Passive Pressure on Retaining Wall supporting c-φ Backfill using Horizontal Slices Method
|
|
- Roland Domenic Shields
- 5 years ago
- Views:
Transcription
1 Cloud Publication Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 2013, Volume 2, Iue 1, pp , Aticle ID Tech-106 Reeach Aticle Open Acce Paive Peue on Retaining Wall uppoting c-φ Backfill uing Hoizontal Slice Method Sima Ghoh and Sumen Deb Civil Engineeing Depatment, National Intitute of Technology, Agatala, Tipua, India Coepondence hould be addeed to Sima Ghoh, Publication Date: 30 Augut 2013 Aticle Link: Copyight 2013 Sima Ghoh and Sumen Deb. Thi i an open acce aticle ditibuted unde the Ceative Common Attibution Licene, which pemit uneticted ue, ditibution, and epoduction in any medium, povided the oiginal wok i popely cited. Abtact An attempt i made to evaluate the paive eath peue on igid etaining wall unde tatic loading condition. The analyi i baed on Hoizontal Slice Method uing c-φ natue of backfill and the analyi geneate non-linea failue uface. The effect of vaiation of all the paamete have been tudied in detail and it i een that the hape of the uptue uface may be hogging o agging in natue. The eult have been given both tabula a well a gaphical epeentation. Keywod Paive Eath Peue, Hoizontal Slice Method, c-φ Backfill, Rigid Retaining Wall, Wall Inclination, Cuvilinea Ruptue Suface 1. Intoduction The pioneeing theoie fo the detemination of lateal eath peue behind etaining wall wee developed by Coulomb (1776) and Rankine (1857). Culmann (1865) intoduced a gaphical method fo the olution of lateal eath peue behind igid etaining wall. Thee analye ae mainly baed on coheion-le backfill and linea failue uface. Bell (1915) equation give the olution of lateal eath peue conideing the effect of coheion. The non-lineaity of the backfill failue uface i taken into account by Tezaghi (1943) conideing a log pial liding uface. A combination of log pial and taight line ha been conideed by Kuma (2001) to how the non-lineaity of failue uface in the detemination of eimic lateal eath peue. Azad et al. (2008) and Ghanbai and Ahmadabadi (2010) have adopted Hoizontal Slice Method (HSM) to calculate the eimic eath peue with the aumption of linea failue uface. In the peent tudy, the Hoizontal Slice Method ha been ued in uch a way that the failue wedge itelf geneate a non-linea uptue uface. The value of paive eath peue coefficient have been optimized conideing the imultaneou effect of unit weight, uchage, coheion and adheion.
2 IJACEAR An Open Acce Jounal 2. Method of Analyi Let u conide a batteed face igid etaining wall of height H (in the paive zone) uppoting a c-φ natue of backfill a hown in Figue 1. The wall on the paive zone i inclined at an angle, α with the vetical. The uptue uface i non-linea having diffeent value of inclination of failue uface with the vetical at bottom and top. The inclination of failue uface with the vetical at the bottom lice i conideed a θ n, wheea; the inclination of the failue uface at the bottom of the top lice i θ 1 with the vetical. If we conide the numbe of hoizontal lice (of thickne ΔH) a n, then the foce acting on the individual lice unde paive tate of equilibium i hown in Figue 2. Active Zone θ 1 Retaining wall c a SLICE -1 SLICE -2 θ 1+θ c P p R δ W Φ H α θ n Paive Zone LAYER -n Fig. 1 Show the foce acting batteed face etaining wall unde paive tate of equilibium Fee body diagam of etaining wall-backfill ytem unde paive tate of equilibium i elaboated in Figue 2. The foce acting on the wall ha been calculated by conideing the following: H i-1, H i = Hoizontal hea acting on the top and bottom of the i th lice W i = Weight of the failue wedge of i th lice V i-1, V i = Vetical load (UDL) on top and bottom of i th lice Ф = the angle of intenal fiction of oil P i = Paive eath peue on i th lice R i = the eaction of the etained oil on i th lice δ = the angle of wall fiction α = the angle of wall inclination c = Coheion acting between the failue uface c a = Adheion acting between the wall and oil uface Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 43
3 IJACEAR An Open Acce Jounal c a1 c 1 R 1 P 1 δ α θ 1 Ф ΔH W 1 H 1 V 1 SLICE - 1 V i-1 H i-1 H P i c ai δ α θ 1+(i-1)θ c i Ф R i ΔH W i V i H i SLICE - i V n-1 H n-1 c an P n δ α θ W n Ф c n R n ΔH SLICE - n Fig. 2 Show foce component acting on the wedge lice unde paive tate of equilibium 3. Deivation of Vaiou Fomulation duing the Paive Cae of Equilibium Applying the peue equilibium condition, we can olve the equation in the following patten, 0 H P co( ) R i ca in [ co Whee, V 0 i c in{ 1 ( i 1) } co{ 1 ( i 1) } co{ ( i 1) } 2 {( H ) }] i ( n i) tan ( i 1)(tan( 1 ( i 1) ) ( H ) n 1 i tan )) {tan( 1 m )} mi 1 2 Pi in( ) Ri in( 1 ( i 1) ) ( i ) (tan 2 c co( 1 ( i 1) ) ca co tan( 1 ( i 1) )) co( ( i 1) ) co 1 1 (1) (2) Solving thee two equation, we find the value of genealized equation fo Paive eath peue fo i th lice a follow: P p i 2 ( ) {(2i 1)(tan tan( 1 ( i 1) ))( co( 1 ( i 1) )) co co( 1 ( 1) ) 2 N M i ( H ) i in( 1 ( i 1) )} co( 1 ( i 1) ) co in( ( i 1) ) 1 (3) Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 44
4 IJACEAR An Open Acce Jounal Whee, ( n i) tan ( i 1)(tan( 1 ( i 1) ) 2 ( H ) n 1 i H tan )) {tan( 1 m )} N (tan tan( 1 ( i 1) )) mi (4) Whee, tan( 1 m ) 0 fo i = n (5) The paive eath peue coefficient can be implified a, kp n P pi i1 2 2 The value of N and M in Eqn 6 ae given by (6) Whee, N M NcH H M ch H (7) (8) 2c N c (9) H M c 2ca (10) H 4. Dicuion on Reult The optimized value of paive eath peue coefficient (K p ) have been evaluated fo the vaiation of diffeent paamete. The eult ae given tabula fom and a detailed paametic tudy i given in gaphical fom. The vaiou paamete conideed fo the pupoe ae a follow: Φ = 10, 20, 30 and 40 ; δ = 0, Φ/2, Φ; N c = 0.1, 0.2; M c = 0, N c /2, N c and α = +20, 0, -20. Optimization of the paive eath peue co-efficient, k p i done fo the vaiable θ 1 and θ n atifying the optimization citeia. The optimum value denoted a K p i given in Table 1. Table 1: Paive Eath Peue Co-Efficient (K p) N c=0.1 N c=0.2 Φ Δ M c α=-20 α=0 α= +20 α=-20 α=0 α= N c/ N c Φ/2 N c/ N c Φ N c/ Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 45
5 IJACEAR An Open Acce Jounal Φ/2 Φ 0 Φ/2 Φ 0 Φ/2 Φ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c Effect of Inclination of the Wall (α) Figue 3 to 5 epeent the effect of inclination of the wall on the paive eath peue fo diffeent value of δ. Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 46
6 IJACEAR An Open Acce Jounal Fom thee figue, it i een that due to deceae in α, the paive eitance inceae. Fo example, at Φ = 20, N c =0.1, M c = N c and α = -20, the value ae found 3.338, and fo δ = 0, Φ/2 and Φ epectively, wheea; with the above condition the value ae1.925, and at Φ=20 and α = +20. When the inclination of wall goe away fom the backfill, then the wall i in a poition to uppot moe load fom the backfill mateial. Thu, the active eath peue inceae and due to thi, the paive eitance i deceaed Effect of Wall Fiction Angle (δ) Figue 6 to 8 epeent the effect of wall fiction angle on the paive eath peue fo diffeent value of α. Fom the plot, it i een that due to the inceae in the value of δ, the paive eitance inceae. The eaon behind thi i the fictional eitance between wall and oil, which inceae with the inceae in the value of δ. Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 47
7 IJACEAR An Open Acce Jounal Fo example, at Φ = 20, N c = 0.1, M c = N c and δ = Φ/2, the value ae 4.781, and fo α= - 20, 0 and +20 epectively, wheea; the value ae found 7.599, and fo α= -20, 0 and +20 epectively fo δ = Φ and all above condition emaining unchanged. Thu, it i found that the inceae in δ i inceaing the incement in the paive eath peue coefficient. The inceae in wall fiction angle inceae the fictional eitance of oil-wall ytem, o the paive eitance inceae Effect of Coheion and Adheion Figue 9 how the vaiation of paive eath peue coefficient (K p ) with epect to oil fiction angle (Ф) at M c = 0, N c /2, N c fo N c =0.1, δ=ф/2 and α=20. Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 48
8 IJACEAR An Open Acce Jounal Fo example, at Φ=30, δ=ф/2, α=20 and M c = N c /2, the value of K p ae 3.325, and epectively fo N c =0.1 and 0.2. Wheea the value inceae up to and fo M c =N c with all othe condition emaining unchanged. Again, fom Figue 10, it i alo found that the value of K p inceae with the inceae of N c value. Fo example, at Φ=20, δ=ф/2, α=20 and N c =0.1, the value of K p ae 2.155, and epectively fo M c =0, N c /2 and N c. wheea; the value inceae up to 2.233, and fo N c =0.2 with all othe condition emaining unchanged Effect of Height (H) Figue 11 how the vaiation of paive eath peue fo diffeent height of etaining wall (5m, 7.5m and 10m). It i obeved that the paive eitance gadually deceae with the inceae in height of etaining wall. Fo highe value of oil fiction angle (Φ), the paive eitance inceae fo the ame height. Fo Φ=20, α=20, N c =0.1, M c =N c and δ=φ /2, the deceae in K p i 10.2% and 15.3% fo 7.5m and 10m high etaining wall epectively compaed to 5m high etaining wall. Alo, fo Φ=40, α=20, N c =0.1, M c =N c and δ=φ/2, the decement in K p i again 5.8% and 12.1% fo 7.5m and 10m high etaining wall epectively compaed to 5m high etaining wall. With the inceae in height, the value of (2c/γH) and (2c a /γh) deceae, o the paive eitance get deceaed. Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 49
9 IJACEAR An Open Acce Jounal 4.5. Wall Inclination and Nonlineaity of Failue Suface Figue 12 how the nonlineaity of failue uface of backfill fo diffeent value of wall inclination (α = -20, 0, +20 ). It i een that the inclination of failue uface with the vetical (α) inceae with the inceae in the wall inclination (α) angle. Fo example, at Φ=30º, δ=φ/2, N c =0.1, M c =N c and α= -20º, the value of angle, α at bottom i 75º wheea the value of angle, α at top i 84º. Figue 13 how the vaiation of failue uface with epect to height of the etaining wall. Fom the plot it i een that peent tudy epeent non-linea failue uface, wheea, Ghoh and Sengupta epeent linea failue uface. The compaion how that the value of inclination of failue uface with the vetical (θ) i 69º in cae of Ghoh and Sengupta (2012) fo the peviouly mentioned condition. Wheea; in the peent tudy, the angle i 77 at bottom and 84 at top of the failue uface. Thu, it how a cuvilinea hape a it pogee upwad. Alo, on the bai of peent tudy, it i een that due to the non-lineaity, the peent tudy epeent paticipation of moe backfill oil in compaion to Ghoh and Sengupta (2012) analyi. Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 50
10 IJACEAR An Open Acce Jounal 4.6. Compaion of Reult Figue 14 how the vaiation of paive eath peue coefficient with epect to oil fiction angle (Φ) at δ=φ/2, N c =0.1, M c =N c fo α =20. K p inceae unifomly with the inceae in the value of oil fiction angle (Φ). The compaion in tabula fom i peented in Table 2. The compaion how that the value of K p obtained fom the peent tudy i 15% lee than the value obtained fom the analyi of Ghoh and Shama (2012). Table 2: Show the Compaion of Reult fo N c = 0.1, M c = N c Φ δ α K p, Peent tudy K p, Ghoh and Shama (2012) Concluion Conideing the cuvilinea uptue uface and uing the hoizontal lice method, an analyi ha been developed fo the detemination paive foce on the back of a etaining wall uppoting c-φ backfill. Vey inteetingly, it i een that the hape of the uptue uface may be agging o hogging in natue. The above tudy of c-φ oil give a geneal olution fo paive eath peue. The paive eitance inceae with the inceae in the value of Φ, δ, c and c a. Geneally, the paive eitance i in an aveage 15% lowe in compaion to Ghoh and Shama (2012). Thi fact ugget the acceptability of the model which may be extended fo the analyi of etaining wall unde eimic loading condition. Notation Φ = oil fiction angle δ = wall fiction angle α = wall inclination angle with the vetical C = coheion C a = adheion P p = paive eath peue W i = weight of i th lice Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 51
11 IJACEAR An Open Acce Jounal R = oil eaction γ = unit weight of oil N = (H/ΔH)*N c M = (H/ΔH)*M c Refeence Azad A., et al. Active Peue Ditibution Hitoy behind Rigid Retaining Wall. Soil Dynamic and Eathquake Engineeing (5) Bell A.L., 1915: Lateal Peue and Reitance of Clay and the Suppoting Powe of Clay Foundation, Minute. Poceeding of the Intitution of Civil Enginee, London, 199. Coulomb C.A., 1776: Eai Su Une Application De Regle De Maximi et Minimi a Queque Poblem De Statique Relatif a1 Achitectue, Memoie d Academie Roy Pe. Diveavant. 7. Culmann K. 1866: Die Gaphiche Statik. Maye and Zelle, Zuich. Ghanbai A., et al. Peudo-Dynamic Active Eath Peue Analyi of Inclined Retaining Wall Uing Hoizontal Slice Method. Tanaction A: Civil Engineeing (2) Ghoh S., et al. Fomulation of Paive Reitance on Non Vetical Retaining Wall Backfilled with c-φ Soil. Civil and Envionmental Reeach (1). Ghoh S., et al. Peudo-Dynamic Evaluation of Paive Repone on the Back of A Retaining Wall Suppoting c-φ Backfill. Geo-mechanic and Geo-engineeing: An Intenational Jounal Kuma J. Seimic Paive Eath Peue Coefficient fo Sand. Can. Geotech. J., Ottawa ; Rankine W.J.M., 1857: On the Stability of Looe Eath. Phil. Ta. Royal Society, London. Shama R.P., et al. Peudotatic Seimic Active Repone of Retaining Wall Suppoting c-φ Backfill. EJGE Tezaghi K., 1943: Theoetical Soil Mechanic. John Wiley & Son, New Yok, 510. Intenational Jounal of Advanced Civil Engineeing and Achitectue Reeach 52
Active Force on Retaining Wall Supporting Φ Backfill Considering Curvilinear Rupture Surface
Cloud Publications International Journal of Advanced Civil Engineering and Architecture Research 2012, Volume 1, Issue 1, pp. 6-15, Article ID Tech-30 Research Article Open Access Active Force on Retaining
More informationPassive Force on Retaining Wall Supporting Φ Backfill Considering Curvilinear Rupture Surface
International Journal of Engineering Inventions ISSN: 2278-7461, ISBN: 2319-6491, www.ijeijournal.com Volume 1, Issue 10 (November2012) PP: 35-42 Passive Force on Retaining Wall Supporting Φ Backfill Considering
More informationone primary direction in which heat transfers (generally the smallest dimension) simple model good representation for solving engineering problems
CHAPTER 3: One-Dimenional Steady-State Conduction one pimay diection in which heat tanfe (geneally the mallet dimenion) imple model good epeentation fo olving engineeing poblem 3. Plane Wall 3.. hot fluid
More informationTheorem 2: Proof: Note 1: Proof: Note 2:
A New 3-Dimenional Polynomial Intepolation Method: An Algoithmic Appoach Amitava Chattejee* and Rupak Bhattachayya** A new 3-dimenional intepolation method i intoduced in thi pape. Coeponding to the method
More informationMATERIAL SPREADING AND COMPACTION IN POWDER-BASED SOLID FREEFORM FABRICATION METHODS: MATHEMATICAL MODELING
MATERIAL SPREADING AND COMPACTION IN POWDER-BASED SOLID FREEFORM FABRICATION METHODS: MATHEMATICAL MODELING Yae Shanjani and Ehan Toyekani Depatment of Mechanical and Mechatonic Engineeing, Univeity of
More informationDevelopment of Model Reduction using Stability Equation and Cauer Continued Fraction Method
Intenational Jounal of Electical and Compute Engineeing. ISSN 0974-90 Volume 5, Numbe (03), pp. -7 Intenational Reeach Publication Houe http://www.iphoue.com Development of Model Reduction uing Stability
More informationEddy Currents in Permanent Magnets of a Multi-pole Direct Drive Motor
Acta Technica Jauineni Vol. 6. No. 1. 2013 Eddy Cuent in Pemanent Magnet of a Multi-pole Diect Dive Moto G. Gotovac 1, G. Lampic 1, D. Miljavec 2 Elaphe Ltd. 1, Univeity of Ljubljana, Faculty of Electical
More informationThin-Walled Tube Extension by Rigid Curved Punch
Engineeing,, 3, 45-46 doi:.436/eng..355 Publihed Online May (http://www.scirp.og/jounal/eng) Thin-Walled Tube Extenion by Rigid Cuved Punch Abtact Rotilav I. Nepehin Platic Defomation Sytem Depatment,
More informationLimit Analysis of Stability of Circular Foundation Pit
5t WSEAS Int. Conf. on ENIRONMENT, ECOSYSTEMS and DEELOPMENT, Teneife, Spain, Decembe 14-16, 27 13 Limit Analyi of Stability of Cicula Foundation Pit CUI XINZHUANG, YAO ZHANYONG, JIN QING, WU SHIMEI Scool
More informationSolutions Practice Test PHYS 211 Exam 2
Solution Pactice Tet PHYS 11 Exam 1A We can plit thi poblem up into two pat, each one dealing with a epaate axi. Fo both the x- and y- axe, we have two foce (one given, one unknown) and we get the following
More informationOn Sextic Equation With Five Unknowns
Intenational Jounal of Scientific and Reeach ublication, Volume 7, Iue 8, Augut 017 ISSN 50-15 On Setic Equation With Five Unknown ( )( ) = 8( w ) S.Vidhalakhmi 1, S. Aath Thangam, G. Dhanalakhmi 1 ofeo,
More informationTheory. Single Soil Layer. ProShake User s Manual
PoShake Ue Manual Theoy PoShake ue a fequency domain appoach to olve the gound epone poblem. In imple tem, the input motion i epeented a the um of a eie of ine wave of diffeent amplitude, fequencie, and
More informationShrinkage Estimation of Reliability Function for Some Lifetime Distributions
Ameican Jounal of Computational and Applied Mathematic 4, 4(3): 9-96 DOI:.593/j.ajcam.443.4 Shinkage Etimation of eliability Function fo Some Lifetime Ditibution anjita Pandey Depatment of Statitic, niveity
More informationThe Analysis of the Influence of the Independent Suspension on the Comfort for a Mine Truck
16 3 d Intenational Confeence on Vehicle, Mechanical and Electical Engineeing (ICVMEE 16 ISBN: 978-1-6595-37- The Analyi of the Influence of the Independent Supenion on the Comfot fo a Mine Tuck JINGMING
More informationThe Normal Stress Dıstribution in an Infinite. Elastic Body with a Locally Curved and Hollow. Fiber under Geometrical Nonlinear Statement
Nonlinea Analyi and Diffeential quation Vol. 4 06 no. 6 95-04 HIKARI td www.m-hikai.com htt://dx.doi.og/0.988/nade.06.656 The Nomal Ste Dıtibution in an Infinite latic Body with a ocally Cuved and Hollow
More informationSimulation of Spatially Correlated Large-Scale Parameters and Obtaining Model Parameters from Measurements
Simulation of Spatially Coelated Lage-Scale Paamete and Obtaining Model Paamete fom PER ZETTERBERG Stockholm Septembe 8 TRITA EE 8:49 Simulation of Spatially Coelated Lage-Scale Paamete and Obtaining Model
More informationSTRENGTH AND DEFORMATION CHARACTERISTICS OF SRC FRAMES HAVING WEAK AXIS BENDING COLUMNS
13 th Wold Confeence on Eathquake Engineeing Vancouve, B.C., Canada Augut 1-6, 24 Pape o. 1214 STREGTH AD DEFORATIO CHARACTERISTICS OF SRC FRAES HAVIG WEAK AXIS BEDIG COLS.Haegawa 1 T.Fujinaga 2, I.itani
More informationGravity. David Barwacz 7778 Thornapple Bayou SE, Grand Rapids, MI David Barwacz 12/03/2003
avity David Bawacz 7778 Thonapple Bayou, and Rapid, MI 495 David Bawacz /3/3 http://membe.titon.net/daveb Uing the concept dicued in the peceding pape ( http://membe.titon.net/daveb ), I will now deive
More informationBoise State University Department of Electrical and Computer Engineering ECE470 Electric Machines
Boie State Univeity Depatment of Electical and Compute Engineeing ECE470 Electic Machine Deivation of the Pe-Phae Steady-State Equivalent Cicuit of a hee-phae Induction Machine Nomenclatue θ: oto haft
More informationNew Analysis for The FGM Thick Cylinders Under Combined Pressure and Temperature Loading
Ameican Jounal of Applied Science 5 (7): 85-859, 008 ISSN 546-939 008 Science Publication New Analyi fo The FGM Thick Cylinde Unde Combined Peue and Tempeatue Loading K. Abinia, H. Naee, F. Sadeghi and
More informationImpulse and Momentum
Impule and Momentum 1. A ca poee 20,000 unit of momentum. What would be the ca' new momentum if... A. it elocity wee doubled. B. it elocity wee tipled. C. it ma wee doubled (by adding moe paenge and a
More informationA NEW VARIABLE STIFFNESS SPRING USING A PRESTRESSED MECHANISM
Poceedings of the ASME 2010 Intenational Design Engineeing Technical Confeences & Computes and Infomation in Engineeing Confeence IDETC/CIE 2010 August 15-18, 2010, Monteal, Quebec, Canada DETC2010-28496
More informationA FORMULATION AND PRELIMINARY RESULTS FOR SIMULATION OF SHIP MOTIONS COUPLED HEAVE, PITCH AND ROLL
8 th Intenational Confeence on the Stability of Ship and Ocean Vehicle Ecuela Técnica Supeio de Ingenieo Navale A FORMUATION AND PREIMINARY RESUTS FOR SIMUATION OF SHIP MOTIONS COUPED HEAVE, PITCH AND
More informationTRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the
Chapte 15 RAVELING WAVES 15.1 Simple Wave Motion Wave in which the ditubance i pependicula to the diection of popagation ae called the tanvee wave. Wave in which the ditubance i paallel to the diection
More informationMathematical Modeling of Metabolic Processes in a Living Organism in Relation to Nutrition
Mathematical Modeling of Metabolic Pocee in a Living Oganim in Relation to Nutition Dimitova N., Makov S. Depatment Biomathematic Intitute of Mathematic and Infomatic Bulgaian Academy of Science 8 Acad.
More informationPearson s Chi-Square Test Modifications for Comparison of Unweighted and Weighted Histograms and Two Weighted Histograms
Peason s Chi-Squae Test Modifications fo Compaison of Unweighted and Weighted Histogams and Two Weighted Histogams Univesity of Akueyi, Bogi, v/noduslód, IS-6 Akueyi, Iceland E-mail: nikolai@unak.is Two
More informationA note on rescalings of the skew-normal distribution
Poyeccione Jounal of Mathematic Vol. 31, N o 3, pp. 197-07, Septembe 01. Univeidad Católica del Note Antofagata - Chile A note on ecaling of the kew-nomal ditibution OSVALDO VENEGAS Univeidad Católica
More informationChapter 15 Slope Stability
Page 15 1 Chapte 15 Slope Stability 1. The oil lope faile in the fom of a lide by tanlation i called (a) fall. (b) topple. (c) pead. (d) flow. 2. The facto of afety of a lope i defined a the atio of (a)
More informationDetermining the Best Linear Unbiased Predictor of PSU Means with the Data. included with the Random Variables. Ed Stanek
Detemining te Bet Linea Unbiaed Pedicto of PSU ean wit te Data included wit te andom Vaiable Ed Stanek Intoduction We develop te equation fo te bet linea unbiaed pedicto of PSU mean in a two tage andom
More informationSupplemental Materials. Advanced Thermoelectrics Governed by Single Parabolic Band Model:
Electonic Supplementay Mateial (ESI) fo Phyical Chemity Chemical Phyic. Thi jounal i The Royal Society of Chemity 04 Supplemental Mateial Advanced Themoelectic Govened by Single Paabolic and Model: Mg
More informationChapter 19 Webassign Help Problems
Chapte 9 Webaign Help Poblem 4 5 6 7 8 9 0 Poblem 4: The pictue fo thi poblem i a bit mileading. They eally jut give you the pictue fo Pat b. So let fix that. Hee i the pictue fo Pat (a): Pat (a) imply
More informationConsiderations Regarding the Flux Estimation in Induction Generator with Application at the Control of Unconventional Energetic Conversion Systems
Conideation Regading the Flux Etimation in Induction Geneato with Application at the Contol of Unconventional Enegetic Conveion Sytem Ioif Szeidet, Octavian Potean, Ioan Filip, Vaa Citian Depatment of
More informationDirect Torque Control of Double Feed Induction Machine (DTC-DFIM)
Jounal of Advanced Reeach in Science and echnology ISSN: 232-9989 Diect oque Contol of Double Feed Induction Machine (DC-DFIM) Zemmit Abdeahim, Sadouni Radhwane 2 and Meoufel Abdelkade 2 Electical Engineeing
More informationψ - exponential type orbitals, Frictional
ew develoment in theoy of Laguee olynomial I. I. Gueinov Deatment of Phyic, Faculty of At and Science, Onekiz Mat Univeity, Çanakkale, Tukey Abtact The new comlete othonomal et of L -Laguee tye olynomial
More informationFracture criterion developed for elastic-plastic Russian materials
ndian Jounal of Engineeing & Mateial Science Vol. 1, Octobe 005, pp. 51-55 Factue citeion developed fo elatic-platic Ruian mateial A Ziliuka Depatment of Mechanic of Solid, Kauna Univeity of Technology,
More informationDuality between Statical and Kinematical Engineering Systems
Pape 00, Civil-Comp Ltd., Stiling, Scotland Poceedings of the Sixth Intenational Confeence on Computational Stuctues Technology, B.H.V. Topping and Z. Bittna (Editos), Civil-Comp Pess, Stiling, Scotland.
More informationDetermination of storage lengths of right-turn lanes at signalized. intersections
Detemination of toage length of ight-tun lane at ignalized inteection By Jinghui Wang Lei Yu Hui Xu ABSTRACT Thi pape develop an analytical method of detemining toage length of ight-tun lane at ignalized
More informationA Neural Network for the Travelling Salesman Problem with a Well Behaved Energy Function
A Neual Netwok fo the Tavelling Saleman Poblem with a Well Behaved Enegy Function Maco Budinich and Babaa Roaio Dipatimento di Fiica & INFN, Via Valeio, 347 Tiete, Italy E-mail: mbh@tiete.infn.it (Contibuted
More informationResearch Article On Alzer and Qiu s Conjecture for Complete Elliptic Integral and Inverse Hyperbolic Tangent Function
Abstact and Applied Analysis Volume 011, Aticle ID 697547, 7 pages doi:10.1155/011/697547 Reseach Aticle On Alze and Qiu s Conjectue fo Complete Elliptic Integal and Invese Hypebolic Tangent Function Yu-Ming
More informationOn Polynomials Construction
Intenational Jounal of Mathematical Analysis Vol., 08, no. 6, 5-57 HIKARI Ltd, www.m-hikai.com https://doi.og/0.988/ima.08.843 On Polynomials Constuction E. O. Adeyefa Depatment of Mathematics, Fedeal
More informationPHYS Summer Professor Caillault Homework Solutions. Chapter 5
PHYS 1111 - Summe 2007 - Pofesso Caillault Homewok Solutions Chapte 5 7. Pictue the Poblem: The ball is acceleated hoizontally fom est to 98 mi/h ove a distance of 1.7 m. Stategy: Use equation 2-12 to
More informationPHYSICS 151 Notes for Online Lecture 2.6
PHYSICS 151 Note fo Online Lectue.6 Toque: The whole eaon that we want to woy about cente of ma i that we ae limited to lookin at point mae unle we know how to deal with otation. Let eviit the metetick.
More informationHistogram Processing
Hitogam Poceing Lectue 4 (Chapte 3) Hitogam Poceing The hitogam of a digital image with gay level fom to L- i a dicete function h( )=n, whee: i the th gay level n i the numbe of pixel in the image with
More informationVECTOR MECHANICS FOR ENGINEERS: STATICS
4 Equilibium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Fedinand P. Bee E. Russell Johnston, J. of Rigid Bodies Lectue Notes: J. Walt Ole Texas Tech Univesity Contents Intoduction Fee-Body Diagam
More informationOn the integration of the equations of hydrodynamics
Uebe die Integation de hydodynamischen Gleichungen J f eine u angew Math 56 (859) -0 On the integation of the equations of hydodynamics (By A Clebsch at Calsuhe) Tanslated by D H Delphenich In a pevious
More informationTHE INFLUENCE OF THE ROTOR ARCHITECTURE OF A ROTATING WORKING MACHINE ON THE DRIVING POWER
U.P.B. Sci. Bull., Seie D, Vol. 77, I. 1, 015 ISSN 1454-358 THE INFLUENCE OF THE ROTOR ARCHITECTURE OF A ROTATING WORKING MACHINE ON THE DRIVING POWER Antonio DETZORTZIS 1, Nicolae BĂRAN, Malik N. HAWAS
More informationNumerical Study on Improving Indoor Thermal Comfort Using a PCM Wall
Numeical Study on Impoving Indoo Themal Comfot Uing a PCM Wall M. Faaji, F. Beoug Abtact A one-dimenional mathematical model wa developed in ode to analyze and optimize the latent heat toage wall. The
More informationInference for A One Way Factorial Experiment. By Ed Stanek and Elaine Puleo
Infeence fo A One Way Factoial Expeiment By Ed Stanek and Elaine Puleo. Intoduction We develop etimating equation fo Facto Level mean in a completely andomized one way factoial expeiment. Thi development
More informationA simplified dynamic method for field capacity estimation and its parameter analysis
Wate Science and Engineeing, 204, 7(4): 35-362 doi:0.3882/j.in.674-2370.204.04.00 http://www.watejounal.cn e-mail: we2008@vip.63.com A implified dynamic method fo field capacity etimation and it paamete
More informationThe Combined Effect of Chemical reaction, Radiation, MHD on Mixed Convection Heat and Mass Transfer Along a Vertical Moving Surface
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-966 Vol. 5, Issue (Decembe ), pp. 53 53 (Peviously, Vol. 5, Issue, pp. 63 6) Applications and Applied Mathematics: An Intenational Jounal (AAM)
More informationInfluences of Interfacial Shear in Turbulent Film Boiling on a Horizontal Tube with External Flowing Liquid
Engineeing, 05, 7, 754-764 Publihe Online Novembe 05 in SciRe. http://www.cip.og/jounal/eng http://x.oi.og/0.46/eng.05.7066 Influence of Intefacial Shea in Tubulent Film Boiling on a Hoizontal Tube with
More informationESTIMATION MODELS USING MATHEMATICAL CONCEPTS AND NEWTON S LAWS FOR CONIC SECTION TRAJECTORIES ON EARTH S SURFACE
Fundamental Jounal of Mathematical Physics Vol. 3 Issue 1 13 Pages 33-44 Published online at http://www.fdint.com/ ESTIMATION MODELS USING MATHEMATICAL CONCEPTS AND NEWTON S LAWS FOR CONIC SECTION TRAJECTORIES
More informationOriginal Method for Stability Analysis of Mechatronic Systems with Asynchronous Machines
Soin Enache, Auel Campeanu, Oiginal Method fo Stability Analyi of Mechatonic Sytem with Aynchonou Machine SORIN ENACHE, AUREL CAMPEANU, ION VLAD, MONICA ADELA ENACHE Electomechanical Faculty Univeity of
More informationMECHANICAL ANALYSIS OF REINFORCED PLATE STRUCTURES
Budapet 9-30Ma 008 MECHANICA ANAYSIS OF REINFORCED PATE STRUCTURES Gábo M Vöö Depatment of Applied Mechanic Budapet Univeit of Technolog and Economic H-151 Budapet Hunga E-mail: voo@mmbmehu Abtact: The
More informationDepartment of Physics, Korea University Page 1 of 5
Name: Depatment: Student ID #: Notice ˆ + ( 1) points pe coect (incoect) answe. ˆ No penalty fo an unansweed question. ˆ Fill the blank ( ) with ( ) if the statement is coect (incoect). ˆ : coections to
More informationRE 7.a. RE 7.b Energy Dissipation & Resonance RE 7.c EP7, HW7: Ch 7 Pr s 31, 32, 45, 62 & CP
Wed. Lab Fi. Mon. Tue. 7.-.4 Macocopic Enegy Quiz 6 4pm, hee Math & Phy Reeach L6 Wok and Enegy 7.5-.9 Enegy Tanfe RE 7.a RE 7.b 7.0-. Enegy Diipation & Reonance RE 7.c EP7, HW7: Ch 7 P 3, 3, 45, 6 & CP
More informationASTR 3740 Relativity & Cosmology Spring Answers to Problem Set 4.
ASTR 3740 Relativity & Comology Sping 019. Anwe to Poblem Set 4. 1. Tajectoie of paticle in the Schwazchild geomety The equation of motion fo a maive paticle feely falling in the Schwazchild geomety ae
More information(U) vanishes. A special case of system (1.1), (1.2) is given by the equations for compressible flow in a variable area duct, a ρv2,
MEHODS AND APPLICAIONS OF ANALYSIS. c 2003 Intenational Pe Vol. 10, No. 2, pp. 279 294, June 2003 007 HE GENERIC SOLUION OF HE RIEMANN PROBLEM IN A NEIGHBORHOOD OF A POIN OF RESONANCE FOR SYSEMS OF NONLINEAR
More informationAERODYNAMIC DESIGN METHOD FOR SUPERSONIC SLENDER BODY USING AN INVERSE PROBLEM
AERODYNAMIC DESIGN METHOD FOR SUPERSONIC SLENDER BODY Kia Matuhima*, Ikki Yamamichi**, Naoko Tokugawa*** * Dept. Engineeing, Univeity of Toyama, Gofuku 3190, Toyama 930-8555, JAPAN. Phone: +81-76-445-6796,
More informationTest 2 phy a) How is the velocity of a particle defined? b) What is an inertial reference frame? c) Describe friction.
Tet phy 40 1. a) How i the velocity of a paticle defined? b) What i an inetial efeence fae? c) Decibe fiction. phyic dealt otly with falling bodie. d) Copae the acceleation of a paticle in efeence fae
More informationFuzzy Speed Regulator for Induction Motor Direct Torque Control Scheme
ACEEE Int. J. on Electical and Powe Engineeing, ol., No., Dec Fuzzy peed Regulato fo Induction Moto Diect Toque Contol cheme Jagadih H. Puja,. F. Kodad Reeach chola JNTU, Anantapu & Faculty Depatment of
More informationChapter 4: The laws of motion. Newton s first law
Chapte 4: The laws of motion gavitational Electic magnetic Newton s fist law If the net foce exeted on an object is zeo, the object continues in its oiginal state of motion: - an object at est, emains
More informationFI 2201 Electromagnetism
FI Electomagnetim Aleande A. Ikanda, Ph.D. Phyic of Magnetim and Photonic Reeach Goup ecto Analyi CURILINEAR COORDINAES, DIRAC DELA FUNCION AND HEORY OF ECOR FIELDS Cuvilinea Coodinate Sytem Cateian coodinate:
More informationAIRCRAFT ENGINE RESPONSE DUE TO FAN UNBALANCE AND TO THE PRESENCE OF CONSUMED GAPS IN THE ENGINE DURING THE PHASE OF WINDMILLING
ICAS CONGRESS AIRCRAF ENGINE RESPONSE DUE O FAN UNBALANCE AND O HE PRESENCE OF CONSUMED GAPS IN HE ENGINE DURING HE PHASE OF WINDMILLING B. Benay AEROSPAIALE MARA AIRBUS 316 ouloue Cedex 3 Fance Abtact
More informationAbove Flux Estimation Issues in Induction Generators with Application at Energy Conversion Systems
Acta Polytechnica Hungaica Vol. 3, No. 3, 2006 Above Flux Etimation Iue in Induction Geneato with Application at Enegy Conveion Sytem Ioif Szeidet, Octavian Potean, Ioan Filip, Vaa Citian Depatment of
More informationV V The circumflex (^) tells us this is a unit vector
Vecto Vecto have Diection and Magnitude Mike ailey mjb@c.oegontate.edu Magnitude: V V V V x y z vecto.pptx Vecto Can lo e Defined a the oitional Diffeence etween Two oint 3 Unit Vecto have a Magnitude
More informationA PHENOMENOLOGICAL DESCRIPTION OF MIXING- SEGREGATION EFFECTS DURING SHEAR
A PHENOMENOLOGICAL DESCRIPTION OF MIXING-SEGREGATION EFFECTS DURING SHEAR DEFORMATION OF PARTICULATE SOLIDS Poceeding of Euopean Conge of Chemical Engineeing (ECCE-6) Copenhagen, 6- Septembe 7 A PHENOMENOLOGICAL
More information7.2.1 Basic relations for Torsion of Circular Members
Section 7. 7. osion In this section, the geomety to be consideed is that of a long slende cicula ba and the load is one which twists the ba. Such poblems ae impotant in the analysis of twisting components,
More informationto point uphill and to be equal to its maximum value, in which case f s, max = μsfn
Chapte 6 16. (a) In this situation, we take f s to point uphill and to be equal to its maximum value, in which case f s, max = μsf applies, whee μ s = 0.5. pplying ewton s second law to the block of mass
More informationSeveral new identities involving Euler and Bernoulli polynomials
Bull. Math. Soc. Sci. Math. Roumanie Tome 9107 No. 1, 016, 101 108 Seveal new identitie involving Eule and Benoulli polynomial by Wang Xiaoying and Zhang Wenpeng Abtact The main pupoe of thi pape i uing
More informationTutorial 5 Drive dynamics & control
UNIVERSITY OF NEW SOUTH WALES Electic Dive Sytem School o Electical Engineeing & Telecommunication ELEC463 Electic Dive Sytem Tutoial 5 Dive dynamic & contol. The ollowing paamete ae known o two high peomance
More informationMomentum is conserved if no external force
Goals: Lectue 13 Chapte 9 v Employ consevation of momentum in 1 D & 2D v Examine foces ove time (aka Impulse) Chapte 10 v Undestand the elationship between motion and enegy Assignments: l HW5, due tomoow
More informationPHYS 1410, 11 Nov 2015, 12:30pm.
PHYS 40, Nov 205, 2:30pm. A B = AB cos φ x = x 0 + v x0 t + a 2 xt 2 a ad = v2 2 m(v2 2 v) 2 θ = θ 0 + ω 0 t + 2 αt2 L = p fs µ s n 0 + αt K = 2 Iω2 cm = m +m 2 2 +... m +m 2 +... p = m v and L = I ω ω
More informationThe Deformation Analysis of the Curved Box Girder Bridges under Different Radius
The Defomation Analsis of the Cuved Bo Gide Bidges unde Diffeent Radius Liu Fangping (Coesponding autho) School of Civil Engineeing & Achitectue, Chongqing Jiao tong Univesit 66 Xuefu Road, Nan an Distict,
More informationA Three-Dimensional Magnetic Force Solution Between Axially-Polarized Permanent-Magnet Cylinders for Different Magnetic Arrangements
Poceedings of the 213 Intenational Confeence on echanics, Fluids, Heat, Elasticity Electomagnetic Fields A Thee-Dimensional agnetic Foce Solution Between Axially-Polaied Pemanent-agnet Cylindes fo Diffeent
More informationTo Feel a Force Chapter 7 Static equilibrium - torque and friction
To eel a oce Chapte 7 Chapte 7: Static fiction, toque and static equilibium A. Review of foce vectos Between the eath and a small mass, gavitational foces of equal magnitude and opposite diection act on
More informationChapter 5 Applications of Newton s Laws
Chapte 5 Application of Newton Law Conceptual Poblem Detemine the Concept Becaue the object ae peeding up (acceleating), thee mut be a net foce acting on them. The foce acting on an object ae the nomal
More informationUniversity of East London Institutional Repository:
Univeity of Eat London Intitutional Repoitoy: http://oa.uel.ac.uk hi pape i made available online in accodance with publihe policie. Pleae coll down to view the document itelf. Pleae efe to the epoitoy
More informationMRAS Based Speed Sensor-less Vector Controlled Induction Motor Using Modified Adaptive Mechanism
Seno & Tanduce, Vol. 55, Iue 8, Augut 23, pp. 8-85 Seno & Tanduce 23 by IFSA http://www.enopotal.com MRAS Baed Speed Seno-le Vecto Contolled Induction Moto Uing Modified Adaptive Mechanim ALIYU Eneji Iah,
More informationThe Influence of Fluid Viscosity on the Driving Power of a Rotating Working Machine
Intenational Jounal of Innovative Reeach in Advanced Engineeing (IJIRAE) ISSN: 349-163 Volume 1 Iue 4 (May 014) http://ijiae.com The Influence of Fluid Vicoity on the Diving Powe of a Rotating Woking Machine
More informationSolution of a Spherically Symmetric Static Problem of General Relativity for an Elastic Solid Sphere
Applied Physics eseach; Vol. 9, No. 6; 7 ISSN 96-969 E-ISSN 96-9647 Published by Canadian Cente of Science and Education Solution of a Spheically Symmetic Static Poblem of Geneal elativity fo an Elastic
More informationChapter 6. NEWTON S 2nd LAW AND UNIFORM CIRCULAR MOTION. string
Chapte 6 NEWTON S nd LAW AND UNIFORM CIRCULAR MOTION 103 PHYS 1 1 L:\103 Phy LECTURES SLIDES\103Phy_Slide_T1Y3839\CH6Flah 3 4 ting Quetion: A ball attached to the end of a ting i whiled in a hoizontal
More information22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 18
.65, MHD Theoy of Fuion Sytem Pof. Feidbeg Lectue 8. Deive δw fo geneal cew pinch. Deive Suydam citeion Scew Pinch Equilibia μ p + + ( ) = μ J = μ J= Stability ( ) m k ξ=ξ e ι +ι ξ=ξ e +ξ e +ξ e =ξ +ξ
More informationThe Millikan Experiment: Determining the Elementary Charge
LAB EXERCISE 7.5.1 7.5 The Elementay Chage (p. 374) Can you think of a method that could be used to suggest that an elementay chage exists? Figue 1 Robet Millikan (1868 1953) m + q V b The Millikan Expeiment:
More informationThen the number of elements of S of weight n is exactly the number of compositions of n into k parts.
Geneating Function In a geneal combinatoial poblem, we have a univee S of object, and we want to count the numbe of object with a cetain popety. Fo example, if S i the et of all gaph, we might want to
More informationChapter 6. NEWTON S 2nd LAW AND UNIFORM CIRCULAR MOTION
Chapte 6 NEWTON S nd LAW AND UNIFORM CIRCULAR MOTION Phyic 1 1 3 4 ting Quetion: A ball attached to the end of a ting i whiled in a hoizontal plane. At the point indicated, the ting beak. Looking down
More informationAnalytical Solutions for Confined Aquifers with non constant Pumping using Computer Algebra
Poceedings of the 006 IASME/SEAS Int. Conf. on ate Resouces, Hydaulics & Hydology, Chalkida, Geece, May -3, 006 (pp7-) Analytical Solutions fo Confined Aquifes with non constant Pumping using Compute Algeba
More informationUsing DEA and AHP for Multiplicative Aggregation of Hierarchical Indicators
Ameican Jounal of Opeation Reeach, 205, 5, 327-336 Publihed Online Septembe 205 in SciRe. http://www.cip.og/jounal/ajo http://dx.doi.og/0.4236/ajo.205.55026 Uing DEA and AHP fo Multiplicative Aggegation
More informationPhysics 201 Homework 4
Physics 201 Homewok 4 Jan 30, 2013 1. Thee is a cleve kitchen gadget fo dying lettuce leaves afte you wash them. 19 m/s 2 It consists of a cylindical containe mounted so that it can be otated about its
More informationFall 2004/05 Solutions to Assignment 5: The Stationary Phase Method Provided by Mustafa Sabri Kilic. I(x) = e ixt e it5 /5 dt (1) Z J(λ) =
8.35 Fall 24/5 Solution to Aignment 5: The Stationay Phae Method Povided by Mutafa Sabi Kilic. Find the leading tem fo each of the integal below fo λ >>. (a) R eiλt3 dt (b) R e iλt2 dt (c) R eiλ co t dt
More informationNetwork Capacity Allocation in Service Overlay Networks
Netwo Capacity Allocation in Sevice Ovelay Netwo Ngo Lam 1, Zbigniew Dziong 2, Lone G. Maon 1 1 Depatment of Electical & Compute Engineeing, McGill Univeity, 3480 Univeity Steet, Monteal, Quebec, Canada
More informationJournal of Mathematical Systems, Estimation, and Control Vol. 8, No. 2, 1998, pp. 1{? c 1998 Birkhauser-Boston A Computational Study of the Representa
Jounal of Mathematical Sytem, Etimation, and Contol Vol. 8, No. 2, 1998, pp. 1{? c 1998 Bikhaue-Boton A Computational Study of the Repeentation Poblem fo Flow Contol Diana Rubio y Abtact The poblem of
More informationSolution of Advection-Diffusion Equation for Concentration of Pollution and Dissolved Oxygen in the River Water by Elzaki Transform
Ameican Jonal of Engineeing Reeach (AJER) 016 Ameican Jonal of Engineeing Reeach (AJER) e-issn: 30-0847 p-issn : 30-0936 Volme-5, Ie-9, pp-116-11 www.aje.og Reeach Pape Open Acce Soltion of Advection-Diffion
More informationPrecessing Ball Solitons as Self-Organizing Systems during a Phase Transition in a Ferromagnet
Applied Mathematics,, 4, 78-8 http://dxdoiog/46/am4a Published Online Octobe (http://wwwscipog/jounal/am) Pecessing Ball Solitons as Self-Oganiing Systems duing a Phase Tansition in a Feomagnet V V Niet
More informationIncreasing the Strength of Standard Involute Gear Teeth with Novel Circular Root Fillet Design
Ameican Jounal of Applied Science 2 (6): 1058-1064, 2005 ISSN 1546-9239 Science Publication, 2005 Inceaing the Stength of Standad Involute Gea Teeth with Novel Cicula Root Fillet Deign V. Spita, Th. Cotopoulo
More informationDeflection of light due to rotating mass a comparison among the results of different approaches
Jounal of Physics: Confeence Seies OPEN ACCESS Deflection of light due to otating mass a compaison among the esults of diffeent appoaches Recent citations - Gavitational Theoies nea the Galactic Cente
More informationPotential Energy and Conservation of Energy
Potential Enegy and Consevation of Enegy Consevative Foces Definition: Consevative Foce If the wok done by a foce in moving an object fom an initial point to a final point is independent of the path (A
More informationDetermination of Excitation Capacitance of a Three Phase Self Excited Induction Generator
ISSN (Online): 78 8875 (An ISO 397: 007 Cetified Oganization) Detemination of Excitation Capacitance of a Thee Phae Self Excited Induction Geneato Anamika Kumai, D. A. G. Thoa, S. S. Mopai 3 PG Student
More informationLECTURE 14. m 1 m 2 b) Based on the second law of Newton Figure 1 similarly F21 m2 c) Based on the third law of Newton F 12
CTU 4 ] NWTON W O GVITY -The gavity law i foulated fo two point paticle with ae and at a ditance between the. Hee ae the fou tep that bing to univeal law of gavitation dicoveed by NWTON. a Baed on expeiental
More informationIntroduction to Laplace Transform Techniques in Circuit Analysis
Unit 6 Introduction to Laplace Tranform Technique in Circuit Analyi In thi unit we conider the application of Laplace Tranform to circuit analyi. A relevant dicuion of the one-ided Laplace tranform i found
More information