form 1 certificate of seismic performance level uc ......mulford hall evaluation august 8, 2011 uc...

Campus: UC Berkeley

Building Name: Mulford Hall

CAAN ID: 1346

Auxiliary Building ID: N/A Date: 6/17/2019

This Form 1 (January 4, 2019) is to be used in connection with Guidebook, Version 1.2, Section III.A.3.c-f

FORM 1

CERTIFICATE OF SEISMIC PERFORMANCE LEVEL

☒ UC-Designed & Constructed Facility

☐ Campus-Acquired or Leased Facility

BUILDING DATA


Address: Core Campus, Univervisty of California, Berkeley

Site location coordinates: Latitude 37.8726 Longitudinal -122.2645

UCOP SEISMIC PERFORMANCE LEVEL (OR “RATING”): V

ASCE 41-17 Model Building Type:

a. Longitudinal Direction: C2 Concrete Shear Wall

b. Transverse Direction: C2 Concrete Shear Wall

Gross Square Footage: 93,547

Number of stories above grade: Four plus Attic (Five Total)

Number of basement stories below grade: None (Lowest level is partially embedded)

Year Original Building was Constructed: 1948

Original Building Design Code & Year: UBC 1946 Assumed

Retrofit Building Design Code & Code (if applicable): N/A

COST RANGE TO RETROFIT It is estimated that the retrofit cost will be High: over $200 per sf and less than

$400 per sf.

FLLING HAZARD RISK: Moderate

SITE INFORMATION

Site Class: C Basis: (Geologic Hazards and Site Classification, Geomatrix, Plate 2)

Geologic Hazards:

Fault Rupture: No Basis: California Geological Survey Website

https://maps.conservation.ca.gov/cgs/informationwarehouse/regulatorymaps/

Liquefaction: No Basis: California Geological Survey Website


Landslide: No Basis: California Geological Survey Website


ATTACHMENT

Seismic Evaluation: (1997 UCB Safer, Forell Elsesser, 1997, FEMA 178; 2011 Seismic Evaluation Report,

Forell Elsesser)

Campus: UC Berkeley


CAAN ID: 1346



CERTIFICATION

I, Russell Berkowitz, a California-licensed structural engineer, am responsible for the completion of this

certificate, and I have no ownership interest in the property identified above. My scope of review to

support the completion of this certificate included both of the following:

a) the review of structural drawings indicating that they are as-built or record drawings, or that they

otherwise are the basis for the construction of the building: Yes ☐ No

b) visiting the building to verify the observable existing conditions are reasonably consistent with

those shown on the structural drawings: Yes ☐ No

Based on my review, I have verified that the UCOP Seismic Performance Level is presumptively

permitted by the following UC Seismic Program Guidebook provision (choose one of the following):

☐ 1) Contract documents indicate that the original design and construction of the aforementioned

building is in accordance with the benchmark design code year (or later) building code seismic design

provisions for UBC or IBC listed in Table 1 below.

2) The existing SPL rating is based on an acceptable basis of seismic evaluation completed in 2006 or

later.

☐ 3) Contract documents indicate that a comprehensive1 building seismic retrofit design was fully-

constructed with a design completed in 2000 or later, and that design was based on ground motion

parameters, at a minimum, corresponding to:

☐ BSE-1E (or BSE-R) and BSE-2E (or BSE-C) as defined in ASCE 41, or the full design basis

ground motion required in the 1997 UBC/1998 CBC or later for EXISTING buildings, and is

presumptively assigned an SPL rating of IV.

☐ BSE-1 (or BSE-1N) and BSE-2 (or BSE-2N) as defined in ASCE 41, or the full design basis

ground motion required in the 1997 UBC/1998 or later CBC for NEW buildings, and is

presumptively assigned an SPL rating of III.

Russell Berkowitz Senior Associate AFFIX SEAL HERE

Print Name Title

S4884

6/30/2020

CA Professional Registration No. License Expiration Date

6/13/2019

Signature Date

Forell / Elsesser Engineers, 415-837-0700, 160 Pine St., 6th Flr.,

San Francisco, CA 94111

Firm Name, Phone Number, and Address

1 A comprehensive retrofit addresses the entire building structural system as indicated by the associated seismic evaluation, as opposed to

addressing selective portions of the structural system.

Campus: UC Berkeley


CAAN ID: 1346



Table 1: Benchmark Building Codes and Standards

UBC IBC

Wood frame, wood shear panels (Types W1 and W2) 1976 2000

Wood frame, wood shear panels (Type W1a) 1976 2000

Steel moment-resisting frame (Types S1 and S1a) 1997 2000

Steel concentrically braced frame (Types S2 and S2a) 1997 2000

Steel eccentrically braced frame (Types S2 and S2a) 1988g 2000

Buckling-restrained braced frame (Types S2 and S2a) f 2006

Metal building frames (Type S3) f 2000

Steel frame with concrete shear walls (Type S4) 1994 2000

Steel frame with URM infill (Types S5 and S5a) f 2000

Steel plate shear wall (Type S6) f 2006

Cold-formed steel light-frame construction—shear wall system (Type CFS1) 1997h 2000

Cold-formed steel light-frame construction—strap-braced wall system (Type CFS2) f 2003

Reinforced concrete moment-resisting frame (Type C1)i 1994 2000

Reinforced concrete shear walls (Types C2 and C2a) 1994 2000

Concrete frame with URM infill (Types C3 and C3a) f f

Tilt-up concrete (Types PC1 and PC1a) 1997 2000

Precast concrete frame (Types PC2 and PC2a) f 2000

Reinforced masonry (Type RM1) 1997 2000

Reinforced masonry (Type RM2) 1994 2000

Unreinforced masonry (Type URM) f f

Unreinforced masonry (Type URMa) f f

Seismic isolation or passive dissipation 1991 2000

Note: UBC = Uniform Building Code . IBC = International Building Code .a Building type refers to one of the common building types defined in Table 3-1 of ASCE 41-17.b Buildings on hillside sites shall not be considered Benchmark Buildings.c not usedd not usede not usedf No benchmark year; buildings shall be evaluated in accordance with Section III.J.

h Cold-formed steel shear walls with wood structural panels only.i Flat slab concrete moment frames shall not be considered Benchmark Buildings.

Building Seismic Design Provisions

g Steel eccentrically braced frames with links adjacent to columns shall comply with the 1994 UBC Emergency Provisions, published September/October

1994, or subsequent requirements.

Building Typea,b

Note: This table has been adapted from ASCE 41-17 Table 3-2. Benchmark Building Codes and Standards for Life Safety Structural Performed at BSE-1E.

SEISMIC EVALUATION REPORT

OF

MULFORD HALL

UNIVERSITY OF CALIFORNIA AT BERKELEY

prepared for University of California at Berkeley Capital Projects 1936 University Avenue, 2ND Floor Berkeley, CA 94720 prepared by FORELL/ELSESSER ENGINEERS, INC. 160 Pine Street San Francisco, CA 94111 **FINAL**

AUGUST 2011

Mulford Hall Evaluation August 8, 2011 UC Berkeley

- 1 - FORELL/ELSESSER ENGINEERS, INC.

1. Executive Summary Mulford Hall has been the subject of two previous evaluation reports issued in 1997 and 2002. Both of the these evaluations rated the building as “Poor” based on the U.C. Berkeley rating system considering the 10%/50 year hazard (475 year return period.) It is recommended that the rating be upgraded to “FAIR”. This recommendation is based on the proposed U.C. Berkeley rating system considering the seismic performance using nonlinear response history analysis. In particular, it is shown that Mulford Hall is expected to meet or exceed Life-Safety and Collapse Prevention performance under the 2/3 x 225 year return period (2/3 x 20%/ 50 year) and 2/3 x 975 year return period (2/3 x 5%/50 year) hazard levels, respectively. It should be noted that the 10%/50 year hazard used in the previous studies falls between the 2/3 x 975 year return period and 975 year return period hazard levels.

2. Goals of Current Evaluation The focus of the current evaluation is to review the “Poor” ratings of the previous studies. The 1997 study is based on a FEMA 178 evaluation, while the 2002 study used Pushover Analysis to evaluate the structural capacity. This study uses nonlinear response history analysis procedures to review the previous report findings. The seismic deficiencies noted previously are evaluated based on the building response to a set ground motions prepared by URS in May, 2009 for the U.C. Berkeley campus, scaled to represent various seismic hazards. The current evaluation and rating is based on the proposed guidelines for the U.C. Earthquake Performance Levels for Existing Buildings. These proposed Guidelines link the current U.C. rating system to the 2010 California Building Code for existing buildings.

3. Existing Building Information This evaluation is based on the historic structural and architectural drawings obtained from U.C. Berkeley Capital Projects. The drawings are dated January 1947. The design team indicated in the title block includes:

Miller & Warnecke Architects Arthur Brown Jr. Supervising Architect William C. Hays Consulting Architect Huber & Knapik Civil Engineers Clyde S. Bentley Mechancial Engineers

The drawings available include:

Structural Sheets S-1 through S-11, and S-13 Architectural Sheets A-1 and A-2

In addition to the drawings, a site visit and walk-through was conducted in November 2010 to verify the information contained in the drawings and to evaluate overall building physical condition.



4. Building Properties 4.1 Building Description, Occupancy and Location Mulford Hall, encompassing 72,000 overall gross square feet, is a four story concrete building with mechanical roof area located just east of the Warren Hall at the northwest corner of the main Berkeley Campus. The building is occupied by the Department of Natural Resources and contains faculty offices, classrooms, a library, and laboratories. The building was originally constructed in 1947 and has had no significant structural modifications since that time. The building is characterized by a C-shaped plan in which the two short transverse wings at either end of the main longitudinal wing project out at orthogonal angles. The building is located on a mildly sloping site, but a perimeter exterior areaway on the uphill side means that all stories are effectively above grade.

Figure 1. Aerial View of Campus and Building Location



Figure 2: North Building Elevation

Figure 3: Typical Building Floor Plan (Blue indicates shear walls, Red indicates perimeter piers) 4.2 Building Construction 4.2.1 Materials Mulford Hall is constructed mainly of reinforced concrete. There is no information given



regarding the strength of concrete on the available drawings. Based on the default lower-bound compressive strength of reinforced concrete values listed in ASCE 41 Table 6-3 the strength is taken as 2,500 psi. Per drawing sheet S-9 all concrete reinforcing consists of deformed bars meeting the A-15-39 specification for Structural Grade. Based on the default lower-bound properties of reinforcing listed in ASCE 41 Table 6-2 the yield and tensile strengths are taken as 33 ksi and 55 ksi, respectively. 4.2.2 Gravity Framing The typical floor construction is a 4-1/2” to 6" thick reinforced concrete (R/C) slab which spans longitudinally between transverse R/C beams. The R/C beams are supported by R/C columns in the interior of the building and bear directly on the exterior R/C walls around the perimeter of the building. The roof is a tile roof on a plywood diaphragm supported by sloping wood beams. The foundation system consists of R/C spread footings at all column locations and grade beams around the perimeter. 4.2.3 Lateral Force Resisting System The primary lateral force resisting system in both the longitudinal and transverse direction consists of a punched pier-and-spandrel system around the exterior and a combination of interior shear walls at the stair cores and shear wall piers at the corners of the building. The perimeter piers vary in thickness from 10” to 12” with boundary elements measuring 12” x 24”. Pier reinforcing is generally two layers of #4 bars at 12” in each direction, with #6 or #7 boundary bars. Spandrel thicknesses vary from 9” to 12” and are reinforced generally two layers of #4 bars at 12” in each direction, with larger longitudinal bars at the edges ranging from #7 to #9. The shear walls at the exterior corners of the building range from 8” to 12” thick and are reinforced similarly to the exterior piers. The interior shear walls at the cores are generally 8” thick with one layer of #4 bars at 10” in both directions. The reinforced concrete gravity beams and columns act as a secondary lateral system. All of the beams and columns are governed by flexural behavior.

5. Key Items for Evaluation The 1997 and 2002 evaluations noted a number of potential deficiencies including:

Inadequate lateral strength / deformation capacity – In the longitudinal direction the base shear capacity was determined to be approximately 25% to 30% of the building weight. In the transverse direction the base shear capacity was determined to be approximately 10% to 12% of the building weight. In both cases the capacity was well below the expected demands. There is a potential for story mechanisms to form as the spandrels and piers lose capacity at larger deformations.

Inadequate overturning resistance at cores – The stair cores are supported by spread footings and small grade beams. Due to the lack of tie downs and low gravity loads it is anticipated that the cores will rock and offer little seismic resistance.

Diaphragm openings, re-entrant corners and lack of collectors – The floor openings at the stair cores limit the ability of the diaphragms to deliver load to the shear walls. The opening at the southern stair core is located adjacent to a re-entrant corner which will lead to large demands on the adjacent diaphragm.



Concrete spalling / deterioration – A survey of the building exterior noted that there are

several locations where the concrete is spalling, leading to exposed reinforcement.

Discontinuous concrete shear wall – There is a shear wall between the Main Level and Level 2 that is discontinuous which may lead to high column and diaphragm shear demands.

Overall lack of ductile detailing. The focus of this evaluation is to assess the overall seismic performance of Mulford Hall considering the issues listed above using a 3D nonlinear computer model for various hazard levels.

6. Acceptance Criteria The structure was analyzed for multiple hazard levels including 225 year (referred to herein as the BSE-R hazard level), 2/3 x 225 year, 975 year (referred to herein as the BSE-C hazard level), and 2/3 x 975 year return periods. The U.C. Berkeley Performance rating system criteria states that for a building to be considered “GOOD” the evaluation must show that the structure meets the S-3 (Life-Safety) performance level for the BSE-R hazard level, and S-5 (Collapse Prevention) for the BSE-C hazard level (where S-3 and S-5 are described in ASCE 41). For a building to considered “FAIR” the evaluation must show what the structure meets the S-3 performance level for the 2/3 BSE-R hazard level, and S-5 performance level for the 2/3 BSE-C hazard level. All nonlinear elements have the full backbone curve including strength degradations and residual strength included in accordance with Section 3.4.3.2 of ASCE 41 Supplement 1. Therefore, the deformation limits are taken as those for Secondary Components in accordance with ASCE 41 Supplement 1.

7. Seismic Hazard and Ground Motions 7.1 Development of Hazard Spectra The 2009 URS report contains site-specific acceleration spectra at four hazard levels for Rock and Thin Soil sites. The Mulford Hall site is consistent with a “Thin Soil” site. Four hazard levels were studied as part of this report, BSE-C, BSE-R, 2/3BSE-C and 2/3BSE-R. Chapter 34 of the California Building Code associates BSE-C with a mean return period of 975 years, and BSE-R with a mean return period equal to 225 years. In order to develop spectra associated with these levels, the 475 year return period values in the URS report are adjusted in accordance with Eq. 1-3 of ASCE 41-06: Si = Si10/50 = (PR / 475)n The BSE-C hazard level has a mean return period of 975 years. Per ASCE 41-06 Table 1-1 the value of the exponent “n” shall be taken as 0.29. Therefore, to compute the 975 year spectrum the 475 URS spectral values are multiplied by (975 / 475)0.29 = 1.23. To compute the 2/3 BSE-C spectrum the 975 values are multiplied by 2/3 (or 1.23 x 2/3 = 0.82 x 475 values.) To determine



the approximate mean return period, ASCE 41-06 states that the exponent “n” shall be taken as 0.44 for probabilities of exceedance greater than 10%/50 years. This produces a mean return period of (0.82)(1/0.44) x 475 = 303 years. The BSE-R hazard level has a mean return period of 225 years. Per ASCE 41-06 Table 1-3 the value of the exponent “n” shall be taken as 0.44. Therefore, to compute the 225 year spectrum the 475 URS spectral values are multiplied by (225 / 475)0.44 = 0.72. To compute the 2/3 BSE-R spectrum the 225 values are multiplied by 2/3 (or 0.72 x 2/3 = 0.48 x 475 values.) To determine the approximate mean return period, ASCE 41-06 states that the exponent “n” shall be taken as 0.44 for probabilities of exceedance greater than 10%/50 years. This produces a mean return period of (0.48)(1/0.44) x 475 = 90 years. The spectra are modified for the base-slab averaging (BSA) effect in accordance with FEMA 440 equation 8-1; RRSbsa = 1- (1/14,100) * (be / T)1.2 >= RRSbsa value @ T = 0.2. For Mulford Hall, be = 135 ft.

Figure 4: Spectral Accelerations for various hazard levels 7.2 Scaling of Acceleration Records The 2009 URS report contained 21 sets of ground-acceleration records to be used at the UC Berkeley campus. For each hazard level, a set of ten records was chosen from the set. These records were scaled by multiplying both horizontal components by a scalar value. The scale factors were computed in accordance with ASCE 7-05 to match the target spectrum. ASCE 7-05 requires that the records be scaled such that the mean of the spectra of the records (taking the SRSS of the two horizontal directions) does not fall below 1.3 times the target spectrum by



more than 10% over the period range of 0.2T to 1.5T, where T is the fundamental period of the building. The ten records selected for the BSE-C and 2/3 BSE-C Hazard Levels are those recommended by the June 2003 U.C. Berkeley Seismic Guidelines for the 5% and 10% in 50 year Hazard Levels. For the BSE-R and 2/3 BSE-R a group of seven of the records from the group described above were used, while three records were replaced with other records recommended by the 2003 UC Berkeley Seismic Guidelines for lower Hazard Levels.

EQ Record 2/3 BSE‐R BSE‐R 2/3 BSE‐C BSE‐C

CL_gil6 0.87 1.28 N/A N/A

EZ_erzi 0.67 1.01 1.19 1.82

LP_cor 0.53 0.81 0.98 1.47

LP_gav 0.80 1.21 1.47 2.17

LP_lgpc 0.53 0.81 0.91 1.4

LP_srtg 0.87 1.35 1.61 2.38

LV_fgnr 1.34 2.09 N/A N/A

MH_clyd 0.50 0.67 N/A N/A

TO_hino 0.50 0.61 0.7 1.05

TO_kofu 0.50 0.67 0.84 1.26

KB_kobj N/A N/A 0.7 1.12

LP_gilb N/A N/A 2.11 3.08

LP_lex1 N/A N/A 1.75 2.59

Table 1: Scale Factors for Time History Records

Figure 5: Scaled Response Spectra for 975 Year Return Period



Figure 6: Scaled Response Spectra for 225 Year Return Period

8. Computer Modeling The structure is analyzed using CSI Perform 3-D software. The model is analyzed using both nonlinear static pushover analysis and nonlinear response history analysis. The pushover analyses were used to check overall model behavior, while the response history analyses are used to check the acceptance of building performance at the various hazard levels. 8.1 Expected Strength of Materials 8.1.1 Concrete The lower-bound concrete compressive strength is taken as 2,500 psi as described earlier. ASCE 41 Table 6-4 recommends a factor of 1.5 to estimate the expected concrete strength from the lower-bound strength. Thus, the expected concrete strength is taken as f’ce = 3,750 psi. 8.1.2 Reinforcement The lower-bound yield and tensile strength are taken as 33ksi and 55ksi, respectively as described earlier. ASCE 41 Table 6-4 recommends a factor of 1.5 to estimate the expected strength from lower-bound strength. Thus, the expected yield and tensile strengths of the reinforcement is taken as fye = 41ksi and fue = 69ksi, respectively. 8.2 Modeling of Structural Elements



Modeling of member behavior and acceptance criteria are taken from ASCE 41-06. 8.2.1 Perimeter Spandrel Elements The perimeter spandrel elements are modeled using nonlinear frame elements. The elements are modeled with nonlinear behavior for both shear and flexure. The nonlinear flexural hinges are located at the face of the piers, while shear hinges are modeled at the midpoint of the frame elements. In general, the spandrels at lowest three levels exhibit shear-critical behavior, while the spandrels at the roof level exhibit flexure-critical behavior. The effective stiffness factor for bending is taken as 0.3 per ASCE 41 Table 6-5. The modeling parameters for this type of element are dependent on the shear demand V / (tw lw f’c

0.5) (see Figures 5 and 6 below.) The shear demand used is taken as the shear forces associated with development of flexural hinges at both ends of the element (note that the shear demand ranged from 2.9 – 5.3 times f’c

0.5.) Modeling of Flexural Hinges – The nonlinear flexural behavior of the perimeter spandrels is modeled using moment-rotation hinges. The backbone and acceptance criteria for these elements is taken from ASCE 41 Table 6-18 for shear wall coupling beams with conventional longitudinal reinforcement with nonconforming transverse reinforcement.

Figure 7: ASCE 41-06 Supplement 1 Modeling Parameters for Spandrel Flexural Hinges



Modeling of Shear Hinges – The nonlinear shear behavior of the perimeter spandrels is modeled using shear hinge – plastic strain. The backbone and acceptance criteria for these elements are taken from ASCE 41 Table 6-19 for shear wall coupling beams with conventional reinforcement and nonconforming transverse reinforcement. The shear hinge in Perform does not give the option for complete strength loss. To approximate the loss in strength the strength ratio is set to 0.01 at point “E”.

Figure 8: ASCE 41-06 Supplement 1 Modeling Parameters for Spandrel Shear Hinges

8.2.2 Perimeter Pier Elements The perimeter spandrel elements are modeled using nonlinear frame elements. The elements are modeled with nonlinear behavior for both shear and flexure. The nonlinear flexural hinges are located at the face of the spandrels, while shear hinges are modeled at the midpoint of the frame elements. In general, the piers exhibit flexure-critical behavior. The effective stiffness factor for in-plane bending is taken as 0.5, and 0.3 for out-of-plane bending per ASCE 41 Table 6-5. The modeling parameters for this type of element are dependent on the axial demand. The axial demand used is taken as the maximum forces associated with the time-history

Strength loss in Perform model



records. These forces, including both gravity and seismic actions, are typically in the range of 0.05Af’ce – 0.1Af’ce. Modeling of Flexural Hinges – The nonlinear flexural behavior of the perimeter piers is modeled using moment-rotation hinges. The backbone and acceptance criteria for these elements are taken from ASCE 41 Table 6-18 for shear walls and wall segments with non-confined boundaries. The shear in the element is taken as that associated with development of flexural hinges at the ends of the piers.

Figure 9: ASCE 41-06 Supplement 1 Modeling Parameters for Pier Flexural Hinges

Modeling of Shear Hinges – The nonlinear shear behavior of the perimeter piers is modeled using shear hinge – plastic strain. The backbone and acceptance criteria for these elements are taken from ASCE 41 Table 6-19 for Shear Wall and Wall Segments. The shear hinge in Perform does not give the option for complete strength loss. To approximate the loss in strength the strength ratio is set to 0.01 at point “E”.



Figure 10: ASCE 41-06 Supplement 1 Modeling Parameters for Pier Shear Hinges

8.2.3 Interior Shear Walls at Cores and Exterior Shear Walls at the Corners The shear walls are modeled using General Wall elements in Perform. The elements are modeled with nonlinear behavior for in-plane loading, and linear elastic behavior for out-of-plane loading. In-plane flexural behavior is modeled using fiber sections with nonlinear behavior. The fibers consist of steel reinforcement (modeled using non-buckling steel behavior) and compression-only concrete fibers.


=

0.0

03

=

0.0

04

=

0.0

06




Figure 11: Stress – Strain Backbone for Concrete Compression In-plane shear behavior is modeled using a nonlinear shear material. This material uses a full loop that may over-estimate the energy dissipation. To account for the pinching of the hysteresis loops energy dissipation factors that adjust the overall energy dissipation to a value consistent with pinching are used. The energy reduction scale factors used range from 0.5 down to 0.1 depending on the deformation level achieved in the current and all previous loading cycles.

Figure 12: ASCE 41-06 Supplement 1 Modeling Parameters for Wall Shear Behavior

8.2.4 Interior Gravity Beams The interior gravity beams are modeled with nonlinear frame elements. A check of the beams shows that they are flexure-critical and not subject to shear failures. Therefore, nonlinearity is only modeled for flexure. Nonlinear moment-rotation hinges are located at the face of the columns on both ends of the beams, with element behavior based on Table 6-7 of ASCE 41. The effective stiffness factor for bending is taken as 0.3 per ASCE 41 Table 6-5.




Figure 13: ASCE 41-06 Supplement 1 Modeling Parameters for Concrete Beam Flexural Behavior

8.2.5 Interior Gravity Columns The interior gravity columns are modeled with linear frame elements. The columns are generally flexure-critical and are not subject to shear failures. The columns are stronger than the beams framing into them for flexure, and thus are assumed to remain essentially elastic. This assumption was checked by looking into the bi-direction flexure induced in the columns by the beams and found to be valid. The columns have low axial demands (approximately 0.1 Agf’c) and are thus modeled using an effective flexural stiffness factor of 0.3 per ASCE 41 Table 6-5.



8.2.6 Reinforced Concrete Diaphragms In general, the diaphragms are modeled as rigid elements. However, due to configuration issues there are portions of the diaphragms that are modeled as nonlinear general wall elements. The diaphragm opening at the Main, 2nd and 3rd Levels at the southern stair core creates a pinch-point in the diaphragm for loading in the transverse (North-South) direction. Therefore, nonlinear floor elements are used in this area to capture any nonlinear behavior. The mass of the Main, 2nd and 3rd Levels on either side of the pinch-point are divided based on tributary areas and applied as point masses to the rigid diaphragms on those levels. At the roof level there is no large opening and all of the mass is applied to one rigid diaphragm. At the Main Level near eastern wing of the building there are some solid shear walls around the perimeter. The diaphragm elements adjacent to these walls are modeled using nonlinear elements to capture any nonlinear behavior. The modeling of these elements is similar to that outlined in Section 8.2.3.

Figure 14: Main Floor Level Diaphragm



Figure 15: Level 2 and 3 Diaprhagms 8.2.7 Soil Spring Elements The behavior of the soil is modeled using compression-only bar elements with no tension capacity. The compression behavior is modeled using bilinear behavior to attempt to capture softening of the soil under high demands. A variety of stiffness and strength values were used to investigate the range of structural behavior to different foundation modeling assumptions. In general, it was determined that the variations in soil characteristics had little impact to overall structural behavior, including mechanism formation, element demands and story drifts. Therefore, the final analyses used soil behavior consistent with the Base Stiffness as shown below.

0

10

20

30

40

50

60

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Soil Bearing Stress (ksf)

Soil Deflection (in)

Range of Soil Spring Stiffness Investigated

Base Stiffness

1/2 x Base Stiffness

2 x Base Stiffness



Figure 16: Soil Spring Behavior 8.3 Seismic Mass The seismic mass properties of the structure were determined by summing up the self and superimposed translational and rotational masses of the structure. The masses are then applied to nodes slaved to the diaphragms as noted above. The seismic weight total is equal to 17,137 kips, which works out to a total weight per unit area of approximately 232 psf.

LevelWeight

(kips)

Rotational

MMI

(kip‐in Units)

Roof / Attic 4447 4.47E+09

3rd Level Diaphragm 1 2588 1.35E+09

3rd Level Diaphragm 2 1520 3.43E+08

2nd Level Diaphragm 1 2552 1.33E+09

2nd Level Diaphragm 2 1668 3.70E+08

Main Level Diaprhagm 1 2765 1.46E+09

Main Level Diaphragm 2 1595 3.55E+08

Table 2: Summary of Seismic Weight by Level and Diaphragm Area

8.4 Gravity Loading Gravity loads are applied to the elements as self-weight and tributary line loads. In general, the floor slabs span one-way between the interior gravity beams. The dead and live loads tributary to the beam elements are applied as uniform line loads. 8.5 Viscous Damping Viscous damping is modeled using Rayleigh damping by specifying damping ratios at two periods. For Mulford Hall, the damping ratio varies from 3% to 4% over the period range of 0.2T to 1.0T.

9. Analysis Results The summary of analysis results is presented below. The building performance is evaluated by looking at interstory drifts to assess overall building stability and local member behavior to assess local collapse potential. 9.1 Interstory Drifts Interstory drifts were tracked at several locations, including the center of mass, each main building corner and the corners at the re-entrant corners. The results shown below are for the maximum drift recorded at any level. In general, the largest drifts occurred at the North-West building corner. As noted earlier, the fault normal and fault parallel motions were applied in both 0 and 90 degree orientations. In general, it can be seen that the drifts associated with the fault normal component are much higher than the fault parallel component. Results for the BSE-R,



2/3 BSE-C and BSE-C hazard levels are presented. The 2/3 BSE-R drifts are quite low and are thus not shown. In general, it can be seen that the Interstory drifts are largest between the Main and 2nd Levels. The drifts are larger here as the spandrels at these levels hinge in shear and create a sway-type mechanism.

0

100

200

300

400

500

600

700

0.00% 0.50% 1.00% 1.50% 2.00%

Elevation (in)

Interstory Drift

Longitudinal Average Interstory Drifts

BSE‐C

BSE‐R

2/3 BSE‐C

0

100

200

300

400

500

600

700

0.00% 0.50% 1.00% 1.50% 2.00%

Elevation (in)

Interstory Drift

Transverse Average Interstory Drifts

BSE‐C

BSE‐R

2/3 BSE‐C

Figure 17: Average Interstory Drifts - Fault Normal Component Oriented Longitudinal



0

100

200

300

400

500

600

700

0.00% 0.50% 1.00% 1.50% 2.00%

Elevation (in)

Interstory Drift

Longitudinal Average Interstory Drifts

BSE‐C

BSE‐R

2/3 BSE‐C

0

100

200

300

400

500

600

700

0.00% 0.50% 1.00% 1.50% 2.00%

Elevation (in)

Interstory Drift

Transverse Average Interstory Drifts

BSE‐C

BSE‐R

2/3 BSE‐C

Figure 18: Average Interstory Drifts - Fault Normal Component Oriented Transverse

Figure 19: Interstory Drift Dispersion for BSE-C Fault-Normal Component



Figure 20: Interstory Drift Dispersion for 2/3 BSE-C Fault-Normal Component

Figure 21: Interstory Drift Dispersion for BSE-R Fault-Normal Component



9.2 Element Results In general, the overall acceptance of elements modeled with nonlinear behavior is checked by defining limit states as part of the nonlinear behavior. After the response history analyses are run the results are averaged over the set of ten time history records. The member acceptance as compared to the hazard level is displayed as a color-coded plot. The gravity column elements are modeled as linear elements, and thus, must be checked for acceptance by investigating their force demands from each analysis. Screen shots of the Perform model are shown below for the BSE-R, 2/3 BSE-C and BSE-C hazard levels. For the BSE-R hazard level, the S-3 (Life Safety) performance level is used. For the 2/3 BSE-C and BSE-C hazard levels, the S-5 (Collapse Prevention) performance level is used. Elements shown in red have demands that exceed the acceptance criteria per ASCE 41.

Figure 22: BSE-R Hazard Level with S-3 (Life Safety) Performance Level



Figure 23: 2/3 BSE-C Hazard Level with S-5 (Collapse Prevention) Performance Level



Figure 24: BSE-C Hazard Level with S-5 (Collapse Prevention) Performance Level 9.2.1 Lack of Detailing The seismic detailing of the concrete elements does not meet the requirements of current seismic design practice. However, the strength and deformation capacities of the existing elements recognize this fact and their behavior and acceptance are adjusted accordingly. See the sections below for discussion of the structural elements. 9.2.2 Perimeter Spandrels In general, the perimeter spandrels exceed the acceptance criteria for the three hazard levels presented. The spandrels yield and lose capacity in shear. They will likely suffer large shear cracking and sliding at the pier interface. However, the spandrel elements only carry their own self-weight and have well distributed reinforcement in both directions that will prevent large chunks of concrete from being dislodged or falling. Therefore, the fact that they are beyond the applicable limit state is not deemed to pose a threat to life safety.



9.2.3 Perimeter Piers In general, only the piers at the lowest level are pushed into the inelastic range. This is due to the deep spandrels at the base of the structure which are much stronger than the piers, causing the piers to yield in flexure just above the base spandrel level. This pier yielding at the base, coupled with the fact that the spandrels above form shear hinges and lose capacity tends to create a rigid body pier rotation mechanism. To investigate whether the rotations imposed at the base of the piers leads to a reduction in the ability of the piers to carry gravity loads, moment-rotation analyses were conducted on the piers. The computer program XTRACT was used to investigate the moment-curvature relationship of the piers for various levels of axial loads. It was found that at the highest anticipated axial loads the piers have a curvature limit of approximately 0.0005 x 1/in. This is the point at which the axial strength begins to deteriorate significantly due to spalling and crushing of concrete across a significant portion of the pier section to the point where the piers lose the ability to support the beams framing into them. For the BSE-R and 2/3 BSE-C hazard levels all of the piers were found to have sufficient curvature capacity to maintain vertical load carrying capacity. For the BSE-C hazard level all of the piers oriented in the longitudinal direction were found to have sufficient curvature capacity to maintain vertical load carrying capacity. However, for the BSE-C hazard level the piers along the West face of the structure in the transverse direction are pushed such that the curvature demands would lead to extensive crushing of the pier concrete. It is possible that these piers would lose their ability to carry their gravity loads at these large deformation demands. 9.2.4 Interior Shear Walls at Cores and Exterior Shear Walls at the Corners In general, the shear wall elements meet the applicable performance level for all hazard levels studied on average. The foundations under the walls typically lack the ability to prevent rocking of the walls, thus protecting them from seeing much inelastic demands at the lower levels. The long shear walls in the eastern portion of the structure have higher overturning capacity due to their overall length, and thus see higher demands. However, the demands on those walls are within the applicable acceptance limits. 9.2.5 Interior Gravity Beams The gravity beams are found to be acceptable for the performance levels associated with all hazards levels investigated. In general, the overall low drift demands (2% or less) produce very minor inelastic demands on the beam elements. Therefore, it is not anticipated that the beam demands will lead to a threat to life safety. 9.2.6 Interior Gravity Columns The gravity columns are flexure-critical and have higher capacities than the flexural demands imposed by the gravity beam elements. These facts, coupled with the overall low drift demands (2% or less) suggest that the gravity load carrying capability of the columns will not be compromised. The sloping slab at the lecture area of the Main Level creates a short column affect for the columns beneath the slab. These columns were checked and found to be flexure-critical even



with their shorter length compared to the typical columns. Similar to the typical columns, these short columns are expected to have sufficient deformation capacity to carry their gravity loads. 9.2.7 Concrete Diaphragms The concrete diaphragms are modeled as nonlinear shell elements at areas where the demands are expected to be high. Overall, the diaphragms show little-to-no yielding and are found to be sufficient for all hazard levels. 9.2.8 Concrete Deterioration In general, the extent of concrete deterioration is minor. It is not expected to have significant effect on the ability of the structure to withstand gravity or lateral loading. 9.2.9 Discontinuous Shear Wall The columns that support the discontinuous shear wall were checked to ensure they have sufficient axial capacity to withstand the forces imposed by the wall above and were found to be adequate. The diaphragm at the base of the wall was checked to ensure that the shear forces could be redistributed through the slab and was found to have adequate capacity.

10. Conclusion In conclusion, it is recommend that the building be rated as “FAIR” based on the proposed UC Rating System. This recommendation is based on the fact that the overall building and local element performance meets the S-3 Performance Limit for the BSE-R hazard level, and the S-5 Performance Limit for the 2/3 BSE-C hazard level. It has been noted that the spandrel elements will likely be significantly damaged, but they only carry their own weight and are not expected to pose a threat to life-safety. The structure is not expected to be a collapse hazard at either of these levels. At the BSE-C hazard level, a number of the piers at the base level could potentially lose the ability to carry gravity loads. This precludes the building from being rated as “GOOD”. It should be noted that the structure will likely be heavily damaged for the 2/3 BSE-C hazard level and above and may not be usable after an event of that magnitude. The building will likely require extensive repair, if it is salvageable at all.

form 1 certificate of seismic performance level uc ......mulford hall evaluation august 8, 2011 uc...

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