University of California at Berkeley Civil and Environmental Engineering Instructor: Stephen A. Mahin Spring Semester 2008 CEE 227 -- Earthquake Resistant Design Introduction to Class Project Building Most of the homework assignments this semester will be related to the design of a hypothetical structure to be constructed in Berkeley or the development and trial applications of simple tools that can be used in the design of such structures. The class homework assignment building is based on a theme building widely used in the literature. The original building was intended to be located in Los Angeles, but for the purposes of this class we will assume it is to be built in Berkeley, on a level rectangular site, located on firm soil approximately 2 km west of the Hayward Fault and 30 km east of the San Andreas Fault. The Hayward fault is assumed capable of generating an earthquake with a Richter magnitude of 7.2 and a magnitude 8+ earthquake is expected eventually on the San Andreas Fault. There are a number of smaller faults in the area. Thus, earthquake loads are a major design consideration in the overall design of this structure. Additional information on the seismic environment will be provided later. For our hypothetical building, we will assume the owner intends to use it as a hightechnology research facility, rather than as a normal office building (as envisioned in the original design of the building). Specifically, the building will have mixed use, housing a variety of nanofabrication labs, high performance computer workstations for computerassisted engineering as well as space for developing and prototyping advanced production systems. It will also house the corporate mainframe computer, which holds much of the company s proprietary software, intellectual property, and financial records. The company believes that a short shutdown of the building of a few days or possibly weeks would be acceptable under a rare event, but that a major shut down of three or more months would make them consider moving their office to Austin, Texas rather than build it in a seismic zone. For truly rare events, they want to minimize but not necessarily avoid damage, but the costs of protecting their intellectual and capital investments in the building would have to be weighed against costs. Based on discussions with the owner, the design life of the structure may be assumed to be 50 years. During the course of the semester, you will carry out a preliminary design of the structure using relatively conventional and more advanced procedures, and evaluate your design using a variety of analytical techniques. Because of the technological orientation of the client, and their active risk management program, this project allows for a lot of latitude in design. The building we will base our starting design upon was initially designed using the 1994 UBC, but now would need to be designed considering the 2003 CBC (equivalent to the 1997 UBC) as the minimum design requirements. We can use more stringent requirements to meet the owner s needs. In this class, we will use FEMA 356 (ASCE 41-06) to evaluate and improve the performance of the structure to satisfy the owner s special requirements. Some information is available about the 1994 design and
CE 227 - Homework Assignment No. 1 page 2 this will be provided throughout the semester, as required. However, you will see that code provisions have changed quite dramatically in the last decade, resulting in more than a doubling of the expected design forces. As such, some creativity is required in achieving an economical as well as safe structure. We will examine how to do this in these problem assignments. It will be assumed that the structure will be constructed from steel, and initially that it will be a moment-resisting frame. Other lateral load systems will be considered later (e.g., braced frames). If you are more comfortable using reinforced concrete, this would be acceptable. However, certain information (floor weights, etc.) will be specified for steel, and homework solutions will be worked out only for steel. Basic Description of the Building In addition to the information provided above, consider the following for the building. Additional information will be supplied later. Building Footprint: Building height: Story height: Column layout: Structural System: Building weights: 120 ft by 180 ft 3 stories; no basement; plus small penthouse 30 ft by 60 ft. in plan. 13 ft - 6 in. typical, including the penthouse a basic 30-ft grid in both directions is considered Special ductile moment frame in steel (see above comments and figures provided below) Steel framing - as designed, but consider 10 psf as a reasonable Estimate since the structure needs to be redesigned. Decking - 3 metal decking with an additional 3-1/4 inch thick NWC fill. Roofing - 7 psf average Ceiling - 3 psf Flooring - 3 psf Mechanical and Electrical - 7 psf on all floors, 50 psf average on floor within penthouse Partitions - 10 psf for seismic weight calculations, 20 psf for gravity load design Exterior cladding - Assume 25 psf of wall surface area on average for the entire building, including the penthouse. Live loads - use UBC provisions for office occupancies - 50 psf (area reduction factors are permitted) Based on these values, it has been estimated that the total weights of each floor are as follows (these values can be used in subsequent calculations of lateral loads and dynamic properties). The weight of the penthouse is included in the roof values given below.
CE 227 - Homework Assignment No. 1 page 3 Floor Dead Load (kips) Live Load (kips) Roof 1940 440 3 2370 1080 2 2370 1080 Soil Conditions: Foundations: stiff soil corresponding to FEMA 368/356 class D sites Spread reinforced concrete footings with allowable stresses of: DL = 4 ksf DL+LL = 6 ksf DL+LL+E = 8 ksf Simply supported beams and girders Penthouse over 4 @ Columns at each grid intersection 3 0 6 @ 30ʼ-0 ʼ - Planar welded moment-resisting space Plan View of Building
CE 227 - Homework Assignment No. 1 page 4 Elevation of Moment Resisting Frames based on 1994 UBC criteria General Notes on CEE 227 Assignments: Many of homework problems in this course are sequential in nature, building upon results obtained in prior solutions. For this reason, when you submit your assignments it is necessary for you to keep a copy of your solutions so you can work on the next week s assignment. Alternatively, you may base your next assignment on the solutions provided by the Teaching Assistant. Generally, it is best to read the entire problem before starting a formal answer to the first part of the problem. Often, the various parts of the problem interact, so thinking about what is needed at the end of the problem will help define, focus and limit the scope of what you do on the earlier parts of a problem. Sometimes a later part simply requests you reiterate a prior answer in the context of the subsequent steps you have taken. You will need to down load FEMA 356 as well as several other FEMA documents to do the problems. Please note that questions asking you to compare, describe or briefly discuss results typically require only a VERY short (on the order of a sentence or paragraph) answer or one or more simple sketches. If you are unclear about the intent of a problem or the solution strategy, please request clarification from the instructor or graduate student instructor.
CE 227 - Homework Assignment No. 1 page 5 Problem 1 Review of Structural Dynamics (Due on January 31, 2008) Review CE 225 (or equivalent) and prepare a short summary sheet containing the relevant matrix equations to estimate using elastic modal dynamic analysis from a spectral displacement response spectrum (and a pseudo-acceleration response spectrum): (a) base shear; (b) peak story level displacements and (c) average inter-story drift ratio (drift ratio is defined here as the difference in horizontal displacements at two adjacent floors divided by the story height); (c) peak inter-story drift and inter-story drift ratio at any story; (d) peak floor level design forces and story shears; (e) peak floor level overturning moments; (f) the elevation above the base for each mode where the base shear for a particular mode would have to be applied if it were to result in the same overturning moment produced by that mode (as a fraction of the total height of the building). This is described in detail in Dynamics of Structures; (g) the contribution of each mode to the story shear and to the interstory drift at each level. There is no precise answer to this since the estimate of maximum response is usually based on SRSS procedures. However, if one takes the modal response value squared and divides by the sum of the squares of the modal values, this will give us an idea of the contribution of each mode to the response. The building can be idealized as a simple elastic multistory shear building with n stories. You can assume you know the mode shapes and natural periods for the structure, and that the appropriate response spectrum is available. In general, try to write these equations so they are suitable for hand solution (i.e., if you want the interstory drift, you really do not want to by hand figure out the lateral displacements at all floors and then subtract them all). We will be using and extending these equations throughout the course, and it will be useful (required) that you develop a simple spreadsheet or Matlab/MathCAD program that can do these calculations, given the dynamic characteristics of the structure and the response spectrum. We will do this for several hazard levels, and the response spectrum will be eventually modified to account for nonlinearity, site effects, ground motion directivity, and so on. Problem 2 - Performance Goals (Due on January 31, 2008) For this problem, you are to begin thinking about the performance goals you will recommend to the client and the types of things you will look into during your design effort. At this stage, you need not be precise, but you need to try to identify those issues and engineering response parameters you believe to be important, what behavior you would accept under different likelihood earthquakes, and what you will need to do to assess the performance in a quantitative sense.
CE 227 - Homework Assignment No. 1 page 6 Using the Vision 2000, FEMA 356 or other limit states format (see class notes) address the questions listed in the following paragraph. Again, you need not have an exact or especially specific quantitative answer. However, the thought process is important. This step will identify questions that need to be answered later in the design process (it will become part of a to do list). For example, it will remind you to find out what displacement will damage the partitions you plan to use, what floor accelerations can be tolerated by computers, what out-of-plane accelerations and in-plane distortions can the cladding take before beginning to leak during rain storms, etc. Similarly, there are other issues that you might want to discuss with the client, such as developing an off-site back up capability for storing critical computer databases, selecting lab components that are seismically resistant or protected, using structural systems like seismic isolation that might mitigate seismic impacts, etc. Please provide very brief narrative responses addressing the following questions: a. What performance would you anticipate if the building were designed according to the 1994 UBC without any special consideration for improved performance in the design process? Does this differ from what you would expect if the structure were designed today according to FEMA 450 (the basis of most current codes) [see chapter 1, FEMA450]? b. Concisely describe the use or occupancy of the building in a few (say < 20) words to convey your characterization of the building. This might correspond to categories used in Vision 2000 or FEMA 356, such as basic facility, hazardous/essential facility, safety critical facility, etc. However, your building and client may not fit nicely into one of the standard categories, so you may wish to develop your own category. What do you suggest? c. Identify in probabilistic terms (recurrence interval or probability of occurrence within the life of structure) what you would mean by a frequent, occasional, rare and very rare earthquake for this building. This need not be different from values identified by others, but this is a decision you must independently make as the designer. d. What are your performance (functional) levels for each of these earthquake probabilities? You may put this in terms of a matrix, like those used in Vision 2000 or FEMA 356. Note that these documents allow a broader range of performance specification than in the FEMA 450 provisions for new buildings. e. Provide specific response parameters that you could, as an engineer, predict and evaluate to determine if each of these functional objectives is satisfied. At this stage, only basic parameters might be listed. What would you be looking for in the case of each of these parameters? Again, you might want to express this in the form of a table, like Table C1-2 in FEMA 356 (Chapter 1). Quantitative values are not required.
CE 227 - Homework Assignment No. 1 page 7 Problem 3 - Preliminary Code-based Estimates of Seismic Design Forces (Due Feb. 7, 2007) You are now to get a quick idea of the level of design forces for which the building was originally designed, and forces that it would be design for with a current model building code. This will give us a baseline against which to compare design forces obtained using other methods, and a set of values upon which to base some preliminary design calculations in subsequent problems. You are NOT expected to be expert related to the 1994 and 1997 UBC provisions. I do not plan on providing copies of these codes for you to examine. For this structure, take the importance factor, I, to equal unity for the time being. 1994 UBC Provisions (Static force provisions of Section 1628): 1. Estimate the period of the structure (T = 0.035h n 3/4 ) with h n (elevation of roof, in feet). 2. Estimate the design base shear for the entire structure. Express your answer as a percentage of the total weight of the structure (i.e., the base shear coefficient), as well as a force. The design Base Shear is computed using the equation shown below: Where V = ZCIW/(R w ) 28-6 C= 1.25S/(T 2/3 ) 2.75 R w = 12, Z= 0.4 and S = 1.2 (for S 2 soils) 3. Distribute the base shear to the individual floors using Equations 28-6 through 28-8 in the UBC. F x = (V -F t )w x h x /(Σw i h i ) 28-8 Where: A force F t is applied at the roof when T > 0.7 sec to approximately account for higher mode effects and F t = 0.07TV 28-7 And where w x and h x are the deadload weight and elevations of the various floors. Do not treat the penthouse as a separate story, but lump its mass at the roof. 4. Make a table and separate graph showing the distribution of floor level lateral forces and story shears. Since the 1994 code is based on working stress design principles, the ultimate strength design values are obtained by multiplying the values of forces and shears obtained above by the earthquake-related load factor (which is 1.4). Tabulate and plot these ultimate values along with the non-amplified values.
CE 227 - Homework Assignment No. 1 page 8 1997 UBC Provisions The 1997 UBC introduced many changes over the 1994 code (while this is not the most recent model code, it is virtually identical to the currently adopted California Building Code). It incorporated special provisions for structures located close to known fault ruptures and makes other significant changes. More information on the reasons and basis for these changes will be presented later in the course. The 1997/2003 codes also express the earthquake design forces as ultimate loads, so the computed loads are numerically higher, but the R values are correspondingly lower. That is Rw is about equal to 1.4R. For now, we need to look at the potential impact of these code changes on our design. The design Base Shear is computed using the equation shown below: V = C v IW/(RT) < 2.5 C a IW/R where R equals 8.5 for steel special moment frames in the 1997 UBC. The change from R w of 12 to and R of 8.5 reflects the 1997 UBC being based on ultimate strength (LRFD) rather than allowable stress design. Thus, to compare results for the 1994 and 1997 codes, the values obtained above for the 1994 UBC should be multiplied by 1.4 to bring them to the ultimate strength level. Also, note that the power on the period term on the base shear equation has also changed (it is now unity, rather than 2/3). To compensate for this at long periods, a minimum design force is now also imposed. V min = 0.11C a IW or 0.8ZN v IW/R Period calculations, distribution of base shear to stories, and other terms are the same as in the 1994 UBC. However, the values of C v and C a depend on soil conditions and fault proximity. For this site, we will assume stiff soil (D) sites and for this soil C a = 0.44N a and C v = 0.64N v, where N is a near source factor. The values of N depend on the type of source (magnitude and slip rate of fault) and distance to closest fault (here 2 km). In our case, the 1997 code stipulates: Distance to closest fault, in km N a N v 2 1.5 2.0 5 1.2 1.6 10 1.0 1.2 15 1.0 1.0 Repeat your solution to the first part of the question done for the 1994 code, but now based on the 1997 code provisions, and tabulate and plot your answers for part 4 on the same tables and graphs as you used for the 1994 code provisions. This facilitates comparison of the results for 1994 and 1997 codes.
CE 227 - Homework Assignment No. 1 page 9 Hint: Recognize that many of your answers for the 1997 code can be obtained by simple proportioning of you previous answers for the 1994 code. Comment on the changes to your design forces (what approximate percentage change do you see and what is the source of the change major change). There are several other changes in the 97 UBC, 2002 IBC and FEMA 365 documents that we will talk about later that will also effect design forces (including redundancy, the likely overstrength of structure, characterization of mode shapes, treatment of higher mode effects, the design/analysis method used, etc.). In general, the 1997 code will require much higher forces and require (through other indirect means) more framing elements than needed for the 1994 code. It is an indication of how fast seismic provisions are changing in the US. Problem 4. Elastic Modal Analysis to Extract Periods and Mode Shapes (Target due date Feb. 8, 2007) For the following problem, you need to download and install a computer program such as Matlab, SAP, OpenSees Navigator, FEDEASlab, CSI Perform and so on. SAP is available on the department server. Here we are to compute the mode shapes and periods for the 1994 design. Two identical moment-resisting frames are located in each principal orientation of the class building (see floor plan in introduction to this assignment packet). If we ignore torsion of the building about a vertical axis and assume the floor diaphragms are rigid in plane, we need only construct a 2D planar model of one frame, and consider half of the total inertial mass of structure applied to each frame. Because we are assuming that the remainder of the framing in the building is pinned connected, it will be ignored for the moment in evaluating the dynamic characteristics. Since we are only interested for this problem in transverse modes of vibration, you may disregard vertical loads and the vertical (or rotational) inertial effects. a. Using a computer program of your choice, model one of the moment-resisting frames designed for the 1994 UBC compliant building, and determine its (three) elastic periods of vibration and mode shapes. b. How does the your computed period for the first mode compare with those used by the 1994 and 1997 UBC, and how does the computed first mode shape compare to that implicitly assumed in the code? c. How do your answers to part a change if the bases of the columns are pin connected to the foundations rather than being fixed? Fixed bases are expensive so this is a design alternative.