269 THE ENEGY DISSIPATION EFFECTS OF EDUNDANT MEMBES IN SILOS UNDE EATHQUAKES Li Zhiming 1 and Geng Shujiang 1 SUMMAY An analytial study is made the response to strong base motion reinfored onrete silo strutures having energy dissipation redundant members. The strutural model onsists an axisymmetri silo body supported by reinfored onrete olumns. Analytial methods used inlude inelasti dynami response history analysis, inelasti stati analysis, and elasti modal spetral analysis (Building Code China). The sensitivity the strutural parameters, suh as the loation redundant members, relative linear stiffness, and reinforement ratios, are examined for lateral fore and ground motions. Based on the data presented, it is onluded that the advantages energy dissipation redundant members are ensuring yielding hinges our in seleted elements, improving the distribution internal fores, and providing inreased dutility. Numerial examples are disussed to show the appliation potential. INTODUCTION Silos are widely used as industrial onstrutions for storage, onveyane and transportation in steel manufatories or mine orporations. During Hai Cheng ity earthquake (1975) and Tang-Shan ity earthquake (1976), about ninety perent the silo strutures were damaged in varying degrees (Fig. 1). Earthquake investigations (1,2) have shown that the onrete raking and rushing at the top olumns and reinforement bukling aused major damage and sometimes even ollapse. Beause the speial features silo strutures, suh as the storage heavy materials, abrupt stiffness hanges at the olumn to silo body joint, the small number strutural elements and low level redundany, the safety fator for lateral resistane against seismi fores was limited. In addition, the speial limitations imposed by the prodution proesses involving the silos gave designers and owners no way inreasing the earthquake resistane by the usual methods, suh as using shear walls or by braing the olumns. The obje tive this study was to determine a suitable type silo struture that would have an improved level lateral resistane against seismi loads. In line with the onept "strutural fuses" (3) and "strong olumn-weak beam" ^ esearh Engineer, Aseismi Engineering Department, Central esearh Institute Building & Constrution, Ministry Metallurgial Industry, P.. China FIG. 1 - SILO COLUMN DAMAGE Silo body Upper olumn V edundani member j\ Lower olumn FIG. 2 - COSS-SECTION OF SILO
270 design onsiderations (4), a weaker beam below the silo body was used as a redundant member for dissipating seismi energy so that the safety the supporting olumns during earthquakes and normal servie loading ould be guaranteed. A study was arried out for a range values for the key parameters and the general harateristis the internal fore distribution, the behaviour and dutility improvement the silo struture with redundant members under the lateral loading and ground motions are presented in this paper. COMPUTATIONAL MODEL AND DIFFEENTIAL EQUATIONS FO THE POBLEM The omputational model has been assumed to be a two mass system, being the silo body and the redundant member. Under the appliation horizontal fores, the rigid silo body was onsidered to be able to displae and rotate in its own plane. Using Lagrange 1 s equation, the system differential equations for the ation horizontal dynami fores on the omplete struture is, in matrix form: [M](U> + [C]{U> + [K]{U} = {P} (1) in whih [M] = m/3 m/6 m/3 sym.,- the mass 0 0 m, matrix; [C] = damping matrix: [K] = stiffness matrix; {P} = generalized load vetors; and {U }, {CO, {U } = aeleration, veloity and displaement vetors. The rotational oupling effets the rigid body was inluded in the stiffness matrix [K] and the mass matrix [M] Eq. (1), and the effets bending, shear and axial fore on the stiffness oeffiients were onsidered as well. Obviously, this analytial model would be more aurate than the normal MDOF or SDOF system (Fig. 3(a)) in whih only translational motion the silo body was taken into aount. ANALYTICAL METHODS AND POCEDUE Three analytial methods were used in this study: (1) Elasti modal spetral analysis (aording to Building Code China (5)); (2) Inelasti stati analysis; and (3) Inelasti dynami response history analysis, designated analyses A, B and C, respetively. The following parameters were varied in the study: (1) Loation oeffiient redundant member (p = h^/h); (2) elative linear stiffness ratio redundant member to olumn (a = J. h/j L) ; and b e (3) einforement ratio redundant member (y A g /bh'). For analysis A, internal fore differenes between the ases with and without redundant members were desribed, and the upper and lower bound key parameters P and a were determined for the reasonable state supporting olumns. In this ase, two basi parameters, earthquake intensity sale and site soil ategory, were equal to E.I. S = 9 and type 2, respetively. Table 1 shows the resulting values olumn end moment redution fator. The top moment the upper olumn redues by 26.1-50.3%, top the lower olumn by 11.8-53.4%, and the bottom moment the upper olumn by 43-96.4%. Clearly, it is more benefiial to have silo strutures with redundant members than without them. It should be pointed out that the trends for olumn end moment redution are presented for hanges p and a. In this study, two fators were required, i.e. (1) suffiient length upper olumn preventing short olumn damage; and (2) suffiient stiffness the redundant member to absorb as muh seismi energy as possible. After general onsideration, the optimum range values p= 0.2-0.4 and a = 1.7-2.55 were adopted. 4 L_4 (a) WITHOUT EDUNDANT MEMBE (b) WITH EDUNDANT MEMBE FIG. 3 - COMPUTATIONAL MODEL
271 TABLE 1 - THE EDUCTION FACTO OF COLUMN END MOMENT (%) Loation Top moment Bottom moment Top moment Bottom moment redundant upper ol. upper ol lower ol lower ol. member ut ub It lb P a a a a 1.00 1.70 2.55 1.00 1.70 2.55 1.00 1.70 2.55 1.00 1.70 2.55 0.1 29.6 39.8 46.4 43.0 51.9 57.5 18.3 14.3 11.8-2.0-3.0-3.8 0.2 33.9 44.1 50.3 70.4 80.9 86.9 28.0 20.8 16.5-2.9-4.5-5.7 0.3 29.6 37.2 41.6 92.7 96.4 90.3 39.1 29.3 23.4-2.2-4.1-5.5 0.4 21.8 26.1 28.4 86.1 74.7 68.1 53.4 41.9 35.0 1.1-0.1-0.2 Note: A positive value indiates a redution, and a negative value an inrease. With analysis B, (1) the ation long-term loads and lateral monotoni loads; (2) the overturning effets lateral loads; (3) the effets stiffness degeneration after raking and hinging on the olumns and beams; and (4) the internal fores redistribution when struture reahes the plasti stage; were taken into aount. During the analysis proess, the loation parameter p, relative linear stiffness ratio a and steel ratio y were ontinually adjusted until hinginf ourred in the redundant member. Plots the relationship between fore and displaement and the orresponding dutility redution oeffiient are presented in Figs. 4 and 5. The relationship shows (1) the silo without redundant members has lowest alues dutility and yield loads; (2) the silo with redundant members designed as weaker elements behaves exellently for both indexes mentioned above; and (3) the behaviour the silo with redundant members not designed as weaker elements lies between that for (1) and (2). For the purpose guaranteeing that yielding hinges our in seleted elements during earthquakes, it is neessary to hoose the parameters p, a and y (shown in Fig. 6, so that the reinforement detailing will permit the first hinge to form there. With analysis C, an examination was arried out whether the dutility silo strutures would satisfy the dutility demand pratial ground motions. For this study, adopting a story-hysteresis model and inputting 20 artifiial earthquake reords (aording to Building Code China, E.I.S = 9 and 9; site soil ategory = type 2), the resulting values average displaement dutility were obtained as shown in Table 2. Table 2 shows the dutility redundant p Without redundant member TABLE 2 - COMPAISONS OF DUCTILITY COEFFICIENT With redundant member a = 0.00 a = 1.00 a = 1. 70 a = 2.55 Cd Cd Cd Cd Cs E.I.S. Cs E.I.S. Cs E.I. S. Cs E.I.S. Note 8 9 8 9 8 9 8 9 0.0 1.03 0.90 6.30 0.1 2.08 0.81 6.53 1.65 0.74 4.56 1.62 0.87 1.90 * 0.1 2.15 0.91 2.22 2.17 0.90 2.23 2.17 0.76 2.62 ** 0.2 2.29 0.81 2.22 2.32 0.81 2.22 2.21 0.78 2.21 ** 0.3 2.43 0. 80 2.21 2.40 0. 82 0.32 2.18 0.76 2.01 ** 0.4 2.75 0.78 1.94 2.55 0.75 1. 86 2.36 0.72 1.76 ** Note: * redundant member not designed as weaker element; ** redundant member designed as weaker element; Cs the dutility oeffiient silo (by analysis B) Cd the dutility demand during an earthquake (by analyis C).
272 Note: With redundant member designed as a weaker element With redundant member not designed as a weaker element FIG. 4 - ELATIONSHIP BETWEEN FOCE AND DISPLACEMENT FO a = 1.0 (top), a = 1.7 (middle) and a= 2.55 (bottom)
273 member designed on weaker element onsideration meets the earthquake dutility demand (E.I.S = 9) over the range values p = 0.2-0.4. 3o0 p- 0*4 /, p, Q.3 / /, p~ 0.2 / _p- o. 1 1.0 ^-P- o.i i. O 1 2 1 -rh 1.0 1.5 2,0 2-o 3j BEFrHXUJm STIFCSS TIG FIG. 5 - DUCTILITY EDUCTION COEFFICIENT NUMEICAL EXAMPLES In this study, three pratial engineering examples are presented: (1) a silo for a magnesium mine (in Hai Cheng ity) without redundant members; (2) a silo for oal storage (in Tang Shan ity) with redundant members whih were not designed as weaker elements; and (3) a oal mine silo (in Tang Shan ity) EFn-mjjm STIFFNESS ATIO a FIG. 6 - ATIONAL EINFOCEMENT ATIO with redundant members designed as weaker elements. The area in whih these were loated was E.I.S = 0 and site soil = type 2. These silos were similar olumn height, olumn ross-setion and beam length, as shown in Table 3 and Fig. 2. The atual earthquake damage sustained by these three buildings is summarised in Table 4, along with the atual dutility the silos and the dutility demand TABLE 3 - DATA FO ANALYTICAL EXAMPLES Desig Height Height Height Whole Whole Length Cross Cross Load nation silo upper lower height height red. se. se. on one body ol. ol. ol. silo mem. ol. red. ol. h h h h H L mem. (m) (m) (m) (m) (m) (m) (m) (m) (t) (1) 5.80 10.40 16.20 6.00 70*70 170 (2) 5.40 3.00 7.60 10.60 16.00 7.00 70*70 40*75 180 (3) 5.40 4.20 6.60 10.80 16.20 7.00 70*70 40*90 180 TABLE 4 - SUMMAY OF ANALYSIS ESULTS AND SEISMIC DAMAGE INVESTIGATIONS Example No. Dutility Silo Cs Dutility demand earthquake Cd Analysis results Seismi damage investigations (1) 1.06 4.36 einforement and dutility were not satisfied (2) 2.07 2.40 yg = 1.2% (exeeds the optimum range reinforement) p = 0.28, a - 1.00 (< 1.70-2.55) (3) 2.36 2.30 P = 0.39, a = 1.87, yg = 1.06%; all three key parameters meet the requirements this study. Conrete rushing at the olumn top end, reinforement bukling Conrete rushing at some lower olumn top ends. Tiny horizontal riks at the lower olumn top end; the ends redundant members were damaged
274 required by the earthquakes used in the analyses. The dutility differenes and the influene the redundant members in reduing the seismi damage an be seen. CONCLUSIONS A rational method designing the redundant members as a weaker element to dissipate the seismi energy has been suggested to improve the dutility silo strutures. In view the results presented, the following onlusions are fered: 1. The redundant members have the effet improving internal fore distribution. 2. By designing redundant members as weaker elements, the dutility the silo strutures and the dissipation seismi energy have been inreased. 3. Three key parameters, whih make full use redundant members have been varied over the ranges p = 0.2-0.4, a = 1.70-2.55 and yg as shown in Fig. 6. EFEENCES (1) "eport: The Silo Damages in Tang Shan Earthquake", 1977. (In Chinese). (2) "Seismi Damage Investigation eport Metallurgial Construtions in Hai Cheng Earthquake", 1975. (In Chinese). (3) Mark Fintel and S.K. Ghosh, "The Strutural Fuse: An Inelasti Approah to Seismi Design Buildings". Div. Civil Engineering, ASCE, Jan. 1981. (4) Hu Qinghang, "The Seismi Design for Some einfored Conrete Buildings". Pro. Earthquake and Hazard Engineering, 1986. (In Chinese). (5) "Building Code China, 1985", Building Industry Press, Peking, China.