Post-Tensioned Two-Way Slab

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Angel Cain
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1 The Medial Oie Building Malvern, PA 13 Post-Tensioned Two-Way Slab Introdution The Filigree beam system reates a thin lightweight loor system that leaves plenty o open plenum spae or mehanial and eletrial equipment. However, the beams divide the plenum spae into hannels, reduing the overall utility. In addition, the system is designed by Filigree Inorporated, making it a blak box or the engineer o reord. A preliminary investigation showed that a onventional two-way slab system an provide slabs that are just as thin, and bring the design bak into the hands o the engineer o reord. It may be possible to ahieve even thinner slabs by introduing pre-stressing or post-tensioning to the system. Solution Overview Proprietary systems have osts and beneits in addition to those assumed by onventional systems. In this ase a onventional two-way slab provides a nearly idential produt to the proprietary Filigree system. Considering that the two-way slab does not have the additional osts o using a proprietary system, it appears to provide a better value. This value an be improved by using prestressing or post-tensioning to redue the overall slab depth, thus inreasing the usable spae. Thereore, a pre-stressed two-way slab may be a very eetive alternative to the proprietary Filigree beam system. In addition to reating more usable spae, the two-way slab system will also eliminate the hanneling o the plenum and allow the ree plaement o lateral resisting systems. Design Criteria The ollowing questions must be addressed regarding the eetiveness o the two-way slab: Can the two-way slab meet ode? Can the two-way slab be onstruted at no greater ost? Will the two-way slab introdue more problems than it orrets? The ode governing the design o the two-way slab will be IBC The ost analysis will be based on data provided by RS Means. The last question will be addressed by omparing the beneits and disadvantages o the two-way slab to the Filigree beam system. For the two-way slab to be onsidered, the irst question must be answered in the airmative. The remaining two questions should also be answered in the airmative i the two-way slab is optimal. I the two-way slab is not optimal, then the relative suess and ailure ompared to the Filigree system will determine the inal deision on whether or not the two-way slab is a reasonable alternative.

2 The Medial Oie Building Malvern, PA 14 Load Analysis When onsidering two-way slabs in a post-tensioned system, it is important to perorm an advaned analysis o the loads and their eets at dierent loations in the building. For the Medial Oie Building, there were three loations onsidered to determine the worst ase loading or a two-way slab system; the longest interior span, an exterior span with edge beams, and an exterior span without edge beams (Figure 2-1). Eah o these areas has a dierent set o design riteria based on ode, and has to be evaluated to ensure the saety o the slab at all loations. In order to simpliy the onstrution o the design, modiiation o the design to respond speiially to eah support was orgone in avor o evaluating only the maximum ondition in eah o the three slab areas and applying the resultant design to all similar loations. Figure 2-1 Typial loor plan highlighting the three areas o the slab evaluated or design In order to determine the requisite loads or the slab an initial guess at the slab thikness was taken as 1/36 th the lear span o the slab, whih is The resulting slab depth o 9 leads to a dead load or normal wiehgt onrete o ps, an additional 15 ps was added or mehanial eletrial and plumbing (MEP) equipment, and an additional 10 ps was added or the ombined raised loor and hung eiling weights. The live load or a typial oie building is 80 ps aording to ASCE 7-02, but this value was inreased to 100 ps to aount or additional loads related to open planning, suh as movable partitions and orridors. The evaluation o the three loads was perormed using ADOSS, the ull results an be ound in Appendix II. A summary o the ritial results or eah setion appears in Table 2-1.

3 The Medial Oie Building Malvern, PA 15 M beam Slab M ol M mid v (t-k) (t-k) (t-k) (psi) Edge with beams 45.3 (-) 37.6 (-) (-) (+) 27.4 (+) (+) Edge without beams (-) 77.8 (-) (+) 91.0 (+) Interior (-) (-) (+) (+) Table 2-1 Critial Shear and Moment as alulated by ADOSS ADOSS does not over wide beam shear analysis, but a brie investigation reveals that the per oot strength is roughly 9.5 kips. Based on the aorementioned loads, the shear on a per oot basis is only 4.5 kips, so wide beam shear does not ontrol. Shearhead Investigation The ADOSS analysis showed that the majority o ross-setions did not meet the neessary requirements or shear strength. The ACI ode states this strength as: ' φ v n = 0.75* 4 (2-1) For 5000 psi onrete, this value is psi. The ode also states that the strength an be taken as: φ v = (2-2) n ' 0.75* 7 i shearheads are used. The shear strength developed on the new shear plane reated by the shearheads must still meet the irst strength requirement. The new apaity or shear in 5000 psi onrete is thus psi at the standard shear plane, and psi at the extended shear plane. The size o the shearheads required to generate the neessary seondary shear plane were determined using a program written in EES (Appendix III). The results o this program show that the exterior shearheads must extend 4-3 rom the enter o the olumns, and that the interior shearheads must extend 3-9 rom the enter o the olumns (Figure 2-2). Figure 2-2 Shearhead details or interior (let) and exterior (right) olumns

4 The Medial Oie Building Malvern, PA 16 Post-Tension Investigation Besides shear strength it is also important to onsider the moment apaity o eah o the setions. An analysis o the bulk ross setion o eah segment o slab is summarized in Table 2-2. Segment A s (in 2 ) Bars Interior Column Top # 4 s Strip Bot # 4 s Interior Middle Top # 4 s Strip Bot # 4 s Exterior Beam Top # 4 s Column Strip Bot # 4 s Exterior Beam Top # 4 s Middle Strip Bot # 4 s Exterior Beams Top # 8 s Bot # 9 s Exterior Top # 4 s Column Strip Bot # 4 s Exterior Middle Top # 4 s Strip Bot # 4 s Table 2-2 Analysis o slab setions Spaing (in) From this analysis, it an be seen that the setions that will most beneit rom post-tensioning are the olumn strips on the exterior suraes without beams and in the interior. Tensioned reinorement must provide the same ore as the untensioned reinorement or the design to be valid. The ode limits the pressure allowed in tension ables in two ways: γ p pu d ( ) ps = pu 1 ρ p w w' ' (2-3) β d p ' ps = se ksi (2-4) 300ρ Using these limitations and hoosing ables with an ultimate strength o 275 ksi and a yield strength o 240 ksi, an iterative design proess was used to ind the required area o able and their posttensioning ore. This proess ound that or the interior olumns, 4 in 2 o able tensioned by 920 kips was adequate, and or exterior olumns, 4 in 2 o able tensioned by 900 kips was adequate. Both o these designs are detailed in Figure 2-3. p

5 The Medial Oie Building Malvern, PA 17 Figure 2-3 Details o the two-way slab: Interior (let), Exterior (right) Deletion Analysis The inal onsideration in the design o the two-way slabs is deletion. Aording to ADOSS, the interior spans due not meet the ode requirements to neglet deletion. Thereore a deletion analysis was perormed on the interior slab setion to determine whether the slab meets the servieability requirements. The tension in the ables generated an initial amber o 0.95 upward. This amber leads to an immediate and long-term deletion o 0.11 downward, whih is less than the limits o 0.93 and 0.70 or immediate and long-term deletion respetively. Conlusions The two-way slab meets all the design and servieability requirements or ode. Thereore, the system an be a reasonable alternative to the Filigree beam system. A diret ost omparison is not possible between the two systems beause o the proprietary nature o the Filigree system. However, omparing the ost o the post-tensioned two-way slab to a typial banded beam system (Table 2-3) should provide a reasonable omparison.

6 The Medial Oie Building Malvern, PA 18 Two-way Banded Slab Formwork $457,050 $457,050 Slab Reinoring (w/ shearheads) $161,020 $33,083 Slab Post-tensioning $165,000 $0 Slab Conrete and Plaement $839,237 $839,237 Beam Formwork $0 $173,765 Beam Reinoring $0 $63,000 Beam Conrete & Plaement $0 $275,229 TOTAL $1,622,307 $1,841,364 Table 2-3 Cost omparison o a two-way slab and a banded beam system The dierene in ost between the two systems is $219,000, whih is nearly the ost o the onrete in the beams. In airness to the Filigree system, less onrete is used than in ast-in-plae onstrution. Assuming that the Filigree beams use 30% less onrete, would result in a $334,000 savings. This makes the Filigree system more avorable by $115,000. However, atory osts, transportation osts, and other ees assoiated with the Filigree tehnology, inluding the harges o the ontrator or working with an unamiliar system may eat up these savings. Due to these speulative expenses, it is diiult to disern whih system is o better eonomi value. Fortunately, the eonomi value alone is not a deiding ator. Although the Filigree system provides a thin loor struture, it is still twie the overall depth o the two-way slab due to the beams. The diret onsequene o the deeper system is the loss o usable spae in the building. The indiret onsequene o the beams hanging down is that they divide the plenum spae o the building into strips, whih means the eilings must be hung deeper to allow enough learane or dutwork and wiring in areas diretly beneath the beams. Beause the twoway slab system is lat, there is no division o the plenum, and the hung eiling may be hung muh loser to the bottom o the slab, thus reovering even more usable spae. Despite an unertain ost advantage, the additional beneits o a two-way slab system make it an appealing alternative, partiularly beause they an be used to optimize the building or Underloor Air Distribution.

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