Studies on Serviceability of Concrete Structures under Static and Dynamic Loads

Transcription

1 ctbuh.org/paper Title: Author: Subject: Keyword: Studie on Serviceability of Concrete Structure under Static and Dynamic Load An Lin, Nanjing Intitute of Technology Ding Dajun, Nanjing Intitute of Technology Structural ngineering Concrete Structure Publication Date: 2001 Original Publication: CTBUH Journal, Spring 2001 Paper Type: 1. Book chapter/part chapter 2. Journal paper 3. Conference proceeding 4. Unpublihed conference paper 5. Magazine article 6. Unpublihed Council on Tall Building and Urban Habitat / An Lin; Ding Dajun

2 Studie on Serviceability of Concrete Structure under Static and Dynamic Load Ding Dajun and An Lin Nanjing Intitute of Technology, Nanjing, China ABSTRACT Thi paper preent a erie of experimental and theoretical tudie on the erviceability of concrete tructure, conducted at Nanjing Intitute of Technology (NIT) for more than 35 year. They include tudie of cracking and deformation of concrete member under tatic loading and of deformation under dynamic loading. For crack width and deformation under tatic loading, the firt author ha uggeted a unified calculation procedure baed on a larger number of experimental tudie, which include the member ubjected to flexure under hort- and long-term loading and under eccentric tenile or compreive force. More than 700 pecimen were teted. Mot of the calculation procedure uggeted have been adopted in relevant Chinee deign code and pecification. For the deformation under dynamic eimic and wind action, the 318m high Nanjing TV Tower wa choen a the cae tudy. INTRODUCTION The tructural deign code current in mot countrie precribe that two limit tate hould be conidered for concrete tructure, i.e., ultimate limit tate and erviceability limit tate. The CB-FIP Model Code (publihed in 1993) claifie the erviceability limit tate into three categorie: 1) limit tate of cracking and exceive compreion, 2) limit tate of deformation, and 3) limitation of vibration. The Chinee Deign Code of Concrete Structure, GBJ10-89, claifie beam of different type (e.g., floor beam, roof beam, crane beam, etc.) according to their circumtantial condition (uch a normal room temperature, outdoor or indoor condition, or very humid condition) in which thee member are placed for ervice. Thu there are three level (I, II, and III) of controlling cracking. Reinforced concrete (RC) member belong to level III becaue they cannot be guaranteed not to crack and maximum crack width could not be limited to a maximum of 0.2, 0.3, and 0.4mm according to different cae of expoure. Pretreed concrete (PC) member may belong to level II or III for pre-treing cold-tenioned teel bar, and to level I or II for high trength wire. The member of level I hould be trictly precluded from crack formation and are not permitted to produce tenile tre in concrete on their tenile face under the combination of the effect of hortterm action. The member of level II hould be generally precluded from crack formation and are not permitted to produce tenile tre in concrete on their tenile face under the combination of the effect of long-term action. Member of level II are permitted to produce tenile tre σ ct under hort-term action but σ ct hould not be larger than σ ct γ ftk, where α i a limitation factor of tenile ct tre in concrete and i equal to 0.3, 0.5 or 1.0. In thi cae, γ i a factor repreenting the influence of platic deformation in tenile concrete depending on the ection hape, determined from the aumption of plane ection hypothei of beam theory and the tenile edge train equal to 2 f / a well a the tenile tre diagram on a tk c rectangular ection, a given in the Deign Code GBJ10-89 (e.g., γ =1.75 for rectangular and T- ection, wherea the value for γ are generally maller than 1.75 for, inverted T- and I-ection, and f tk i the characteritic tenile trength of concrete). For calculating the deflection of imply upported member, the Chinee Deign Code precribe uing the principle of minimal tiffne (i.e., that of a cracked ection with M max ), for the length near the upport in a beam under uniform load- CTBUH RVIW/VOLUM 1, NO. 2: FBRUARY

3 ing or for the hear-pan in a beam under concentrated load though the tiffne i larger than that at mid-pan. Minimal tiffne i determined by evaluating bending along normal ection. However, the increaed influence of tenile teel train due to the bending along diagonal ection and the influence of hear deformation hould alo be conidered, o the above principle can be adopted along the entire beam length (Ding, et. al., 1986). For calculating the deflection of a continuou beam, the repective minimal tiffne along the length with maximum poitive and negative moment hould be ued (Ding, 1989 and 1990). For conidering the reditribution of internal force in continuou beam under ervice loading, with two fixed end (for middle pan) and one fixed end and one imply upported end (for end pan), the firt author uggeted adjutment factor µ for the upport moment (Ding, 1989 and 1990). In determining µ, the hift of inflection point after the adjutment of the upport moment wa conidered, o the propoed value are more precie a compared with the value of tet in China and elewhere, including the tet conducted at NIT in which the diagram for deflection factor of continuou beam were given (Ding, 1989). The allowable deflection [f] of flexural member lited in the Chinee Code, depending on pan ( ), are given a <7m, [f] = /200 and >9m, [f] = /300. XPRIMNTAL STUDIS ON STIFFNSS AND CRACKS In the early 1960, the firt author began conducting experimental tudie on tiffne and cracking of RC flexural member under hort-term loading. Since the late 1970, he began teting member ubjected to eccentric force under hortterm loading (Ding, et. al.,1985 and 1986; Ding, 1992a). In 1965, the firt erie of beam tet under long-term loading wa carried out. He per- Fig.1 Reult of 8th Serie of Tet on 3pc Beam CTBUH RVIW/VOLUM 1, NO. 2: FBRUARY

4 formed10 ucceful tet erie of long-term experimental tudie on RC beam, and another erie of tet over a 23-year period of cracked and intact (without crack) PC beam (Ding, et. al., 1985; Ding, 1992a). For the teted beam, the average train along beam depth and the crack width of every crack on the level of tenile teel in pure length of beam and the deflection f 0 at pan center were meaured, a well a their temperature and relative humidity level. For the firt ix erie of tet, deflection and the temperature and humidity were recorded almot every day. The firt erie of long-term teting wa utained over a 6-year period (from December, 1965 to February, 1972). More complete data have been accumulated ince then. Fig.1 how the detailed record of 3 PC beam in the 8th erie of tet. The curve are drawn from the tet point of average value of each week. From the large number of meaured data, four concluion can be drawn (Ding, et. al., 1985 and 1986; Ding,1992a): (1) The average train along ection depth in pure bending length are conitent with the plane ection hypothei, not only under hort-term loading, but alo under long-term loading. (2) The curve of ε - ε ( ε = calculated teel train at cracked ection, ε = average teel train meaured) appear to be linear, and all the lineat curve for all beam in the ame erie are approximately parallel to one another, regardle of ection hape and teel ratio, i.e., the ctgø of ε ε line (ø = lope of line) i approximately equal to a contant, although in other erie of tet the outcome may be different due to the exitence of a different bond. Generally, ctgø can be taken a 1.1 (for plain bar, it hould be lightly larger). Becaue the hrinkage of concrete in beam i relatively larger than that of other material and the material bond i not trong, ctgø may reach a value a high a 1.3. (3) The factor defining the ection modulu for calculating the average concrete train edge of the compreive zone, M ζ = 2 ε b h c 0 c ε at the of a given ection can be taken a a contant in the ervice tage and i the function of ρ = c ρα and ection hape, where b and h 0 are the web width and the effective depth of member ection, repectively;, c are the moduli of elaticity of teel and concrete, repectively, α i the modular ratio and the teel ratio ρ = A /bh 0. Thi applie to all cae of rectangular, T, inverted T, and I ection. A i the cro-ectional area of tenile teel. In annular ection, ρ = ( A ) / A, in which ( A ) i the cro- ectional area of total reinforcement, and A i the entire ectional area of the member. (4) After crack formation, the M-f curve for a PC beam and an RC beam with the ame condition except with the preence of pre-treing are approximately parallel, f being the deflection at the center of the beam. In thi paper, only the calculation of flexural member with rectangular, T, inverted T and I (all with concentrated reinforcement) and annular ection (with uniformly ditributed reinforcement), are conidered. Member ubjected to eccentric force are not included. From the concluion preented in 1-3, it follow that the tiffne B under hort-term loading can be derived a (Ding, et. al., 1985 and 1986; Ding, 1992a): B A h ord = 0( 2 2 ) ψ η + α ρ ζ (1) where: d i the diameter around which the total teel reinforcement i uniformly placed in an annular ection; ψ i a non-uniformity factor defining tenile teel train, and i given by: ψ = 1.1(1 M cr / M ) (2) M cr i the cracking moment of concrete ection without teel, which hould be calculated uing elatic theory technique, then multiplied by the factor γ for conidering the platic deformation CTBUH RVIW/VOLUM 1, NO. 2: FBRUARY

5 tenile concrete: γ =1.75 for rectangular and T ection; γ <1.75 for inverted T and I ection (definite value of γ are lited in the China Code); and,γ = 2-0.4d 1 /d for annular ection, where d and d 1, repectively, are the outer and inner diameter. The calculated value of M cr multiplied by 0.8 i taken to conider the influence of hrinkage; η i the factor defining internal moment arm z, i.e., the ditance between internal force related to tenion (T) and compreion (C) in ection with cracking, where η =z/h 0 ; for member with rectangular., T, inverted T, and I ection reinforced concentrically, η =0.87; for annular ection reinforced uniformly,η =1/3.2 due to uing the total value of A in the calculation and the higher location of the reultant reiting force in the tenile teel. For member with rectangular., T, inverted T, and I ection, αρ α ρ = ζ 1+ 2γ (3) where, γ i the trengthening factor of compreive cantilever flange in a T- or I-ection to the effective ection of web, γ =(b f -b)h f /bh 0 ; and b f, h f are the width and thickne of the compreion flange, repectively. For member with annular ection, α ρ = α ρ ζ (4) For cracked PC flexural member, deflection can be calculated by uing concluion 4 or another formula, uggeted alo by the firt author (Ding, 1992b). For PC flexural member without crack, B can be taken a 0.85 c I 0, where I 0 i the moment of inertia of the tranformed ection. For long-term tiffne, Chinee deign code adopt an amplification factor θ for deflection, the value of which were alo given by the firt author through hi tet; θ = 2.0 in general cae. Another formula for long-term tiffne of flexural member with the conideration of creep and hrinkage of concrete i repreented by q.(1) (Ding, 1992b). The formula (Ding, et. al., 1985 and 1986; Ding, 1992a) applied to cracking in flexural member, propoed by the firt author baed on ignificant teting and analyi, are ummarized here. The general formula for average crack pacing: (5) = ( 1+ γ )( a bd/ ρ) ν cr cr + where: a and b are parameter, different for variou hape of member: for member with rectangular, T, inverted T, and I ection, a = 6 cm and b = 0.06 (1+2γ γ 1 ), γ 1 = (b f -b) h f / bh; b f and h f are, repectively, the width and thickne of a tenile flange and h i the overall depth of the ection, and γ 1 = (b f -b) h f /bh. For annular ection, a = 0.5 and b = 0.1, where repreent the tirrup pacing, which hould not be le than 10cm and more than 20cm. γ cr repreent a pecial factor for tenion member; γ cr = 0 for flexural member and member in eccentric compreion. In thi paper only the calculation for flexural member are introduced, and therefore, γ cr and the other relevant parameter will be neglected. Calculated value of cr were checked with thoe obtained from a large number of tet by the firt author and were found to be in good agreement. The average crack width can then be calculated a follow: w ψ (σ ) cr= cr (6) M σ = (7) A ηl ( ord ) 0 Finally, ν i a factor for conidering urface configuration of teel bar: for plain bar, ν = 1.0, and for deformed bar, ν = 0.7 (in fly-ah ceramite concrete ν = 0.8). When conidering the non-uniform ditribution of crack and the influence of long-term loading, CTBUH RVIW/VOLUM 1, NO. 2: FBRUARY

6 Fig. 2 Nanjing TV Tower tet reult revealed that w cr hould be multiplied by 2.0. Thee propoal for calculating tiffne and cracking of flexural member with rectangular, T, inverted T, and I ection were accepted by the previou Chinee Deign Code TH10-74 and are ued continuouly in the current code GBJ10-89 after ome adjutment. SRVICABILITY RQUIRMNTS UNDR DYNAMIC XCITATIONS It i neceary to limit the acceleration of the ky cabin of tall TV tower ubjected to eimic and Fig. 3a and 3b Section (a) taken through Sky-Cabin and Floor Plan (b) of Fan Room. wind action o a not to caue dicomfort to viitor and operator. In the PC patial frame tructure of the 318m high Nanjing TV Tower (Fig.2), for example, two ky-cabin, one large and the other mall are upported by 3 PC branche (Ding and Maoquan, 1995; Ding and Zhenhua, 1994). The branch of Nanjing Tower i a box ection with multiple cell (in the bottom part of the tower, there are 4 cell which are gradually tranformed into 3, and then 2 cell at the junction with the large ky-cabin due to the battering of the branch). The Nanjing TV Tower i generally recognized a the firt tall pace-frame PC tower in the world (Ding and Maoquan, 1995). For verifying the maximum acceleration of ky-cabin under wind- CTBUH RVIW/VOLUM 1, NO. 2: FBRUARY

7 1993). From the calculation it can be hown that the acceleration of the mall ky-cabin under wind-pule loading cannot meet the erviceability requirement. The upper level of the mall kycabin i reerved a a mechanical floor (Fig.3a) and the lower level i ued a a ight-eeing floor for ditinguihed guet (the general ight-eeing hall i located in the large ky-cabin). For controlling the acceleration of the maller ky-cabin, Reng (1993) uggeted to et Tuned Liquid Damper (TLD) with diameter of 2.4m and 3.5m on the floor of the fan room (Fig.3b). The dynamic analyi in Fig. 4a how the enveloping curve of the maximum acceleration of each ma point before the addition of control damper. The envelope of maximum acceleration of each ma point after the intallation of control damper i hown in Fig. 4b (Zhenhua, 1993) where the acceleration of the mall ky-cabin i reduced to 0.183m/ 2 (Ding and Zhenhua, 1994). ven with damper, the controlling effect i only 12.4% and i till below the ervice requirement. Thi problem hould be tudied further. Fig. 4a and 4b Acceleration Diagram of Sky-Cabin ubjected to Dynamic Wind Load before (a) and after (b) intallation of Tuned Liquid Damper pule, one doctoral tudent and two mater degree tudent, upervied by the firt author at NIT, tudied the dynamic behavior of thi tower (Zhenhua, 1993; Meixiao, 1993). It wa alo invetigated for eimic action (Lin, 1993). Following the tipulation of the Chinee Code, the acceleration of tower ky cabin under wind-pule hould not be over 0.15m/ 2. Ding Dajun and Ren Zhenhua adopted artificial pule ample to conduct direct dynamic analyi and determined the acceleration of the mall and large ky-cabin to be equal to 0.209m/ 2 and 0.1m/ 2, repectively (Ding and Zhenhua, 1994; Zhenhua, Cheng Mexiao mater thei (Meixio, 1993) tudied the ue of Tuned Ma Damper (TMD) for controlling the pulating wind repone of the Nanjing TV Tower. She pointed out that the controlling effect for the mall ky-cabin i larger with the increae of the ma of the TMD ytem. However, he alo found that if the economic ma ratio (i.e., the ratio of the ma of the TMD ytem to that of the mall ky-cabin) of 0.05 i ued, then the optimum damping ratio i 0.1 and the optimum frequency ratio (i.e., the ratio of frequency of TMD to the 1t frequency of the tructure) i An Lin thei (Lin, 1993) applied the TMD ytem to control the vibration due to wind-pule and obtained the optimum controlling parameter by uing the optimum controlling program. Fig. 5 how the time-hitory-acceleration repone curve before and after controlling (Lin, et. al., 1995). The maximum acceleration of the mall ky-cabin i 0.24m/ 2 and i reduced to 0.21m/ 2 after controlling. The controlling effect i 12.5% which i the ame a given in by Ding and Maoquan CTBUH RVIW/VOLUM 1, NO. 2: FBRUARY

8 Fig. 5 Analyi with and without Tuned Ma Damper intalled in the Nanjing TV Tower (1995) and Ding and Zhenhua (1994). The maximum acceleration i lightly different due to the fact that the wind-pule ample ued and the mae calculated were lightly different. The eimic action wa alo invetigated and the controlling effect reached 50% (Lin, et. al., 1995; Lin and Ding, 2000). CONCLUSIONS For the calculation of tiffne and cracking of concrete member under tatic loading, the firt author uggeted a erie of propoal, which are applicable to rectangular, T, inverted T, I, and annular ection currently ued in engineering practice. They alo can be ued for RC, PC, and light-weight concrete member ubjected to flexure and eccentric force under hort- and longterm loading. Thi method of calculation appear to be more convenient, eem to provide a high degree of accuracy (Ding, 1989, 1990, 1992and 1992b; Ding, et. al., 1985 and 1986) and can atifactorily meet deign requirement. It i important to note that the tudy of the Nanjing TV Tower a tall tructure ubjected to dynamic action i preliminary and, therefore, it i neceary to conduct more reearch before definitive concluion can be drawn. RFRNCS Ding, D., 1989 CALCULATION FOR DFLCTION OF CONTINU- OUS RINFORCD CONCRT BAMS IN CON- SIDRATION OF MOMNT RDISTRIBUTION (IN- CLUDING CHINS CONGRATULATORY POM WITH NGLISH TRANSLATION), 75 o compleanno di Franco Levi, Tetimonianze, Politecnico di Torino, September, p. 43, pp Ding, D., 1990 CALCULATION FOR DFLCTION OF CONTINU- OUS RINFORCD CONCRT BAMS IN CON- SIDRATION OF MOMNT RDISTRIBUTION, Proceeding of JSC, pp Ding, D., 1992a RSARCH IN CHINA ON TH STIFFNSS AND CRACKING CHARACTRISTICS OF CONCRT MMBRS, Proceeding of the Intitution of Civil ngineer; Structure & Building, pp CTBUH RVIW/VOLUM 1, NO. 2: FBRUARY

9 Ding, D., 1992b XPRIMNTAL STUDIS AND CALCULATION PROPOSALS FOR STIFFNSS OF PPC FLXURAL MMBRS, Proceeding of the FIP Sympoium 92, Budapet, Hungary, May, pp Ding, D. and Maoquan, X., 1995 SPATIAL FRAM TV TOWR, NANJING, CHINA, Structural ngineering International, Journal of IABS, No.3, pp Ding, D. and Zhenhua, R., 1994 DSIGN TSTING AND ANALYSS OF NANJING TV TOWR, Concrete International, November, pp Meixiao, C., 1993 SIMULATION OF MULTIDIMNSIONAL ARTIFI- CIAL PULSATING WIND AND RSARCH FOR WIND-PULS CONTROL OF P-TMD ON HIGH- RIS STRUCTURS (in Chinee), thei for MS degree from NIT, China, February, p. 72. Zhenhua, R., 1993 FUNDAMNTALS OF A TLD DVIC AND ITS APPLICATION TO VIBRATION CONTROL OF TH NJTV TOWR (in Chinee), Ph.D. diertation from NIT, May, p. 57. Ding, D., et al., 1985 XPRIMNTAL RSARCH OF RINFORCD CONCRT AND PR-STRSSD CONCRT BAMS UNDR LONG TRM LOADING, Stavebnicky Caopi (Building Journal of Slovakian Academy), 33, pp Ding, D., et al., 1986 XPRIMNTAL RSARCH AND CALCULATION PROPOSALS FOR STIFFNSS AND CRACK WIDTH OF RINFORCD CONCRT MMBRS, Stavebnicky Caopi (Building Journal of Slovakian Academy), 34, pp Lin, A., 1993 STUDY OF A SISMIC CONTROL OF P-TMD AND OPTIMAL CONTROL FOR NJTV TOWR (in Chinee), thei for MS degree from NIR, China, February, p. 77. Lin, A., Ding, D., 2000 A STUDY ON TH P-TMD CONTROL FOR SISMIC AND WIND VIBRATION OF TH NANJING TV TOWR, Journal of Structural ngineering, Vol. 26, No. 4, January, pp Lin, A., Ding, D., Qin, L., 1995 STUDY OF VIBRATION CONTROL OF TH NANJING TV TOWR BY P-TMD, Building Structure (in Chinee), No. 7, pp CTBUH RVIW/VOLUM 1, NO. 2: FBRUARY