be available to contribute in resisting an externally applied load depends on the amount of force diverted to the supports. If cracks extend through the entire depth of a slab, it is reasonable to assume that the entire prestressing intended for the slab has been diverted away into the restraining supports, or well away from the cracked location that is subject to strength evaluation. SELECTION OF INVESTIGATION REGION The method of strength evaluation starts with selection of the load path that has been used in the original design of the structure. Should the load path selected prove to be inadequate, progressively more refined methods will be adopted (ADAPT TN311). Review of the plan of the floor system and its supports suggests that the slab panel bounded between grid lines X5 and X6 (Fig. 3) is a representative critical region for investigation. The associated support line (Support Line 5 along the first row of columns next to perimeter) for the representative panel and the bounds of the panel are illustrated in Fig. 4. Note that the support line along the perimeter wall is not considered critical, since the wall provides the support. FIGURE 3 PLAN OF SLAB 3
FIGURE 4 SUPPORT LINES AND THE IDENTIFICATION OF REPRESENTATIVE PANEL Figure 5 shows the design strips along the left-right direction. The Investigation panel is highlighted between the faces of the two supports along grid lines X5 and X6 and the associated tributary of the design strip. FIGURE 5 DESIGN STRIPS AND IDENTIFICATION OF INVESTIGATION PANEL SERVICEABILITY To restore, the following recommendations were made: Seal the cracks that are larger than 0.20 mm in order to: o Guard the reinforcement against exposure to corrosive elements; and o Improve the appearance of the slab (cosmetic). Take level measurements of the entire slab soffit at quarter spans along the line of columns and diagonals of each panel. Measurements should have an accuracy of not less than 0.5mm. 4
When taking measurements, there shall be no construction material or load on top of the entire floor. Unless the superimposed loads are evaluated and allowed for in the computations, their presence will invalidate the comparison between the calculated and measured levels. Level measurements taken along the diagonals of the panels at the soffit of the floor are shown in Fig. 6. The readings show an out-of-flat values for panel center of 2 to 3 mm. For the panel under consideration, the center of panel has a measured 2mm downward elevation difference with respect to its supports. The calculated deflection for the selfweight and prestressing give a deflection just over 1mm (Fig. 7). Neither the calculated, nor the measured values are of significance to be critical for inservice performance of the slab, since they are well below the allowable values. It is concluded that the crack formation has not impaired the flexural stiffness of the slab to a degree that would call for further investigation. 5
FIGURE 6 LEVEL MEASUREMENTS AT SLAB SOFFIT Technical Note The calculated deflection of the same panel under selfweight and prestressing is between 1 and 2 mm (Fig. 7). FIGURE 7 DEFORMATION OF THE SLAB UNDER SELFWEIGHT AND PRESTRESSING (ADAPT Floor Pro) (Maximum deflection for the representative panel is between 1 and 2 mm) STRENGTH EVALUATION The following steps define the method of strength calculation. Three design sections are selected in the representative span, one at the face of each of the two supports, and one at midspan. The design sections extend through the entire tributary of the design strip. The sections are marked 1, 2,3 and shown in Fig. 8. Using the geometry, material, and other details of the structure, including the amount and location of the post-tensioned tendons, a solution was obtained for the strength load combination of the slab. 3 From the solution obtained, the demand moments (Fig. 9) for the strength limit state were evaluated for the three critical design sections 1, 2 and 3. 3 Used computer program ADAPT-PULT 6
FIGURE 8 IDENTIFICATION OF THE CRITICAL DESIGN SECTIONS 1, 2 AND 3 FOR THE REPRESENTATIVE PANEL FIGURE 9 DISTRIBUTION OF DESIGN MOMENTS The values of the design moments reported by the program are reproduced in Table 1. The design values are based on elastic solution, with due allowance for hyperstatic moments from the tendons shown on the drawings. The typical tendon profile is shown in Fig. 10. TABLE 1 DESIGN (DEMAND) MOMENTS FOR THE CRITICAL DESIGN SECTIONS 1, 2 AND 3 (strength condition) Design section Moment Shear Axial Torsion kn-m kn kn kn-m Design Section 1-896.451-704.192-242.879 287.381 Design Section 2-676.711 625.925-327.028-605.344 Design Section 3 435.296 6.440-270.082-92.123 7
Using the post-tensioning (Fig. 10) and the reinforcement (Fig. 11) shown on the structural drawings 4, the design capacities of the three design sections were calculated using an in-house computer program, and assuming no cracking from support restraints. FIGURE 10 TENDON PROFILE THROUGH THE CRITICAL SPAN 20-13mm strands FIGURE 11 AVAILABLE REINFORCEMENT IN THE CRITICAL PANEL Bottom mesh: 10mm @ 300 spacing each way Top bar over each column: 6 16mm A plot of the representative span demand moment and its associated capacity is shown in Fig. 12-a. It is noted that in the original design the provided capacity exceeded the demand at all locations, in particular by a significant margin at midspan. A presentation of the span s overall demand and the capacity based on no restraint of supports is shown in part (b) of Fig. 12. Observe that the total demand of the panel is 1221.50 knm compared to the calculated capacity of 1872.85 knm. The available capacity, however, is less due to loss of prestressing to the restraining supports. The available capacity is calculated next. 4 Drawing No. S/R/002, revision 3, dated March 24, 2006 8
FIGURE 12 Using the geometry, and friction characteristics of the tendons (20 strands) for the design strip of the critical span, the distribution of force along the tendon length immediately at completion of stressing is calculated and shown in Fig. 13. The calculated stresses at the three design sections immediately after seating of the tendons is listed in the first row of Table 2. This information is extracted from the stress distribution shown in Fig. 13 The original calculation was based on a total long-term losses due to shrinkage, creep, elastic shortening and relaxation of prestressing equal to 75 MPa. On the assumption that tendons were stressed and grouted 5 Days after concrete was cast, the loss of long-term losses will be 25% of its total value 5, namely 18.75 MPa (see Table 2). 5 The percentage of stress loss is read off from page 3 Figure 2-2 of ADAPT Technical Note on Prestressing Losses and Elongation Calculations [ADAPT-TN186} 9
7.00E+05 6.00E+05 5.00E+05 Force (N) 4.00E+05 3.00E+05 2.00E+05 1.00E+05 0.00E+00 1.89E+04 2.89E+04 3.89E+04 4.89E+04 5.89E+04 6.89E+04 7.89E+04 8.89E+04 X (mm) FIGURE 13 DISTRIBUTION OF FORCE ALONG THE TENDONS (Force shown is for 20-12.7 mm strands after seating of tendons, from ADAPT-FELT) TABLE 2 STRESSES AND MOMENTS AFTER CRACKING Face of support at left Design section 1 Mid-span Design section 2 Face of support at right Design section 3 Stress (MPa) 412.59 428.57 472.24 Losses (MPa) 18.75 18.75 18.75 Net stress (MPa) 393.84 409.82 453.49 Available stress (MPa) 1466.16 1450.18 1406.51 746.1 800.7 735 Available moment capacity (knm) Conservatively, based on cracks through the slab depth, it is assumed that the entire tendon force is absorbed by the restraint of the supports. Thus at limit state, the available stress in a strand contributory to a design section s capacity is the strand s ultimate strength (fpu = 1860 MPa) minus the stress in strand at time of grouting. This stress is calculated and entered in the last, but one, row of Table 2. Using the balance of stress that is available at strength limit state to resist applied moments at each of the design sections, along with the reinforcement shown on the drawing (Figs. 9 and 10), the design capacity of each section was calculated and entered on the last row of Table 2. The span capacity of the representative panel is calculated and compared with demand as follows: Span capacity = 800.7 + 0.5(746.1 +735) = 1541.25 knm Span demand = 1221.50 knm < 1541.25 knm OK Since the capacity is greater than the demand on the panel, the structure is deemed to exceed the code stipulated factor of safety for strength limit state. 10
APPENDIX A This appendix contains the basic properties of the floor system used in the calculations. Concrete: Weight = 2500 kg/m 3 Cylinder Strength at 28 days for slabs = 36.0 MPa Modulus of Elasticity = 28.4 kn/mm 2 Creep Coefficient = 2 Post-Tensioning: MATERIAL Low Relaxation, seven wire strand Strand Diameter = 12.7 mm nominal Strand Area = 99 mm 2 Modulus of Elasticity = 200000MPa Guaranteed ultimate strength (f pu ) = 1860 MPa Average effective stress (f se ) = 1200 MPa SYSTEM System grouted Maximum number of strands per tendon = 5 (per anchorage device) Duct width and depth = 80x20 mm Distance of duct centroid to centroid of strand z = 3 mm STRESSING Assumed Angular Friction = 0.20 Assumed Wobble Friction = 0.025 rad/m Stress on day 3 (Approx) Minimum concrete cube strength at full stressing = 25.0 MPa Non-prestressed Reinforcement: Yield Strength Modulus of Elasticity = 450.0 MPa = 200000 MPa Design Loading Self weight = based on volume Superimposed dead load = 2.5 kn/m 2 LIVE LOAD (6) Parking = 5.0 kn/m 2 Load Combination The following load combination is used for strength check limit state U = 1.40DL + 1.60LL + 1.00Secondary 6 Live load is conservatively not reduced 11
Where secondary consists of the secondary moments, shears and reactions due to posttensioning. The overall arrangement of tendons and details of the profile used in are shown in the following two illustrations OVERALL ARRANGEMENT OF TENDONS DETAILS OF TENDON PROFILES 12
REFERENCES ADAPT TN224, (2006), Impact of Restraint Cracks on Serviceability and Safety of Post- Tensioned Floor System, ADAPT Corporation, Redwood City, California, www. Adaptsoft.com, 5 pp., 2006 ADAPT TN311, (2009), Basic Concepts in Adequacy Investigation of Floor Systems, ADAPT Corporation, Redwood City, California, www.adaptsoft.com, 23pp, (2009) ADAPT TN186, (2004), Prestressing Losses and Elongation Calculations, ADAPT Corporation, Redwood City, California, www.adaptsoft.com, 16 pp. (2004) 13