Experimental Investigation and Numerical Analysis of New Multi-Ribbed Slab Structure
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1 Experimenta Investigation and Numerica Anaysis of New Muti-Ribbed Sab Structure Jie TIAN Xi an University of Technoogy, China Wei HUANG Xi an University of Architecture & Technoogy, China Junong LU Xi an University of Technoogy, China ABSTRACT: Muti-ribbed sab structure (MRSS) is a new type of composite structura system which is composed of prefabricated muti-ribbed composite wa sab and cast-in-pace foor sab as we as cast-in-suit conceaed outer frame whie the muti-ribbed composite wa sab is composed of reinforced concrete frame and buit-in infi siicate bocks or ight-weight infi panes. This paper presents the resuts of experimenta investigation and numerica anaysis resuts of MRSS. The specimen is four scaed modes in which there are three 1/2 scae two-storey two-bay modes and one 1/3 scae three-storey two-bay mode. The pseudo-static experiments of the specimens have been executed. The noninear numerica anaysis of four specimens is carried out with two simpified anaysis modes proposed in the paper. The anayses show that numerica resuts are good coincidence with the experimenta resuts. The pseudo-static tests and noninear numerica modeing show that the muti-ribbed sab structure has a good earthquake-coapse resistant capacity. Keywords: muti-ribbed sab structure; pseudo-static experiment; noninear numerica anaysis 1. INTRODUCTION Muti-ribbed sab structure (MRSS) is a new type of composite structura system which is composed of prefabricated muti-ribbed composite wa sab and cast-in-pace foor sab as we as cast-in-suit conceaed outer frame, in which the muti-ribbed composite wa sab is composed of reinforced concrete frame made up of rib beams and rib coumns and buit-in infi siicate bocks or ight-weight infi panes [1-2]. This paper presents the resuts of experimenta investigation and numerica anaysis of MRSS. The specimens are four scaed modes in which there are three 1/2 scae two-storey two-bay modes and one 1/3 scae three-storey two-bay mode. The pseudo-static experiments of the specimens have been executed. The faiure phenomena, faiure modes, bearing capacity and hysteretic property of the specimens were studied. The noninear numerica anaysis of four specimens was carried out. Two simpified anaysis modes such as an equivaent strut mode and shear wa mode were proposed. The rationaity and accuracy of numerica modes were vaidated through comparing with the experimenta resuts. The anayses show that numerica resuts are good coincidence with the experimenta resuts, especiay for forecast of the vaues of oad carrying capacity at feature points. The pseudo-static tests and noninear numerica anaysis show that the muti-ribbed sab structure has a good earthquake coapse resistant capacity. 2. EXPERIMENTAL INVESTIGATION 2.1 Specimen Design The prototype of specimen is an eight-storey frame-supported muti-ribbed sab structure designed according to China buiding criterion [3-4]. For simpicity, specimens were designed to be a pane structures where bottom frame was one storey and upper muti-ribbed sab structure was 1~2 storey.
2 The seria numbers of specimens were KZML-1, KZML-2, KZML-3 and KZML-4 respectivey. KZML-1 was a 1/2scae two-storey two-equa-bay modes. KZML-2 was a 1/2scae two-storey two-unequa-bay modes. KZML-3 was a 1/2 scae two-storey two-unequa-bay modes with hoow. KZML-4 was a 1/3 scae three-storey two-unequa-bay modes. The wa thickness of 1/2scae modes was 1mm whie 1/3 scae mode was 75mm. The materias of specimen were homoogous with prototype. The construction and dimensions as we as reinforcement detais of specimens were shown in Figure1. (a) KZML-1 3 (b) KZML-2
3 (c) KZML-3 (d) KZML-4 Figure1. The construction and dimensions as we as reinforcement detais of specimens 2.2. Loading System The pseudo-static experiments of the specimens have been carried out. The test oading system was shown in Figure 2. Firsty, vertica oading 331kN, 385kN, 385kN and 236kN were oaded on KZML-1, KZML-2, KZML-3 and KZML-4 respectivey. Secondy, horizonta oading were oaded by using oading-dispacement mixing contro method, in which oading contro was adopted by using monotone oading with every step of 1kN/2kN before the specimens yieding, and then after yieding dispacement contro was adopted with mutipes of yieding dispacement cycing three times under every step.
4 Jack Reaction wa Actuator Aot beam Loading frame 298(319) Anchor bot 2.3. Faiure Procedure Figure 2. Loading system Faiure phenomena of the specimens are shown in Figure 3.The faiure modes of the specimens presented shearing faiure characteristic. Under ow cycic oadings, for specimen KZML-1, at initia stages of oading, infied siicate bocks of muti-ribbed wa sab appeared severa sight cracks; oading to metaphase, the cracks of infied siicate bocks increased markedy, and extended to reinforced concrete rib beams and rib coumns; continuing oading, there is a sma cracking and sipping between interface of the wa and trimmer beam; oading to yieding of the specimen, interface of the wa and trimmer beam arose big cracking and apparent sipping; faiure of specimen KZML-1 mainy took pace in the bottom frame post, occurring of post root pasticity hinge brought on serious deformation resuting in specimen not being continued oading. Faiure of specimen KZML-2, KZML-3 and KZML-4 mainy concentrated on second storey whie damage of frame post was sight; faiure procedure of second storey wa took pace in the order of infied siicate bocks, reinforced concrete rib beams and rib coumns, outer frame unti the infied siicate bocks desquamated in a big area, the wa degenerated into sma frame, end of numerous rib beams came into being pasticity hinges, and oca concrete of outer frame post root was crushed party. (a)kzml-1 (b) KZML-2 (b)kzml-3 (b) KZML-4 Figure 3. Faiure phenomena of specimens
5 3. NUMERICAL ANALYSIS 3.1. Structura Anaysis Mode There are two simpified modes that are an equivaent strut mode and shear wa mode to be proposed for muti-ribbed wa sab. (a)the equivaent strut mode, considering a fundamenta infied frame eement with infi siicate bocks in muti-ribbed wa sab shown in Figure 4(a), based on the mode of masonry infi pane (Madan and Reinhorn et a., 1997)[5], was presented. Since the tension strength of siicate bocks is negigibe, the individua siicate bocks strut is considered to be ineffective in tension. However, the combination of both diagona struts provides a atera oad-resisting mechanism for the opposite atera directions of oading. (b) The equivaent shear wa mode consider muti-ribbed wa sab to be equivaent as a shear wa sab by two steps of equivaent[3].the first step, according to equivaent principe of compressive stiffness such as ratio of the eastic modue of siicate bocks to concrete, siicate bocks is equivaent as concrete wa. The second step, using equivaent principe of fexura stiffness, the equivaent concrete was and rib coumns are equivaent as an integra concrete shear wa shown in Figure 4(b). The fexura stiffness is cacuated according to: E I = c eq ( E I + E I ) (3-1) c c c w 1 Where, I eq the section moments of inertia of the integra concrete shear wa after second equivaent. I w1 the section moments of inertia of the concrete wa after first equivaent. I c the section moments of inertia of the rib coumn. E the eastic modue of concrete. c Rib Beam frame Beam Shear wa Rib Coumn Rib Beam Rib Coumn frame coumn frame coumn frame Beam (a) Equivaent strut mode (b) Equivaent shear wa mode Figure 4. Simpified modes of muti-ribbed wa sab 3.2. Pseudo-Static Anaysis The Pseudo-Static anaysis of KZML-1~KZML-4 has been carried out by using an equivaent shear wa mode. The computing oading system and testing oading system was basicay the same shown in Figure 5. The dispacement contro method was adopted, firsty monotone oading to yieding dispacement, secondy cycing under every step with mutipes of yieding dispacement after yieding.
6 KZML-1 cyce number KZML-2 KZML-3 cyce number KZML-4 cyce number (a)kzml-1 (b) KZML-2, KZML-3 (c) KZML-4 Figure 5. The computing oading system Testing -4 Cacuating Testing -4 Cacuating (a) KZML-1 (b) KZML Testing Cacuating Testing Cacuating (c) KZML-3 (d) KZML-4 Figure 6. Hysteretic curves of the specimens The Pseudo-Static anaysis was carried out by using program IDARC2D Version 7. [6-7]. Figure 6 give separatey the hysteretic curves of the testing and cacuating of specimens whie its crack, yied, utimate and faiure oad-resisting capacity are shown in Tabe 3.1. The anaysis shows that numerica resuts are in good coincidence with the experimenta resuts, especiay in forecast of the vaues of
7 oad carrying capacity at feature points. Therefore, the equivaent shear wa mode proposed in the paper is practicabe. Tabe 3.1. Load Carrying Capacity of Test and Cacuating with Pseudo-Static Anaysis Crack Yied Utimate Faiure Specimen V c (kn) V y (kn) V u (kn) V m (kn) Test Cacuating Test Cacuating Test Cacuating Test Cacuating KZML KZML KZML KZML Noninear Dynamic Time-History Anaysis The noninear dynamic time-history anaysis of KZML-1~KZML-4 under E-Centro wave has been carried out by using separatey an equivaent strut mode and shear wa mode. The computing time of structure is t =3s. The computing time of compression for 1/2 scae modes is as t / 2 = s, and the computing time of compression for 1/3 scae mode is as t / 3 = s. The skeeton curves of shearing force and dispacement of test modes KZML-1~KZML-4 are shown in Figure Equivaent strut mode Equivaent shear wa mode KZML Equivaent strut mode Equivaent shear wa mode KZML (a)kzml-1 (b) KZML Equivaent strut mode Equivaent shear wa mode KZML Equivaent strut mode Equivaent shear wa mode KZML (c)kzml-3 (d) KZML-4 Figure 7. Force-dispacement reation curves
8 Figure 7 (a)~(d) show that the computing resuts for an equivaent strut mode and shear wa mode are in good coincidence with the testing resuts, especiay in oad-resisting capacity of yieding point and utimate point (see Tabe 3.2). Error of cacuating yieding oad for KZML-1~ KZML-4 using an equivaent strut mode are respectivey.71%,13.64%,8.14% and 5.77% whie error of cacuating utimate oad are respectivey1.56%, 2.93%, 2.33% and 5.77%. Error of cacuating yieding oad for KZML-1~ KZML-4 using an equivaent shear wa mode are respectivey 4.29%,1.23%,2.33% and 8.46% whie error of cacuating utimate oad are respectivey 7.81%,6.9%,1.16% and 3.85%. The equivaent strut mode and shear wa mode proposed above is feasibe. Specimen Tabe 3.2. Load Carrying Capacity of Test and Cacuating with Dynamic Anaysis Yied(kN) Utimate(kN) Strut mode Shear wa mode Strut mode Shear wa mode Test Cacuating Cacuating Test Cacuating Cacuating KZML KZML KZML KZML Push-Over Anaysis The noninear static incrementa anaysis was carried out using force contro. Latera force distribution was seected using four force distributions avaiabe in the program IDARC 2D version 7.: inverted trianguar distribution, uniform distribution, generaized power distribution and moda adaptive distribution [6-7]. a) The inverse trianguar distribution considers that the structure is subjected to a inear distribution of the acceeration throughout the buiding height. The force increment at each step for story i is cacuated according to: wihi ΔFi = ΔV N b (3-2) w h =1 where wi and hi are the story weight and the story eevation, respectivey, and ΔVb is the increment of the buiding base shear. b) The uniform distribution considers a constant distribution of the atera forces throughout the height of the buiding, regardess of the story weights. The force increment at each step for story i is given by: ΔVb ΔFi = N (3-3) Where ΔV b is the increment in the base shear of the structure, and N is the tota number of stories in the buiding. c) The generaized power distribution was introduced to consider different variation of the story acceerations with the story eevation. This distribution was introduced to capture different modes of deformation, and the infuence of higher modes in the response. The force increment at foor i is cacuated according to: k wihi ΔFi = ΔV N b (3-4) k w h =1 where k is the parameter that contros the shape of the force distribution. The recommended vaue for k may be cacuated as a function of the fundamenta period of the structure ( T ): k = 1. (T.5s)
9 T.5 k = 1. + (.5s<T <2.5s) k = 2. ( T 2.5s), Nevertheess, any vaue for k may be used to consider different acceeration profies. Note that k = produces a constant variation of the acceeration, whie k = 1. produces a inear variation (inverted triange distribution), and k = 2. yieds a paraboic distribution of story acceerations. d) The moda adaptive distribution differs significanty from a the previous ones in that the story force increments are not constant. The moda adaptive distribution was deveoped (Reinhorn, 1996, 1997) to capture the changes in the distribution of atera forces. Instead of a poynomia distribution, the instantaneous mode-shapes of the structure are considered. Since the ineastic response of the structure wi change the stiffness matrix, the mode shapes wi aso be affected, and a distribution proportiona to the mode shapes wi capture this change. The increment in the force distribution is cacuated according to: ΔF = i w [ n i j= 1 m m w [ ( Φ j= 1 ij ( Φ Γ ij j ) Γ j ) ] ] V b F od i (3-5) Where Φ ij is the vaue of instantaneous mode shape j at story i, Γj is the moda od participation factor for mode j, V b is the new base shear of the structure, and F i is the force at foor i in the previous oading step. The noninear static incrementa anaysis of KZML-1~KZML-4 under four force distributions has been carried out by using an equivaent shear wa mode. The push-over curves as we as test skeeton curves of KZML-1~KZML-4 are shown in Figure 8. From Figure 8 (a)~(d) it can been seen that push-over curves of four force distributions are in good coincidence with the experimenta resuts, which the uniform distribution gives the upper imit of push-over curves and the moda adaptive distribution gives the ower imit of push-over curves. Base Shear Force(V/W) Inverse trianguar Uniform Moda adaptive Generaized power Top Dispacement(Δ /H %) Base Shear Force(V/W) Inverse trianguar.6 Uniform.4 Moda adaptive Generaized power Top Dispacement(Δ /H %) (a) KZML-1 (b) KZML-2
10 Base Shear Force(V/W) Inverse trianguar.6 Uniform.4 Moda adaptive Generaized power Top Dispacement(Δ /H %) Base Shear Force(V/W) Inverse trianguar 1. Uniform Moda adaptive.5 Generaized power Top Dispacement(Δ /H %) (c) KZML-3 (d) KZML-4 Figure 8. The push-over curves of KZML-1~KZML-4 4. CONCLUSIONS The pseudo-static tests and noninear numerica modeing show that the muti-ribbed sab structure has a good earthquake-coapse resistant capacity. The pseudo-static anaysis, noninear dynamic time -history anaysis and push-over anaysis show that numerica cacuating resuts are in good coincidence with the experimenta resuts, especiay in forecast of the vaues of the oad carrying capacity at feature points, which indicated that the equivaent strut mode and shear wa mode proposed in the paper are practicabe. AKCNOWLEDGEMENT Current research has been financiay supported by the Nationa Natura Science Foundation of China Research Project(No )and Scientific Research Program Funded by Shaanxi Provincia Education Department (No. 21JK729). REFERENCES [1] Scientific and Technica Report (2). Study on Theory and appication of muti-ribbed wa sab structure with ight-weight outer frame, Xi an University of Architecture & Technoogy, China. [2] YAO Qianfeng, Huang Wei, TIAN Jie and DING Yong-gang. (24).Experimenta anayses of mechanica characteristics and seismic performance of muti-ribbed pane wa. Journa of Buiding structure25:6, [3] TIAN Jie. (27). The noninear earthquake response anaysis of frame-supported muti-ribbed sab structure and damage performance based seismic evauation methods. PhD dissertation, Schoo of Civi Engineering, Xi an University of Architecture & Technoogy, Xi an, China. [4] GB Code for Seismic Design of Buidings (21).China Architecture and Buiding Press. [5] Madan, A., Reinhorn, A.M., Mander, J.B. and Vaes, R.E. (1997). Modeing of masonry infi panes for structura anaysis. Journa of Structura Engineering123:1, [6] Reinhorn A.M., Roh H., Sivasevan M., Kunnath S.K.,Vaes R.E.,Madan A., Lobo C. Li, R.and Park Y.J. (21). IDARC2D version 7.: A program for the ineastic damage anaysis of structures. State University of New York at Buffao. [7] Reinhorn A.M., Roh H., Sivasevan M., Kunnath S.K.,Vaes R.E.,Madan A., Lobo C. Li, R. and Park Y.J. (21). IDARC2D version 7.: User's guide. State University of New York at Buffao.
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