Comparison of One- and Two-Way Slab Minimum Thickness Provisions in Building Codes and Standards

Transcription

1 ACI STRUCTURAL JOURNAL Tite no. 107-S15 TECHNICAL PAPER Comparison of One- and Two-Way Sab Minimum Thickness Provisions in Buiding Codes and Standards by Young Hak Lee and Andrew Scanon Minimum thickness provisions for one- and two-way sabs provide a we-estabished approach for defection contro. Various nationa design codes and specifications have approached these provisions from different perspectives. Concerns have been raised about the range of the vaidity of current ACI Code provisions. This paper compares the ACI Code provisions with severa nationa codes and an equation proposed by the authors to incorporate the main design variabes affecting defection contro. Based on the resuts of the comparison, a recommendation is made to adopt the proposed equation, retaining the current vaues as upper imits. Keywords: defection; minimum thickness; reinforced concrete; serviceabiity. INTRODUCTION The ACI Code (ACI Committee ) provides minimum thickness vaues for one- and two-way sabs, under prescribed conditions, as a function of span ength, boundary conditions, and stee yied strength as a basis for defection contro. These provisions have remained essentiay unchanged since 1971 and are attractive due to their simpicity. A number of authors have raised questions about the vaidity of the current provisions under certain design conditions (Grossman 1981; Rangan 1982; Gibert 1985; Hwang and Chang 1996; Scanon and Choi 1999; Scanon et a. 2001; Bondy 2005). To address these questions, the authors proposed a unified equation that coud be appied to one- and two-way sabs as we as beams (Scanon and Lee 2006). Buiding codes and standards in other parts of the word aso provide minimum thickness or span-depth criteria for defection contro. The objective of this paper is to compare the current ACI provisions with the authors proposed equation and provisions currenty used in other codes and standards. The provisions seected for comparison are those incorporated in the British Standard for Design of Concrete Structures (British Standards Institution 1997), Eurocode 2: Design of Concrete Structures (British Standards Institution 2004), and the Austraian Standard for Concrete Structures (AS Committee BD ). Simiarities and differences among the various provisions are identified and recommendations for changes to the ACI Code are presented. The scope of this paper is restricted to one- and two-way sab systems covered by provisions of the ACI Code. Fat pates with sma shear caps that do not quaify as drop panes according to ACI coud be considered as fat pates with an appropriate definition of cear span using Section of ACI A separate study is being conducted to compare code provisions for defection contro of beams. RESEARCH SIGNIFICANCE Minimum thickness provisions in ACI have remained unchanged since This paper presents a review of the current provisions, incuding comparisons with severa nationa codes, and provides recommendations for changes to ACI provisions for one- and two-way nonprestressed construction. MINIMUM THICKNESS PROVISIONS Minimum thickness provisions are attractive as a means of defection contro due to their simpicity. In this paper, four different codes, incuding ACI , BS :1997, Eurocode 2, and Austraian Standard AS and the proposed approach of Scanon and Lee (2006) are compared for one- and two-way sabs. The seected codes have been used for many construction projects, not ony for their homeands but aso in other countries incuding those in Africa, Asia, and South America. ACI 318 provisions are based on member depth, whereas other codes are based on reinforcement effective depth. To aow for comparison of the various methods considered, 1 in. (25.4 mm) was added to the effective depth for cases where minimum thickness was based on effective depth. Comparisons were thus based on tota member depth. A brief description of the various code provisions is provided as foows with reference to the summary provided in Tabe 1. ACI Buiding Code (ACI ) ACI provides minimum thickness provisions as a fraction of span ength for both one- and two-way sabs, as shown in Tabe 1. The minimum thickness vaues are independent of appied oad incuding ive and dead oads, and no imits are specified on the appicabe range of span engths. Modification factors are provided for stee yied strength and ightweight concrete. British Standard Code (BS EN :1997) For the minimum thickness requirements, BS EN :1997 provides basic span-to-effective depth ratios that vary according to support conditions, incuding simpy supported, continuous, and cantiever. In addition to the basic span-toeffective depth ratio, a modification factor is provided for tension reinforcement determined by tensie strength of reinforcements and design utimate moment at the center of the member (for cantiever, at the support). A modification factor for compression reinforcement is aso used. Additionay, BS EN :1997 specifies modification factors for spans ACI Structura Journa, V. 107, No. 2, March-Apri MS No. S R1 received Apri 17, 2009, and reviewed under Institute pubication poicies. Copyright 2010, American Concrete Institute. A rights reserved, incuding the making of copies uness permission is obtained from the copyright proprietors. Pertinent discussion incuding author s cosure, if any, wi be pubished in the January-February 2011 ACI Structura Journa if the discussion is received by September 1, ACI Structura Journa/March-Apri

2 ACI member Young Hak Lee is an Assistant Professor in the Department of Architectura Engineering at Kyung Hee University, Yongin, Korea. He is a member of ACI Committee 435, Defection of Concrete Buiding Structures. His research interests incude the serviceabiity of reinforced and prestressed concrete members, and deveoping anaytica modes of concrete structures. Andrew Scanon, FACI, is a Professor in the Department of Civi and Environmenta Engineering at the Pennsyvania State University, University Park, PA. He is Chair of ACI Committee 435, Defection of Concrete Buiding Structures, and a member of ACI Committees 224, Cracking; 342, Evauation of Concrete Bridges and Bridge Eements; and 348, Structura Safety. greater than 32.8 ft (10 m) and for fat pates, as indicated in Tabe 1. Eurocode 2 (BS EN :2004) Minimum thickness in the Eurocode 2 provisions is based on a reinforcement ratio depending on whether the actua reinforcement ratio is arger than or smaer than a given reference reinforcement ratio. Because the reinforcement ratio cannot be determined unti the member depth is estabished, an initia estimate must be made of the reinforcement ratio. If the span ength exceeds 23.0 ft (7 m), the depth is mutipied by 23.0/span ength (7/span ength) to account for an increased sef-weight of the member as span ength increases. For fat pates, the depth is mutipied by 27.9/span ength (8.5/span ength). The minimum thickness requirement of Eurocode 2 can be appied to both beams and sabs and depends on the reinforcement ratio cacuated from moment at the center of the member and compressive strength of the concrete. The difference between one- and two-way construction, however, is not we-defined in the appication of the minimum thickness equations. Austraian Standard (AS ) The current Austraian Standard, AS , provides a span-to-effective depth equation as isted in Tabe 1, taking into account the effects of cracking, ong-term effects, and oad conditions. The equation is simiar in form to the equation proposed by Scanon and Choi (1999) which, in turn, is based on a simpification of the form originay proposed by Rangan (1982). Unified equation proposed by Scanon and Lee (2006) Scanon and Lee (2006) proposed a generaized minimum thickness equation for one- and two-way nonprestressed construction in terms of span-depth ratios considering Tabe 1 Minimum thickness provisions for sabs ACI Simpy supported Minimum thickness of nonprestressed one-way sabs uness defections are cacuated One end continuous Both ends continuous Cantiever /20 /24 /28 /10 Minimum thickness of two-way sabs without interior beams Without drop panes f y,psi Exterior panes Interior panes Without edge With edge beams beams 60,000 n /30 n /33 n /33 is span ength of one-way sab n is ength of cear span measured face-to-face of supports For sabs with beams spanning between supports on a sides α fm 0.2 Sabs without drop panes - 5 in. Sabs with drop panes - 4 in. 0.2 α fm 2 α fm > 2 f y n , 000 h = β( α fm 0.2) Not ess than 5 in. f y n , 000 h = β Not ess than 3.5 in. AS α fm is average vaue of α f for a beams on edges of pane α f is ratio of fexura stiffness of beam section to fexura stiffness of width of sab L ef ( Δ L d k 3 k ef )E = c F d.ef L ef is effective span, taken as ess of ( n + d) and ; d is effective depth of cross section; Δ / L ef is defection imit; F d.ef is effective design oad, per unit area; k 3 = 1.0 for one-way sab, rectanguar sabs supported on four sides = 0.95 for two-way fat sab without drop panes; k 4 is defection constant which may be taken as: (a) for simpy supported sabs, 1.6; or (b) for continuous sabs, where in adjoining spans ratio of onger span to shorter span does not exceed 1.2 where no end span is onger than an interior span-(i) 2.0 in an end span; or (ii) 2.4 in interior spans; and (c) for edge-supported sabs k 4 varies from 1.7 to 2.0 (Tabe in AS ). 158 ACI Structura Journa/March-Apri 2010

3 Tabe 1 Minimum thickness provisions for sabs (cont.) Basic span/effective depth ratios for rectanguar section Support conditions Rectanguar section Modification factor for tension reinforcement ( 477 f 0.55 s ) = f s = 2 --f y M bd 2 BS Eurocode 2 Scanon and Lee s proposa If ρ ρ ο If ρ > ρ ο Cantiever Simpy supported Continuous --- n β Δ inc = h ρ -- K f ck ---- o + 32 f ρ ck ---- o = + d ρ ρ d -- = K f ρ o ck ρ ρ aow --- n β Δ inc = h 2400k DP E c ( b 12) κk AR k ss ( λw s + W L ( add) ) aow f ck ---- ρ k DP E c b κk AR k ss ( λw s + W L ( add) ) M is design utimate moment at center of span or, for cantiever, at support; f s is estimated design service stress in tension reinforcement; f y is yied strength of reinforcement; b is effective width of rectanguar beam; d is effective depth; For spans exceeding 10 m, Tabe 3.9 shoud be mutipied by 10/span, except for cantievers where the design shoud be justified by cacuation. For fat pate, span/effective depth ratio shoud be mutipied by 0.9. ρ o (U.S. Customary Units) 1 3 (SI Units) K is factor to take into account different structura systems: (a) simpy supported 1.0; (b) one end continuous 1.3; and (c) both end continuous 1.5; 10 f 3 ck ρ o is reference reinforcement ratio, = ; ρ is required tension reinforcement ratio at midspan to resist moment due to design oads (at support for cantievers); ρ is required compression reinforcement ratio at midspan to resist moment due to design oads (at support for cantievers); f ck is specified compressive strength of concrete, in MPa units; and is span ength. W s is sustained oad (psf [sabs]; pf [beams]); (Pa [sabs]; N/m [beams]); W L(add) is additiona ive oad (psf [sabs]; pf [beams]); (Pa[sabs]; N/m [beams]); β = 1, except β is ong span/short span 2.0 for edge-supported sabs; κ is defection coefficient depending on support condition: equas 5 for simpy supported, 1.4 for both ends continuous, 2 for one end continuous, and 48 for fixed end cantiever; k DP = 1, except k DP = 1.35 for sab with drop panes; k SS = 1, except k SS = 1.35 for coumn supported two-way sab systems; k AR = 1, except k AR = β for edge-supported sabs; b = 12 in. (1000 mm for SI) for one- and two-way sabs = beam width (= web width, b w for T-beams) (in. for U.S. Customary Units and mm for SI Units); (Δ inc ) aow is required incrementa defection imit; and λ is ong-time mutipier for sustained oads (ACI 318, Section ). appied oads, ong-term mutipiers, effects of cracking, and target defection-to-span imitations. The equation is based on using an effective moment of inertia, I e, equa to one-haf of the gross moment of inertia, I g. This approximation aows the thickness to be seected without knowing the reinforcement ratio, athough an initia estimate of the depth is required to compute dead oad due to sef-weight. The unified equation was deveoped from the equation suggested by Scanon and Choi (1999) for one-way sabs based on a simpified form of the approach proposed by Rangan (1982) for one-way construction and extended to two-way construction by Gibert (1985). PARAMETRIC STUDY A parametric study was performed to evauate the effects of design variabes on the minimum thickness and to compare vaues cacuated from the various design codes and the Scanon and Lee (2006) unified equation. The parameters considered herein incude the foowing. Span ength The foowing span engths were used to represent ranges typicay encountered in practice: 10, 15, 20, 25, 30, 35, and 40 ft (3.05, 4.57, 6.10, 7.62, 9.14, 10.67, and m) for one-way sabs; 10, 15, 20, 25, and 30 ft (3.05, 4.57, 6.10, 7.62, and 9.14 m) for fat pates (square); 10, 15, and 20 ft (3.05, 4.57, and 6.10 m) for edge supported two-way sabs; and Live oad Live oads are based on ASCE/SEI 7 (2005) provisions for: a) office occupancy pus aowance for partitions: 70 psf (3.4 kpa); (b) for exampe, assemby and restaurant: 100 psf (4.87 kpa); and (c) storage (ight to heavy): 200 psf (9.74 kpa). The foowing design parameters were hed constant: Concrete compressive strength: 4000 psi (27.58 MPa); Yied strength of reinforcement: 60,000 psi ( MPa); Superimposed dead oad: 15 psf (0.73 kpa); Sustained ive oad: (a) 20 psf (0.97 kpa) for ive oad equa to 70 psf (3.4 kpa) and 100 psf (4.87 kpa); and (b) 50 psf (2.44 kpa) for ive oad equa to 200 psf (9.74 kpa); and Long-time mutipier λ: 2. Target aowabe defections for AS and the unified equation were taken as /240 and /480. A of the provisions considered except ACI 318 consider variation of ive oad in estabishing minimum thickness. Design parameters considered in the various codes are summarized in Tabe 2. Resuts of the parametric study are presented in the foowing for one-way sabs, fat pates, and edge-supported sabs. Defection imits are those corresponding to defections occurring after instaation of nonstructura eements. ACI Structura Journa/March-Apri

4 Tabe 2 Design parameters considered in minimum thickness provisions Design parameters considered Design parameters ACI BS Eurocode 2 AS Scanon and Lee s proposa Boundary condition Yes Yes Yes Yes Yes Span ength Yes Yes Yes Yes Yes Live oad No Yes Yes Yes Yes Superimposed dead oad No No No No Yes Aowabe defection imit No No No Yes Yes Fig. 1 Span-depth ratio as function of span ength one-way sabs, /240: (a) simpy supported: ive oad = 70 psf (3.4 kpa); (b) one end continuous: ive oad = 70 psf (3.4 kpa); and (c) both ends continuous: ive oad = 70 psf (3.4 kpa). Fig. 2 Span-depth ratio as function of span ength one-way sabs, /480: (a) simpy supported: ive oad = 70 psf (3.4 kpa); (b) one end continuous: ive oad = 70 psf (3.4 kpa); and (c) both ends continuous: ive oad = 70 psf (3.4 kpa). One-way sabs Figures 1(a) to (c) show span-depth ratios versus span ength for one-way sabs with various end conditions for a constant ive oad of 70 psf (3.4 kpa) and a defection imit of /240. For this case, ACI 318 vaues are consistenty ower than a others for spans up to approximatey 40 ft (12.19 m). A provisions, except ACI 318, show a genera trend of decreasing span-depth ratio with increasing span ength. Figures 2(a) to (c) show the corresponding resuts for a defection imit of /480. It shoud be noted that the minimum thickness vaues given in ACI 318 are intended for use with sabs not supporting or attached to nonstructura eements ikey to be damaged by arge defections, that is, the /240 imit. These resuts suggest, however, that ACI 318 vaues shoud be satisfactory in most cases to satisfy the /480 imit for ive oad up to 70 psf (3.4 kpa), except for the simpy supported case where the ACI 318 vaues are conservative compared with other provisions up to a span of approximatey 20 ft (6.10 m). Effects of varying ive oad according to the provisions considered are shown in Fig. 3 for a defection imit of / ACI Structura Journa/March-Apri 2010

5 Fig. 3 Span-depth ratio as function of span ength and variabe ive oads one-way sabs: (a) BS : simpy supported, /480; (b) Eurocode 2: simpy supported, /480; (c) AS : simpy supported, /480; and (d) unified equation proposed by Scanon and Lee (2006): simpy supported, /480. Vaues obtained using ACI 318, Tabe 9.5(a), are used as a reference, athough stricty speaking, the ACI 318 vaues are not appicabe to the defection imit of /480. The simpy supported case is seected as the basis for comparison. In a cases except ACI 318, the cacuated span-depth ratio decreases as ive oad increases. The BS :1997 spandepth ratios are ess conservative than ACI 318 up to a span of approximatey 40 ft (12.19 m). Eurocode 2 provides spandepth ratios that are higher than the ACI 318 vaues for spans greater than 35 ft (10.67 m) and ive oad ess than 100 psf (4.87 kpa). For the 200 psf (9.74 kpa) ive oad case, Eurocode 2 provides ower span-depth ratio than ACI 318 for spans greater than approximatey 22 ft (6.71 m). AS and Scanon and Lee (2006) show simiar trends providing span-depth ratios that are more conservative than the ACI 318 vaues over a wider range of span engths than BS :1997 and Eurocode 2. Fat pates Figure 4 shows the span-depth ratio potted against span ength for an interior pane of a fat pate for /240 and /480 defection imits, and a ive oad of 70 psf (3.4 kpa). Figure 4(a) shows that the ACI Code vaues are conservative compared to the other provisions for the /240 defection imit. For the /480 case, however, the AS and Scanon and Lee (2006) vaues are more conservative for spans greater than approximatey 15 ft (4.57 m). Figure 5 shows the effect of increasing ive oad for the /480 imit. In a cases for heavy ive oads (200 psf [9.74 kpa]), the ACI vaues are unconservative compared with the other provisions. Edge-supported two-way sabs Figures 6 and 7 show the comparison between ACI 318 and the other provisions for two-way edge-supported sabs of varying aspect ratios and ive oads. In genera, the ACI 318 vaues are seen to be conservative compared to the other provisions whie there is a wide variation in the vaues obtained with the various provisions. Fig. 4 Span-depth ratio as function of span ength fat pates: (a) ive oad = 70 psf (3.4 kpa), /240; and (b) ive oad = 70 psf (3.4 kpa), /480. DISCUSSION OF RESULTS Resuts of the parametric study indicate that ACI minimum thickness vaues for one-way sabs and edgesupported two-way sabs are generay conservative compared with the other provisions considered for span engths up to approximatey 40 ft (12.19 m) for both the /240 and /480 defection imits. It shoud be noted that, stricty speaking, the ACI minimum thickness vaues for one-way sabs shoud ony be used for sabs not supporting ACI Structura Journa/March-Apri

6 Fig. 5 Span-depth ratio as function of span ength and variabe ive oads fat pates: (a) BS , /480; (b) Eurocode 2, /480; (c) AS , /480; and (d) unified equation proposed by Scanon and Lee (2006), /480. The situation with respect to fat pates is somewhat different. For the /240 imit, the ACI minimum thickness vaues appear to be adequate for the span range considered and a specified ive oad of 70 psf (3.4 kpa). For the /480 case, however, the AS and Scanon and Lee (2006) provisions suggest that the current ACI 318 vaues are generay unconservative for the span and ive oad range considered. This is particuary the case for onger spans and higher oad eves. These resuts suggest that the current ACI minimum thickness vaues need to be reevauated in terms of their appicabiity to sabs supporting non-structura eements ikey to be damaged by arge defections. Fig. 6 Span-depth ratio as function of span ength: edgesupported sabs (short span = 15 ft [4.57 m] and α fm = 2 for ACI requirement): (a) ive oad = 70 psf (3.4 kpa), /240; and (b) ive oad = 70 psf (3.4 kpa), /480. or attached to non-structura eements ikey to be damaged by arge defections. This is consistent with the generay acceptabe performance over the years of one-way sabs and edge-supported two-way sabs. For heavy ive oads and heavy superimposed dead oads (greater than 100 psf [4.87 kpa]), a more detaied defection evauation is recommended. CONCLUSIONS AND RECOMMENDATIONS Various design provisions incuding ACI , BS :1997, Eurocode 2, and AS and the unified equation proposed by Scanon and Lee (2006) are compared in terms of minimum thickness for one- and two-way sabs. The effects of design parameters such as support condition, span ength, and appied oad are evauated. The resuts indicate that ACI 318 provisions need to be revised to cover the range of design parameters that are prevaent in current practice. The resuts of the parametric study suggest that whie these minimum thickness vaues are easy to appy, imitations need to be paced on the appicabiity of current ACI vaues. In particuar, the ACI vaues for fat pates (and fat sabs) seem to be adequate for the /240 imit for typica spans and oading but may be inadequate in many cases to satisfy the /480 imit. It is recommended that the Scanon/Lee equation for minimum thickness of one-way sabs, fat pates, and fat sabs be adopted by ACI 318 but not ess than vaues given by the current imits. The advantage of the proposed equation is that it is reativey easy to appy and covers a wider range of design conditions than seems to have been anticipated when the current provision were introduced. Given the approximations invoved in the proposed equation and many years of experience with the current provisions, however, it is considered prudent to retain the current minimum thickness vaues when the proposed equation produces a ower thickness vaue than the current 162 ACI Structura Journa/March-Apri 2010

7 Fig. 7 Span-depth ratio as function of span ength and variabe ive oads: edge-supported sabs (short span = 15 ft [4.57 m] and α fm = 2 for ACI requirement): (a) BS , /480; (b) Eurocode 2 (BS EN 2004), /480; (c) AS , /480; and (d) unified equation proposed by Scanon and Lee (2006), /480. provisions. The proposed minimum thickness equation shoud not be appied when sabs are over-oaded before the specified 28-day concrete strength has been reached uness appropriate adjustments to the equation have been made to account for such eary age oading. ACKNOWLEDGMENTS This work was supported by a grant from the Kyung Hee University in 2009 (KHU ). REFERENCES ACI Committee 318, 2008, Buiding Code Requirements for Structura Concrete (ACI ) and Commentary, American Concrete Institute, Farmington His, MI, 473 pp. AS , 2001, Austraian Standard for Concrete Structures, Standards Austraia, Sydney, Austraia, 175 pp. ASCE/SEI 7, 2005, Minimum Design Loads for Buidings and Other Structures, American Society of Civi Engineers, 388 pp. Bondy, K. B., 2005, ACI Code Defection Requirements Time for a Change? Serviceabiity of Concrete: A Symposium Honoring Dr. Edward G. Nawy, SP-255, F. Barth, ed., American Concrete Institute, Farmington His, MI, pp BS EN :1997, 1997, British Standard Code: Design of Concrete Structures, British Standards Institution, London, UK, 159 pp. BS EN :2004, 2004, Eurocode 2: Design of Concrete Structures. Genera Rues and Rues for Buidings, British Standards Institution, London, UK, 230 pp. Gibert, R. I., 1985, Defection Contro of Sabs Using Aowabe Spanto-Depth Ratios, ACI Structura Journa, V. 82, No. 1, Jan.-Feb., pp Grossman, J. S., 1981, Simpified Computations for Effective Moment of Inertia, I e and Minimum Thickness to Avoid Defection Cacuations, ACI Structura Journa, V. 78, No. 6, Nov.-Dec., pp Hwang, S.-J., and Chang, K.-Y., 1996, Defection Contro of Two-Way Reinforced Concrete Sabs, Journa of Structura Engineering, ASCE, V. 122, No. 2, pp Rangan, B. V., 1982, Contro of Beam Defections by Aowabe Spanto-Depth Ratios, ACI Structura Journa, V. 79, No. 5, Sept.-Oct., pp Scanon, A.; Cagey Orsak, D. R.; and Buettner, D. R., 2001, ACI 318 Code Requirements for Defection Contro: A Critica Review, Code Provisions for Defection Contro in Concrete Structures, SP-203, E. G. Nawy and A. Scanon, eds., American Concrete Institute, Farmington His, MI, pp Scanon, A., and Choi, B.-S., 1999, Evauation of ACI 318 Minimum Thickness Requirements for One-Way Sabs, ACI Structura Journa, V. 96, No. 4, Juy-Aug., pp Scanon, A., and Lee, Y. H., 2006, Unified Span-to-Depth Ratio Equation for Nonprestressed Concrete Beams and Sabs, ACI Structura Journa, V. 103, No. 1, Jan.-Feb., pp ACI Structura Journa/March-Apri