SIMPLE DESIGN METHOD FOR OPENING WALL WITH VARIOUS SUPPORT CONDITIONS

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1 SIMPLE DESIGN METHOD FOR OPENING WALL WITH VARIOUS SUPPORT CONDITIONS Jeng-Han Doh 1, Nhat Minh Ho 1, Griffith School of Engineering, Griffith University-Gold Coast Camps, Qeensland, Astralia ABSTRACT De to recent poplarity of tilt-p constrction and concrete cores in tall bildings, reinforced concrete (RC) alls are no considered jst as important strctral element as beams, slabs and colmns. The Astralian Concrete Standard, AS for the simplified design of axially loaded alls allos for increased capacity de to side restraints compared ith previos code of AS and crrent American Concrete Institte Code, ACI Nevertheless, all of these codes do not significantly accont for openings sch as doors or indos. In vie of the limitation, it is necessary to iden the scope of the methods and rectify the inadeqacies hich exist in these major national design codes. This paper presents shortcomings of the AS and also revies existing experimental tests by previos researches. It incldes all ith varios opening configrations and spport conditions sbjected to eccentric axial loading. Using the reslts obtained from previos experimental stdies, a simple design method for varios opening alls ith spport conditions has been derived. Comparisons are then made ith the other available empirical eqations to highlight its accracy, reliability and otstanding performance. Keyords: Wall, openings, axial, segment, PDM. 1. INTRODUCTION RC all panels have become as poplar today as the traditional strctral elements sch as beams, slabs and colmns. They are sed extensively for their strctral capacity particlarly in tilt-p constrction and core alls in tall bildings. RC alls ith eccentric axial loads can be designed sing simplified design method. The previos AS and crrent ACI are intended for load-bearing alls spported at top and bottom only. Extensive experimental researches on alls sbject to in-plane vertical loads ere condcted by Fragomeni (1995), Sanjayan and Mahesaran (1999), Doh and Fragomeni (005) in Astralia. These orks contribted to significant revision of the AS for providing extended rles for the se of simplified all design eqation for alls ith varios spport conditions, in addition to its applicability for higher concrete strengths. As a reslt of architectral reqirements and/or fnctional modifications of the strctres, provision of openings for doors and indos or paths for ventilation systems is navoidable. Several stdies have been ndertaken on this area by Saheb and Desayi (1990), Doh and Fragomeni (006) and introdced some formlae to estimate the load capacity of alls ith openings. More recently, 1

2 comprehensive stdies have been condcted by Lee (008) and Fragomeni et al. (01) on the behavior of opening alls focsing on the inflence of opening size, location and slenderness ratio. Nonetheless, there are still limited provisions for alls ith openings in the AS SIMPLIFIED WALL DESIGN METHOD Section 11 of the AS specifies a simplified eqation to calclate the axial load capacity of alls. The eqation applies to alls ith varios spport conditions as shon in Figre 1. A design formla proposed by Doh and Fragomeni (005) is capable of analyzing alls ith H e /t > 30. (a) OW (b) TW3 (c) TW4 Figre 1: Walls ith varios side restraints (Doh & Fragomeni, 010). For the simplified design method proposed by AS , the ltimate design axial strength per nit length (in N/mm) of a braced all in compression is given by the folloing formla: N = (t -1.e-e )0.6f (1) a c here t is the all thickness (mm), is the strength redction factor and 0.6, e is the load eccentricity (mm) hich has a minimm of 0.05t, f c (MPa) is concrete strength and e a =H e /(500t ). The effective height as specified in Clase 11.4, shall be taken as H e = kh in hich the factor k for one-ay action all are 1 and 0.75 for no restraint and fll lateral restraint at both ends, respectively. To-ay bckling ith three side lateral spport alls are k 1/ 1 H / 3L and for side lateral spport provided by floors and intersecting alls are k 1/(1 H /L ) here H L and k L / H here H > L in hich, H is the floor-to-floor nspported height and L is the horizontal length. The empirical formla proposed Doh & Fragomeni (005) to predict the axial strength of alls is:

3 0.7 N.0f (t 1.e e ) () c a here all variable ere defined earlier. ect that in the calclation of e a, the variable H e = H e in hich, 1 or 18/ 0.88 for H/t or < 7 simply spported top and bottom only and H/t β α/1 H/L or αl/h depending on aspect rations for alls ith for all sides restraint. is an eccentricity parameter and is eqal to α 1/(1 (e/t )) and α 1/(1 (e/t ) 18/ 0.88 for H/t < 7 and H/t > 7, respectively. H/t The AS only allos the effects of openings in all ith for all sides restraint as shon in Figre 1(c) (TW4), and it can be neglected if the total area of openings is less than 1/10 of the area of the all, and the height of any opening is less than 1/3 of the height of the all. In other cases, the area of all beteen opening and spport shall be designed as TW3, or the area beteen to openings shall be designed as spported on to sides (OW). 3. WALL DESIGN FORUMLAE FOR WALLS WITH OPENINGS Many researchers have investigated the behavior of reinforced concrete alls ith openings either in OW and TW4. Table 1 presents design formlae proposed by Saheb & Desayi (1990), Doh & Fragomeni (006) and Lee (008),here N o is the ltimate load for all ith openings; N is the ltimate load for solid all (N in Eqs (4a) & (4b), (5a) & (5b) is defined by Eq ()); A g is the gross cross sectional area of all in plane (mm ); f yv is the yield strength of steel (MPa); A sv is the area of vertical steel in all (mm ); χ is the opening geometry parameter; χ xy is the opening parameter defined by the opening size and location in both horizontal and vertical directions and the spacing beteen openings (if applicable); s x is the opening spacing parameter for alls ith to openings located side by side (mm); χ x and χ y is the opening parameter ith respect to the inflence of opening size and location in the horizontal and vertical direction respectively. Figre : Geometric parameters for all ith openings (Saheb and Desayi, 1990). 3

4 Figre identifies some of the symbols sed in those eqations here G 1 and G are the centres of gravity of all cross section ith and ithot opening, respectively; G 3 is the centre of gravity of the opening. Table 1: Wall ith openings design eqations Nmber of test f c (MPa) H/t H/L Saheb & Desayi (1990) For OW: N ( )N o Lt o A o o L o o A L Lt Lot here in hich A L t,a Lt, and H H H N 0.55 Agf c (fyv f c )A sv for.0 3t 10L L H H N 0.55 Agf c (fyv fc )A sv 1 for.0 3t L For TW4: N ( )N o L H H L N 0.67Agf c for and 60 10t L L t Lt (3a) (3b) Doh & Fragomeni (006) 1 35~51 30~40 1 For OW: For TW4: N ( )N o N ( )N o (4a) (4b) Lee (008) 47 47~93 30~40 1 For OW: For TW4: N N o xys N N o xys (5a) (5b) A s / A ox x x oy y A o ox x L Ay H Lt Aox x L xys and x here Aox Lot,Ax Lt and x (1 ) Ax L Lt Lot Ht A o oy oy Ht y H y here A oy Hot,Ay Ht and y Ay H Ht Hot Lt 4

5 4. PROPOSED DESIGN METHOD (PDM) The all panel ith opening shall be divided into several segments considered as OW and TW3 solid alls. The ltimate strength of OW alls is calclated based on Eq () hile the ltimate strength of TW3 alls is based on Eq (1). It is proposed that for the opening hose total area is not greater than 1.5% of the all ithot opening, the contribtion of all segments above and belo opening is taken into accont and considered as OW. Its length is sggested to be L o / One-ay Action Wall ith Opening For OW all panel ith opening, the all is divided into segments hich shall behave as OW solid alls (Figres 3a). 4.. To-ay Action Wall Spported on For Sides ith Opening For TW4 all panel ith opening, the all is divided into segments hich shall behave as TW3 solid alls (Figre 3b). OW OW TW3 TW3 H L1 Lo L L1 Lo L (a) OW (b) TW4 Figre 3: Wall segments for OW and TW4 alls ith opening. 5. COMPARATIVE STUDY To verify the proposed method, predicted ltimate loads based on PDM are compared to experimental tests by Saheb & Desayi (1990), Doh & Fragomeni (006) and Lee (008). Additionally, comparisons are made ith previosly available design eqations to sho its accracy, reliability and otstanding performance. The dimensions, material properties and ltimate failre loads of OW and TW4 alls are smmarized in Table. 5

6 Table : Dimensions, material properties and experimental failre loads of OW and TW4 alls ith opening Spport condition Panel Designation Size of opening Size of all panel (mm) (mm) H L t Ho Lo f c (MPa) failre load Saheb & Desayi (1990) Doh & Fragomeni (006) OW WWO WWO TW4 WWO-P WWO-5P OW OW TW4 TW O90W1C O95W1C OW O65W1W O65W1L Lee (008) O65D1C T50W1C T70W1C TW4 T65W1W T65W1U T65D1L Table 3 presents the comparison of predicted failre loads of all panels sing different design methods ith the experimental tests. The reslts indicated that the ratio of the crrent method (PDM) to the test reslts ith a mean of 0.94 and a standard deviation of 0.13 as in a good agreement ith the test reslts. Frthermore, PDM as a better prediction of the failre load compared to the Astralian Standard, hich had a mean of 1.10 and a standard deviation of 0.9, and Eqs (3a) & (3b), hich had a mean of 1.41 ith very high standard deviation of Althogh Eqs (4a) & (4b) had a better mean vale than PDM (0.96 compared to 0.94), the standard deviation as slightly high. In addition, PDM is obviosly mch simpler design tool as opposed to the complicated Eqs (5a) & (5b). The reslts revealed that PDM had the same standard deviation and less conservative than Eqs (5a) & (5b). 6

7 Table 3: Comparison of predicted failre loads of all panels sing different design methods ith the experimental tests Panel Designation AS * PDM Eq (3) Eq (4) Eq (5) AS * PDM Eq (3) Eq (4) Eq (5) WWO- N/A N/A WWO-5 N/A N/A WWO-P WWO-5P OW11 N/A N/A TW O90W1C1. N/A N/A O95W1C1. N/A N/A O65W1W1. N/A N/A O65W1L1. N/A N/A O65D1C1. N/A N/A T50W1C T70W1C T65W1W T65W1U T65D1L Mean Standard Deviation * AS CONCLUSION The design formla recommended in the Astralian Concrete Standard, AS does not significantly accont for alls ith openings nder different restraint conditions. The simple design method is, therefore, developed to overcome this barrier. Comparisons ith the available test reslts shoed that the PDM is acceptable and reliable. Moreover, it as fond that PDM is a simpler and more convenient design method for engineering practitioner in opposition ith other complicated empirical eqations. REFERENCES ACI (014). Bilding Code Reqirements for Reinforced Concrete. American Concrete Institte, Detroit, USA. AS (001). Concrete Strctres. Standards Astralia, Sydney, Astralia. 7

8 AS (009). Concrete Strctres, Standards Astralia, Sydney, Astralia. Doh, J.H., Fragomeni, S. (005). Evalation of experimental ork on concrete alls in one-ay and to-ay action. Astralian Jornal of Strctral Engineering, 6(1), Doh, J.H., and Fragomeni, S. (006). Ultimate load formla for reinforced concrete all panels ith openings. Advances in Strctral Engineering, 9(1), Doh, J.H., Loo YC, Fragomeni, S. (010). Concrete alls ith and ithot openings spported on three sides. Incorporating sstainable practice in mechanics and strctres of materials, Fragomeni, S. (1995). Design of normal and high strength reinforced concrete alls. Ph.D Thesis, University of Melborne, Astralia. Fragomeni, S., Doh, J.H., and Lee, D.J. (01). Behavior of axially loaded concrete all panels ith openings: An experimental stdy, Advances in Strctral Engineering, 15(8), Lee, D.J. (008). erimental and theoretical stdy of normal and high strength concrete all panels ith openings. Ph.D Thesis, Griffith University, Gold Coast, Astralia. Saheb S.M., Desayi, P. (1990). Ultimate strength of RC all panels ith openings. Jornal of Strctral Engineering, ASCE, 16(6), Sanjayan, J.G., Mahesaran, T. (1999). Load capacity of slender high-strength concrete all ith side spports. ACI Strctral Jornal, 96(4),