PROFESSIONALDEVELOPMENTSERIES

Post-Tensioning for Two-WayFlat Plate Construction

By Amy Reineke Trygestad, P.E.

October 2005

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The post-tensioning systemThe most common post-tensioning system for two-way

slab building construction uses mono-strand unbondedtendons. In this type of construction, the prestressing steel iscomposed generally of high-strength, single-wire steel,wrapped with another six wires to form a seven-wire strand.

The common strand has a specified tensile strength, fpu, of 270kips per square inch (ksi), a nominal diameter of 1/2 inch, andan area of steel, Aps, equaling 0.153 square inch (Figure 1). Bydesign, unbonded tendons have a continuous plastic sheath-ing to prevent the strand from bonding with the concretealong its length. This sheathing serves as the bond breaker;provides protection during handling, shipping, and construc-tion; and limits intrusion of corrosive elements. Corrosion-inhibiting grease coats the strands to reduce friction betweenthe strand and the sheathing during stressing.

The force in a stressed tendon is transferred to the concretevia serrated wedges that lock into anchor plates provided atits ends. Anchors are classified as either live (stressing) ends ordead ends. Dead end anchors are embedded into theconcrete and will not be stressed. These anchors are mountedto the tendon at the fabrication plant. Live end anchors aremounted and stressed in the field. Each tendon is stressedindividually and has its own anchor plate (thus, mono-strand)with approximate dimensions of 2-1/4 inches by 5-1/4inches. This small, ductile iron casting transfers 33 kips offorce for a seven-wire, 1/2-inch-diameter, 270-ksi tendon in aconcentrated area. Since this involves high local stresses, it isessential to place the anchors accurately, consolidate thesurrounding concrete, limit or eliminate penetrations in theimmediate vicinity, and sufficiently reinforce the anchoragezone to preserve its long-term integrity.

Analysis Computers have increased the speed of post-tensioning design significantly, but it is still important tounderstand the concepts and calculations to arrive at anaccurate output. When performing manual calculations, theEquivalent Frame Method (EFM) of the American ConcreteInstitutes Building Code Requirements for StructuralConcrete (ACI 318-05) within Section 13.7 (excludingsections 13.7.7.4-5) often is used for the structural analysis ofa post-tensioned, two-way, flat slab structure.

EFM models a 3-D slabsystem as a series of equiva-lent 2-D frames along thesupport lines, taken longitu-dinally and transverselythrough the structure. Eachequivalent frame then canbe analyzed individually asan isolated plane frame,consisting of a row ofcolumns or supports and

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Learning ObjectivesUpon reading this article and completing the quiz,

you should be able to understand the design processfor post-tensioned two-way slabs and recognizeconstructibility issues involved when using a post-tensioning system.

Professional Development Series SponsorPortland Cement Association

Every major metropolitan area is getting a facelift. Old buildings are beingrenovated and converted, while new construction continues to add tothe skyline. Downtown living is making its resurgence, and with thisbooming residential construction, two-way post-tensioned flat plates are the structural system of choice.

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Figure 1: Tendon showinganchor, strand, and sheathing

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the corresponding tributary slab width, bounded laterally bythe centerlines of the adjacent slab panels (Figure 2). Theanalysis and design of post-tensioned, two-way slabs incorpo-rate the full tributary slab width without the distribution offorces and reinforcement between column strips and middlestrips, synonymous with mild reinforced two-way slabdesigns. This allowance eases the structural engineers designprocess and ultimately simplifies construction.

Preliminary sizing Before design can begin on thestructure, there needs to be a starting point for the slab thick-ness. For common occupancy structures with live load todead load (LL/DL) ratios less than 1.0, a preliminary slabthickness can be estimated using a longest span to thicknessratio, L/h, of 45 for floors and 48 for roofs. For example, an8-inch-thick slab is typical for a 30-foot-long floor span (30feet x (12 inches/foot) / 45 = 8 inches).

Because of post-tensionings ability to balance loads andgreatly reduce service load deflections, there is a 25 percentto 35 percent reduction in slab thickness in post-tensionedstructures compared with mild reinforced structures.Therefore, in addition to the ability to span further, thereduced structural depth economizes material quantities forthe slabs and consequently the columns and foundations.

Design for prestressing The amount of prestressing in a slab system is guided by

parameters and requirements given in ACI 318 as well asnumerous other references, but the engineer has flexibility inadjusting the design for optimization of an individual project.Tendons for building construction usually are placed with aparabolic vertical profile to counteract a portion of the grav-

ity loads on the structure (Figure 3). Thisundulating profile places the center of grav-ity, CGS, of the tendon force, P, eccentric tothe neutral axis of the concrete section creatingthe primary moment, P x e. The eccentricity, e, isthe distance from the tendon CGS to the sections neutral axisat any examined cross section.

The high and low points are governed by several parame-ters. The ends of the tendons usually are located at thesections neutral axis (mid-height for a slab), so as to notinduce additional moment at the anchors. In buildingconstruction, minimum cover requirements per ACI 318 aresufficient for slabs not exposed to a corrosive environment.Fire protection often governs the minimum concrete cover ofthese structures. Fire resistance issues are addressed in modelbuilding codes, assigned at the local level for a given struc-ture, and should be evaluated during the preliminary design.As it pertains to prestressed concrete two-way slabs, fire resist-ance requirements are dependent on the restrained versusunrestrained conditions. For most applications, the interiorspans in the direction of frame design are consideredrestrained. That is, they are restrained against moving duringa fire loading. However, the end spans for a flat slab systemare considered unrestrained in the direction of the tendondesign. The fire resistance provisions do not match the mini-mum cover requirements per ACI 318 for reinforcementprotection, so it is necessary to reference the governing build-ing code (most likely Section 720 of the International CodeCouncils 2003 International Building Code) for settingconcrete cover parameters of the prestressed tendons. Typicaltwo-hour bottom covers to the tendons for slabs are 3/4 inchfor restrained, interior spans and 1-1/2 inches for unre-strained, exterior spans.

When the design is performed manually, the post-tension-ing force typically is selected to balance a specified percent-age of the floor self weight. Superimposed dead loads suchas partitions, flooring, mechanical equipment, and live loadsare not included, since they are not present at the time ofstressing. Common load-balancing percentages are in the65-percent to 80-percent range and should be kept relativelyconsistent between spans. Codes do not prescribe limita-tions for these percentages, but engineers still need todesign to appropriate balancing loads to limit slab deflec-tions and cracking.

The load-balancing effects reduce the amount of flexuralstresses for ultimate requirements, helping economizemember sizes and materials. Another advantage is the signif-icantly reduced deflections. With a percentage of the dead

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Post-Tensioning for Two-Way Flat Plate Construction

Figure 2: Tributary slab widths for equivalent frames (Aalami, B.and Bommer, A., Design Fundamentals of Post-Tensioned ConcreteFloors, Post-Tensioning Institute, Phoenix, AZ, 1999)

Figure 3: Tendon profile of a continuous post-tensioned beam.

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load being balanced by an upward unif