A Modal Pushover Analysis Procedure to Estimate Seismic Demands for Buldings
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by:
Anil K. Chopra, University of California - Berkeley
Rakesh K. Goel, California Polytechnic State University - San Luis Obispo
The principal objective of this investigation is to develop a pushover analysis procedure based on structural dynamics theory, which retains the conceptual simplicity and computational attractiveness of current procedures with invariant force distribution, but provides superior accuracy in estimating seismic demands on buildings.
The standard response spectrum analysis (RSA) for elastic buildings is reformulated as a Modal Pushover Analysis (MPA). The peak response of the elastic structure due to its nth vibration mode can be exactly determined by pushover analysis of the structure subjected to lateral forces distributed over the height of the building according to s*n = mφn, where m is the mass matrix and φn its nth-mode, and the structure is pushed to the roof displacement determined from the peak deformation Dn of the nth-mode elastic SDF system. Combining these peak modal responses by modal combination rule leads to the MPA procedure.
The MPA procedure is extended to estimate the seismic demands for inelastic systems: First, a pushover analysis determines the peak response rno of the inelastic MDF system to individual modal terms, peff,n(t) = −snüg (t) , in the modal expansion of the effective earthquake forces, peff,n (t) = −mιüg (t) . The base shear-roof displacement (Vbn −um ) curve is developed from a pushover analysis for force distributions*n. This pushover curve is idealized as bilinear and converted to the force-deformation relation for the nth-“mode” inelastic SDF system. The peak deformation of this SDF system is used to determine the roof displacement, at which the seismic response, rno , is determined by pushover analysis. Second, the total demand, ro , is determined by combining the rno (n= 1, 2,…) according to an appropriate modal combination rule.
Comparing the peak inelastic response of a 9-story SAC building determined by the approximate MPA procedure with rigorous nonlinear response history analysis (RHA) demonstrates that the approximate procedure provides good estimates of floor displacements and story drifts, and identifies locations of most plastic hinges; plastic hinge rotations are less accurate. The results presented for El Centro ground motion scaled by factors varying from 0.25 to 3.0, show that MPA estimates the response of buildings responding well into the inelastic range to a similar degree of accuracy when compared to standard RSA for estimating peak response of elastic systems. Thus the MPA procedure is accurate enough for practical application in building evaluation and design.
Comparing the earthquake-induced demands for the selected 9-story building determined by pushover analysis using three force distributions in FEMA-273, MPA, and nonlinear RHA, it is demonstrated that the FEMA force distributions greatly underestimate the story drift demands, and the MPA procedure is more accurate than all the FEMA force distributions methods in estimating seismic demands. However, all pushover analysis procedures considered do not seem to compute to acceptable accuracy local response quantities, such as hinge plastic rotations. Thus the present trend of comparing computed hinge plastic rotations against rotation limits established in FEMA-273 to judge structural performance does not seem prudent. Instead, structural performance evaluation should be based on story drifts known to be closely related to damage and can be estimated to a higher degree of accuracy by pushover analyses.
Capacity Demand Diagram Methods for Estimating Seismic Deformation of Inelastic Structures: SDF Systems
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by:
Anil K. Chopra, University of California - Berkeley
Rakesh K. Goel, California Polytechnic State University - San Luis Obispo
The ATC-40 and FEMA-274 documents contain simplified nonlinear analysis procedures to determine the displacement demand imposed on a building expected to deform inelastically. The Nonlinear Static Procedure in these documents, based on the capacity spectrum method, involves several approximations: The lateral force distribution for pushover analysis and conversion of these results to the capacity diagram are based only on the fundamental vibration mode of the elastic system. The earthquake-induced deformation of an inelastic SDF system is estimated by an iterative method requiring analysis of a sequence of equivalent linear systems, thus avoiding the dynamic analysis of the inelastic SDF system. This last approximation is first evaluated in this report, followed by the development of an improved simplified analysis procedure, based on capacity and demand diagrams, to estimate the peak deformation of inelastic SDF systems.
Several deficiencies in ATC-40 Procedure A are demonstrated. This iterative procedure did not converge for some of the systems analyzed. It converged in many cases, but to a deformation much different than dynamic (nonlinear response history or inelastic design spectrum) analysis of the inelastic system. The ATC-40 Procedure B always gives a unique value of deformation, the same as that determined by Procedure A if it converged.
The peak deformation of inelastic systems determined by ATC-40 procedures are shown to be inaccurate when compared against results of nonlinear response history analysis and inelastic design spectrum analysis. The approximate procedure underestimates significantly the deformation for a wide range of periods and ductility factors with errors approaching 50%, implying that the estimated deformation is about half the “exact” value.
Surprisingly, the ATC-40 procedure is deficient relative to even the elastic design spectrum in the velocity-sensitive and displacement-sensitive regions of the spectrum. For periods in these regions, the peak deformation of an inelastic system can be estimated from the elastic design spectrum using the well-known equal displacement rule. However, the approximate procedure requires analyses of several equivalent linear systems and still produces worse results.
Finally, an improved capacity-demand-diagram method that uses the well-known constant-ductility design spectrum for the demand diagram has been developed and illustrated by examples. This method gives the deformation value consistent with the selected inelastic design spectrum, while retaining the attraction of graphical implementation of the ATC-40 methods. One version of the improved method is graphically similar to ATC-40 Procedure A whereas a second version is graphically similar to ATC-40 Procedure B. However, the improved procedures differ from ATC-40 procedures in one important sense. The demand is determined by analyzing an inelastic system in the improved procedure instead of equivalent linear systems in ATC-40 procedures.
The improved method can be conveniently implemented numerically if its graphical features are not important to the user. Such a procedure, based on equations relating Ry and µ for different T n ranges, has been presented, and illustrated by examples using three different Ry - µ - T n relations.
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In this course includes the program Rosetta Stone 3.3.5 and levels of English (American) 1-2-3. Rosetta Stone - No.1 in the world among linguistic software. Rosetta Stone is the most natural and native, and therefore the most effective way to study for a man of almost any foreign language. The company uses specially developed technology Dynamic Immersion - dynamic immersion.
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Run the main installation file RosettaStoneSetup.exe, after installation copy RosettaStoneVersion3.exe from folder Crack in a folder with the program. Do not update the program on the Internet and do not click on the registration, if the program you are asked. In the window of activation / registration, press the "Later" (Later).
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Open the Rosetta Stone Setup.dmg, run and install the program (script Update), after installation copy the file mdm.dat from folder Crack in the directory/Applications/Rosetta Stone Version 3.app/Contents/Resources (with the replacement of an existing file). Do not update the program from the network and not register/activate the program, with press queries always "Later" (Later).
Setting English (American) 1-2-3:
1. Install the program "RosettaStoneSetup.exe" in the folder "Application"
2. Do not start the program after the installation.
3. Copy the crack "RosettaStoneVersion3.exe" in the installation folder (C:\Program Files\Rosetta Stone\Rosetta Stone Version 3).
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8. For other levels of version 3 to repeat steps 4-7
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SAP2000 Detailed Tutorial Including Pushover Analysis
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169 pages
1061 kb
This tutorial is quite detailed. It is intended to introduce and demonstrate many of the capabilites of SAP2000. Because we are trying to demonstrate as many different capabilities as reasonable, the example problem is not necessarily created and the results are not necessarily reviewed in the most efficient and expedient manner. Often with computer programs, what is efficient for one person may not be the best method for the next person. It is assumed that once introduced to the SAP2000 capabilities and methods in this tutorial, users will decide which methods work best for them in their particular
circumstances.
CSi - Practical Three Dimensional Nonlinear Static Pushover Analysis
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By Ashraf Habibullah and Stephen Pyle
(Published in Structure Magazine, Winter 1998.
4 pages.
150 kb.
The recent advent of performance based design has brought the nonlinear static pushover analysis procedure to the forefront. Pushover analysis is a static, nonlinear procedure in which the magnitude of the structural loading is incrementally increased in accordance with a certain predefined pattern.
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Alton D. Romig, Jr.
President, ASM International
Michael J. DeHaemer
Managing Director, ASM International
2571 pages - PDF Format - 26 MB
Preface
The Metals Handbook Desk Edition is intended to serve as a comprehensive single-volume reference source on the properties, selection, processing, testing, and characterization of metals and their alloys. Although the information presented in this Volume is drawn principally from the 20 volumes of the ASM Handbook series, it should not be considered simply an abridged version of the larger work. Instead, the Metals Handbook Desk Edition draws upon the complete arsenal of ASM products--both print and electronic--as well as other key sources of information originating from other publications, company literature, technical societies, and government agencies.
Volume Content
Because of the familiarity, success, and ease-of-use of the original Desk Edition published in 1984, it was determined from the outset of the project that the editorial approach and outline for the new edition should follow in a similar manner.
The challenge in successfully revising the first edition was to determine what strategic additions (or reductions) and improvements should be made. Complicating this task was the fact that a complete edition cycle of the ASM Handbook (including completely new volumes on corrosion, tribology, materials characterization, and other topics) had been published since the earlier edition was produced. To ensure that the best product possible resulted from the revision/updating process, a 12-member Editorial Advisory Board representing industry, academia, and research laboratories was formed. All board members have been key contributors to the Handbook series or have been involved with other important ASM activities over the past decade. Under their guidance, an outline was established for the second edition that divided the book into five major parts: General Information; Irons, Steels, and High-Performance Alloys; Nonferrous Alloys and Special-Purpose Materials; Processing; and Testing, Inspection, and Materials Characterization.
General Information contains a glossary of more than 3000 terms, a collection of common engineering tables, and graphs
comparing properties of metals and nonmetals. It also includes contributions on crystal structure, practical uses of phase diagrams, engineering design, and factors to be considered in the materials selection process.
Irons, Steels, and High-Performance Alloys. Emphasis is placed on properties and selection of ferrous alloys and heatresistant superalloys. Important relationships between structure and properties in irons and steels are described. The effects of modern steelmaking practices on properties are examined, as is the influence of improved melting/refining methods on superalloy performance. New or expanded information is presented on austempered ductile irons, highstrength low-alloy steels, stainless steels(including duplex stainless steels), and powder metallurgy steels.
Nonferrous Alloys and Special-Purpose Materials comprises 14 major sections that describe the properties and selection of
conventional (structural) nonferrous alloys and materials used for such special-purpose applications as magnetic or electrical devices, biomedical devices, and advanced aircraft/aerospace components. Metal-matrix composites and structural intermetallics--more recently developed materials not covered in the previous Desk Edition--are also described.
Processing. Processes extending through the entire life-cycle of a component are described, including extractive metallurgy, casting, forming, heat treatment, joining, surface cleaning, finishing and coating, and recycling. An entirely new section on powder metallurgy has also been added. The increased coverage of recycling technology reflects the response of the metals industry to environmental concerns.
Testing, Inspection, and Materials Characterization. In addition to offering information on failure analysis, fractography, nondestructive testing, mechanical testing, and metallography, a new section describes in practical terms the selection of characterization methods for bulk elemental analysis, bulk microstructural analysis, and surface analysis. New information on wear testing and tests for evaluating stress-corrosion cracking and hydrogen embrittlement is also presented.
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Hi, I have a bridge of postensionig concrete, this bridhe have a span 20m and I have characteristics of this span. I required the characteristics for 35m span, Is there a simple procedure for a preliminary design.
Please help me
Regards
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E.030 EarthQuake-Resistant Design: National Building Code
Technical Standard of Building
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anybody have a copy of the design of rectangular and or circular tank concrete design by the Portland Cement Association (PCA) ...pls share....thanks noelda2
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