Module 1. Energy Methods in Structural Analysis. Version 2 CE IIT, Kharagpur
|
|
- Eustace Morton
- 7 years ago
- Views:
Transcription
1 Module 1 Energy Methods n Structural Analyss Verson 2 CE IIT, Kharagpur
2 Lesson 6 Engesser s Theorem and Truss Deflectons by Vrtual Work Prncples Verson 2 CE IIT, Kharagpur
3 Instructonal Objectes After readng ths lesson, the reader wll be able to: 1. State and proe Crott-Engesser theorem. 2. Dere smple expressons for calculatng deflectons n trusses subjected to mechancal loadng usng unt-load method. 3. Dere equatons for calculatng deflectons n trusses subjected to temperature loads. 4. Compute deflectons n trusses usng unt-load method due to fabrcaton errors. 6.1 Introducton In the preous lesson, we dscussed the prncple of rtual work and prncple of rtual dsplacement. Also, we dered unt load method from the prncple of rtual work and unt dsplacement method from the prncple of rtual dsplacement. In ths lesson, the unt load method s employed to calculate dsplacements of trusses due to external loadng. Intally the Engesser s theorem, whch s more general than the Castglano s theorem, s dscussed. In the end, few examples are soled to demonstrate the power of rtual work. 6.2 Crott-Engesser Theorem The Crott-Engesser theorem states that the frst partal derate of the * U expressed n terms of appled forces s complementary stran energy ( equal to the correspondng dsplacement. F j U * n = ajk Fk = uj (6.1 F j k = 1 For the case of ndetermnate structures ths may be stated as, U F j * = 0 (6.2 Note that Engesser s theorem s ald for both lnear and non-lnear structures. When the complementary stran energy s equal to the stran energy (.e. n case of lnear structures the equaton (6.1 s nothng but the statement of Castglano s frst theorem n terms of complementary stran energy. Verson 2 CE IIT, Kharagpur
4 In the aboe fgure the stran energy (area OACO s not equal to complementary stran energy (area OABO Area OACO = U u = F du (6.3 0 Dfferentatng stran energy wth respect to dsplacement, du = F (6.4 du Ths s the statement of Castglano s second theorem. Now the complementary energy s equal to the area enclosed by OABO. U * F = 0 u df (6.5 Dfferentatng complementary stran energy wth respect to force F, * du = u df (6.6 Verson 2 CE IIT, Kharagpur
5 Ths ges deflecton n the drecton of load. When the load dsplacement relatonshp s lnear, the aboe equaton concdes wth the Castglano s frst theorem gen n equaton ( Unt Load Method as appled to Trusses External Loadng In case of a plane or a space truss, the only nternal forces present are axal as the external loads are appled at jonts. Hence, equaton (5.7 may be wrtten as, n L δp Pds δ F u = (6.7 EA j j j= 1 0 wheren, δ Fj s the external rtual load, u j are the actual deflectons of the truss, L P δ P s the rtual stress resultant n the frame due to the rtual load and ds 0 EA s the actual nternal deformaton of the frame due to real forces. In the aboe equaton L, E, A respectely represent length of the member, cross-sectonal area of a member and modulus of elastcty of a member. In the unt load method, δ F j = 1 and all other components of rtual forces δ F ( = 1,2,..., j 1, j + 1,..., n are zero. Also, f the cross sectonal area A of truss remans constant throughout, then ntegraton may be replaced by summaton and hence equaton (6.7 may be wrtten as, u j = m = 1 (δp j P L (6.8 where m s the number of members, (δ P j s the nternal rtual axal force n P member due to unt rtual load at j and ( L s the total deformaton of EA member due to real loads. If we represent total deformaton by, then m u j = (δ P j Δ (6.9 = 1 Δ where, Δ s the true change n length of member due to real loads Temperature Loadng Due to change n the enronmental temperature, the truss members ether expand or shrnk. Ths n turn produces jont deflectons n the truss. Ths may be Verson 2 CE IIT, Kharagpur
6 calculated by equaton (6.9. In ths case, the change n length of member calculated from the relaton, Δ s Δ = αtl (6.10 where α s the co-effcent of thermal expanson member, member and T s the temperature change. L s the length of Fabrcaton Errors and Camber Sometmes, there wll be errors n fabrcatng truss members. In some cases, the truss members are fabrcated slghtly longer or shorter n order to prode camber to the truss. Usually camber s proded n brdge truss so that ts bottom chord s cured upward by an equal to ts downward deflecton of the chord when subjected to dead. In such nstances, also, the truss jont deflecton s calculated by equaton (6.9. Here, Δ = (6.11 e where, e s the fabrcaton error n the length of the member. e s taken as poste when the member lengths are fabrcated slghtly more than the actual length otherwse t s taken as negate. 6.4 Procedure for calculatng truss deflecton 1. Frst, calculate the real forces n the member of the truss ether by method of jonts or by method of sectons due to the externally appled forces. From ths P L determne the actual deformaton ( Δ n each member from the equaton. E A Assume tensle forces as poste and compresse forces as negate. 2. Now, consder the rtual load system such that only a unt load s consdered at the jont ether n the horzontal or n the ertcal drecton, where the deflecton s sought. Calculate rtual forces ( δ P j n each member due to the appled unt load at the j-th jont. 3. Now, usng equaton (6.9, ealuate the j-th jont deflecton u j. 4. If deflecton of a jont needs to be calculated due to temperature change, then determne the actual deformaton ( Δ n each member from the equaton Δ = αtl. The applcaton of equaton (6.8 s shown wth the help of few problems. Verson 2 CE IIT, Kharagpur
7 Example 6.1 Fnd horzontal and ertcal deflecton of jont C of truss ABCD loaded as shown n Fg. 6.2a. Assume that, all members hae the same axal rgdty. The gen truss s statcally determnate one. The reactons are as shown n Fg 6.2b along wth member forces whch are determned by equatons of statc equlbrum. To ealuate horzontal deflecton at C, apply a unt load as shown n Fg 6.2c and ealuate the rtual forces δ P n each member. The magntudes of nternal forces are also shown n the respecte fgures. The tensle forces are shown as +e and compresse forces are shown as e. At each end of the bar, arrows hae been drawn ndcatng the drecton n whch the force n the member acts on the jont. Verson 2 CE IIT, Kharagpur
8 Horzontal deflecton at jont C s calculated wth the help of unt load method. Ths may be stated as, 1 u H c ( δp c P L = (1 For calculatng horzontal deflecton at C,, apply a unt load at the jont C as shown n Fg.6.2c. The whole calculatons are shown n table 6.1. The calculatons are self explanatory. u c Verson 2 CE IIT, Kharagpur
9 Table 6.1 Computatonal detals for horzontal deflecton at C Member Length L / A E P (δ P (δp E A unts m m/kn kn kn kn.m AB 4 4/AE BC 4 4/AE CD 4 4/AE /AE DA 4 4/AE AC /AE /AE AE ( 1( u H C = = (Towards rght (2 AE Vertcal deflecton at jont C 1 u c ( δp c P L = In ths case, a unt ertcal load s appled at jont C of the truss as shown n Fg. 6.2d. Table 6.2 Computatonal detals for ertcal deflecton at C Member Length L / A E P (δ P (δp unts m m/kn kn kn kn.m AB 4 4/AE BC 4 4/AE CD 4 4/AE /AE DA 4 4/AE AC /AE AE ( 1( u C = = (Downwards (4 AE P L P L 2 (3 Verson 2 CE IIT, Kharagpur
10 Example 6.2 Compute the ertcal deflecton of jont b and horzontal dsplacement of jont D of the truss shown n Fg. 6.3a due to a Appled loadng as shown n fgure. 0 b Increase n temperature of 25 C n the top chord BD. Assume α = per C, E = N / mm. The cross sectonal areas of the members n square centmeters are shown n parentheses. Verson 2 CE IIT, Kharagpur
11 Verson 2 CE IIT, Kharagpur
12 The complete calculatons are shown n the followng table. Table 6.3 Computatonal detals for example 6.2 Mem L L / A E P P H (δ (δp Δ t = αtl (δp P L H (δ P PL H (δ (δp t Δ t P Δ unts m (10-5 m/kn kn kn kn m (10-3 kn.m (10-3 kn.m (10-3 kn.m (10-3 kn.m ab ab bc Bc BD cd cd de De Bb Dd Verson 2 CE IIT, Kharagpur
13 a Vertcal deflecton of jont b Applyng prncple of rtual work as appled to an deal pn jonted truss, ( δ P PL 1 m j δ Fu j j = j= 1 = 1 EA (1 For calculatng ertcal deflecton at b, apply a unt rtual load δ F b = 1. Then the aboe equaton may be wrtten as, 1 u 1 Due to external loads b ( δp P L = (2 u b = KNm 1 KN = m = 4.38 mm 2 Due to change n temperature t ( 1( u = ( δ P Δ b KN. m u t b = = m 1 KN u t b = mm t b Horzontal dsplacement of jont D 1 Due to externally appled loads u H D 1 u H b H ( δp P L = KNm = = m 1 KN = 0.68 mm Verson 2 CE IIT, Kharagpur
14 2 Due to change n temperature Ht H ( 1( u = ( δ P Δ D KN. m D = = m 1 KN u Ht u Ht D = mm t Summary In ths chapter the Crott-Engessor s theorem whch s more general than the Castglano s theorem has been ntroduced. The unt load method s appled statcally determnate structure for calculatng deflectons when the truss s subjected to arous types of loadngs such as: mechancal loadng, temperature loadng and fabrcaton errors. Verson 2 CE IIT, Kharagpur
Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More information+ + + - - This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More information21 Vectors: The Cross Product & Torque
21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rght-hand rule for the cross product of two vectors dscussed n ths chapter or the rght-hand rule for somethng curl
More informationUniversity Physics AI No. 11 Kinetic Theory
Unersty hyscs AI No. 11 Knetc heory Class Number Name I.Choose the Correct Answer 1. Whch type o deal gas wll hae the largest alue or C -C? ( D (A Monatomc (B Datomc (C olyatomc (D he alue wll be the same
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationModule 9.1 Software toepassing 4 (SAFIR) Toelichten van de mogelijkheden met SAFIR
TETRA Module 9.1 Software toepassng 4 (SAFIR) Toelchten van de mogeljheden met SAFIR Jean-Marc Franssen jm.franssen@ulg.ac.be Sept. 15, 009 Queston: what s an advanced calculaton model? Accordng to EN
More informationwhere the coordinates are related to those in the old frame as follows.
Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationChapter 11 Torque and Angular Momentum
Chapter 11 Torque and Angular Momentum I. Torque II. Angular momentum - Defnton III. Newton s second law n angular form IV. Angular momentum - System of partcles - Rgd body - Conservaton I. Torque - Vector
More informationSETTLEMENT PREDICTION OF PILE-SUPPORTED STRUCTURES IN LIQUEFIABLE SOILS DURING EARTHQUAKE
SETTLEMENT PREDICTION OF PILE-SUPPORTED STRUCTURES IN LIQUEFIABLE SOILS DURING EARTHQUAKE Chandra Dev Raman 1, Subhamoy Bhattacharya 2 and A Blakeborough 3 1 Research Scholar, Department of Engneerng Scence,Unversty
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationHomework: 49, 56, 67, 60, 64, 74 (p. 234-237)
Hoework: 49, 56, 67, 60, 64, 74 (p. 34-37) 49. bullet o ass 0g strkes a ballstc pendulu o ass kg. The center o ass o the pendulu rses a ertcal dstance o c. ssung that the bullet reans ebedded n the pendulu,
More informationFaraday's Law of Induction
Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy
More informationGoals Rotational quantities as vectors. Math: Cross Product. Angular momentum
Physcs 106 Week 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap 11.2 to 3 Rotatonal quanttes as vectors Cross product Torque expressed as a vector Angular momentum defned Angular momentum as a
More informationPeak Inverse Voltage
9/13/2005 Peak Inerse Voltage.doc 1/6 Peak Inerse Voltage Q: I m so confused! The brdge rectfer and the fullwae rectfer both prode full-wae rectfcaton. Yet, the brdge rectfer use 4 juncton dodes, whereas
More informationStudy of the mechanical behavior of the optical fiber by a mark-tracking method
EPJ Web of Conferences 6, 6 34002 (2010) DOI:10.1051/epjconf/20100634002 Owned by the authors, publshed by EDP Scences, 2010 Study of the mechancal behavor of the optcal fber by a mark-trackng method V.
More information(6)(2) (-6)(-4) (-4)(6) + (-2)(-3) + (4)(3) + (2)(-3) = -12-24 + 24 + 6 + 12 6 = 0
Chapter 3 Homework Soluton P3.-, 4, 6, 0, 3, 7, P3.3-, 4, 6, P3.4-, 3, 6, 9, P3.5- P3.6-, 4, 9, 4,, 3, 40 ---------------------------------------------------- P 3.- Determne the alues of, 4,, 3, and 6
More informationSection C2: BJT Structure and Operational Modes
Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationThe circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are:
polar Juncton Transstor rcuts Voltage and Power Amplfer rcuts ommon mtter Amplfer The crcut shown on Fgure 1 s called the common emtter amplfer crcut. The mportant subsystems of ths crcut are: 1. The basng
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationRate Monotonic (RM) Disadvantages of cyclic. TDDB47 Real Time Systems. Lecture 2: RM & EDF. Priority-based scheduling. States of a process
Dsadvantages of cyclc TDDB47 Real Tme Systems Manual scheduler constructon Cannot deal wth any runtme changes What happens f we add a task to the set? Real-Tme Systems Laboratory Department of Computer
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationA machine vision approach for detecting and inspecting circular parts
A machne vson approach for detectng and nspectng crcular parts Du-Mng Tsa Machne Vson Lab. Department of Industral Engneerng and Management Yuan-Ze Unversty, Chung-L, Tawan, R.O.C. E-mal: edmtsa@saturn.yzu.edu.tw
More informationLogical Development Of Vogel s Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME, ISSUE, FEBRUARY ISSN 77-866 Logcal Development Of Vogel s Approxmaton Method (LD- An Approach To Fnd Basc Feasble Soluton Of Transportaton
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationProject Networks With Mixed-Time Constraints
Project Networs Wth Mxed-Tme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationChapter 9. Linear Momentum and Collisions
Chapter 9 Lnear Momentum and Collsons CHAPTER OUTLINE 9.1 Lnear Momentum and Its Conservaton 9.2 Impulse and Momentum 9.3 Collsons n One Dmenson 9.4 Two-Dmensonal Collsons 9.5 The Center of Mass 9.6 Moton
More informationn + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)
MATH 16T Exam 1 : Part I (In-Class) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationLevel Annuities with Payments Less Frequent than Each Interest Period
Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annuty-mmedate 2 Annuty-due Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annuty-mmedate 2 Annuty-due Symoblc approach
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.
More informationLecture 2 Sequence Alignment. Burr Settles IBS Summer Research Program 2008 bsettles@cs.wisc.edu www.cs.wisc.edu/~bsettles/ibs08/
Lecture 2 Sequence lgnment Burr Settles IBS Summer Research Program 2008 bsettles@cs.wsc.edu www.cs.wsc.edu/~bsettles/bs08/ Sequence lgnment: Task Defnton gven: a par of sequences DN or proten) a method
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and
More informationPhysics 110 Spring 2006 2-D Motion Problems: Projectile Motion Their Solutions
Physcs 110 Sprn 006 -D Moton Problems: Projectle Moton Ther Solutons 1. A place-kcker must kck a football from a pont 36 m (about 40 yards) from the oal, and half the crowd hopes the ball wll clear the
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σ-algebra: a set
More informationNMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING. Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582
NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582 7. Root Dynamcs 7.2 Intro to Root Dynamcs We now look at the forces requred to cause moton of the root.e. dynamcs!!
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationRisk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008
Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationWe assume your students are learning about self-regulation (how to change how alert they feel) through the Alert Program with its three stages:
Welcome to ALERT BINGO, a fun-flled and educatonal way to learn the fve ways to change engnes levels (Put somethng n your Mouth, Move, Touch, Look, and Lsten) as descrbed n the How Does Your Engne Run?
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More informationVisa Smart Debit/Credit Certificate Authority Public Keys
CHIP AND NEW TECHNOLOGIES Visa Smart Debit/Credit Certificate Authority Public Keys Overview The EMV standard calls for the use of Public Key technology for offline authentication, for aspects of online
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More information8 Algorithm for Binary Searching in Trees
8 Algorthm for Bnary Searchng n Trees In ths secton we present our algorthm for bnary searchng n trees. A crucal observaton employed by the algorthm s that ths problem can be effcently solved when the
More informationRotation and Conservation of Angular Momentum
Chapter 4. Rotaton and Conservaton of Angular Momentum Notes: Most of the materal n ths chapter s taken from Young and Freedman, Chaps. 9 and 0. 4. Angular Velocty and Acceleraton We have already brefly
More informationThe Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1
EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 9-2, 24, pp. 546-555. The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons
More informationSeries Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3
Royal Holloway Unversty of London Department of Physs Seres Solutons of ODEs the Frobenus method Introduton to the Methodology The smple seres expanson method works for dfferental equatons whose solutons
More informationAn interactive system for structure-based ASCII art creation
An nteractve system for structure-based ASCII art creaton Katsunor Myake Henry Johan Tomoyuk Nshta The Unversty of Tokyo Nanyang Technologcal Unversty Abstract Non-Photorealstc Renderng (NPR), whose am
More informationImplementation of Deutsch's Algorithm Using Mathcad
Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"
More informationSUMMARY. Topology optimization, buckling, eigenvalue, derivative, structural optimization 1. INTRODUCTION
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 0000; 00:1 20 Publshed onlne n Wley InterScence (www.nterscence.wley.com). A fast method for solvng bnary programmng
More informationtotal A A reag total A A r eag
hapter 5 Standardzng nalytcal Methods hapter Overvew 5 nalytcal Standards 5B albratng the Sgnal (S total ) 5 Determnng the Senstvty (k ) 5D Lnear Regresson and albraton urves 5E ompensatng for the Reagent
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationPolitecnico di Torino. Porto Institutional Repository
Poltecnco d orno Porto Insttutonal Repostory [Proceedng] rbt dynamcs and knematcs wth full quaternons rgnal Ctaton: Andres D; Canuto E. (5). rbt dynamcs and knematcs wth full quaternons. In: 16th IFAC
More informationA fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng (2012) Publshed onlne n Wley Onlne Lbrary (wleyonlnelbrary.com)..4367 A fast method for bnary programmng usng frst-order
More informationActivity Scheduling for Cost-Time Investment Optimization in Project Management
PROJECT MANAGEMENT 4 th Internatonal Conference on Industral Engneerng and Industral Management XIV Congreso de Ingenería de Organzacón Donosta- San Sebastán, September 8 th -10 th 010 Actvty Schedulng
More informationElastic Systems for Static Balancing of Robot Arms
. th World ongress n Mechans and Machne Scence, Guanajuato, Méco, 9- June, 0 _ lastc Sstes for Statc alancng of Robot rs I.Sonescu L. uptu Lucana Ionta I.Ion M. ne Poltehnca Unverst Poltehnca Unverst Poltehnca
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationCHAPTER 8 Potential Energy and Conservation of Energy
CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and non-conservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More informationDamage detection in composite laminates using coin-tap method
Damage detecton n composte lamnates usng con-tap method S.J. Km Korea Aerospace Research Insttute, 45 Eoeun-Dong, Youseong-Gu, 35-333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The con-tap test has the
More informationThe Games of Cournot Sports
Appled Mathematcal Scences, Vol. 7, 013, no. 4, 01-09 Managers Compensaton and Colluse Behaour under Cournot Olgopoly Marco A. Marn Department of Computer, Control and Management Engneerng Unerstà d Roma
More informationA Performance Analysis of View Maintenance Techniques for Data Warehouses
A Performance Analyss of Vew Mantenance Technques for Data Warehouses Xng Wang Dell Computer Corporaton Round Roc, Texas Le Gruenwald The nversty of Olahoma School of Computer Scence orman, OK 739 Guangtao
More informationTraffic-light a stress test for life insurance provisions
MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationAn Analysis of Central Processor Scheduling in Multiprogrammed Computer Systems
STAN-CS-73-355 I SU-SE-73-013 An Analyss of Central Processor Schedulng n Multprogrammed Computer Systems (Dgest Edton) by Thomas G. Prce October 1972 Techncal Report No. 57 Reproducton n whole or n part
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationOptical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems
Applcaton ote: FA-9.0. Re.; 04/08 Optcal Sgnal-to-ose Rato and the Q-Factor n Fber-Optc Communcaton Systems Functonal Dagrams Pn Confguratons appear at end of data sheet. Functonal Dagrams contnued at
More informationMultiple stage amplifiers
Multple stage amplfers Ams: Examne a few common 2-transstor amplfers: -- Dfferental amplfers -- Cascode amplfers -- Darlngton pars -- current mrrors Introduce formal methods for exactly analysng multple
More informationAddendum to: Importing Skill-Biased Technology
Addendum to: Importng Skll-Based Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More information8.4. Annuities: Future Value. INVESTIGATE the Math. 504 8.4 Annuities: Future Value
8. Annutes: Future Value YOU WILL NEED graphng calculator spreadsheet software GOAL Determne the future value of an annuty earnng compound nterest. INVESTIGATE the Math Chrstne decdes to nvest $000 at
More informationA Three-Point Combined Compact Difference Scheme
JOURNAL OF COMPUTATIONAL PHYSICS 140, 370 399 (1998) ARTICLE NO. CP985899 A Three-Pont Combned Compact Derence Scheme Peter C. Chu and Chenwu Fan Department o Oceanography, Naval Postgraduate School, Monterey,
More informationSystemic Behaviour of Plane Reciprocal Frame Structures
Systemc Behavour of Plane Recprocal Frame Structures Thomas Kohlhammer, Char of Structural Desgn, ETH Zurch, Zurch, Swtzerland; Ton Kotnk, Char of Structural Desgn, ETH Zurch, Zurch, Swtzerland Contact:
More informationPOLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and
POLYSA: A Polynomal Algorthm for Non-bnary Constrant Satsfacton Problems wth and Mguel A. Saldo, Federco Barber Dpto. Sstemas Informátcos y Computacón Unversdad Poltécnca de Valenca, Camno de Vera s/n
More information1 Battery Technology and Markets, Spring 2010 26 January 2010 Lecture 1: Introduction to Electrochemistry
1 Battery Technology and Markets, Sprng 2010 Lecture 1: Introducton to Electrochemstry 1. Defnton of battery 2. Energy storage devce: voltage and capacty 3. Descrpton of electrochemcal cell and standard
More informationConsider a 1-D stationary state diffusion-type equation, which we will call the generalized diffusion equation from now on:
Chapter 1 Boundary value problems Numercal lnear algebra technques can be used for many physcal problems. In ths chapter we wll gve some examples of how these technques can be used to solve certan boundary
More informationTraffic-light extended with stress test for insurance and expense risks in life insurance
PROMEMORIA Datum 0 July 007 FI Dnr 07-1171-30 Fnansnspetonen Författare Bengt von Bahr, Göran Ronge Traffc-lght extended wth stress test for nsurance and expense rss n lfe nsurance Summary Ths memorandum
More informationSection 2 Introduction to Statistical Mechanics
Secton 2 Introducton to Statstcal Mechancs 2.1 Introducng entropy 2.1.1 Boltzmann s formula A very mportant thermodynamc concept s that of entropy S. Entropy s a functon of state, lke the nternal energy.
More informationActuator forces in CFD: RANS and LES modeling in OpenFOAM
Home Search Collectons Journals About Contact us My IOPscence Actuator forces n CFD: RANS and LES modelng n OpenFOAM Ths content has been downloaded from IOPscence. Please scroll down to see the full text.
More informationThe Full-Wave Rectifier
9/3/2005 The Full Wae ectfer.doc /0 The Full-Wae ectfer Consder the followng juncton dode crcut: s (t) Power Lne s (t) 2 Note that we are usng a transformer n ths crcut. The job of ths transformer s to
More informationChapter 31B - Transient Currents and Inductance
Chapter 31B - Transent Currents and Inductance A PowerPont Presentaton by Paul E. Tppens, Professor of Physcs Southern Polytechnc State Unversty 007 Objectves: After completng ths module, you should be
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationRotation Kinematics, Moment of Inertia, and Torque
Rotaton Knematcs, Moment of Inerta, and Torque Mathematcally, rotaton of a rgd body about a fxed axs s analogous to a lnear moton n one dmenson. Although the physcal quanttes nvolved n rotaton are qute
More informationChapter 6 Inductance, Capacitance, and Mutual Inductance
Chapter 6 Inductance Capactance and Mutual Inductance 6. The nductor 6. The capactor 6.3 Seres-parallel combnatons of nductance and capactance 6.4 Mutual nductance 6.5 Closer look at mutual nductance Oerew
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationIT09 - Identity Management Policy
IT09 - Identty Management Polcy Introducton 1 The Unersty needs to manage dentty accounts for all users of the Unersty s electronc systems and ensure that users hae an approprate leel of access to these
More information