a) Calculate the seismic weights for all floors including level 1 and roof (use centreline dimensions in calculations).
b) Calculate the Seismic Horizontal Design Action Coefficient and distribute the calculated base shear to all levels on Frames A to C using the Equivalent Static Method. Estimate direct shear only and ignore torsion.
. . Design Data: Refer to Drawings of Typical Floor Plan and Section shown in the Figure below: Building use: Office Building type: Concrete moment frame Location: Auckland (at 25km away from the nearest fault) Design working life: 50 year Site Subsoil: shallow soil Ductility: p= 2 Period: T=0.45 Permanent load on each floor (level 1 and roof) including columns, beams, floors, cladding and super dead load (SDL) = 4 kPa. The rigidity of frames: along axes A and C is half B. . . . a) Calculate the seismic weights for all floors including level 1 and roof (use centreline dimensions in calculations). (15 marks) b) Calculate the Seismic Horizontal Design Action Coefficient and distribute the calculated base shear to all levels on Frames A to C using the Equivalent Static Method. Estimate direct shear only and ignore torsion. (30 marks) 4.2 SEISMIC WEIGHT AND SEISMIC MASS The seismic weight at each level shall be given by: W = G+IVE Q: ... 4.2(1) where G; and V:Q are summed between the mid-heights of adjacent storeys G the permanent action (self-weight or dead' action) at level i VE 0.6 is the earthquake imposed action (live load) combination factor for storage applications WE 0.3 is the earthquake imposed action (live load) combination factor for all other applications Q = the imposed action for each occupancy class on level i, (refer AS/NZS 1170.1) Q: for roofs shall include an allowance of 1.0 kPa for ice on roofs where required by AS/NZS 1170.3. The seismic mass at each level, mi, shall be taken as W/g. 6.2 EQUIVALENT STATIC METHOD 6.2.1 Equivalent static forces 6.2.1.1 General The set of equivalent static forces in the direction being considered that are specified in this Clause shall be assumed to act simultaneously at each level of the structure. 6.2.1.2 Horizontal seismic shear The horizontal seismic shear, V, acting at the base of the structure in the direction being considered shall be calculated from: V = C(TW, 6.2(1) where C,(T= the horizontal design action coefficient as given in Clause 5.2.1.1 for the ultimate limit state and Clause 5.2.1.2 for the serviceability limit state W = the seismic weight of the structure defined in Clause 4.2 6.2.1.3 Equivalent static horizontal force at each level The equivalent static horizontal force, F; at each level, i, shall be obtained from Equation 6.2(2) F = F, +0.92V Wh; w, h;) ... 6.2(2) i=1 where F= 0.08V at the top level and zero elsewhere. TABLE 3.1 REFERENCE VALUES OF IMPOSED FLOOR ACTIONS Uniformly distributed actions Concentrated actions KN kPa Type of activity/oceupaney for part of the building or Specific uses structure A Domestic and residential activities (also see Category C) Al Self-contained General areas, private kitchens and dwellings laundries in self-contained dwellings Balconies, and roofs used for floor type activities, in self-contained dwellings- (a) less than 1 m above ground level 1.5 1.8(1) 1.5 1.5 kN/m run along edge 2.0 1.811) 2.0 2.7 0.5 (b) other Stairs) and landings in self-contained dwellings Non-habitable roof spaces in self- contained dwellings General areas, bedrooms, hospital wards, hotel rooms, toilet areas Communal kitchens Balconies, and roofs used for floor type activities, with community access A2 Other 2.0 1.81) 3.0 2.7 same as areas providing access but not less than 4.0 1.8 B Offices and work areas not covered elsewhere Operating theatres, X-ray rooms, utility rooms 3.0 4.5 3.0 3.5 3.0 2.73) 3.0 2.7 5.0 Work rooms (light industrial) without storage Offices for general use Communal kitchens Commercial/institutional kitchens Laundries Laboratories Factories, workshops and similar buildings (general industrial) Balconies, and roofs used for floor type activities 4.5 4.5 3.0 3.0 4.5 5.0 4.5 1.8 Fly galleries in theatres, etc.) same as areas providing access but not less than 4.0 4.5 kN/m run uniformly distributed over the width 2.8 Grids (over the area of proscenium width by stage depth) AS/NZS 1170.1:2002 12 3.4.2| Reduction of uniformly distribution imposed actions The reduction factor (V.) shall be as follows: (a) va = 1.0 for the following: (i) Areas covered by activity or occupancy types C3, C4 and C5 (see Table 3.1). (ii) Storage areas on which imposed floor actions exceed 5 kPa. (iii) Light and medium traffic areas (activity or occupancy types F and G). (iv) Imposed actions from machinery and equipment for which specific design allowance has been made. (v) One-way slabs. 3 (b) but not greater than 1.0 and not less than 0.5. VA (b) V = 0.3 + where A = sum of all areas supported by a structural element, in square metre, for which reduction is not restricted under Clause 3.4.2(a) C4.1.2.2 Empirical method A (Ref. 5) 1.Ok, 0.75 1.25k, 10.75 = Il T for the serviceability limit state T for the ultimate limit state where ki 0.075 for moment-resisting concrete frames 0.11 for moment-resisting steel frames = 0.06 for eccentrically braced steel frames = 0.05 for all other frame structures H = height in m from the base of the structure to the uppermost seismic weight or mass. TABLE 3.3 ANNUAL PROBABILITY OF EXCEEDANCE Annual probability of exceedance for Annual probability of ultimate limit states exceedance Importance for serviceability limit states level SLS2 SESI Wind Snow Earthquake Importance level 4 only Design working life Construction equipment, e. props, scaffolding. braces and similar 2 1/100 1/50 1/100 1/25 1/25 1/25 1 2 3 4 1/25 Less than 6 months 1/50 1/100 1/250 1/25 1/25 5 years 1 2 3 4 1/25 1/25 1/25 1/250 1/25 1/50 1/100 1/250 1/25 1/50 1/100 1/250 1/25 1/100 1/250 1/1000 1/25 1/250 1/500 1/1000 1/50 1/250 1/500 1/1000 1/100 1/500 1/1000 1/2500 1/100 1/250 1/1000 1/25 1/250 1/500 1/1000 1/50 1/250 1/500 1/1000 1/100 1/500 1/1000 1/2500 1/250 1/1000 1/2500 25 years 1 2 3 4 1/25 1/25 1/25 1/250 .IIIIIIIIIIII 50 years 1 2 3 4 1/50 1/150 1/250 1/500 1/23 1/25 1/25 1/500 1 100 years or more 1/150 1/250 1/500 1/250 1/1000 1/2500 1/25 1/25 1/25 For importance level 4 structures with a design working life of 100 years or more, the design events are determined by a hazard analysis but need to have probabilities less than or equal to those for importance level 3. Design events for importance level 5 structures should be determined on a case by case basis. SECTION 3 SITE HAZARD SPECTRA 3.1 ELASTIC SITE SPECTRA FOR HORIZONTAL LOADING 3.1.1 Elastic site spectra The elastic site hazard spectrum for horizontal loading, C(T), for a given return period shall be as given by Equation 3.1(1): () = C(D) ZRN(TD) ... 3.1(1) where C.(T) = the spectral shape factor determined from Clause 3.1.2 z = the hazard factor determined from Clause 3.1.4 = the return period factor Ror R, for the appropriate limit state determined from Clause 3.1.5 but limited such that ZR does not exceed 0.7 N(T.D) = the near-fault factor determined from Clause 3.1.6 3.1.2 Spectral shape factor, Ch(T) The spectral shape factor, C(T). shall be selected from Table 3.1, for the site subsoil class defined in Clause 3.1.3. The spectral shape factor functions are graphed in Figure 3.1 for general cases and in Figure 3.2 for values for the modal response spectrum and the numerical integration time history methods, to determine the C(T) values required for vertical loading, and to determine the Co) values required to evaluate C(O) for parts in Clause 8.2. R TABLE 3.1 SPECTRAL SHAPE FACTOR, C. (T) Spectral shape factor, CT 3.00 Period, T Site subsoil class (seconds) c D E Strong rock and Shallow soil Deep or soft soll Very soft soil B rock 0.0 1.89 (100) 2.36 (1.33) 3.00 (1.12) 0.1 1.89 (2.35) 2.36 (2.93) 3.00 0.2 1.89 (2.35) 2.36 (293) 3.00 0.3 1.89 (2.35) 2.36 (2.93) 0.4 1.89 2.36 3.00 0.5 1.60 2.00 3.00 0.6 1.40 1.74 2.84 3.00 0.7 1.24 1.55 2.53 3.00 0.8 1.12 1.41 2.29 3.00 0.9 1.03 1.29 2.09 3.00 1.0 0.95 1.19 1.93 3.00 1.5 0.70 0.88 1.43 2.21 2.0 0.53 0.66 1.07 1.66 2.5 0.42 0.53 0.86 1.33 3.0 0.35 0.44 0.71 1.11 3.5 0.26 0.32 0.52 0.81 4.0 0.20 0.25 0.40 0.62 4.5 0.16 0.20 0.32 0.49 NOTE: 1 Values in brackets correspond to spectral values for the modal response spectrum and the numerical integration time history methods, to the C(7) values required for vertical loading, and to the GCO) values required to evaluate C(O) for parts in Clause 8.2. NZS 1170.5:2004 12 3.5 3.0 2.5 2.0 Spectral shape factor, C.(T) Solltype D Soil type 1.5 Soil type 1.0 Soil types A&B 0.5 0.0 0 0.5 1 1.5 2.5 3 3.5 4.5 2 Period, T (5) FIGURE 3.1 SPECTRAL SHAPE FACTOR, ChiT) - GENERAL SIDO TABLE 3.3 Z-VALUES AND SHORTEST MAJOR FAULT DISTANCES D FOR NEW ZEALAND LOCATIONS (North to South) # Location Z D(km) # Location Z D(km) 1 Kaitaia 0.13 48 Raetihi 0.26 2 Paihia/Russell 0.13 49 Ohakune 0.27 3 Kaikohe 0.13 50 Waiouru 0.29 4 Whangarei 0.13 51 Napier 0.38 5 Dargaville 0.13 52 Hastings 0.39 6 Warkworth 0.13 53 Wanganui 0.25 7 Auckland 0.13 54 Waipawa 0.41 8 Manakau City 0.13 55 Waipukurau 0.41 9 Waiuku 0.13 56 Taihape 0.33 10 Pukekohe 0.13 57 Marton 0.30 11 Thames 0.16 58 Bulls 0.31 12 Paeroa 0.18 59 Feilding 0.37 13 Waihi 0.18 60 Palmerston North 0.38 8-16 14 Huntly 0.15 61 Dannevirke 0.42 10 15 Ngaruawahia 0.15 62 Woodville 0.41 32 16 Morrinsville 0.18 63 Pahiatua 0.42 8 17 Te Aroha 0.18 64 Foxton/Foxton 0.36 18 Tauranga 0.20 Beach 19 Mount Maunganui 0.20 65 Levin 0.40 20 Hamilton 0.16 66 Otaki 0.40 21 Cambridge 0.18 67 Waikanae 0.40 15-20 22 Te Awamutu 0.17 68 Paraparaumu 0.40 14-20 olol Woolpololesale Vio Etnogaas TABLE 3.5 RETURN PERIOD FACTOR Required annual probability of R or R, exceedance 1/2500 1.8 1/2000 1.7 1/1000 1.3 1.0 1/500 1/250 0.75 1/100 0.5 1/50 0.35 1/25 0.25 1/20 0.20 NOTE: Shaded rows correspond to annual probabilities of exceedance related to a 50 year design working life in Table 3.3 of AS/NZS 1170.0. 3.1.6 Near-fault factor The near-fault factor, N(T.D), shall be determined from Equations 3.1(2) and 3.1(3) for locations at shortest distance, D. of less than 20 km from the nearest major fault listed in Table 3.6. The locations of these faults are shown in Figure 3.5. 3.1.6.1 Annual probability of exceedance 2250 NT.D) - 1.0 ... 3.1(2) 3.1.6.2 Annual probability of exceedance 20 km 3.1(3) where the shortest distance (in kilometres) from the site to the nearest fault listed in Table 3.6 Nmas(T) = the maximum near-fault factor and is linearly interpolated for period T from Table 3.7. = D 5.2 HORIZONTAL DESIGN ACTION COEFFICIENTS AND DESIGN SPECTRA 5.2.1 Equivalent static method - Horizontal design action coefficient 5.2.1.1 Ulrimare limir state For the ultimate limit state, the horizontal design action coefficient. CdT). shall be as given by Equation 5.2(1): crise C, (T) ky ...5.201) (2/20+ 0.02)R, but not less than 0.03R. ..5.2(2) where C (7) the ordinate of the elastic site hazard spectrum determined from Clause 3.1.1 S, = the structural performance factor determined by Clause 4.4 Z the hazard factor determined from Clause 3.1.4 taking account of the limitation on the value of ZR, given by Clause 3.1.1 For soil classes A, B, C and D ky for T, 2 0.75 = u (1-1)7 +1 for T, 20 km 3.1(3) where the shortest distance (in kilometres) from the site to the nearest fault listed in Table 3.6 Nmas(T) = the maximum near-fault factor and is linearly interpolated for period T from Table 3.7. = D 5.2 HORIZONTAL DESIGN ACTION COEFFICIENTS AND DESIGN SPECTRA 5.2.1 Equivalent static method - Horizontal design action coefficient 5.2.1.1 Ulrimare limir state For the ultimate limit state, the horizontal design action coefficient. CdT). shall be as given by Equation 5.2(1): crise C, (T) ky ...5.201) (2/20+ 0.02)R, but not less than 0.03R. ..5.2(2) where C (7) the ordinate of the elastic site hazard spectrum determined from Clause 3.1.1 S, = the structural performance factor determined by Clause 4.4 Z the hazard factor determined from Clause 3.1.4 taking account of the limitation on the value of ZR, given by Clause 3.1.1 For soil classes A, B, C and D ky for T, 2 0.75 = u (1-1)7 +1 for T,
