THE ANALYSIS OF SOIL RESISTANCE DURING SCREW DISPLACEMENT PILE INSTALLATION

Size: px
Start display at page:

Download "THE ANALYSIS OF SOIL RESISTANCE DURING SCREW DISPLACEMENT PILE INSTALLATION"

Transcription

1 Sudia Geoechnica e Mechanica, Vol. XXXVI, No. 3, 014 DOI: /sgem THE ANALYSIS OF SOIL RESISTANCE DURING SCREW DISPLACEMENT PILE INSTALLATION ADAM KRASIŃSKI Gdańsk Universiy of Technology, Deparmen of Geoechnics, Geology and Mariime Engineering, ul. Naruowicza 11/1, Gdańsk, Poland, akra@pg.gda.pl Absrac: The applicaion of screw displacemen piles (SDP) is sill increasing due o heir high efficiency and many advanages. However, one echnological problem is a serious disadvanage of hose piles. I relaes o he generaion of very high soil resisance during screw auger peneraion, especially when piles are insalled in non-cohesive soils. In many siuaions his problem causes difficulies in creaing piles of designed lengh and diameer. I is necessary o find a proper mehod for predicion of soil resisance during screw pile insallaion. The analysis of screw resisances based on model and field ess is presened in he paper. The invesigaions were carried ou as par of research projec, financed by he Polish Minisry of Science and Higher Educaion. As a resul of ess and analyses he empirical mehod for predicion of roaion resisance (orque) during screw auger peneraion in non-cohesive subsoil based on CPT is proposed. Key words: screw displacemen pile, pile insallaion, pile auger, orque, soil resisance 1. INTRODUCTION During he insallaion of SDP pile, when he auger peneraes he non-cohesive subsoil, high soil resisance is observed. This screw resisance is one of he bigges problems of SDP pile echnology and is a subjec of ongoing scienific invesigaions and analyses. I was also he reason ha many ypes of screw auger have already been inroduced ino pracice. I is believed ha soil resisance could be reduced by appropriae auger consrucion. Due o he difficulies conneced wih he insallaion of screw displacemen piles in various ypes of soil condiions, hese piles are ofen omied in geoechnical projecs. High soil resisance during screw auger peneraion means he high value of orque (M T ), which should be applied o roae he auger. Therefore, very massive drilling machines wih high orque (a leas 00 knm) need o be used for screw displacemen pile insallaion. The analysis of insallaion effor conneced wih SDP piles was carried ou, among ohers, by NeSmih [10]. The problem is addiionally complicaed due o he fac ha high soil resisances during he insallaion no always mean he high bearing capaciy of screw pile. The analogy o driven piles, where he high blowing resisances indicae he high pile bearing capaciy, canno be aken in he case of SDP piles. This resuls from he fac ha he load bearing capaciy of screw displacemen piles is primarily based on he shaf resisance Q s, [4 6]. Learning from pracice shows ha we raher will no be able o reduce significanly he soil resisances by changing he shape or he consrucion of screw auger. The only way o solve he problem seems o idenify he phenomena occurring in he soil during he screwing process and o propose a mehod for predicing he soil resisances. This paper presens he resuls of he auhor s own model and field ess as well as heoreical analyses concerning soil resisances during screw auger peneraion in non-cohesive soil. Model and field ess were correlaed wih CPT ess. Thanks o hese resuls, he empirical mehod of screw orque M T value predicion based on CPT ess has been developed and presened.. DESCRIPTION OF SCREW AUGER PENETRATION PROCESS The main ask of screw pile auger is o creae a hole in he ground by radial soil displacemen and o fill he hole wih he concree. Boom par of he

2 50 A. KRASIŃSKI auger is helical bu in he upper par he diameer of auger core gradually increases. Thanks o is shape he auger peneraes he soil during roaion and displaces he soil radially. Someimes, a verical compressive force is added from drilling machine o iniiae he auger peneraion. In oher cases a ension force is used o decrease he peneraion velociy and o reduce he orque value. Screwing process iniiaes a significan increase of radial sresses in he surrounding soil. These sresses are he main reason of high soil fricion around he auger surface. There are also soil resisances under he auger base. The inserion of a drilling ool ino he ground is a complex process, difficul o heoreical describe. Therefore, a simplified scheme of he auger was aken for analysis. In his scheme, presened in Fig. 1, he real auger is represened by he equivalen cylinder. I is assumed ha he oal value of orque M T consiss of wo componens: M Ts and M M = M + M. (1) T Ts M Ts is conneced wih soil fricion Ts around he auger shaf and is generaed by he auger roaion. M is conneced wih soil uni fricion under he auger base and is generaed by he roaion and auger verical movemen. Componens M Ts and M are defined by he formulas π Ds = Ts; i hs i, () M Ts ; M 3 π Ds = 1. (3) Fig. 1. Simplified scheme of SDP auger aken for analysis Screw resisance is also defined by he number of auger roaions n T per uni deph of peneraion. In he auhor s opinion M T and n T are he mos imporan parameers of SDP pile insallaion. In pracice, in he repors of screw displacemen pile insallaion here is given he informaion abou: oil pressure in he hydraulic roary ool, roaion velociy RPM (roaion per minue) and peneraion velociy (meers per hour). M T and n T values are obained from recalculaing he Fig.. Tes and measuremen resuls concerning example of SDP pile, [6]

3 The analysis of soil resisance during screw displacemen pile insallaion 51 hree parameers menioned. In mos drilling machines, he value of orque M T depends on hydraulic oil pressure and on RPM (he smaller he RPM, he higher he M T for a given oil pressure). Figure presens he example of measuremen resuls concerning SDP pile insallaion in correlaion wih CPT es of subsoil. CPT was carried ou before and afer pile insallaion. The pile was insalled by drilling machine of maximal orque M T = 00 knm and by he auger of shape presened in he figure. In he CPT diagram one may noe ha afer pile insallaion here is an increase of q c resisances in he region around he pile shaf, bu under he pile base ha increase is no very high. Similar phenomenon was observed wih regard o he oher SDP piles esed. This allowed us o conclude ha screw displacemen piles affec he soil condiions (densiy and sress level) mainly around heir shafs. In he M T and n T diagrams one may noice ha during auger peneraion ino he bearing sraum an inensive increase of orque is observed wih consan value of he roaion number n T (abou 4 roaions per meer). When he orque reached he maximal value of 00 knm, a he deph of 7.5 m under he ground level, he peneraion velociy was reduced. As a resul, he n T value increased whereas he M T value decreased. Thanks o such acions i was possible o creae a pile of lengh L = 8.85 m. This example shows ha he orque value can be influenced by regulaion of auger peneraion velociy, hus by roaion number n T. 3. MODEL TESTS Model ess were conduced using SDP auger models prepared in 1:7.5 scale in wo diameers (Fig. 3). Auger model SDP1 represens he original auger of 400 mm in diameer, while model SDP represens he original auger of 500 mm in diameer. The experimens were carried ou a he Geoechnical Laboraory in Gdańsk Universiy of Technology. The research device consiss of seel conainer (.0 m diameer and.0 m high) for soil. Mois fine sand was prepared wih appropriae densiy achieved by vibraion and conrolled by CPT ess. The augers were screwed ino he soil using hand operaed device and verical load of consan value of 0.5 kn. Soil resisances during screwing were measured in erms of orque M T and number of roaions n T per each 0.1 m of auger peneraion. Several series of ess were carried ou. Apar from he measuremens of soil resisances during auger peneraion also he SDP and Alas pile models were insalled and esed in respec of heir bearing capaciy. A deailed descripion of pile model ess is presened also in oher auhor s work [3]. Fig. 3. Models of SDP augers (model scale 1:7.5) During screw auger peneraion usually only he oal value of orque M T is measured, and i is difficul o divide is value ino M Ts and M componens. Therefore, in one of he ess he measuring of screwing resisances was performed in a special way. I was assumed ha if he auger verical peneraion was blocked, hen during roaion only he M Ts componen was measured. Before blocking he oal M T value was measured. M componen was hen calculaed as a difference beween M T and M Ts. During he es, which is shown in Fig. 4, also he value of verical force Q Tv was measured. The auhor named his ension force as auger hrus. The measuremens of M T, M Ts and Q Tv were carried ou every 0.1 m of peneraion from 0.5 m o 1.0 m of deph. The resuls of measuremens, which were done for boh augers SDP1 and SDP, are presened as he diagrams in Fig. 5, ogeher wih diagrams of cone resisances q c and roaion numbers n T. Nex, using he auger scheme presened in Fig. 1, he values of uni soil resisances Ts and were calculaed and presened in Fig. 6 as diagrams ogeher wih diagrams of raios Ts /q cs and /q cb. The q cs value was aken as an average q c from he auger lengh h s, whereas q cb was aken as an average q c of D s o +D s region around he auger base level.

4 5 A. KRASIŃSKI Fig. 4. Measuremen of orque componen M Ts and auger hrus Q Tv in model es Fig. 5. The resuls of auger SDP screwing ess wih measuremens of orques M T, M Ts, M and force Q Tv Fig. 6. Uni fricion resisances Ts and and heir relaions o cone resisances q c

5 The analysis of soil resisance during screw displacemen pile insallaion 53 I can be noed ha raio Ts /q cs is consan along he whole deph, which means ha uni resisance Ts is proporional o cone resisance q c. On his basis he following relaion is creaed = (4) Ts q cs The raio /q cb is no consan bu is increasing wih deph. I was assumed ha his increase is caused by auger hrus Q Tv. The mechanism of auger hrus iniiaion can be explained by analogy o ordinary screw. In such a screw, when he fricion on he hread is negleced, a relaion beween M Ts componen of orque and hrus Q Tv resuls from he principle of energy conservaion. In he case of auger which is peneraed ino he soil he following relaion is assumed π MTs QTv = a (5) nt s where s pich of he auger helix, a reducion facor, aking ino accoun he losses caused by he soil fricion and by he fac ha verical velociy of auger inserion is less han i would resul from pich of helix s (a < 1.0, he exac value of a is no known). The number of auger roaion per 1.0 m (n T ) should be aken ino accoun as a value wihou unis. The hrus Q Tv causes he auger base impac on he soil by verical pressure q which can be expressed by he formula q 4Q MTs = = a. (6) π D n s D Tv 8 s The verical pressure q influences direcly he soil fricion under he auger base. The following relaion is assumed q T s = μ (7) where μ fricion coefficien of he soil under he auger base. On he basis of model es resuls i was concluded ha he value μ is no consan bu increases wih deph approximaely proporionally o he increase of cone resisance q c. The following relaion is assumed qcb μ = b, (8) p ref where p ref = 1.0 MPa reference sress, b conversion facor (no known). and Equaion (7) akes he form M Ts cb = 8 a b. (9) nt s Ds pref Afer inroducing wo new coefficiens m Ts Ts s ref q = M s D p (10) m we receive a new form of equaion (9) T = 8 a b (11) = 1 mts m qcb. (1) n The coefficien m was deermined experimenally from es resuls by using back analysis mehod. I was no necessary o deermine values of a and b coefficiens separaely. The m value was found o be abou 4.40 and was approximaely consan in relaion o deph and similar in he case of boh augers SDP1 and SDP. Finally, from he analysis one can obain empirical equaions for he calculaion of orque componens M Ts and M and oal orque M T of screw displacemen augers on he basis of cone resisances q c. Moreover, he analysis has shown ha M Ts componen depends mainly on he cone resisance q c, whereas M componen depends on M Ts value, cone resisance and number of auger roaions per uni deph n T. 4. FIELD TESTS A mehod for predicion of soil resisance during screw auger peneraion was prepared also for piles in naural scale. This mehod concerns SDP and CMC (Conrolled Modulus Column) augers. There were applied he same assumpions and very similar equaions as in he model es analyses, bu several addiional facors and effecs had o be aken ino accoun. These facors concerned he auger shape, nonhomogeneiy of soil profile and sress level in he subsoil. The same scheme of auger as presened in Fig. 1 and he same equaions (1) (3) of M T, M Ts and M calculaions were applied. Afer many rial replicaions of orque values measured in he field ess, he following formulas for Ts and resisances were deermined

6 54 A. KRASIŃSKI Fig. 7. Diagrams for deerminaion of η1, η and η4 coefficiens Fig. 8. Torque MT predicion for he SDP pile insallaion on he field sie Fig. 9. Torque MT predicion for he CMC pile insallaion on he field sie

7 The analysis of soil resisance during screw displacemen pile insallaion 55 Ts = η η3 q cs η [kpa], (13) q cb = 1. η 3 η4 mts [kpa], (14) nt where η 1, η 4 coefficiens dependen on he deph of auger peneraion in bearing soil layer, η coefficien of auger shape influence, η 3 coefficien of sress level in he subsoil. Coefficiens η 1, η and η 4 are read from diagrams presened in Fig. 7, whereas η 3 coefficien is calculaed from he formula σ v 0 η3 = (15) 100 kpa where σ v 0 is a verical effecive sress in he subsoil. The value of m Ts coefficien is calculaed using formula (10). The number of auger roaions per uni deph n T which has o be applied in equaion (14) is unknown and we mus assume is value. I was menioned earlier ha he n T value can be conrolled during screwing process by he piling machine operaor. In he calculaion we should ake he planned or maximal acceped value of n T (usually no more han 0 o 40 roaions per meer) COMPARISON OF PREDICTED AND MEASURED SCREW RESISTANCES Figures 8 and 9 presen he resuls of calculaed replicaions of real screw resisances measured during he insallaion of wo seleced piles in he field. Paricular emphasis was placed on M T value predicion in he boom par of subsoil when he auger was peneraed in he bearing sandy layer. The organic soils in he upper pars of subsoil were less imporan, hen he screw resisances in hese layers were aken approximaely as: Ts = f s and = 5 f s, where f s is he sleeve fricion measured in CPT es. The values of η 1, η, η 3 and η 4 coefficiens were aken as equal o 1.0 in organic soil. The values of n T were aken as equal o hose read from he pile insallaion repors. On he basis of diagrams presened in Figs. 8 and 9 i can be concluded ha he proposed mehod for predicion of soil resisance during SDP and CMC auger peneraion in non-cohesive soils provides good resuls. 5. CONCLUSIONS The ess and analyses presened in he paper showed ha roaion resisances during screw displacemen auger peneraion in non-cohesive soils depend on soil srengh properies (expressed by CPT cone resisances q c ), auger geomery and screw echnique (he velociy of roaion and peneraion). The oal value of orque M T generaed by screwing process can be divided ino wo componens: M Ts momen resuling from soil fricion around he auger shaf and M momen resuling from soil resisances under he auger base. The calculaion mehod developed as a resul of ess and analyses allows us o predic he roaion resisances (a value of orque M T ) during SDP auger peneraion ino non-cohesive subsoil on he basis of CPT resuls. The mehod was verified posiively wih several pracical examples of SDP and CMC pile insallaion in he field. On he base of i, we will be able o know wha energy of piling machine is required o insall he designed screw displacemen pile. This predicion mehod can be applied o design screw displacemen piles ogeher wih he auhor s own mehod for pile bearing capaciy calculaion [7] or wih oher calculaion mehods, proposed, for example, by Busamane and Gianeselli [1], [], Maerens and Huybrechs [8] or by NeSmih [9]. I should be underlined ha many elemens of he calculaion mehod proposed were assumed in a simplified way. Due o his fac i may no work well in every case. This mehod should raher be considered as a preliminary proposal, which require many ess and verificaions and will cerainly be subjeced o modificaions. REFERENCES [1] BUSTAMANTE M., GIANESELLI L., Design of auger displacemen piles from in siu ess, Proceedings of Inernaional Geoechnical Seminar on Deep Foundaions on Bored and Auger Piles, BAP II, Balkema, Roerdam 1993, pp [] BUSTAMANTE M., GIANESELLI L., Insallaion parameers and capaciy of screwed piles, Proceedings of Inernaional Geoechnical Seminar on Deep Foundaions on Bored and Auger Piles, BAP III, Balkema, Roerdam 1998, pp [3] KRASIŃSKI A., Model ess of screwed piles, Proc. of he XIV Danube-European Conf. on Geoechnical Engineering, Braislava, Slovak Republic, June 4, 010, 37+CD. [4] KRASIŃSKI A., Field ess of screw displacemen piles and columns SDP and SDC, Drogi i Mosy, 011a, No. 1, pp (in Polish).

8 56 A. KRASIŃSKI [5] KRASIŃSKI A., Resuls of field ess of screw displacemen pile and columns, Inżynieria Morska i Geoechnika, 011b, No. 6, pp (in Polish). [6] KRASIŃSKI A., Bearing capaciy and ineracion wih soil of screw displacemen piles, Final repor of research projec No. N N for he Polish Minisry of Science and Higher Educaion, Gdansk (in Polish, no published), 011c. [7] KRASIŃSKI A., Proposal for calculaing he bearing capaciy of screw displacemen piles in non-cohesive soils based on CPT resuls, Sudia Geoechnica e Mechanica, 01, Vol. XXXIV, No. 4, pp [8] MAERTENS J., HUYBRECHTS N., Belgian screw pile echnology. Design and recen developmens, Swes & Zeilinger B.V., Lisse, The Neherlands, 003, p. 37. [9] NESMITH W.M., Saic capaciy analysis of augered, pressure-injeced displacemen piles, Proc. of he In. Deep Foundaion Congress 00, Geoechnical Special Publicaion, 00, No. 116, Vol., ASCE, pp [10] NESMITH W.M., Insallaion effor as an indicaor of displacemen screw pile capaciy, Deep Foundaion on Bored and Auger Piles, BAP IV, Van Impe (ed.), Millpress, Roerdam 003, pp

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,

More information

At the end of this lesson, the students should be able to understand

At the end of this lesson, the students should be able to understand Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress concenraion facor; experimenal and heoreical mehods.

More information

Navneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi

Navneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi Creep in Viscoelasic Subsances Numerical mehods o calculae he coefficiens of he Prony equaion using creep es daa and Herediary Inegrals Mehod Navnee Saini, Mayank Goyal, Vishal Bansal (23); Term Projec

More information

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should Cambridge Universiy Press 978--36-60033-7 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion

More information

Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture

Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture Scienific Herald of he Voronezh Sae Universiy of Archiecure and Civil Engineering. Consrucion and Archiecure UDC 625.863.6:551.328 Voronezh Sae Universiy of Archiecure and Civil Engineering Ph. D. applican

More information

Some Basic Information about M-S-D Systems

Some Basic Information about M-S-D Systems Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,

More information

Curling Stress Equation for Transverse Joint Edge of a Concrete Pavement Slab Based on Finite-Element Method Analysis

Curling Stress Equation for Transverse Joint Edge of a Concrete Pavement Slab Based on Finite-Element Method Analysis TRANSPORTATION RESEARCH RECORD 155 35 Curling Sress Equaion for Transverse Join Edge of a Concree Pavemen Slab Based on Finie-Elemen Mehod Analysis TATSUO NISHIZAWA, TADASHI FUKUDA, SABURO MATSUNO, AND

More information

1. VELOCITY AND ACCELERATION

1. VELOCITY AND ACCELERATION 1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under

More information

Electrical and current self-induction

Electrical and current self-induction Elecrical and curren self-inducion F. F. Mende hp://fmnauka.narod.ru/works.hml mende_fedor@mail.ru Absrac The aricle considers he self-inducance of reacive elemens. Elecrical self-inducion To he laws of

More information

MATHEMATICAL DESCRIPTION OF THEORETICAL METHODS OF RESERVE ECONOMY OF CONSIGNMENT STORES

MATHEMATICAL DESCRIPTION OF THEORETICAL METHODS OF RESERVE ECONOMY OF CONSIGNMENT STORES MAHEMAICAL DESCIPION OF HEOEICAL MEHODS OF ESEVE ECONOMY OF CONSIGNMEN SOES Péer elek, József Cselényi, György Demeer Universiy of Miskolc, Deparmen of Maerials Handling and Logisics Absrac: Opimizaion

More information

Vehicle Arrival Models : Headway

Vehicle Arrival Models : Headway Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where

More information

The motions of the celt on a horizontal plane with viscous friction

The motions of the celt on a horizontal plane with viscous friction The h Join Inernaional Conference on Mulibody Sysem Dynamics June 8, 18, Lisboa, Porugal The moions of he cel on a horizonal plane wih viscous fricion Maria A. Munisyna 1 1 Moscow Insiue of Physics and

More information

Friction (kpa) Cross correlation between qc qc & & fs fs

Friction (kpa) Cross correlation between qc qc & & fs fs CPT: CPT- Toal deph:. m, Dae: -- Surface Elevaion:. m Coords: X:., Y:. Cone Cone resisance Sleeve Sleeve fricion Pore Pore pressure Tip resisance (MPa), Fricion (kpa) Cross correlaion beween qc qc & &

More information

23.2. Representing Periodic Functions by Fourier Series. Introduction. Prerequisites. Learning Outcomes

23.2. Representing Periodic Functions by Fourier Series. Introduction. Prerequisites. Learning Outcomes Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals

More information

Sub Module 2.6. Measurement of transient temperature

Sub Module 2.6. Measurement of transient temperature Mechanical Measuremens Prof. S.P.Venkaeshan Sub Module 2.6 Measuremen of ransien emperaure Many processes of engineering relevance involve variaions wih respec o ime. The sysem properies like emperaure,

More information

Combined Bending with Induced or Applied Torsion of FRP I-Section Beams

Combined Bending with Induced or Applied Torsion of FRP I-Section Beams Combined Bending wih Induced or Applied Torsion of FRP I-Secion Beams MOJTABA B. SIRJANI School of Science and Technology Norfolk Sae Universiy Norfolk, Virginia 34504 USA sirjani@nsu.edu STEA B. BONDI

More information

Involute Gear Tooth Bending Stress Analysis

Involute Gear Tooth Bending Stress Analysis Involue Gear Tooh Bending Sress Analysis Lecure 21 Engineering 473 Machine Design Gear Ineracion Line of Ceners Line Tangen o s Line Normal o Line of Ceners 1 s Close Up of Meshed Teeh Line of Conac W

More information

Modeling the Dynamics of an Ice Tank Carriage

Modeling the Dynamics of an Ice Tank Carriage Modeling he Dynamics of an Ice Tank Carriage The challenge: To model he dynamics of an Ice Tank Carriage and idenify a mechanism o alleviae he backlash inheren in he design of he gearbox. Maplesof, a division

More information

Final Spring 2007

Final Spring 2007 .615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o

More information

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still. Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in

More information

KINEMATICS IN ONE DIMENSION

KINEMATICS IN ONE DIMENSION KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec

More information

On Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature

On Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature On Measuring Pro-Poor Growh 1. On Various Ways of Measuring Pro-Poor Growh: A Shor eview of he Lieraure During he pas en years or so here have been various suggesions concerning he way one should check

More information

Econ107 Applied Econometrics Topic 7: Multicollinearity (Studenmund, Chapter 8)

Econ107 Applied Econometrics Topic 7: Multicollinearity (Studenmund, Chapter 8) I. Definiions and Problems A. Perfec Mulicollineariy Econ7 Applied Economerics Topic 7: Mulicollineariy (Sudenmund, Chaper 8) Definiion: Perfec mulicollineariy exiss in a following K-variable regression

More information

Lab #2: Kinematics in 1-Dimension

Lab #2: Kinematics in 1-Dimension Reading Assignmen: Chaper 2, Secions 2-1 hrough 2-8 Lab #2: Kinemaics in 1-Dimension Inroducion: The sudy of moion is broken ino wo main areas of sudy kinemaics and dynamics. Kinemaics is he descripion

More information

SPH3U: Projectiles. Recorder: Manager: Speaker:

SPH3U: Projectiles. Recorder: Manager: Speaker: SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0

More information

v A Since the axial rigidity k ij is defined by P/v A, we obtain Pa 3

v A Since the axial rigidity k ij is defined by P/v A, we obtain Pa 3 The The rd rd Inernaional Conference on on Design Engineering and Science, ICDES 14 Pilsen, Czech Pilsen, Republic, Czech Augus Republic, 1 Sepember 1-, 14 In-plane and Ou-of-plane Deflecion of J-shaped

More information

d 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3

d 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3 and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or

More information

Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro. Category: Isotropic Linear Elasticity, Dynamics, Member

Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro. Category: Isotropic Linear Elasticity, Dynamics, Member Verificaion Example Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro Caegory: Isoropic Linear Elasiciy, Dynamics, Member Verificaion Example: 0104 Canilever Beam wih Periodic Exciaion 0104 Canilever Beam

More information

CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK

CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 175 CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 10.1 INTRODUCTION Amongs he research work performed, he bes resuls of experimenal work are validaed wih Arificial Neural Nework. From he

More information

Estimation of Kinetic Friction Coefficient for Sliding Rigid Block Nonstructural Components

Estimation of Kinetic Friction Coefficient for Sliding Rigid Block Nonstructural Components 7 Esimaion of Kineic Fricion Coefficien for Sliding Rigid Block Nonsrucural Componens Cagdas Kafali Ph.D. Candidae, School of Civil and Environmenal Engineering, Cornell Universiy Research Supervisor:

More information

IB Physics Kinematics Worksheet

IB Physics Kinematics Worksheet IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?

More information

5.2. The Natural Logarithm. Solution

5.2. The Natural Logarithm. Solution 5.2 The Naural Logarihm The number e is an irraional number, similar in naure o π. Is non-erminaing, non-repeaing value is e 2.718 281 828 59. Like π, e also occurs frequenly in naural phenomena. In fac,

More information

Decimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0.

Decimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0. PHYSICS 20 UNIT 1 SCIENCE MATH WORKSHEET NAME: A. Sandard Noaion Very large and very small numbers are easily wrien using scienific (or sandard) noaion, raher han decimal (or posiional) noaion. Sandard

More information

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile

More information

MEASUREMENTS AND THEORETICAL CALCULATIONS OF DIFFUSED RADIATION AND ATMOSPHERE LUCIDITY

MEASUREMENTS AND THEORETICAL CALCULATIONS OF DIFFUSED RADIATION AND ATMOSPHERE LUCIDITY ENGINEERING FOR RURAL DEVELOPMENT Jelgava, 8.-9.5.9. MEASUREMENTS AND THEORETICAL CALCULATIONS OF DIFFUSED RADIATION AND ATMOSPHERE LUCIDITY Ilze Pelēce, Uldis Iljins, Imans Ziemelis Lavia Universiy of

More information

The Simple Linear Regression Model: Reporting the Results and Choosing the Functional Form

The Simple Linear Regression Model: Reporting the Results and Choosing the Functional Form Chaper 6 The Simple Linear Regression Model: Reporing he Resuls and Choosing he Funcional Form To complee he analysis of he simple linear regression model, in his chaper we will consider how o measure

More information

Structural Dynamics and Earthquake Engineering

Structural Dynamics and Earthquake Engineering Srucural Dynamics and Earhquae Engineering Course 1 Inroducion. Single degree of freedom sysems: Equaions of moion, problem saemen, soluion mehods. Course noes are available for download a hp://www.c.up.ro/users/aurelsraan/

More information

- If one knows that a magnetic field has a symmetry, one may calculate the magnitude of B by use of Ampere s law: The integral of scalar product

- If one knows that a magnetic field has a symmetry, one may calculate the magnitude of B by use of Ampere s law: The integral of scalar product 11.1 APPCATON OF AMPEE S AW N SYMMETC MAGNETC FEDS - f one knows ha a magneic field has a symmery, one may calculae he magniude of by use of Ampere s law: The inegral of scalar produc Closed _ pah * d

More information

04. Kinetics of a second order reaction

04. Kinetics of a second order reaction 4. Kineics of a second order reacion Imporan conceps Reacion rae, reacion exen, reacion rae equaion, order of a reacion, firs-order reacions, second-order reacions, differenial and inegraed rae laws, Arrhenius

More information

Robust estimation based on the first- and third-moment restrictions of the power transformation model

Robust estimation based on the first- and third-moment restrictions of the power transformation model h Inernaional Congress on Modelling and Simulaion, Adelaide, Ausralia, 6 December 3 www.mssanz.org.au/modsim3 Robus esimaion based on he firs- and hird-momen resricions of he power ransformaion Nawaa,

More information

Development of a new metrological model for measuring of the water surface evaporation Tovmach L. Tovmach Yr. Abstract Introduction

Development of a new metrological model for measuring of the water surface evaporation Tovmach L. Tovmach Yr. Abstract Introduction Developmen of a new merological model for measuring of he waer surface evaporaion Tovmach L. Tovmach Yr. Sae Hydrological Insiue 23 Second Line, 199053 S. Peersburg, Russian Federaion Telephone (812) 323

More information

R t. C t P t. + u t. C t = αp t + βr t + v t. + β + w t

R t. C t P t. + u t. C t = αp t + βr t + v t. + β + w t Exercise 7 C P = α + β R P + u C = αp + βr + v (a) (b) C R = α P R + β + w (c) Assumpions abou he disurbances u, v, w : Classical assumions on he disurbance of one of he equaions, eg. on (b): E(v v s P,

More information

Influence of High Axial Tension on the Shear Strength of non-shear RC Beams

Influence of High Axial Tension on the Shear Strength of non-shear RC Beams Influence of High Axial Tension on he Shear Srengh of non-shear RC Beams Henrik B. JOERGENSEN PhD candidae Univ. of Souhern Denmark hebj@ii.sdu.dk Joergen MAAGAARD Associae Professor Univ. of Souhern Denmark

More information

Computation of the Effect of Space Harmonics on Starting Process of Induction Motors Using TSFEM

Computation of the Effect of Space Harmonics on Starting Process of Induction Motors Using TSFEM Journal of elecrical sysems Special Issue N 01 : November 2009 pp: 48-52 Compuaion of he Effec of Space Harmonics on Saring Process of Inducion Moors Using TSFEM Youcef Ouazir USTHB Laboraoire des sysèmes

More information

Module 2 F c i k c s la l w a s o s f dif di fusi s o i n

Module 2 F c i k c s la l w a s o s f dif di fusi s o i n Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms

More information

Numerical Simulation of the Overall Flow Field for Underwater Vehicle with Pump Jet Thruster

Numerical Simulation of the Overall Flow Field for Underwater Vehicle with Pump Jet Thruster Available online a www.sciencedirec.com Procedia Engineering 31 (2012) 769 774 Inernaional Conference on Advances in Compuaional Modeling and Simulaion Numerical Simulaion of he Overall Flow Field for

More information

DESIGN OF TENSION MEMBERS

DESIGN OF TENSION MEMBERS CHAPTER Srcral Seel Design LRFD Mehod DESIGN OF TENSION MEMBERS Third Ediion A. J. Clark School of Engineering Deparmen of Civil and Environmenal Engineering Par II Srcral Seel Design and Analysis 4 FALL

More information

Keywords: thermal stress; thermal fatigue; inverse analysis; heat conduction; regularization

Keywords: thermal stress; thermal fatigue; inverse analysis; heat conduction; regularization Proceedings Inverse Analysis for Esimaing Temperaure and Residual Sress Disribuions in a Pipe from Ouer Surface Temperaure Measuremen and Is Regularizaion Shiro Kubo * and Shoki Taguwa Deparmen of Mechanical

More information

20. Applications of the Genetic-Drift Model

20. Applications of the Genetic-Drift Model 0. Applicaions of he Geneic-Drif Model 1) Deermining he probabiliy of forming any paricular combinaion of genoypes in he nex generaion: Example: If he parenal allele frequencies are p 0 = 0.35 and q 0

More information

Lecture 4 Kinetics of a particle Part 3: Impulse and Momentum

Lecture 4 Kinetics of a particle Part 3: Impulse and Momentum MEE Engineering Mechanics II Lecure 4 Lecure 4 Kineics of a paricle Par 3: Impulse and Momenum Linear impulse and momenum Saring from he equaion of moion for a paricle of mass m which is subjeced o an

More information

ON THE BEAT PHENOMENON IN COUPLED SYSTEMS

ON THE BEAT PHENOMENON IN COUPLED SYSTEMS 8 h ASCE Specialy Conference on Probabilisic Mechanics and Srucural Reliabiliy PMC-38 ON THE BEAT PHENOMENON IN COUPLED SYSTEMS S. K. Yalla, Suden Member ASCE and A. Kareem, M. ASCE NaHaz Modeling Laboraory,

More information

UNC resolution Uncertainty Learning Objectives: measurement interval ( You will turn in two worksheets and

UNC resolution Uncertainty Learning Objectives: measurement interval ( You will turn in two worksheets and UNC Uncerainy revised Augus 30, 017 Learning Objecives: During his lab, you will learn how o 1. esimae he uncerainy in a direcly measured quaniy.. esimae he uncerainy in a quaniy ha is calculaed from quaniies

More information

Application of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing

Application of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing Applicaion of a Sochasic-Fuzzy Approach o Modeling Opimal Discree Time Dynamical Sysems by Using Large Scale Daa Processing AA WALASZE-BABISZEWSA Deparmen of Compuer Engineering Opole Universiy of Technology

More information

Physics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.

Physics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs. Physics 180A Fall 2008 Tes 1-120 poins Name Provide he bes answer o he following quesions and problems. Wach your sig figs. 1) The number of meaningful digis in a number is called he number of. When numbers

More information

A DELAY-DEPENDENT STABILITY CRITERIA FOR T-S FUZZY SYSTEM WITH TIME-DELAYS

A DELAY-DEPENDENT STABILITY CRITERIA FOR T-S FUZZY SYSTEM WITH TIME-DELAYS A DELAY-DEPENDENT STABILITY CRITERIA FOR T-S FUZZY SYSTEM WITH TIME-DELAYS Xinping Guan ;1 Fenglei Li Cailian Chen Insiue of Elecrical Engineering, Yanshan Universiy, Qinhuangdao, 066004, China. Deparmen

More information

EE100 Lab 3 Experiment Guide: RC Circuits

EE100 Lab 3 Experiment Guide: RC Circuits I. Inroducion EE100 Lab 3 Experimen Guide: A. apaciors A capacior is a passive elecronic componen ha sores energy in he form of an elecrosaic field. The uni of capaciance is he farad (coulomb/vol). Pracical

More information

Cumulative Damage Evaluation based on Energy Balance Equation

Cumulative Damage Evaluation based on Energy Balance Equation Cumulaive Damage Evaluaion based on Energy Balance Equaion K. Minagawa Saiama Insiue of Technology, Saiama S. Fujia Tokyo Denki Universiy, Tokyo! SUMMARY: This paper describes an evaluaion mehod for cumulaive

More information

Mechanical Fatigue and Load-Induced Aging of Loudspeaker Suspension. Wolfgang Klippel,

Mechanical Fatigue and Load-Induced Aging of Loudspeaker Suspension. Wolfgang Klippel, Mechanical Faigue and Load-Induced Aging of Loudspeaker Suspension Wolfgang Klippel, Insiue of Acousics and Speech Communicaion Dresden Universiy of Technology presened a he ALMA Symposium 2012, Las Vegas

More information

On Multicomponent System Reliability with Microshocks - Microdamages Type of Components Interaction

On Multicomponent System Reliability with Microshocks - Microdamages Type of Components Interaction On Mulicomponen Sysem Reliabiliy wih Microshocks - Microdamages Type of Componens Ineracion Jerzy K. Filus, and Lidia Z. Filus Absrac Consider a wo componen parallel sysem. The defined new sochasic dependences

More information

V AK (t) I T (t) I TRM. V AK( full area) (t) t t 1 Axial turn-on. Switching losses for Phase Control and Bi- Directionally Controlled Thyristors

V AK (t) I T (t) I TRM. V AK( full area) (t) t t 1 Axial turn-on. Switching losses for Phase Control and Bi- Directionally Controlled Thyristors Applicaion Noe Swiching losses for Phase Conrol and Bi- Direcionally Conrolled Thyrisors V AK () I T () Causing W on I TRM V AK( full area) () 1 Axial urn-on Plasma spread 2 Swiching losses for Phase Conrol

More information

Shiva Akhtarian MSc Student, Department of Computer Engineering and Information Technology, Payame Noor University, Iran

Shiva Akhtarian MSc Student, Department of Computer Engineering and Information Technology, Payame Noor University, Iran Curren Trends in Technology and Science ISSN : 79-055 8hSASTech 04 Symposium on Advances in Science & Technology-Commission-IV Mashhad, Iran A New for Sofware Reliabiliy Evaluaion Based on NHPP wih Imperfec

More information

0 time. 2 Which graph represents the motion of a car that is travelling along a straight road with a uniformly increasing speed?

0 time. 2 Which graph represents the motion of a car that is travelling along a straight road with a uniformly increasing speed? 1 1 The graph relaes o he moion of a falling body. y Which is a correc descripion of he graph? y is disance and air resisance is negligible y is disance and air resisance is no negligible y is speed and

More information

ACE 562 Fall Lecture 8: The Simple Linear Regression Model: R 2, Reporting the Results and Prediction. by Professor Scott H.

ACE 562 Fall Lecture 8: The Simple Linear Regression Model: R 2, Reporting the Results and Prediction. by Professor Scott H. ACE 56 Fall 5 Lecure 8: The Simple Linear Regression Model: R, Reporing he Resuls and Predicion by Professor Sco H. Irwin Required Readings: Griffihs, Hill and Judge. "Explaining Variaion in he Dependen

More information

Some Ramsey results for the n-cube

Some Ramsey results for the n-cube Some Ramsey resuls for he n-cube Ron Graham Universiy of California, San Diego Jozsef Solymosi Universiy of Briish Columbia, Vancouver, Canada Absrac In his noe we esablish a Ramsey-ype resul for cerain

More information

!!"#"$%&#'()!"#&'(*%)+,&',-)./0)1-*23)

!!#$%&#'()!#&'(*%)+,&',-)./0)1-*23) "#"$%&#'()"#&'(*%)+,&',-)./)1-*) #$%&'()*+,&',-.%,/)*+,-&1*#$)()5*6$+$%*,7&*-'-&1*(,-&*6&,7.$%$+*&%'(*8$&',-,%'-&1*(,-&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',-9*(&,%)?%*,('&5

More information

Principle and Analysis of a Novel Linear Synchronous Motor with Half-Wave Rectified Self Excitation

Principle and Analysis of a Novel Linear Synchronous Motor with Half-Wave Rectified Self Excitation Principle and Analysis of a Novel Linear Synchronous Moor wih Half-Wave Recified Self Exciaion Jun OYAMA, Tsuyoshi HIGUCHI, Takashi ABE, Shoaro KUBOTA and Tadashi HIRAYAMA Deparmen of Elecrical and Elecronic

More information

Chapter 1 Rotational dynamics 1.1 Angular acceleration

Chapter 1 Rotational dynamics 1.1 Angular acceleration Chaper Roaional dynamics. Angular acceleraion Learning objecives: Wha do we mean by angular acceleraion? How can we calculae he angular acceleraion of a roaing objec when i speeds up or slows down? How

More information

Diebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles

Diebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles Diebold, Chaper 7 Francis X. Diebold, Elemens of Forecasing, 4h Ediion (Mason, Ohio: Cengage Learning, 006). Chaper 7. Characerizing Cycles Afer compleing his reading you should be able o: Define covariance

More information

Morning Time: 1 hour 30 minutes Additional materials (enclosed):

Morning Time: 1 hour 30 minutes Additional materials (enclosed): ADVANCED GCE 78/0 MATHEMATICS (MEI) Differenial Equaions THURSDAY JANUARY 008 Morning Time: hour 30 minues Addiional maerials (enclosed): None Addiional maerials (required): Answer Bookle (8 pages) Graph

More information

Designing Information Devices and Systems I Spring 2019 Lecture Notes Note 17

Designing Information Devices and Systems I Spring 2019 Lecture Notes Note 17 EES 16A Designing Informaion Devices and Sysems I Spring 019 Lecure Noes Noe 17 17.1 apaciive ouchscreen In he las noe, we saw ha a capacior consiss of wo pieces on conducive maerial separaed by a nonconducive

More information

Mathcad Lecture #7 In-class Worksheet "Smart" Solve Block Techniques Handout

Mathcad Lecture #7 In-class Worksheet Smart Solve Block Techniques Handout Mahcad Lecure #7 In-class Workshee "Smar" Solve Block echniques Handou A he end of his lecure, you will be able o: use funcions in solve block equaions o improve convergence consruc solve blocks wih minimal

More information

2001 November 15 Exam III Physics 191

2001 November 15 Exam III Physics 191 1 November 15 Eam III Physics 191 Physical Consans: Earh s free-fall acceleraion = g = 9.8 m/s 2 Circle he leer of he single bes answer. quesion is worh 1 poin Each 3. Four differen objecs wih masses:

More information

Inventory Control of Perishable Items in a Two-Echelon Supply Chain

Inventory Control of Perishable Items in a Two-Echelon Supply Chain Journal of Indusrial Engineering, Universiy of ehran, Special Issue,, PP. 69-77 69 Invenory Conrol of Perishable Iems in a wo-echelon Supply Chain Fariborz Jolai *, Elmira Gheisariha and Farnaz Nojavan

More information

Nature Neuroscience: doi: /nn Supplementary Figure 1. Spike-count autocorrelations in time.

Nature Neuroscience: doi: /nn Supplementary Figure 1. Spike-count autocorrelations in time. Supplemenary Figure 1 Spike-coun auocorrelaions in ime. Normalized auocorrelaion marices are shown for each area in a daase. The marix shows he mean correlaion of he spike coun in each ime bin wih he spike

More information

We just finished the Erdős-Stone Theorem, and ex(n, F ) (1 1/(χ(F ) 1)) ( n

We just finished the Erdős-Stone Theorem, and ex(n, F ) (1 1/(χ(F ) 1)) ( n Lecure 3 - Kövari-Sós-Turán Theorem Jacques Versraëe jacques@ucsd.edu We jus finished he Erdős-Sone Theorem, and ex(n, F ) ( /(χ(f ) )) ( n 2). So we have asympoics when χ(f ) 3 bu no when χ(f ) = 2 i.e.

More information

Chapter 12: Velocity, acceleration, and forces

Chapter 12: Velocity, acceleration, and forces To Feel a Force Chaper Spring, Chaper : A. Saes of moion For moion on or near he surface of he earh, i is naural o measure moion wih respec o objecs fixed o he earh. The 4 hr. roaion of he earh has a measurable

More information

Time series Decomposition method

Time series Decomposition method Time series Decomposiion mehod A ime series is described using a mulifacor model such as = f (rend, cyclical, seasonal, error) = f (T, C, S, e) Long- Iner-mediaed Seasonal Irregular erm erm effec, effec,

More information

15210 RECORDING TIMER - AC STUDENT NAME:

15210 RECORDING TIMER - AC STUDENT NAME: CONTENTS 15210 RECORDING TIMER - AC STUDENT NAME: REQUIRED ACCESSORIES o C-Clamps o Ruler or Meer Sick o Mass (200 g or larger) OPTIONAL ACCESSORIES o Ticker Tape Dispenser (#15225) o Consan Speed Vehicle

More information

8. Basic RL and RC Circuits

8. Basic RL and RC Circuits 8. Basic L and C Circuis This chaper deals wih he soluions of he responses of L and C circuis The analysis of C and L circuis leads o a linear differenial equaion This chaper covers he following opics

More information

STATE-SPACE MODELLING. A mass balance across the tank gives:

STATE-SPACE MODELLING. A mass balance across the tank gives: B. Lennox and N.F. Thornhill, 9, Sae Space Modelling, IChemE Process Managemen and Conrol Subjec Group Newsleer STE-SPACE MODELLING Inroducion: Over he pas decade or so here has been an ever increasing

More information

R.#W.#Erickson# Department#of#Electrical,#Computer,#and#Energy#Engineering# University#of#Colorado,#Boulder#

R.#W.#Erickson# Department#of#Electrical,#Computer,#and#Energy#Engineering# University#of#Colorado,#Boulder# .#W.#Erickson# Deparmen#of#Elecrical,#Compuer,#and#Energy#Engineering# Universiy#of#Colorado,#Boulder# Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance,

More information

ACE 562 Fall Lecture 5: The Simple Linear Regression Model: Sampling Properties of the Least Squares Estimators. by Professor Scott H.

ACE 562 Fall Lecture 5: The Simple Linear Regression Model: Sampling Properties of the Least Squares Estimators. by Professor Scott H. ACE 56 Fall 005 Lecure 5: he Simple Linear Regression Model: Sampling Properies of he Leas Squares Esimaors by Professor Sco H. Irwin Required Reading: Griffihs, Hill and Judge. "Inference in he Simple

More information

MEI STRUCTURED MATHEMATICS 4758

MEI STRUCTURED MATHEMATICS 4758 OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Cerificae of Educaion Advanced General Cerificae of Educaion MEI STRUCTURED MATHEMATICS 4758 Differenial Equaions Thursday 5 JUNE 006 Afernoon

More information

Suggested Practice Problems (set #2) for the Physics Placement Test

Suggested Practice Problems (set #2) for the Physics Placement Test Deparmen of Physics College of Ars and Sciences American Universiy of Sharjah (AUS) Fall 014 Suggesed Pracice Problems (se #) for he Physics Placemen Tes This documen conains 5 suggesed problems ha are

More information

( ) = b n ( t) n " (2.111) or a system with many states to be considered, solving these equations isn t. = k U I ( t,t 0 )! ( t 0 ) (2.

( ) = b n ( t) n  (2.111) or a system with many states to be considered, solving these equations isn t. = k U I ( t,t 0 )! ( t 0 ) (2. Andrei Tokmakoff, MIT Deparmen of Chemisry, 3/14/007-6.4 PERTURBATION THEORY Given a Hamilonian H = H 0 + V where we know he eigenkes for H 0 : H 0 n = E n n, we can calculae he evoluion of he wavefuncion

More information

LabQuest 24. Capacitors

LabQuest 24. Capacitors Capaciors LabQues 24 The charge q on a capacior s plae is proporional o he poenial difference V across he capacior. We express his wih q V = C where C is a proporionaliy consan known as he capaciance.

More information

Comparing Means: t-tests for One Sample & Two Related Samples

Comparing Means: t-tests for One Sample & Two Related Samples Comparing Means: -Tess for One Sample & Two Relaed Samples Using he z-tes: Assumpions -Tess for One Sample & Two Relaed Samples The z-es (of a sample mean agains a populaion mean) is based on he assumpion

More information

Reasonable compensation coefficient of maximum gradient in long railway tunnels

Reasonable compensation coefficient of maximum gradient in long railway tunnels Journal of Modern Transporaion Volume 9 Number March 0 Page -8 Journal homepage: jm.swju.edu.cn DOI: 0.007/BF0335735 Reasonable compensaion coefficien of maximum gradien in long railway unnels Sirong YI

More information

MATHEMATICAL MODELING OF THE TRACTOR-GRADER AGRICULTURAL SYSTEM CINEMATIC DURING LAND IMPROVING WORKS

MATHEMATICAL MODELING OF THE TRACTOR-GRADER AGRICULTURAL SYSTEM CINEMATIC DURING LAND IMPROVING WORKS Bullein of he Transilvania Universiy of Braşov Series II: Foresry Wood Indusry Agriculural Food Engineering Vol. 5 (54) No. 1-2012 MATHEMATICA MODEING OF THE TRACTOR-GRADER AGRICUTURA SYSTEM CINEMATIC

More information

10. State Space Methods

10. State Space Methods . Sae Space Mehods. Inroducion Sae space modelling was briefly inroduced in chaper. Here more coverage is provided of sae space mehods before some of heir uses in conrol sysem design are covered in he

More information

236 CHAPTER 3 Torsion. Strain Energy in Torsion

236 CHAPTER 3 Torsion. Strain Energy in Torsion 36 CHAPER 3 orsion Srain Energy in orsion Problem 3.9-1 A solid circular bar of seel (G 11. 1 6 psi) wih lengh 3 in. and diameer d 1.75 in. is subjeced o pure orsion by orques acing a he ends (see figure).

More information

Excel-Based Solution Method For The Optimal Policy Of The Hadley And Whittin s Exact Model With Arma Demand

Excel-Based Solution Method For The Optimal Policy Of The Hadley And Whittin s Exact Model With Arma Demand Excel-Based Soluion Mehod For The Opimal Policy Of The Hadley And Whiin s Exac Model Wih Arma Demand Kal Nami School of Business and Economics Winson Salem Sae Universiy Winson Salem, NC 27110 Phone: (336)750-2338

More information

Modal identification of structures from roving input data by means of maximum likelihood estimation of the state space model

Modal identification of structures from roving input data by means of maximum likelihood estimation of the state space model Modal idenificaion of srucures from roving inpu daa by means of maximum likelihood esimaion of he sae space model J. Cara, J. Juan, E. Alarcón Absrac The usual way o perform a forced vibraion es is o fix

More information

Circuit Variables. AP 1.1 Use a product of ratios to convert two-thirds the speed of light from meters per second to miles per second: 1 ft 12 in

Circuit Variables. AP 1.1 Use a product of ratios to convert two-thirds the speed of light from meters per second to miles per second: 1 ft 12 in Circui Variables 1 Assessmen Problems AP 1.1 Use a produc of raios o conver wo-hirds he speed of ligh from meers per second o miles per second: ( ) 2 3 1 8 m 3 1 s 1 cm 1 m 1 in 2.54 cm 1 f 12 in 1 mile

More information

Hall effect. Formulae :- 1) Hall coefficient RH = cm / Coulumb. 2) Magnetic induction BY 2

Hall effect. Formulae :- 1) Hall coefficient RH = cm / Coulumb. 2) Magnetic induction BY 2 Page of 6 all effec Aim :- ) To deermine he all coefficien (R ) ) To measure he unknown magneic field (B ) and o compare i wih ha measured by he Gaussmeer (B ). Apparaus :- ) Gauss meer wih probe ) Elecromagne

More information

not to be republished NCERT MATHEMATICAL MODELLING Appendix 2 A.2.1 Introduction A.2.2 Why Mathematical Modelling?

not to be republished NCERT MATHEMATICAL MODELLING Appendix 2 A.2.1 Introduction A.2.2 Why Mathematical Modelling? 256 MATHEMATICS A.2.1 Inroducion In class XI, we have learn abou mahemaical modelling as an aemp o sudy some par (or form) of some real-life problems in mahemaical erms, i.e., he conversion of a physical

More information

Flow-Induced Vibration Analysis of Supported Pipes with a Crack

Flow-Induced Vibration Analysis of Supported Pipes with a Crack Flow-Induced Vibraion Analsis of Suppored Pipes wih a Crack Jin-Huk Lee, Samer Masoud Al-Said Deparmen of Mechanical Engineering American Universi of Sharjah, UAE Ouline Inroducion and Moivaion Aeroacousicall

More information

Chapter 15: Phenomena. Chapter 15 Chemical Kinetics. Reaction Rates. Reaction Rates R P. Reaction Rates. Rate Laws

Chapter 15: Phenomena. Chapter 15 Chemical Kinetics. Reaction Rates. Reaction Rates R P. Reaction Rates. Rate Laws Chaper 5: Phenomena Phenomena: The reacion (aq) + B(aq) C(aq) was sudied a wo differen emperaures (98 K and 35 K). For each emperaure he reacion was sared by puing differen concenraions of he 3 species

More information

Theory of! Partial Differential Equations!

Theory of! Partial Differential Equations! hp://www.nd.edu/~gryggva/cfd-course/! Ouline! Theory o! Parial Dierenial Equaions! Gréar Tryggvason! Spring 011! Basic Properies o PDE!! Quasi-linear Firs Order Equaions! - Characerisics! - Linear and

More information

Pressure Loss Analysis of the Perforated Tube Attenuator

Pressure Loss Analysis of the Perforated Tube Attenuator Purdue Universiy Purdue e-pubs Inernaional Refrigeraion and Air Condiioning Conference chool of Mechanical Engineering 014 Pressure Loss Analysis of he Perforaed Tube Aenuaor Zhan Liu Xi'an Jiaoong universiy,

More information