The given “Level” in the first column of Table 4.3-3 identifies items relevant to properties or results associated with that level. Items related to story drift (presented later in this chapter) are identified at the relevant “Story” of the building because these quantities represent the deformations between levels. Table 4.3-3 includes a mass computed for Level G of the building. This mass is associated with an extremely stiff story (the basement level) and is dynamically excited by the earthquake in very high frequency modes of response. As shown later, this mass is not included in equivalent lateral force computations, and can complicate modal response spectrum and modal response history analysis. Table 4.3-1. Area weights contributing to masses on diaphragms (See Fig. 4.3-5) Mass Source Area A Area B Area C Area D Area E Slab and Deck (psf) Structure (psf) Ceiling and Mechanical (psf) Partition (psf) Roofing (psf) Special (psf) Total (psf) 50 20 15 10 0 0 95 75 20 15 10 0 0 120 50 20 15 0 15 0 100 75 20 15 0 15 60 185 75 50 15 10 0 25 175 Table 4.3-2. Line weights contributing to masses on diaphragms (See Fig. 4.3-5) Mass Source Line 1 Line 2 Line 3 Line 4 Line 5 From Story Above (plf) From Story Below (plf) Total (plf) 60.0 93.8 153.8 93.8 93.8 187.6 93.8 0.0 93.8 93.8 135.0 228.8 135.0 1,350.0 1,485.0 Figure 4.3-5. Key diagram for computation of floor weights
Table 4.3-23b. Matching parameters for Loma Prieta earthquake Parameter Original G03000 Modified G03000 Original G03090 Modified G03090 PGA (g) 0.555 0.433 0.367 0.402 PGV (in./s.) 14.1 17.1 17.6 17.4 PGD (in.) 2.91 4.68 7.59 5.06 Dominant Frequency (Hz) 0.873 0.403 0.256 0.958 Correlation Coefficient 0.0451 0.1126 0.0451 0.1126 Duration of Corrective Acceleration (s.) 0.00 5.975 0.00 7.205 Duration of Blank Padding (s.) 7.205 1.230 7.205 0.00 Table 4.3-23c. Matching parameters for Chi Chi earthquake Parameter Original TCU045-E Modified TCU04-E Original TU045-N Modified TU045-N PGA (g) 0.474 0.447 0.512 0.435 PGV (in./s.) 14.5 17.5 10.8 10.2 PGD (in.) 8.45 9.41 5.28 6.69 Dominant Frequency (Hz) 0.781 0.708 0.659 0.760 Correlation Coefficient 0.335 0.122 0.335 0.122 Duration of Corrective Acceleration (s.) N.A. 0.00 N.A. 0.00 Duration of Blank Padding (s.) N.A. 0.0 N.A. 0.00 (a) Unmatched
Loma Prieta: GO3090 VEY min=-3701 VEY max=3623 Y=1114/(3701/8)=2.41 Chi Chi TCU045-N VEY min=-2080 VEY max=3140 Y=1114/(3140/8)=2.84 Calculation of Scale Factors for results including P-Delta Northridge: MUL009 VEX min=-2289 VEX max=2213 X =1114/(2289/8)=3.89 Loma Prieta: GO3000 VEX min=-3263 VEX max=3088 X =1114/(3263/8)=2.73 Chi Chi TCU045-E VEX min=-2478 VEX max=2519 X =1114/(2519/8)=3.54 Northridge: MUL2799 VEY min=-3300 VEY max=3403 Y =1114/(3403/8)=2.62 Loma Prieta: GO3090 VEY min=-3651 VEY max=3401 Y =1114/(3651/8)=2.44 Chi Chi TCU045-N VEY min=-2402 VEY max=3047 Y =1114/(3047/8)=2.93 Results for all analyses are presented in Tables 4.3-24 through 4.3-39. These include story drifts in Frames 1 and 5 and shears in the middle bays beams of Frames 1 and 5. Analysis either did not or did include P-delta effects as indicated, and accidental torsion and orthogonal load effects were included as appropriate. Results are discussed in the context of the other methods of analysis in Section 4.3.6.4 of this example. Combinations shown in the Tables are relative to Figure 4.3-12 as follows:
zs = 1.0 Rs = 3.0 (12.10-11) (12.10-12) (12.10-8) (12.10-9) (12.10-10a) (12.10-6) (12.10-7) Roof - Strength Level: (12.10-4) But not less than: Fpr = 0.2SDSIewpr = 0.2(1.0)(1.0)(194.1) = 38.8 kips (12.10-5) Roof - ASD Level: Fpr = 0.7(44 kips) = 30.8 kips 3rd Floor - Strength Level: Cp3 = 0.40 (12.10-4) But not less than: Fp3 = 0.2SDSIewp3 = 0.2(1.0)(1.0)(180.2) = 36 kips (12.10-5) 3rd Floor - ASD Level: Fp3 = 0.7(36.0 kips) = 25.2 kips 2nd Floor - Strength Level: Cp2 = 0.40 (12.10-4) But not less than: Fp2 = 0.2SDSIewp2 = 0.2(1.0)(1.0)(180.2) = 36 kips (12.10-5) 2nd Floor - ASD Level: Fp2 = 0.7(36.0 kips) = 25.2 kips Comparison Summary - ASD Level Fpx Forces (#) Level ASCE 7-16 2015 NEHRP Provisions Roof 30,800 30,800 3rd 25,200 25,200 2nd 25,200 25,200
Table 7.1-1 Geotechnical Parameters Parameter Value Basic soil properties Medium dense sand (SPT) N = 20  = 125 pcf Angle of internal friction = 33 degrees Bearing capacity (Nominal foundation geotechnical capacity) 3,000B psf for concentrically loaded square footings 4,000B' psf for eccentrically loaded footings where B and B' are in feet, B is the footing width and B' is an average width for the compressed area. Resistance factor,  = 0.45 per Table 12.13-1 of the Standard Lateral properties Earth pressure coefficients: Active, KA = 0.3 At-rest, K0 = 0.46 Passive, KP = 3.3 Sliding friction coefficient at base of footing = 0.65 Resistance factor,  = 0.85 per Table 12.13-1 of the Standard Allowable soil bearing for sustained loads to control settlement (serviceability verification) ≤ 2,000 psf for B ≤ 20 feet ≤ 1,000 psf for B ≤ 40 feet (may interpolate for intermediate dimensions) The structural material properties assumed for this example are as follows: f'c = 4,000 psi fy = 60,000 psi 7.1.1.2 Seismic Parameters. The complete set of parameters used in applying the Provisions to design of the superstructure is described in Section 6.2.2.1 of this volume of design examples. The following parameters, which are used during foundation design, are duplicated here.
The structural material properties assumed for this example are as follows: f'c = 3,000 psi fy = 60,000 psi 7.2.1.2 Seismic Parameters. Site Class = C and E (both conditions considered in this example) SDS = 1.1 Seismic Design Category = D (for both conditions) 7.2.1.3 Demands. The unfactored demands from the moment frame system are shown in Table 7.2-2. Table 7.2-2 Gravity and Seismic Demands Location Load Vx Vy P Mxx Myy Corner D -460.0 L -77.0 Vx 55.5 0.6 193.2 4.3 624.8 Vy 0.4 16.5 307.5 189.8 3.5 ATx 1.4 3.1 26.7 34.1 15.7 ATy 4.2 9.4 77.0 103.5 47.8 Side D -702.0 L -72.0 Vx 72.2 0.0 0.0 0.0 723.8 Vy 0.0 13.9 181.6 161.2 1.2 ATx 0.4 1.8 2.9 18.1 4.2 ATy 1.2 5.3 8.3 54.9 12.6 Note: Units are kips and feet. Load Vy is for loads applied toward the east. ATx is the corresponding accidental torsion case. Load Vx is for loads applied toward the north. ATy is the corresponding accidental torsion case. Using Load Combinations 5 and 7 from Section 12.4.2.3 of the Standard (with 0.2SDSD = 0.22D and taking  = 1.0), considering orthogonal effects as required for Seismic Design Category D and including accidental torsion, the following 32 load conditions must be considered. 1.42D + 0.5L ± 1.0Vx ± 0.3Vy ± max(1.0ATx, 0.3ATy) 1.42D + 0.5L ± 0.3Vx ± 1.0Vy ± max(0.3ATx, 1.0ATy)
While it is not explicitly required, site specific response spectra, is recommended for soil-structure interaction. Because the soil structure interaction effects alter the foundation input motion or seismic demands on a structure due to changes in damping, it is important to have an accurate representation of the free field motion at the site. Site specific response spectra can even be developed at the foundation depth, directly incorporating embedment effects instead of using the equations in Chapter 19 to estimate those effects. 8.3 A four story reinforced concrete shear wall building with one basement will be used to illustrate the soil structure interaction provisions of the Standard. The building is located in a region of very high seismicity, within 5 miles of an active fault with subsurface material that would be characterized as Site Class D. The average shear wave velocity for 100 feet below the ground is 800 ft/s based on the geotechnical investigation at the site. A site specific response spectrum was developed in accordance with Chapter 21 of the Standard and shown below in Figure 8-1. SDS and SD1 are 1.0 and 0.71 respectively, placing the building in Seismic Design Category E. Figure 8.3-1: Site Specific Spectra The building used for the example is approximately 53 feet tall and the basement is 15 feet below grade. Figure 8-2 shows an elevation of the building. The building is rectangular with a north south dimension of 180 feet and an east-west dimension of 150 feet. Floor slabs are reinforced concrete flat plates and the columns are rectangular cast-in-place concrete situated on spread footings. The lateral forces are resisted by cast-in-place special reinforced concrete shear walls. There is a reinforced concrete wall around the entire basement. The interior walls and columns are founded on spread footings and the basement wall is founded on a continuous strip footing. Figure 8-3 shows a foundation plan of the building. The weight of each floor is summarized in Table 1. Table 1: Story Weight Story Weight Fourth 4,000 kips Third 4,100 kips Second 4,100 kips First 4,400 kips
The following parameters will be needed to calculate radiation damping B = Half the shorter dimension of the structure’s foundation footprint = 150 ft / 2 = 75 ft for this structure L = Half the longer dimension of the structure’s overall foundation footprint = 180 ft / 2 = 90 ft for this structure T = Fixed base period = 0.39 s = Flexible base period = 0.49 s (typically the upper bound value since it will produce the least reduction) vs = Effective shear wave velocity over a depth equal to ‘B’ below the foundation = 570 ft/s G = Effective shear modulus over a depth equal to ‘B’ below the foundation = 1,200 k/ft2 ν = Poisson’s ratio of the soil = 0.3 M* = Fundamental mode effective mass = 14,500 kips (from the analysis model) h* = Effective structure height at the fundamental mode = h / (Γϕroof) = 41.5 ft (from the analysis model) To determine the translational contribution to radiation damping, first the fictitious periods Ty is calculated. Where Then the translational contribution to radiation damping is computed as