KINETICS Pipe & Duct Seismic Application Manual
|
|
- Blake Barker
- 5 years ago
- Views:
Transcription
1 KINETIC pe & Duct esmc Applcton Mnul CODE BAED EIMIC DEIGN FORCE 5.1 Introducton: The code bsed horzontl sesmc force requrements for ppe nd duct re ether clculted by the sesmc restrnt mnufcturer s prt of the selecton nd certfcton process, or vlble through convenent nd esy method provded by the mnufcturer. Knetcs Nose Control provdes onlne tools tht wll clculte the horzontl sesmc force nd mke recommendtons for the proper sesmc restrnts for the ppe or duct n queston. These tools wll be dscussed n the next secton. Ths secton s n nformtonl secton. It wll dscuss the code bsed horzontl sesmc force demnd equtons nd the vrbles tht go nto them. Ths dscusson wll provde deeper understndng for the desgner responsble for selectng the sesmc restrnts for ppe or duct nd the nture of the sesmc forces nd the fctors tht ffect them. 5.2 Code Bsed Horzontl esmc Desgn Force ACE/EI 7-05 ecton 13.3: The sesmc force s mss, or weght, bsed force, nd s such s ppled to the ppe or duct t ts center of grvty, whch s usully t the center of the cross-secton of the ppe or duct. Keep n mnd tht the erthquke ground moton moves the bse of the buldng frst. Then the moton of the buldng wll ccelerte the ppe or duct through the hngers. The horzontl sesmc force ctng on ppe or duct wll be determned n ccordnce wth Equton of ACE/EI F 0.4 = R I W z h Equton 5-1 ACE/EI 7-05 defnes nd upper nd lower bound for the horzontl force tht s to be ppled to the center of grvty of ppe or duct. The horzontl sesmc force ctng on ppe or duct s not requred to be greter thn; AGE 1 of 7 ECTION 5.0
2 KINETIC pe & Duct esmc Applcton Mnul F = 1. 6 I W Equton 5-2 And the horzontl sesmc force ctng on ppe or duct s not to be less thn; F = 0. 3 I W Equton 5-3 Where: F = the desgn horzontl sesmc force ctng on ppe or duct ctng t ts center of grvty. = the short perod desgn spectrl ccelerton. =the component mplfcton fctor. Ths fctor s mesure of how close to the nturl perod of the buldng the nturl perod of the component s expected s expected to be. Typclly ths wll vry from 1.0 to 2.5, nd s specfed by component type n ACE/EI 7-05 nd lsted n Tble 5-3. I = the component mportnce fctor whch be ether 1.0 or 1.5. W = the opertng weght of the ppe or duct tht s beng restrned. R = the response modfcton fctor whch usully wll vry from 1.0 to Ths fctor s mesure of the blty of the component nd ts ttchments to the structure to bsorb energy. It s relly mesure of how ductle or brttle the component nd ts ttchments re. The vlues re specfed by component type n ACE 7-05 nd lsted n Tble 5-3. z = the structurl ttchment mountng heght of the ppe or duct hnger n the buldng reltve to the grde lne of the buldng. h= the verge heght of the buldng roof s mesured from the grde lne of the buldng. The 0.4 fctor ws ntroduced s modfer for AGE 2 of 7 ECTION 5.0 s recognton tht the ME components nsde the buldng would rect more strongly to the long perod erthquke ground moton thn to the short perod moton. The 0.4 fctor brngs the desgn level ccelerton for the ME components more n lne wth the desgn level ccelerton tht s ppled to the buldng structure tself.
3 KINETIC pe & Duct esmc Applcton Mnul The weght of the ppe or duct beng restrned wll depend on the sesmc restrnt spcng. For the trnsverse sesmc restrnts, the weght of the ppe or duct beng restrned s; W Equton 5-4 = T w For the longtudnl sesmc restrnts, the weght of the ppe or duct beng restrned s; W Equton 5-5 = L w Where: L = the longtudnl sesmc restrnt spcng. T = the trnsverse sesmc restrnt spcng. w = the sum of the weghts of ll of the ndvdul ppes or ducts beng restrned over dstnce equl to the restrnt spcng. w = the weght per foot of n ndvdul ppe or duct over the dstnce equl to the restrnt spcng. z The term n Equton 5-1 s recognton of the fct tht ll buldngs nd structures h become more flexble s they ncrese n heght. Tht s they re much stffer t the foundton level thn the roof. nce the ground moton from n erthquke enters the buldng structure t the foundton level, the ctul ccelertons mprted to the ppe nd duct wll be greter the hgher n the buldng they re ttched. A buldng my be lkened to vertclly mounted cntlever bem tht s beng shken by the bottom. It s vbrtng system tht wll hve certn nturl perod tht s, n generl fshon, bsed on ts mss nd stffness. If the nturl perod of the buldng s t, or close too, the erthquke perod, the moton of the buldng could be extreme. Ths ws the cse n the Mexco Cty erthquke of eptember 19, AGE 3 of 7 ECTION 5.0
4 KINETIC pe & Duct esmc Applcton Mnul The ppe or duct, long wth ts hngers, wll lso form vbrtng system wth nturl perod tht depends on the mss of the ppe or duct nd the stffness of the hngers. The component mplfcton fctor ( ) s mesure of how closely the nturl perod of the ppe or duct mtches the nturl perod of the buldng. For = 1. 0 the nturl perods re not close, whle for p = 2.5 the nturl perod of the ppe or duct s very close to tht of the buldng. The component response modfcton fctor( R )s mesure of how much energy the ppe or duct long wth the hnger nd ttchments cn bsorb wthout sustnng crpplng dmge. A common term used throughout the HVAC ndustry s frglty. As the term mples, t s concerned wth how frgle component mght be. Tht s, how esly component my be dmged, nd to wht degree t mght be dmged by specfed lod nd lodng rte. The R fctor, then, s consdered to be n ndctor of how frgle ppe or duct mght be. For R = 1. 0 the component s extremely frgle. For R = 12. 0, on the other hnd, would be component tht s very robust. The vlues for nd R re ssgned by the ACE 7 commttee bsed on ccumulted experence throughout the buldng ndustry. The evoluton of these fctors my be trced through Tbles 5-1; 5-2, nd 5-3 whch represent 2000 IBC/ACE 7-98, 2003 IBC/ACE 7-02, nd 2006/2009 IBC/ACE 7-05 respectvely. The consensus of opnon ppers to be tht ppng nd ductwork, n generl, cn bsorb more energy thn hd orgnlly been thought. Indeed ppng nd ductwork tht s constructed of hghly deformble mterls wth jonts mde wth weldng or brzng cn bsorb gret del of energy wthout sustnng enough dmge to cuse loss of servce. These fcts re reflected by the lrger vlues for R whch wll led to the use of fewer nd smller sesmc restrnts on run or ppe or duct. AGE 4 of 7 ECTION 5.0
5 KINETIC pe & Duct esmc Applcton Mnul Tble 5-1; Component Amplfcton nd Response Modfcton Fctors for 2000 IBC (ACE 7-98) Component R png ystems Hgh deformblty elements nd ttchments (welded steel ppe & brzed copper ppe) Lmted deformblty elements nd ttchments (steel ppe wth screwed connectons, no hub connectons, nd Vctulc type connectons). Low deformblty elements nd ttchments (ron ppe wth screwed connectons, nd glss lned ppe) HVAC ystems Vbrton solted Non-vbrton solted Mounted-n-lne wth ductwork Other Tble 5-2; Component Amplfcton nd Response Modfcton Fctors for 2003 IBC (ACE 7-02) Component R png ystems Hgh deformblty elements nd ttchments (welded steel ppe & brzed copper ppe) Lmted deformblty elements nd ttchments (steel ppe wth screwed connectons, no hub connectons, nd Vctulc type connectons). Low deformblty elements nd ttchments (ron ppe wth screwed connectons, nd glss lned ppe) HVAC ystems Vbrton solted Non-vbrton solted Mounted-n-lne wth ductwork Other AGE 5 of 7 ECTION 5.0
6 KINETIC pe & Duct esmc Applcton Mnul Tble 5-3; Component Amplfcton nd Response Modfcton Fctors for 2006/2009 IBC (ACE 7-05) Component R Dstrbuton ystems png n ccordnce wth AME B31, ths ncludes n-lne components, wth jonts mde by weldng or brzng. png n ccordnce wth AME B31, ths ncludes n-lne components, constructed of hgh or lmted deformblty mterls wth jonts mde by thredng, bondng, compresson couplngs, or grooved couplngs. png & tubng tht s not n ccordnce wth AME B31, ths ncludes n-lne components, constructed wth hgh deformblty mterls wth jonts mde by weldng or brzng. png & tubng tht s not n ccordnce wth AME B31, ths ncludes n-lne components, constructed of hgh or lmted deformblty mterls wth jonts mde by thredng, bondng, compresson couplngs, or grooved couplngs. png & tubng of low deformblty mterls, such s cst ron, glss, or non-ductle plstcs. Ductwork, ncludng n-lne components, constructed of hgh deformblty mterls, wth jonts mde by weldng or brzng. Ductwork, ncludng n-lne components, constructed of hgh or lmted deformblty mterls, wth jonts mde by mens other thn weldng or brzng. Duct work constructed of low deformblty mterls such s cst ron, glss, or non-ductle plstcs Code Bsed Vertcl esmc Desgn Force ACE/EI 7-05 ecton 13.3: ACE/EI 7-05 requres tht vertcl sesmc lod be ppled to the ppe or duct concurrently wth the horzontl sesmc lod from Equton 5-1. The vertcl sesmc lod ctng on the ppe or duct wll be; F = ±0. 2 W Equton 5-6 V Ths force s to be ppled n the drecton tht cuses the worst cse condton. In ths nstnce t s to be ppled downwrd to the hnger(s) tht re closest to the sesmc restrnt loctons. Ths lod wll dd to the tenson lod n the hnger generted by the supported weght of the ppe of duct. A check should be performed to mke sure tht the vertcl sesmc force does not overlod the hnger(s). AGE 6 of 7 ECTION 5.0
7 KINETIC pe & Duct esmc Applcton Mnul 5.4 LRFD versus AD ACE/EI 7-05 ectons 2.3, 2.4 nd The Cvl nd tructurl Engneerng communty hs dopted the LRFD, Lod Resstnce Fctor Desgn, phlosophy. Wth ths desgn phlosophy the fctors controllng the servceblty of the structure s ssgned to the desgn lods. AD, Allowble tress Desgn, s the desgn phlosophy whch preceded LRFD. In AD, the fctors controllng the servceblty of the structure re ssgned to the yeld strength or to the ultmte strength of the mterl. Trdtonlly the fctors controllng the servceblty of the structure hve been known s the fety Fctors, or Fctors of fety. The forces clculted usng Equtons 5-1, 5-2, 5-3, nd 5-6 wll hve mgntudes tht correspond to LRFD. Mny stndrd components such concrete nchors, bolts, screws, nd etc. wll hve ther cpctes lsted s AD vlues. Components whose cpctes re lsted s AD vlues my be compred to the LRFD results from Equtons 5-1 through 5-6 by multplyng the AD vlues by ummry: Ths secton hs provded n nsght nto the wy n whch the sesmc desgn forces for ppe nd duct dstrbuton systems my be computed. It s generlly not necessry for desgner to ctully run the computtons for the sesmc desgn forces. Knetcs Nose Control provdes web bsed computer tools to help the desgner responsble for the sesmc restrnt selecton determne the sesmc forces tht wll be ctng on the ppe or duct dstrbuton system nd to mke the proper selecton for the sesmc restrnts. More bout the selecton process nd the web bsed tools wll be sd n the followng sectons. AGE 7 of 7 ECTION 5.0
4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
More informationApplied Statistics Qualifier Examination
Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng
More informationDemand. Demand and Comparative Statics. Graphically. Marshallian Demand. ECON 370: Microeconomic Theory Summer 2004 Rice University Stanley Gilbert
Demnd Demnd nd Comrtve Sttcs ECON 370: Mcroeconomc Theory Summer 004 Rce Unversty Stnley Glbert Usng the tools we hve develoed u to ths ont, we cn now determne demnd for n ndvdul consumer We seek demnd
More informationRank One Update And the Google Matrix by Al Bernstein Signal Science, LLC
Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses
More informationDCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
More informationUNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II
Mcroeconomc Theory I UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS MSc n Economcs MICROECONOMIC THEORY I Techng: A Lptns (Note: The number of ndctes exercse s dffculty level) ()True or flse? If V( y )
More informationChapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
More information6 Roots of Equations: Open Methods
HK Km Slghtly modfed 3//9, /8/6 Frstly wrtten t Mrch 5 6 Roots of Equtons: Open Methods Smple Fed-Pont Iterton Newton-Rphson Secnt Methods MATLAB Functon: fzero Polynomls Cse Study: Ppe Frcton Brcketng
More information523 P a g e. is measured through p. should be slower for lesser values of p and faster for greater values of p. If we set p*
R. Smpth Kumr, R. Kruthk, R. Rdhkrshnn / Interntonl Journl of Engneerng Reserch nd Applctons (IJERA) ISSN: 48-96 www.jer.com Vol., Issue 4, July-August 0, pp.5-58 Constructon Of Mxed Smplng Plns Indexed
More information? plate in A G in
Proble (0 ponts): The plstc block shon s bonded to rgd support nd to vertcl plte to hch 0 kp lod P s ppled. Knong tht for the plstc used G = 50 ks, deterne the deflecton of the plte. Gven: G 50 ks, P 0
More informationHaddow s Experiment:
schemtc drwng of Hddow's expermentl set-up movng pston non-contctng moton sensor bems of sprng steel poston vres to djust frequences blocks of sold steel shker Hddow s Experment: terr frm Theoretcl nd
More informationDefinition of Tracking
Trckng Defnton of Trckng Trckng: Generte some conclusons bout the moton of the scene, objects, or the cmer, gven sequence of mges. Knowng ths moton, predct where thngs re gong to project n the net mge,
More information13 Design of Revetments, Seawalls and Bulkheads Forces & Earth Pressures
13 Desgn of Revetments, Sewlls nd Bulkheds Forces & Erth ressures Ref: Shore rotecton Mnul, USACE, 1984 EM 1110--1614, Desgn of Revetments, Sewlls nd Bulkheds, USACE, 1995 Brekwters, Jettes, Bulkheds nd
More informationTorsion, Thermal Effects and Indeterminacy
ENDS Note Set 7 F007bn orson, herml Effects nd Indetermncy Deformton n orsonlly Loded Members Ax-symmetrc cross sectons subjected to xl moment or torque wll remn plne nd undstorted. At secton, nternl torque
More informationINTRODUCTION TO COMPLEX NUMBERS
INTRODUCTION TO COMPLEX NUMBERS The numers -4, -3, -, -1, 0, 1,, 3, 4 represent the negtve nd postve rel numers termed ntegers. As one frst lerns n mddle school they cn e thought of s unt dstnce spced
More information1 Module for Year 10 Secondary School Student Logarithm
1 Erthquke Intensity Mesurement (The Richter Scle) Dr Chrles Richter showed tht the lrger the energy of n erthquke hs, the lrger mplitude of ground motion t given distnce. The simple model of Richter
More informationInitial Imperfections of Steel and Steel-Concrete Circular Columns
Recent dvnces n Contnuum echncs, Hdrolog nd colog Intl Imperectons o Steel nd Steel-Conete Crculr Columns RCL KRZÍOVÁ nd JIDRICH LCHR Fcult o Cvl ngneerng Brno Unverst o Technolog Veveří St. 33/95, 6 Brno
More informationEvaluation of Liquefaction Return Period for Bangalore Based on Standard Penetration Test Data: Performance Based Approach
Amercn J. of Engneerng nd Appled Scences 2 (3): 537-543, 2009 ISSN 1941-7020 2009 Scence Publctons Evluton of Lquefcton Return Perod for Bnglore Bsed on Stndrd Penetrton Test Dt: Performnce Bsed Approch
More informationQuiz: Experimental Physics Lab-I
Mxmum Mrks: 18 Totl tme llowed: 35 mn Quz: Expermentl Physcs Lb-I Nme: Roll no: Attempt ll questons. 1. In n experment, bll of mss 100 g s dropped from heght of 65 cm nto the snd contner, the mpct s clled
More informationMath 131. Numerical Integration Larson Section 4.6
Mth. Numericl Integrtion Lrson Section. This section looks t couple of methods for pproimting definite integrls numericlly. The gol is to get good pproimtion of the definite integrl in problems where n
More informationKatholieke Universiteit Leuven Department of Computer Science
Updte Rules for Weghted Non-negtve FH*G Fctorzton Peter Peers Phlp Dutré Report CW 440, Aprl 006 Ktholeke Unverstet Leuven Deprtment of Computer Scence Celestjnenln 00A B-3001 Heverlee (Belgum) Updte Rules
More informationApplications of Bernoulli s theorem. Lecture - 7
Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.
More informationRemember: Project Proposals are due April 11.
Bonformtcs ecture Notes Announcements Remember: Project Proposls re due Aprl. Clss 22 Aprl 4, 2002 A. Hdden Mrov Models. Defntons Emple - Consder the emple we tled bout n clss lst tme wth the cons. However,
More informationName: SID: Discussion Session:
Nme: SID: Dscusson Sesson: hemcl Engneerng hermodynmcs -- Fll 008 uesdy, Octoer, 008 Merm I - 70 mnutes 00 onts otl losed Book nd Notes (5 ponts). onsder n del gs wth constnt het cpctes. Indcte whether
More informationChapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson
More informationJens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers
Jens Sebel (Unversty of Appled Scences Kserslutern) An Interctve Introducton to Complex Numbers 1. Introducton We know tht some polynoml equtons do not hve ny solutons on R/. Exmple 1.1: Solve x + 1= for
More informationWork and Energy (Work Done by a Varying Force)
Lecture 1 Chpter 7 Physcs I 3.5.14 ork nd Energy (ork Done y Vryng Force) Course weste: http://fculty.uml.edu/andry_dnylov/techng/physcsi Lecture Cpture: http://echo36.uml.edu/dnylov13/physcs1fll.html
More informationfractions Let s Learn to
5 simple lgebric frctions corne lens pupil retin Norml vision light focused on the retin concve lens Shortsightedness (myopi) light focused in front of the retin Corrected myopi light focused on the retin
More informationThe graphs of Rational Functions
Lecture 4 5A: The its of Rtionl Functions s x nd s x + The grphs of Rtionl Functions The grphs of rtionl functions hve severl differences compred to power functions. One of the differences is the behvior
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More informationADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS
ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:
More informationLecture 36. Finite Element Methods
CE 60: Numercl Methods Lecture 36 Fnte Element Methods Course Coordntor: Dr. Suresh A. Krth, Assocte Professor, Deprtment of Cvl Engneerng, IIT Guwht. In the lst clss, we dscussed on the ppromte methods
More informationIntroduction to Numerical Integration Part II
Introducton to umercl Integrton Prt II CS 75/Mth 75 Brn T. Smth, UM, CS Dept. Sprng, 998 4/9/998 qud_ Intro to Gussn Qudrture s eore, the generl tretment chnges the ntegrton prolem to ndng the ntegrl w
More informationPrinciple Component Analysis
Prncple Component Anlyss Jng Go SUNY Bufflo Why Dmensonlty Reducton? We hve too mny dmensons o reson bout or obtn nsghts from o vsulze oo much nose n the dt Need to reduce them to smller set of fctors
More informationChapter 0. What is the Lebesgue integral about?
Chpter 0. Wht is the Lebesgue integrl bout? The pln is to hve tutoril sheet ech week, most often on Fridy, (to be done during the clss) where you will try to get used to the ides introduced in the previous
More information5.7 Improper Integrals
458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the
More informationState space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies
Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response
More informationAcceptance Sampling by Attributes
Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire
More informationGoals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite
Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite
More informationLecture 1: Introduction to integration theory and bounded variation
Lecture 1: Introduction to integrtion theory nd bounded vrition Wht is this course bout? Integrtion theory. The first question you might hve is why there is nything you need to lern bout integrtion. You
More information1 Probability Density Functions
Lis Yn CS 9 Continuous Distributions Lecture Notes #9 July 6, 28 Bsed on chpter by Chris Piech So fr, ll rndom vribles we hve seen hve been discrete. In ll the cses we hve seen in CS 9, this ment tht our
More informationSolution Manual. for. Fracture Mechanics. C.T. Sun and Z.-H. Jin
Solution Mnul for Frcture Mechnics by C.T. Sun nd Z.-H. Jin Chpter rob.: ) 4 No lod is crried by rt nd rt 4. There is no strin energy stored in them. Constnt Force Boundry Condition The totl strin energy
More informationSampling Theory MODULE VII LECTURE - 23 VARYING PROBABILITY SAMPLING
Samplng heory MODULE VII LECURE - 3 VARYIG PROBABILIY SAMPLIG DR. SHALABH DEPARME OF MAHEMAICS AD SAISICS IDIA ISIUE OF ECHOLOGY KAPUR he smple random samplng scheme provdes a random sample where every
More informationKinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!
Knemtc Quntte Lner Phyc 11 Eyre Tme Intnt t Fundmentl Tme Interl t Dened Poton Fundmentl Dplcement Dened Aerge g Dened Aerge Accelerton g Dened Knemtc Quntte Scler: Mgntude Tme Intnt, Tme Interl nd Speed
More informationThe Number of Rows which Equal Certain Row
Interntonl Journl of Algebr, Vol 5, 011, no 30, 1481-1488 he Number of Rows whch Equl Certn Row Ahmd Hbl Deprtment of mthemtcs Fcult of Scences Dmscus unverst Dmscus, Sr hblhmd1@gmlcom Abstrct Let be X
More informationA Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls
A Mechancs-Based Approach for Determnng Deflectons of Stacked Mult-Storey Wood-Based Shear Walls FPINNOVATIONS Acknowledgements Ths publcaton was developed by FPInnovatons and the Canadan Wood Councl based
More informationVariable time amplitude amplification and quantum algorithms for linear algebra. Andris Ambainis University of Latvia
Vrble tme mpltude mplfcton nd quntum lgorthms for lner lgebr Andrs Ambns Unversty of Ltv Tlk outlne. ew verson of mpltude mplfcton;. Quntum lgorthm for testng f A s sngulr; 3. Quntum lgorthm for solvng
More informationAP Calculus Multiple Choice: BC Edition Solutions
AP Clculus Multiple Choice: BC Edition Solutions J. Slon Mrch 8, 04 ) 0 dx ( x) is A) B) C) D) E) Divergent This function inside the integrl hs verticl symptotes t x =, nd the integrl bounds contin this
More information( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that
Arc Length of Curves in Three Dimensionl Spce If the vector function r(t) f(t) i + g(t) j + h(t) k trces out the curve C s t vries, we cn mesure distnces long C using formul nerly identicl to one tht we
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationa = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114
Lner Accelerton nd Freell Phyc 4 Eyre Denton o ccelerton Both de o equton re equl Mgntude Unt Drecton (t ector!) Accelerton Mgntude Mgntude Unt Unt Drecton Drecton 4/3/07 Module 3-Phy4-Eyre 4/3/07 Module
More information8. INVERSE Z-TRANSFORM
8. INVERSE Z-TRANSFORM The proce by whch Z-trnform of tme ere, nmely X(), returned to the tme domn clled the nvere Z-trnform. The nvere Z-trnform defned by: Computer tudy Z X M-fle trn.m ued to fnd nvere
More information1. Weak acids. For a weak acid HA, there is less than 100% dissociation to ions. The B-L equilibrium is:
th 9 Homework: Reding, M&F, ch. 15, pp. 584-598, 602-605 (clcultions of ph, etc., for wek cids, wek bses, polyprotic cids, nd slts; fctors ffecting cid strength). Problems: Nkon, ch. 18, #1-10, 16-18,
More informationIdentification of Robot Arm s Joints Time-Varying Stiffness Under Loads
TELKOMNIKA, Vol.10, No.8, December 2012, pp. 2081~2087 e-issn: 2087-278X ccredted by DGHE (DIKTI), Decree No: 51/Dkt/Kep/2010 2081 Identfcton of Robot Arm s Jonts Tme-Vryng Stffness Under Lods Ru Xu 1,
More informationLecture 4: Piecewise Cubic Interpolation
Lecture notes on Vrtonl nd Approxmte Methods n Appled Mthemtcs - A Perce UBC Lecture 4: Pecewse Cubc Interpolton Compled 6 August 7 In ths lecture we consder pecewse cubc nterpolton n whch cubc polynoml
More informationChapter 1: Fundamentals
Chpter 1: Fundmentls 1.1 Rel Numbers Types of Rel Numbers: Nturl Numbers: {1, 2, 3,...}; These re the counting numbers. Integers: {... 3, 2, 1, 0, 1, 2, 3,...}; These re ll the nturl numbers, their negtives,
More informationPurpose of the experiment
Newton s Lws II PES 6 Advnced Physics Lb I Purpose of the experiment Exmine two cses using Newton s Lws. Sttic ( = 0) Dynmic ( 0) fyi fyi Did you know tht the longest recorded flight of chicken is thirteen
More informationIs there an easy way to find examples of such triples? Why yes! Just look at an ordinary multiplication table to find them!
PUSHING PYTHAGORAS 009 Jmes Tnton A triple of integers ( bc,, ) is clled Pythgoren triple if exmple, some clssic triples re ( 3,4,5 ), ( 5,1,13 ), ( ) fond of ( 0,1,9 ) nd ( 119,10,169 ). + b = c. For
More informationPhysics 121 Sample Common Exam 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7. Instructions:
Physcs 121 Smple Common Exm 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7 Nme (Prnt): 4 Dgt ID: Secton: Instructons: Answer ll 27 multple choce questons. You my need to do some clculton. Answer ech queston on the
More informationEvaluation of Allowable Hold Loading of, Hold No. 1 with Cargo Hold No. 1 Flooded, for Existing Bulk Carriers
(997) (Rev. 997) (Rev.2 ept. 2000) (Rev.3 July 2004) Evlution of Allowble Hold Loding of Crgo, Hold No. with Crgo Hold No. Flooded, for Existing Bulk Crriers. - Appliction nd definitions These requirements
More informationThe Schur-Cohn Algorithm
Modelng, Estmton nd Otml Flterng n Sgnl Processng Mohmed Njm Coyrght 8, ISTE Ltd. Aendx F The Schur-Cohn Algorthm In ths endx, our m s to resent the Schur-Cohn lgorthm [] whch s often used s crteron for
More informationSmart Motorways HADECS 3 and what it means for your drivers
Vehcle Rentl Smrt Motorwys HADECS 3 nd wht t mens for your drvers Vehcle Rentl Smrt Motorwys HADECS 3 nd wht t mens for your drvers You my hve seen some news rtcles bout the ntroducton of Hghwys Englnd
More informationReview of linear algebra. Nuno Vasconcelos UCSD
Revew of lner lgebr Nuno Vsconcelos UCSD Vector spces Defnton: vector spce s set H where ddton nd sclr multplcton re defned nd stsf: ) +( + ) (+ )+ 5) λ H 2) + + H 6) 3) H, + 7) λ(λ ) (λλ ) 4) H, - + 8)
More information7.2 The Definite Integral
7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where
More informationEffects of polarization on the reflected wave
Lecture Notes. L Ros PPLIED OPTICS Effects of polrzton on the reflected wve Ref: The Feynmn Lectures on Physcs, Vol-I, Secton 33-6 Plne of ncdence Z Plne of nterfce Fg. 1 Y Y r 1 Glss r 1 Glss Fg. Reflecton
More informationLATTICE TOWER DYNAMIC RESPONSE CALCULATION TO HUMAN INDUCED LOADS: CASE STUDY
Proceedngs of the Interntonl Conference Innovtve Mterls, Structures nd Technologes do: 0750/scconstrs0407 LATTICE TOWER DYNAMIC RESPONSE CALCULATION TO HUMAN INDUCED LOADS: CASE STUDY Lg Gle, Ivrs Rdnsh,
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationMath 113 Exam 2 Practice
Mth Em Prctice Februry, 8 Em will cover sections 6.5, 7.-7.5 nd 7.8. This sheet hs three sections. The first section will remind you bout techniques nd formuls tht you should know. The second gives number
More informationSolution of Tutorial 5 Drive dynamics & control
ELEC463 Unversty of New South Wles School of Electrcl Engneerng & elecommunctons ELEC463 Electrc Drve Systems Queston Motor Soluton of utorl 5 Drve dynmcs & control 500 rev/mn = 5.3 rd/s 750 rted 4.3 Nm
More informationPrecalculus Spring 2017
Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify
More informationModel Fitting and Robust Regression Methods
Dertment o Comuter Engneerng Unverst o Clorn t Snt Cruz Model Fttng nd Robust Regresson Methods CMPE 64: Imge Anlss nd Comuter Vson H o Fttng lnes nd ellses to mge dt Dertment o Comuter Engneerng Unverst
More informationSolubilities and Thermodynamic Properties of SO 2 in Ionic
Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,
More informationTHREE-DIMENSIONAL KINEMATICS OF RIGID BODIES
THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES 1. TRANSLATION Figure shows rigid body trnslting in three-dimensionl spce. Any two points in the body, such s A nd B, will move long prllel stright lines if
More informationStatistics 423 Midterm Examination Winter 2009
Sttstcs 43 Mdterm Exmnton Wnter 009 Nme: e-ml: 1. Plese prnt your nme nd e-ml ddress n the bove spces.. Do not turn ths pge untl nstructed to do so. 3. Ths s closed book exmnton. You my hve your hnd clcultor
More informationACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER /2019
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS MATH00030 SEMESTER 208/209 DR. ANTHONY BROWN 7.. Introduction to Integrtion. 7. Integrl Clculus As ws the cse with the chpter on differentil
More informationUniform Circular Motion
Unfom Ccul Moton Unfom ccul Moton An object mong t constnt sped n ccle The ntude of the eloct emns constnt The decton of the eloct chnges contnuousl!!!! Snce cceleton s te of chnge of eloct:!! Δ Δt The
More informationNumerical Analysis: Trapezoidal and Simpson s Rule
nd Simpson s Mthemticl question we re interested in numericlly nswering How to we evlute I = f (x) dx? Clculus tells us tht if F(x) is the ntiderivtive of function f (x) on the intervl [, b], then I =
More informationx=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions
Knemtc Quntte Lner Moton Phyc 101 Eyre Tme Intnt t Fundmentl Tme Interl Defned Poton x Fundmentl Dplcement Defned Aerge Velocty g Defned Aerge Accelerton g Defned Knemtc Quntte Scler: Mgntude Tme Intnt,
More informationConcept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B]
Conept of Atvty Equlbrum onstnt s thermodynm property of n equlbrum system. For heml reton t equlbrum; Conept of Atvty Thermodynm Equlbrum Constnts A + bb = C + dd d [C] [D] [A] [B] b Conentrton equlbrum
More informationMTH 146 Class 7 Notes
7.7- Approxmte Itegrto Motvto: MTH 46 Clss 7 Notes I secto 7.5 we lered tht some defte tegrls, lke x e dx, cot e wrtte terms of elemetry fuctos. So, good questo to sk would e: How c oe clculte somethg
More informationBernoulli Numbers Jeff Morton
Bernoulli Numbers Jeff Morton. We re interested in the opertor e t k d k t k, which is to sy k tk. Applying this to some function f E to get e t f d k k tk d k f f + d k k tk dk f, we note tht since f
More informationMeasuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
More informationInfinite Geometric Series
Infinite Geometric Series Finite Geometric Series ( finite SUM) Let 0 < r < 1, nd let n be positive integer. Consider the finite sum It turns out there is simple lgebric expression tht is equivlent to
More informationExponents and Logarithms Exam Questions
Eponents nd Logrithms Em Questions Nme: ANSWERS Multiple Choice 1. If 4, then is equl to:. 5 b. 8 c. 16 d.. Identify the vlue of the -intercept of the function ln y.. -1 b. 0 c. d.. Which eqution is represented
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
More informationSecond Order Analysis
Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to
More informationNUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.
NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with
More informationImproper Integrals. Type I Improper Integrals How do we evaluate an integral such as
Improper Integrls Two different types of integrls cn qulify s improper. The first type of improper integrl (which we will refer to s Type I) involves evluting n integrl over n infinite region. In the grph
More informationExperiment 1 Mass, volume and density
Experment 1 Mass, volume and densty Purpose 1. Famlarze wth basc measurement tools such as verner calper, mcrometer, and laboratory balance. 2. Learn how to use the concepts of sgnfcant fgures, expermental
More informationLecture 3. In this lecture, we will discuss algorithms for solving systems of linear equations.
Lecture 3 3 Solving liner equtions In this lecture we will discuss lgorithms for solving systems of liner equtions Multiplictive identity Let us restrict ourselves to considering squre mtrices since one
More informationM/G/1/GD/ / System. ! Pollaczek-Khinchin (PK) Equation. ! Steady-state probabilities. ! Finding L, W q, W. ! π 0 = 1 ρ
M/G//GD/ / System! Pollcze-Khnchn (PK) Equton L q 2 2 λ σ s 2( + ρ ρ! Stedy-stte probbltes! π 0 ρ! Fndng L, q, ) 2 2 M/M/R/GD/K/K System! Drw the trnston dgrm! Derve the stedy-stte probbltes:! Fnd L,L
More informationp-adic Egyptian Fractions
p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction
More informationStructural Dynamics and Earthquake Engineering
Structural Dynamcs and Earthuake Engneerng Course 9 Sesmc-resstant desgn of structures (1) Sesmc acton Methods of elastc analyss Course notes are avalable for download at http://www.ct.upt.ro/users/aurelstratan/
More informationFig. 1. Open-Loop and Closed-Loop Systems with Plant Variations
ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses
More informationEffect of Wind Speed on Reaction Coefficient of Different Building Height. Chunli Ren1, a, Yun Liu2,b
4th Interntonl Conference on Senor, Meurement nd Intellgent Mterl (ICSMIM 015) Effect of Wnd Speed on Recton Coeffcent of Dfferent Buldng Heght Chunl Ren1,, Yun Lu,b 1 No.9 Dxuexdo. Tnghn Cty, Hebe Provnce,
More informationChapter 4 Contravariance, Covariance, and Spacetime Diagrams
Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More information4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve
Dte: 3/14/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: Use your clcultor to solve 4 7x =250; 5 3x =500; HW Requests: Properties of Log Equtions
More informationVyacheslav Telnin. Search for New Numbers.
Vycheslv Telnin Serch for New Numbers. 1 CHAPTER I 2 I.1 Introduction. In 1984, in the first issue for tht yer of the Science nd Life mgzine, I red the rticle "Non-Stndrd Anlysis" by V. Uspensky, in which
More information13.4 Work done by Constant Forces
13.4 Work done by Constnt Forces We will begin our discussion of the concept of work by nlyzing the motion of n object in one dimension cted on by constnt forces. Let s consider the following exmple: push
More information