CUNY City - EE - 312

CUNY City - EE - 312

Canisius College - EDU - EDU250

Dylan Stawarek EDU 250 9/11/2007Chapter 1 1. What are the six key characteristics of teachers as professionals? There are six key characteristics of teachers as professionals. The first key characteristic of teachers as professionals is the fact th

USC - POSC - 220

POSC 220g Lecture Notes 9.4.07 Chaco Canyon settlement -New Mexico -similar to LA -desolate region with few available resources -center of a "mini empire"; centralized government; quite prosperous -rapidly used up available resources on site. -comple

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Fourier Series Example0 t 2 sec 0 lb F (t ) = , F (t + 5) = F (t ) 200 lb 2 t 5 sec rad T = 5 seconds =2 /5 sec .Constant term:ao = = 1 5 sec 1 2 sec 1 5 sec F (t ) dt = ( 0 lb ) dt + ( 200 lb ) dt 5 sec 5 sec

Purdue - CIVIL ENGI - CE 573

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Characteristics of Structural Dynamic Systems Restoring Forces "Inertial Forces": Newton's 2nd Law and D'Alembert's Principle Damping Dynamic Forces

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Numerical Evaluation of Dynamic Response Forcing Interpolation ExampleGiven: Mass of tank m = 0.2533 kip-sec2 / in , stiffness k = 10 kips/in, undamped natural period T = 1.0 sec ( = 6.283 rad/sec ), and = 0.05 . Tan

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Equivalent Viscous Damping Energy Dissipation in GeneralED =cycleFD du =cycleFD (t ) du dt ED = FD (t ) u (t ) dt dt cycle Energy Dissipation for Viscous DampingFd (t ) = cx (t ) = cX cos( t )FD

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Response to Arbitrary Dynamic Excitationmu + ku = F (t ) u (t ) = 1 t F ( ) sin (t - ) d m 0(In all the examples, assume that the system starts at rest.) Example #1: Step Force u (t ) = Fo t 1 t Fo sin (t - ) d

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Structural Control Devices Supplemental DampersIdea: Add damping to the structural system by inserting dampers directly into the structure.Advantages: Fairly cheap and easy to install good for seismic retrofitting. D

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Example: Solving the Forced Vibration ProblemGiven: A three story building is modeled using shear frames. The property matrices and modal information for this structure are: 0 0 0 0.1035 405.57 -349.63 0 kip-sec2 ;

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Example: Solving the Free Vibration ProblemGiven: A three-story building is modeled as shown. The dead load per unit length for each horizontal girder varies with each floor; you may assume that the weight of each column

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Example: Response Spectrum Analysis using Modal CombinationsGiven: A four story building is modeled using shear frames. The mass and stiffness properties are expressed in terms of m = 12 103 kg and k = 4 106 N/m; prope

Purdue - CIVIL ENGI - CE 573

Problem 10.1:Given: A uniform beam of flexural stiffness EI = 109 lb-in 2 and length 300 in has one end fixed and theother simply supported.Required: Determine the system stiffness matrix considering three beam segments and the nodal coordinates

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#2 SolutionProblem #1Given: A viscously damped structure is set into free vibration with an initial velocity. The resultingdamped oscillations are shown above.Required: (a) Determine the logarithmic decrement, the

Berkeley - CIV ENG - CE 227

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Overview of Finite Element Analysis IdealizationIdea: Model the structure as a collection of small elements (beams, plates, rods, springs, .) connected at nodes. Define the global degrees of freedom at each node as appr

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Earthquake Response Spectrum Analysis: SDOF Case Recall: Spectral Displacement and Response Spectrumx (t ) = 1 t F ( )e - (t - ) sin [ d (t - ) ] d S d max x(t ) = S d ( m, c, k , F (t ) ) . m d 0 Earthquake Respon

Berkeley - CIV ENG - CE 227

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2002; 31:539560 (DOI: 10.1002/eqe.143)Evaluation of approximate methods to estimate maximum inelastic displacement demandsEduardo Miranda; and Jorge Ruiz-GarcaDepartmen

Berkeley - CIV ENG - CE 227

BISPEC: Interactive Software for the Computation of Unidirectional and Bidirectional Nonlinear Earthquake Spectra Mahmoud M. Hachem1, PhD, PE1Wiss, Janney, Elstner Associates, Inc., 2200 Powell Street, Suite 925, Emeryville, CA 94608; PH (510) 428

Berkeley - CIV ENG - CE 227

Journal of Earthquake Engineering, Vol. 8, No. 2 (2004) 175207 c Imperial College PressTHE VERTICAL-TO-HORIZONTAL RESPONSE SPECTRAL RATIO AND TENTATIVE PROCEDURES FOR DEVELOPING SIMPLIFIED V/H AND VERTICAL DESIGN SPECTRAYOUSEF BOZORGNIA Applied T

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Solutions to HW#4Problem #1Given: A response spectrum is a plot of the maximum dynamic load factor (DLF) as a function of the(nondimensional) duration of the loading. See Figures 4.4 and 4.5 in the text for examples. W

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#6 SolutionsProblem #1Given: A popular method for limiting the effects of earthquakes on structures is to base isolate them; that is, to put in supports underneath the structure that isolate the main part of the struc

Berkeley - CIV ENG - CE 227

University of California, Berkeley Civil and Environmental EngineeringInstructor: Stephen Mahin Spring Semester 2006CEE 227 Earthquake Engineering Design Reading Assignments FEMA 356 Generally Topic Earthquake Engineering Borzorgnia and BerteroS

Berkeley - CIV ENG - CE 227

University of California at Berkeley Civil and Environmental EngineeringInstructor: Stephen A. Mahin Spring Semester 2006CEE 227 - Earthquake Resistant DesignProblem 4 - Conceptual Design (due in Discussion Section, Feb. 16) In this problem, you

Berkeley - CIV ENG - CE 227

Jeffrey Hunt CE 227 Problem 8 Part (a) The zip code for the site was chosen as 94704-1209LOCATION 37.870925 Lat. -122.268424 Long. The interpolated Probabilistic ground motion values, in %g, at the requested point are: 10%PE in 50 yr 5%PE in 50 yr 2

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Response to Harmonic Forcing: Damped Systems Complementary Solution + Particular Solutionmu + cu + ku = Fo sin ( t + ) u + 2 u + 2u =Complementary solution:uc (t ) = e - t [ A cos d t + B sin d t ]Fo sin ( t +

Berkeley - CIV ENG - CE 227

FEMA Program to Reduce Earthquake Hazards in Steel Moment-Frame Structures A New Paradigm for Design and Evaluation of Steel Moment Frame Buildings Stephen MahinNishkian Professor of Structural Engineering University of California at Berkeley Chair,

Berkeley - CIV ENG - CE 227

Statistical Evaluation of Approximate Methods for Estimating Maximum Deformation Demands on Existing StructuresSinan D. Akkar1 and Eduardo Miranda, M.ASCE2Abstract: A statistical study is presented to evaluate the accuracy of five approximate metho

Berkeley - CIV ENG - CE 227

Seismic Design Based on the Yield DisplacementMark Aschheim,a) M.EERIAlthough seismic design traditionally has focused on period as a primary design parameter, relatively simple arguments, examples, and observations discussed herein suggest that th

Berkeley - CIV ENG - CE 227

CE 227 Homework #1 SolutionsAdapted from: Troy MorganProblem 1 Performance GoalsThis problem primarily deals with seismic performance goals, as implied by the Uniform Building Code (UBC) and as implemented in performance-based earthquake engine

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Logarithmic Decrement Matlab Example> u1 = udata(2) u1 = 96.5749 > u2 = udata(10) u2 = 83.9971(Located from the plot.)(Located from the plot.)> delta = log(u1/u2) delta = 0.1395 u = log k , k = 1. uk +1 >

Berkeley - CIV ENG - CE 227

Problem 1119% reduction in mass, or a 23%Problem 12

Berkeley - CIV ENG - CE 227

CE 227 Homework #2 SolutionsAdpated from: Troy MorganProblem 4 Conceptual DesignIn this problem, we investigate various structural configurations for our building. I've presented a sketch of possible solutions here, but obviously yours may (and

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Numerical Evaluation of Dynamic Response Newmark Methods ExampleGiven: Mass of tank m = 0.2533 kip-sec2 / in , stiffness k = 10 kips/in, undamped natural period T = 1.0 sec ( = 6.283 rad/sec ), and = 0.05 . Tank star

Berkeley - CIV ENG - CE 227

Problem 13Problem 13Problem 14Problem 15Problem 16

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#5 Supplemental ProblemGiven: Another common model used for buildings is the portal frame model, which tries to account forflexibility of both horizontal and vertical members by allowing for rotations at connections.

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Solution to HW#1Problem #1Given: A concrete slab (mass = 20,000 kg) forms the floor of a manufacturing facility. To preventexcessive vibrations from reaching the equipment placed on this floor, the slab is supported by

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics MDOF Earthquake Response Spectrum ExampleGiven: A three story building is modeled using shear frames. The mass and stiffness properties are as indicated. Assume = 0.02 for all modes. Each story has a height of 14 ft. Re

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Example on Orthogonality and Modal MatricesGiven: A three-story building is modeled as shown. The dead load per unit length for each horizontal girder varies with each floor; you may assume that the weight of each column

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Example: MDOF Damped Forced VibrationGiven: A six story shear frame model building has the following mass and stiffness properties: m = 66 lb-sec 2 / in , E = 30 106 psi and I = 882 in 4 for each column. The property ma

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Example: Rayleigh QuotientGiven: A six-story building is modeled as a shear-frame structure. Parameters are m = 66 lb-sec 2 / in , E = 30 106 psi, and I = 882 in 4 . Required: Estimate the fundamental natural frequency

Purdue - CIVIL ENGI - CE 573

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Transmissibility

Berkeley - CIV ENG - CE 227

Characterizing Near Fault Ground Motion For The Design And Evaluation Of BridgesPaul SomervilleABSTRACT Near-fault ground motions are different from ordinary ground motions in that they often contain strong coherent dynamic long period pulses and p

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#6 Supplemental ProblemsProblem #1Given: A popular method for limiting the effects of earthquakes on structures is to base isolate them; that is, to put in supports underneath the structure that isolate the main part

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#1 Supplemental ProblemsProblem #1Given: A concrete slab (mass = 20,000 kg) forms the floor of a manufacturing facility. To preventexcessive vibrations from reaching the equipment placed on this floor, the slab is su

Auckland - CIVIL ENGI - Civil 416

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#5 SolutionsGiven: Another common model used for buildings is the portal frame model, which tries to account forflexibility of both horizontal and vertical members by allowing for rotations at connections. In this pro

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Example on Natural Frequencies and ModesGiven: A two-story building is modeled as a shear-frame structure. Parameters are m = 35 103 kg and k = 17.5 106 N/m. Required: Determine the natural frequencies and natural vibr

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Degrees of Freedom Modeling Options Examples

Auckland - CIVIL ENGI - Civil 416

Structural Mechanics 3 - Worksheet 1

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Numerical Evaluation of Dynamic Response Elastoplastic Behavior ExampleGiven: Mass of frame m = 0.5 kip-sec2 / in , stiffness k = 20 kips/in, and = 0.02 . Tank starts at rest and is subjected to pulse F(t) as shown. A

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#2 Supplemental ProblemsProblem #1Given: A viscously damped structure is set into free vibration with an initial velocity. The resultingdamped oscillations are shown above.Required: (a) Determine the logarithmic de

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Solutions to HW#3Problem #1m Y(t) y(t)v = constantCenter of MasskcFramegh yo y (x)RWheelxGiven: A car can be (crudely) modeled as a single degree of freedom system having the entire car's mass m lumpe

Purdue - CIVIL ENGI - CE 573

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#4 Supplemental ProblemGiven: A response spectrum is a plot of the maximum dynamic load factor (DLF) as a function of the(nondimensional) duration of the loading. See Figures 4.4 and 4.5 in the text for examples. We w

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics General Periodic Response Theorymu + cu + ku = F ( t ) ao + an cos ( n t ) + bn sin ( n t )n =1 n =1 N NComplementary Solution: uc (t ) = e - t [ A cos D t + B sin D t ]. Particular Solution:For constant term: u

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics HW#3 Supplemental Problemv = constantm Y(t) y(t)Center of MasskcFramegh yo y (x)RWheelxGiven: A car can be (crudely) modeled as a single degree of freedom system having the entire car's massm lumped a

Purdue - CIVIL ENGI - CE 573

CE 573: Structural Dynamics Example: Inverse Vector Iteration for Higher ModesGiven: A six-story building is modeled as shown. Parameters are m = 66 lb-sec 2 / in , E = 30 106 psi, and I = 882 in 4 . Required: Use inverse vector iteration to find