Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading
|
|
- Alexia April Sims
- 6 years ago
- Views:
Transcription
1 xpermental Study on Ultmate Strength of Flexural-Falure-Type RC Beams under Impact Loadng N. Ksh 1), O. Nakano 2~, K. G. Matsuoka 1), and T. Ando 1~ 1) Dept. of Cvl ngneerng, Muroran Insttute of Technology, Muroran, , Japan 2) Muroran Development & Constructon Department, Hokkado Development Bureau, Muroran, , Japan ABSTRACT In ths paper, to estmate the ultmate strength of flexural-falure-type Renforced Concrete (RC) beams under mpact loadng, fallng-weght mpact tests were conducted. ght smply supported rectangular RC beams were used, each wth a clear-span length of 2 m. Impact load was surcharged onto the md-span by flee-fallng 2 kg steel weght. Cross sectonal dmensons, rebar rato, and mpact velocty were taken as varables. In ths experment, mpact force excted n steel weght, reacton force, and md-span dsplacement were measured and recorded by wde-band analog data recorder. The tests show that the ultmate strength of flexural-falure-type RC beams subjected to mpact load can be estmated by usng the maxmum reacton force at falure and that ths type of RC beam can be ratonally desgned wth a certan safety margn usng the relatonshp between maxmum reacton force and statc bendng capacty. INTRODUCTION Renforced Concrete (RC) and Prestressed Concrete (PC) structures such as nuclear power plants should be desgned wth a certan safety margn aganst mpact load. However, n Japan, these structures usually are constructed based on statc desgn, because desgn manuals for mpact-resstant RCPC structural members (beam, slab, column) have never yet been drafted, even for RC beams. In ths study, to establsh a ratonal mpact-resstant desgn procedure of flexural-falure-type RC beams, fallng-weght mpact tests were conducted for eght RC beams. The mpact-resstant behavor of RC beams of ths type was nvestgated by analyzng the followng expermental results: 1) tme hstores of mpact force, reacton force, and md-span dsplacement; 2) hysteretc loops of mpact force - dsplacement and reacton force - dsplacement; 3) relatonshp between dynamc responses (maxmum reacton force and cumulatve resdual dsplacement) and mpact velocty; and ) dynamc response rato of maxmum reacton force to statc bendng capacty and rato of absorbed energy to nput knetc energy. XPRIMNTAL OVRVIW Dmensons and statc desgn values of RC beams Fgure 1 shows the dmensons of RC beams used n ths study. All RC beams are of rectangular cross secton wth two deformed man rebars. The clear-span length s 2 m. The cross sectonal dmensons and rebar rato were vared. The statc desgn values for all these RC beams are lsted n Table 1. ach specmen s desgnated by cross sectonal type (A: 16 2 ram, B: 2 22 mm, C: mm) and man rebar dameter (1, 13, 19, and 22 mm). Statc bendng capacty P, sc and statc shear capacty V, sc are calculated accordng to the Japan Concrete Standard [1], and statc shear-bendng capacty rato a s obtaned by dvdng V,,~,c by P, sc. Accordng to the manual, all RC beams consdered here wll collapse n bendng-falure mode under statc loadng because ther a ratos exceed 1.. At commencement of the experments, the average concrete compressve strength was approxmately 26.5 MPa. Test procedure ach RC beam was smply supported at a pont 25 mm nsde from the ends and was pnched on the top and bottom surface at the support ponts to prevent the beam from reboundng (Photo 1). Impact tests were conducted by teratve loadng of a free-fallng 2 kg steel weght, n whch mpact velocty was ncreased n ncrements of 1 ms from 1 ms ntal mpact velocty untl the RC beam reached the ultmate state. Impact velocty was defned as the velocty at whch the steel weght mpacts onto the RC beam. The ultmate state s assumed to be that when the cumulatve resdual dsplacement of RC beam approaches 2. % of clear-span length (Photo 1). Impact load was surcharged onto the md-span of RC beam for all test cases. Impact force excted n steel weght, reacton force, and md-span dsplacement (herenafter, dsplacement) were measured and recorded by wde-band analog data recorder. The allowable frequences of load cells and LVDT are khz and 915 Hz, respectvely. All these analog data were converted to dgtal wth 1,us samplng tme.
2 6O 1 8O o=, Type A Type B Type C Strrup D6 I Man Rebar Type A ( D19, D22 ) Type B, C ( D1, D13, D19 ) " A 3@ =,15{ =3 11@ 1=11 ' I. =31 -,~ =)5 ~, 2 ] '- (mm) Fg. 1 Dmensons of RC beams Table 1 Statc desgn values and mpact velocty Specmen A-19 A-22 B-1 B-13 B-19 C-1 C-13 C-19 Dmensons of Cross Secton (mm) (Type A) 2 x 22 (Type B) 16 X 16 (Type C) Dameter of Man Rebar (mm) Rebar Rato p~ (%) Statc Bendng Capacty P.~ (kn) Statc Shear Capacty V.~ (kn) Shear-Bendng Capacty Rato a(=v.~ P.~) Impact Velocty V( ms ) !',',q!,. %~ :~:~:~:,-~::- ~: "... :.::::N... :-::-:... ~.,'... ~-~::::~... :.:...: :::... ::...? }:!::::!::;~ ~,~l;: ::..::~.:~;::!!!tl;~:~;:::::~;::::? ~ :7%:::~!l:;}:: ::~:~*~:::..... #:::}::::::::: :;!::; K:! ~).;!:.:;:.% %; :::>:%::::::~!!!!};::: Photo 1 xpermental setup
3 V= lms 2ms 3ms ms (kn) Impact Force, P LC'2ml (kn) '... L,r-"--.,-..= ~ ~ ~''~'~ Tme(msec) IWm_-~ Reacton Force, R ~ldlr (cm) Md- Span Dsp., '' 2 ~ ~ 2. ~"~~'--' J o Tme(msec) Tme(msec) Fg. 2 Tme hstores of mpact force, reacton force and md-span dsplacement (B-IO) XPRIMNTAL RSULTS AND DISCUSSION Tme hstores of mpact force, reacton force, and md-span dsplacement Fgure 2 shows the tme hstores of mpact force P, reacton force R, and md-span dsplacement 6 for beam B-1. Here, reacton force was evaluated summng up the values obtaned from both supportng ponts. These fgures plot the mpact force as two half-sne waves: an ncdental wave havng extremely short duraton at the begnnng of mpact, and a man wave havng relatvely longer duraton rrespectve of the magntude of mpact velocty. The maxmum mpact force s ncreased and the duraton of man wave s prolonged accordng to ncrease n the mpact velocty. In contrast, reacton force s plotted as only one half-sne wave, and the confguraton of the wave durng mpact loadng resembles that of dsplacement wave. Regardng dsplacement wave, n the case of V = 1 ms mpact velocty, t can be seen that only one half-sne wave s excted. In the cases of V > 1 ms, maxmum dsplacement s ncreased and duraton of man wave s prolonged wth ncrease n mpact velocty. After mpact force s unloaded, the dsplacement fluctuates fantly accompaned by drft. Also, the resdual dsplacement s ncreased wth each ncrement of mpact velocty. Ths suggests that the damage to RC beams progresses. Hysteretc loops of mpact force - dsplacement and reacton force - dsplacement Hysteretc loops of mpact force - dsplacement P-6 and reacton force - dsplacement R,6 for beam B-1 are shown n Fg. 3. The fgure shows that n the case of V = 1 ms mpact velocty, the RC beam may behave almost elastcally because the absorbed energy estmated by ntegratng the looped area s very small. In the cases of V > 1 ms, the absorbed energy s ncreased wth each ncrement of mpact velocty. Fgure shows the hysteretc loops of P-6 and R-6 for all RC beams at the fnal mpact test. These fgures show that the dstrbuton characterstcs of P-6 and R-6 loops dffer from each other. Impact force ncreases very rapdly up to the maxmum value at very begnnng of mpact, and decreases almost to zero, rrespectve of the beam type. After that, mpact force ncreases agan to the second peak and then decreases to zero. In ths way, the confguratons of P-6 loops are complex. In contrast, reacton force ncreases lnearly up to the maxmum value. After that, almost the same value s contnuously kept untl the dsplacement reaches ts maxmum value, and then decreases to zero. The R-6 loops may be assumed to be a parallelogram whose confguraton s smple. From the precedng observatons, t s consdered that the ultmate strength of flexural-falure-type RC beams may be more ratonally estmated by usng the maxmum reacton force than the maxmum mpact force. In the followng nvestgatons, the maxmum reacton force s used for estmaton of the ultmate strength of RC beams under mpact loadng.
4 15[ ~'.~ 1 I V=lms V=2ms V=3ms V=ms 2 ~ ( c m ) ½ (~,.) ~ (~m) ~ (~m) Fg. 3 Hysteretc loops of mpact force - dsplacement and reacton force - dsplacement (B-l ) 25 ] v:,,. 125 P, e(cm) (a) A-19 V=Sms P-a R-# ' V= 2 a' (,:m) V-Oms r 2 ~(c~) (b) A-22 (c) B-1 V=3ms l ' V=ms r - 2 a, (cr.) (d) B-T I,, ' V=6ms [ V=3ms ' V=3ms ' V=Sms e~ =2 125 O 2 a' (,:m) (e) B-19 2 a (~,.) (f) C-1 2 (~) ~ (~) (g) c-13 (h) c-19 Fg. Hysteretc loops of mpact force - dsplacement and reacton force - dsplacement at fnal mpact test for all RC beams Relatonshp between dynamc responses and mpact velocty Maxmum reacton force R,d and cumulatve resdual dsplacement 3c,-each s plotted aganst mpact velocty n Fg. 5. Here, to nvestgate the effect of cross sectonal dmensons and rebar rato on dynamc response characterstcs of RC beams, two pars of RC beams (beams A-19 and B-19, and beams B-1 and C-13) are compared. ach beam n the par has a statc bendng capacty smlar to the other beam n the same par. These fgures show that the maxmum reacton force ncreases monotoncally wth the ncrease n mpact velocty. In contrast, the cumulatve resdual dsplacement ncreases steeply wth each ncrement of mpact velocty. Comparng the dynamc responses between A-19 and B-19, and between B-1 and C-13, t can be observed that the values of maxmum reacton force andor the cumulatve resdual dsplacement are almost same between the RC beams, when the statc bendng capactes of RC beams are smlar to each other. Relatonshp between the maxmum reacton force and statc bendng capacty The relatonshp between the maxmum reacton force Ru~ and statc bendng capacty Pu,~.c for each RC beam at falure s shown n Fg. 6. R,~ s obtaned from the fnal mpact tests; P,.~,c s based on Japan Concrete Standard. The dotted lne represents maxmum reacton force of 2. tmes statc bendng capacty. Ths fgure shows that the maxmum reacton force Ru~ for all RC beams exceeds 2. tmes statc bendng capacty P~.~,c. Ths suggests that the ultmate strength of flexural-falure-type RC beams under mpact loadng can be estmated by doublng the value of statc bendng capacty to ensure a margn of safety.
5 2 ~e 2 = 16 LL '~ 12 = 8 O A-19 B B-1 C-13..D,,~ Impact Velocty, V (ms) (,J e,o m_ r~ e I.'2_ r,n ~J ty = t~ l = = o n O A-19 v B-19 D B-1 C-13..v t s6! Impact Velocty, V (ms) (a) Fg. 5 Maxmum reacton force (b) Cumulatve resdual dsplacement Relatonshp between maxmum reacton force and mpact velocty and between cumulatve resdual dsplacement and mpact velocty Z 3 u x.. 2 O L O = ~" A'-1'9 :A-22 A :B-1 Q :B-13 O :B-19 '.-o "C-13.C-19 O.." J J 1 a l X t~ 1 Q - A. I 2O ' ' go 2 Pusc '13' Statc Bendng Capacty, Pusc(kN) Fg. 6 Relatonshp between maxmum reacton force and statc bendng capacty Rato of absorbed energy to nput knetc energy The rato of absorbed energy to nput knetc energy a k for each RC beam at falure s plotted n Fg. 7, where a s absorbed energy estmated usng looped area of reacton force - dsplacement curve (Fg. ) and k s nput knetc energy (= mv22; m" mass of steel weght, V: mpact velocty). The fgure shows that these values are dstrbuted n the regon from.5 through.9. The mean value s about.7. PROPOSAL OF IMPACT-RSIsTANT DSIGN PROCDUR The confguraton of reacton force - dsplacement loops of RC beams at falure (Fg. ) can be smplfed as a
6 ua 1. U tl,b x ua. T o.2 x_ o. - (3).8 ~e, () \ \.... ; _~:... ~, \ \ \ l (3) ~ (o) ~e' (o) (6) (5) ( )" Impact Velocty, V (ms) A9 A2 Bo B3 B9 co c3 c9 Type of Specmen - Fg. 7 Rato of absorbed energy to nput knetc energy Rud L e~ Md-Span Dsplacement r Fg. 8 A smplfed model for reacton force- dsplacement loop parallelogram (Fg. 8). Usng ths smplfed model, the requred statc bendng capacty P,.~.j of RC beams aganst mpact load can be derved settng desgn nput knetc energy ~e and resdual dsplacement 6,.j as follows: Assumng that the maxmum reacton force R,a s 2. tmes the requred statc bendng capacty P,~.a, and the absorbed energy a s.7 tmes the desgn nput knetc energy,a based on the results n sectons 3.5 and 3.6, the followng equatons are derved: R,,~ = 2.P,,, (1),, =. 7k~l (2) Here, absorbed energy, can be wrtten, by referrng to the smplfed model shown n Fg. 8, as:, = R,e6,.,t (3) Substtutng qs. (1) and (2) nto q. (3) yelds the requred statc bendng capacty P,,~,~l"
7 .7 ~ l _.35 ~ () P,,,l- 2 6,-,1 6,-d Usng q. (), flexural-falure-type RC beams may be ratonally desgned aganst mpact load usng the statc bendng capacty. CONCLUSIONS In ths study, toward establshment of a ratonal mpact-resstant desgn procedure of flexural-falure-type RC beams, fallng-weght mpact tests were conducted on eght RC beams. They revealed the followng: 1) Dynamc response characterstcs of flexural-falure-type RC beams are roughly the same for beams of smlar statc bendng capactes calculated based on Japan Concrete Standard. 2) Ultmate strength of flexural-falure-type RC beams subjected to mpact load can be estmated by usng the maxmum reacton force at falure. 3) Confguraton of the hysteretc loop between reacton force and the md-span dsplacement at falure of an RC beam can be approxmated by a parallelogram. ) Flexural-falure-type RC beams under mpact load may be desgned wth a margn of safety by assumng dynamc response rato as 2. and rato of absorbed energy to nput knetc energy as.7. 5) Requred statc bendng capacty for RC beams aganst mpact load may be evaluated by a proposed smple equaton. RFRNC 1. JSC, Japan Concrete Standard, 1996, n Japanese.
CHAPTER 9 CONCLUSIONS
78 CHAPTER 9 CONCLUSIONS uctlty and structural ntegrty are essentally requred for structures subjected to suddenly appled dynamc loads such as shock loads. Renforced Concrete (RC), the most wdely used
More informationSecond Order Analysis
Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to
More informationEffect of loading frequency on the settlement of granular layer
Effect of loadng frequency on the settlement of granular layer Akko KONO Ralway Techncal Research Insttute, Japan Takash Matsushma Tsukuba Unversty, Japan ABSTRACT: Cyclc loadng tests were performed both
More informationFUZZY FINITE ELEMENT METHOD
FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments
More informationNON LINEAR ANALYSIS OF STRUCTURES ACCORDING TO NEW EUROPEAN DESIGN CODE
October 1-17, 008, Bejng, Chna NON LINEAR ANALYSIS OF SRUCURES ACCORDING O NEW EUROPEAN DESIGN CODE D. Mestrovc 1, D. Czmar and M. Pende 3 1 Professor, Dept. of Structural Engneerng, Faculty of Cvl Engneerng,
More informationTHE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD
Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS
More informationEVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES
EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES Manuel J. C. Mnhoto Polytechnc Insttute of Bragança, Bragança, Portugal E-mal: mnhoto@pb.pt Paulo A. A. Perera and Jorge
More informationTorsion Stiffness of Thin-walled Steel Beams with Web Holes
Torson Stffness of Thn-walled Steel Beams wth Web Holes MARTN HORÁČEK, JNDŘCH MELCHER Department of Metal and Tmber Structures Brno Unversty of Technology, Faculty of Cvl Engneerng Veveří 331/95, 62 Brno
More informationAssessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion
Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,
More informationORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp.
Clck to Vew Mathcad Document 2011 Knovel Corp. Buldng Structural Desgn. homas P. Magner, P.E. 2011 Parametrc echnology Corp. Chapter 3: Renforced Concrete Slabs and Beams 3.2 Renforced Concrete Beams -
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationImpact-resistant behavior of shear-failure-type RC beams under falling-weight impact loading
Impact-resistant behavior of shear-failure-type RC beams under falling-weight impact loading N. Kishil, H. Mikami2 & T. Ando3 Civil Engineering, A4uroran Institute of Technology, Japan. 2TechnicalResearch
More informationI have not received unauthorized aid in the completion of this exam.
ME 270 Sprng 2013 Fnal Examnaton Please read and respond to the followng statement, I have not receved unauthorzed ad n the completon of ths exam. Agree Dsagree Sgnature INSTRUCTIONS Begn each problem
More informationχ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body
Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown
More informationModule 3: Element Properties Lecture 1: Natural Coordinates
Module 3: Element Propertes Lecture : Natural Coordnates Natural coordnate system s bascally a local coordnate system whch allows the specfcaton of a pont wthn the element by a set of dmensonless numbers
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Experment-I MODULE VII LECTURE - 3 ANALYSIS OF COVARIANCE Dr Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Any scentfc experment s performed
More informationIncrease Decrease Remain the Same (Circle one) (2 pts)
ME 270 Sample Fnal Eam PROBLEM 1 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 1A. (5 ponts) FIND: A 2000 N crate (D) s suspended usng ropes AB and AC and s n statc equlbrum. If θ = 53.13, determne
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationPeridynamic Modeling of plain concrete structures under monotonic loading Jiezhi Lu1, a, Yaoting Zhang1, b, Zhijun Chen1
Second Internatonal Conference on Mechancs, Materals and Structural Engneerng (ICMMSE 7) Perdynamc Modelng of plan concrete structures under monotonc loadng Jezh Lu, a, Yaotng Zhang, b, Zhjun Chen School
More informationProbability, Statistics, and Reliability for Engineers and Scientists SIMULATION
CHATER robablty, Statstcs, and Relablty or Engneers and Scentsts Second Edton SIULATIO A. J. Clark School o Engneerng Department o Cvl and Envronmental Engneerng 7b robablty and Statstcs or Cvl Engneers
More informationSIMPLIFIED PREDICTION METHOD FOR SEISMIC RESPONSE OF ROCKING STRUCTURAL SYSTEMS WITH YIELDING BASE PLATES
13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 4 Paper No. 371 SIMPLIFIED PREDICTION METHOD FOR SEISMIC RESPONSE OF ROCKING STRUCTURAL SYSTEMS WITH YIELDING BASE PLATES
More informationTHE EFFECT OF BEAM TO COLUMN CONNECTION IN ARC PORTAL FRAME
THE EFFECT OF BEAM TO COLUMN CONNECTON N ARC PORTAL FRAME Asko Keronen Rakenteden Mekankka, Vol. 26 No 2 1993, ss. 35-5 SUMMARY A full scale rc (renforced concrete) portal frame has been bult n order to
More informationSTUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION
STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION CAO Wanln 1, CHANG Wehua 2, ZHANG Janwe 1 1 College of archtecture and Cvl Engneerng, Bejng
More informationPressure Measurements Laboratory
Lab # Pressure Measurements Laboratory Objectves:. To get hands-on experences on how to make pressure (surface pressure, statc pressure and total pressure nsde flow) measurements usng conventonal pressuremeasurng
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name and Secton: (Crcle Your Secton) Sectons:
More informationONE-DIMENSIONAL COLLISIONS
Purpose Theory ONE-DIMENSIONAL COLLISIONS a. To very the law o conservaton o lnear momentum n one-dmensonal collsons. b. To study conservaton o energy and lnear momentum n both elastc and nelastc onedmensonal
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationWinter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan
Wnter 2008 CS567 Stochastc Lnear/Integer Programmng Guest Lecturer: Xu, Huan Class 2: More Modelng Examples 1 Capacty Expanson Capacty expanson models optmal choces of the tmng and levels of nvestments
More informationLecture 4 Hypothesis Testing
Lecture 4 Hypothess Testng We may wsh to test pror hypotheses about the coeffcents we estmate. We can use the estmates to test whether the data rejects our hypothess. An example mght be that we wsh to
More informationDetermining the Temperature Distributions of Fire Exposed Reinforced Concrete Cross-Sections with Different Methods
Research Journal of Envronmental and Earth Scences 4(8): 782-788, 212 ISSN: 241-492 Maxwell Scentfc Organzaton, 212 Submtted: May 21, 212 Accepted: June 23, 212 Publshed: August 2, 212 Determnng the Temperature
More informationAGC Introduction
. Introducton AGC 3 The prmary controller response to a load/generaton mbalance results n generaton adjustment so as to mantan load/generaton balance. However, due to droop, t also results n a non-zero
More informationChapter Newton s Method
Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve
More informationLAB 4: Modulus of elasticity
LAB 4: Modulus of elastcty 1. Preparaton: modulus of elastcty (chapter15, p.79) Hook s law graphcal determnaton of modulus of elastcty (p.8) determnaton of modulus of elastcty n tenson and flexural stress
More information829. An adaptive method for inertia force identification in cantilever under moving mass
89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,
More informationStatistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA
14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton
More informationChapter 12 Analysis of Covariance
Chapter Analyss of Covarance Any scentfc experment s performed to know somethng that s unknown about a group of treatments and to test certan hypothess about the correspondng treatment effect When varablty
More informationAnnexes. EC.1. Cycle-base move illustration. EC.2. Problem Instances
ec Annexes Ths Annex frst llustrates a cycle-based move n the dynamc-block generaton tabu search. It then dsplays the characterstcs of the nstance sets, followed by detaled results of the parametercalbraton
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationIdentification of Instantaneous Modal Parameters of A Nonlinear Structure Via Amplitude-Dependent ARX Model
Identfcaton of Instantaneous Modal Parameters of A Nonlnear Structure Va Ampltude-Dependent ARX Model We Chh Su(NCHC), Chung Shann Huang(NCU), Chng Yu Lu(NCU) Outlne INRODUCION MEHODOLOGY NUMERICAL VERIFICAION
More informationChapter 12. Ordinary Differential Equation Boundary Value (BV) Problems
Chapter. Ordnar Dfferental Equaton Boundar Value (BV) Problems In ths chapter we wll learn how to solve ODE boundar value problem. BV ODE s usuall gven wth x beng the ndependent space varable. p( x) q(
More informationAPPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS
6th ICPT, Sapporo, Japan, July 008 APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS James MAINA Prncpal Researcher, Transport and Infrastructure Engneerng, CSIR Bult Envronment
More information( ) = ( ) + ( 0) ) ( )
EETOMAGNETI OMPATIBIITY HANDBOOK 1 hapter 9: Transent Behavor n the Tme Doman 9.1 Desgn a crcut usng reasonable values for the components that s capable of provdng a tme delay of 100 ms to a dgtal sgnal.
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS
More informationNovember 5, 2002 SE 180: Earthquake Engineering SE 180. Final Project
SE 8 Fnal Project Story Shear Frame u m Gven: u m L L m L L EI ω ω Solve for m Story Bendng Beam u u m L m L Gven: m L L EI ω ω Solve for m 3 3 Story Shear Frame u 3 m 3 Gven: L 3 m m L L L 3 EI ω ω ω
More informationSimulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests
Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth
More informationChapter 9: Statistical Inference and the Relationship between Two Variables
Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,
More informationPHYS 1101 Practice problem set 12, Chapter 32: 21, 22, 24, 57, 61, 83 Chapter 33: 7, 12, 32, 38, 44, 49, 76
PHYS 1101 Practce problem set 1, Chapter 3: 1,, 4, 57, 61, 83 Chapter 33: 7, 1, 3, 38, 44, 49, 76 3.1. Vsualze: Please reer to Fgure Ex3.1. Solve: Because B s n the same drecton as the ntegraton path s
More informationDynamic analysis of fibre breakage in singleand multiple-fibre composites
JOURNAL OF MATERIALS SCIENCE 31 (1996) 4181-4187 Dynamc analyss of fbre breakage n sngleand multple-fbre compostes M.L. ACCORSI, A. PEGORETTI**, A.T. DIBENEDETTO * Department of Cvl Engneerng, and ~ Department
More informationIn this section is given an overview of the common elasticity models.
Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp
More informationANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)
Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of
More informationFirst Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.
Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act
More informationThe optimal delay of the second test is therefore approximately 210 hours earlier than =2.
THE IEC 61508 FORMULAS 223 The optmal delay of the second test s therefore approxmately 210 hours earler than =2. 8.4 The IEC 61508 Formulas IEC 61508-6 provdes approxmaton formulas for the PF for smple
More informationEN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st
EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to
More informationPrinciples of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer
Prncples of Food and Boprocess Engneerng (FS 31) Solutons to Example Problems on Heat Transfer 1. We start wth Fourer s law of heat conducton: Q = k A ( T/ x) Rearrangng, we get: Q/A = k ( T/ x) Here,
More informationCHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation:
HPT 3 xercses 3. The emtter current s gen by the Shockley equaton: S exp VT For operaton wth, we hae exp >> S >>, and we can wrte VT S exp VT Solng for, we hae 3. 0 6ln 78.4 mv 0 0.784 5 4.86 V VT ln 4
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More informationTHE SMOOTH INDENTATION OF A CYLINDRICAL INDENTOR AND ANGLE-PLY LAMINATES
THE SMOOTH INDENTATION OF A CYLINDRICAL INDENTOR AND ANGLE-PLY LAMINATES W. C. Lao Department of Cvl Engneerng, Feng Cha Unverst 00 Wen Hwa Rd, Tachung, Tawan SUMMARY: The ndentaton etween clndrcal ndentor
More informationModule 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur
Module 11 Desgn o Jonts or Specal Loadng Verson ME, IIT Kharagpur Lesson 1 Desgn o Eccentrcally Loaded Bolted/Rveted Jonts Verson ME, IIT Kharagpur Instructonal Objectves: At the end o ths lesson, the
More informationLecture 8 Modal Analysis
Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal 1 2015 ANSYS, Inc. February 27, 2015 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal
More informationClock-Gating and Its Application to Low Power Design of Sequential Circuits
Clock-Gatng and Its Applcaton to Low Power Desgn of Sequental Crcuts ng WU Department of Electrcal Engneerng-Systems, Unversty of Southern Calforna Los Angeles, CA 989, USA, Phone: (23)74-448 Massoud PEDRAM
More informationWeek 9 Chapter 10 Section 1-5
Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationLab 2e Thermal System Response and Effective Heat Transfer Coefficient
58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),
More informationSIMPLIFIED APPROACH TO THE NON-LINEAR BEHAVIOR OF RC MEMBERS
SIMPLIFIED APPROACH TO THE NON-LINEAR BEHAVIOR OF RC MEMBERS Shahd NASIR 1, Supratc GUPTA 2 And Hdetaka UMEHARA 3 SUMMARY In ths paper, a smplfed one-dmensonal analytcal tool based on fnte dfference technque
More information2 Finite difference basics
Numersche Methoden 1, WS 11/12 B.J.P. Kaus 2 Fnte dfference bascs Consder the one- The bascs of the fnte dfference method are best understood wth an example. dmensonal transent heat conducton equaton T
More informationStructural Dynamics and Earthquake Engineering
Structural Dynamcs and Earthuake Engneerng Course 9 Sesmc-resstant desgn of structures (1) Sesmc acton Methods of elastc analyss Course notes are avalable for download at http://www.ct.upt.ro/users/aurelstratan/
More informationIndeterminate pin-jointed frames (trusses)
Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all
More informationPhysics 114 Exam 2 Fall 2014 Solutions. Name:
Physcs 114 Exam Fall 014 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem Answer each of the followng questons. Ponts for each queston are ndcated n red. Unless otherwse ndcated,
More informationTHE CURRENT BALANCE Physics 258/259
DSH 1988, 005 THE CURRENT BALANCE Physcs 58/59 The tme average force between two parallel conductors carryng an alternatng current s measured by balancng ths force aganst the gravtatonal force on a set
More informationChapter 3. Estimation of Earthquake Load Effects
Chapter 3. Estmaton of Earthquake Load Effects 3.1 Introducton Sesmc acton on chmneys forms an addtonal source of natural loads on the chmney. Sesmc acton or the earthquake s a short and strong upheaval
More informationA large scale tsunami run-up simulation and numerical evaluation of fluid force during tsunami by using a particle method
A large scale tsunam run-up smulaton and numercal evaluaton of flud force durng tsunam by usng a partcle method *Mtsuteru Asa 1), Shoch Tanabe 2) and Masaharu Isshk 3) 1), 2) Department of Cvl Engneerng,
More informationMECHANICS OF MATERIALS
Fourth Edton CHTER MECHNICS OF MTERIS Ferdnand. Beer E. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech Unversty Stress and Stran xal oadng Contents Stress & Stran: xal oadng
More informationA Robust Method for Calculating the Correlation Coefficient
A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal
More informationSampling Theory MODULE V LECTURE - 17 RATIO AND PRODUCT METHODS OF ESTIMATION
Samplng Theory MODULE V LECTURE - 7 RATIO AND PRODUCT METHODS OF ESTIMATION DR. SHALABH DEPARTMENT OF MATHEMATICS AND STATISTICS INDIAN INSTITUTE OF TECHNOLOG KANPUR Propertes of separate rato estmator:
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationBoise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab
Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment
More informationPRATICAL STATIC CALCULATION METHOD FOR ESTIMATING ELASTO-PLASTIC DYNAMIC RESPONSES OF SPACE FRAMES
th World Congress on Computatonal Mechancs (WCCM XI) 5th European Conference on Computatonal Mechancs (ECCM V) 6th European Conference on Computatonal lud ynamcs (EC VI) E. Oñate, J. Olver and A. Huerta
More informationBoise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab
Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationDEVELOPMENT OF REAL-TIME RESIDUAL SEISMIC CAPACITY EVALUATION SYSTEM -INTEGRAL METHOD AND SHAKING TABLE TEST WITH PLAIN STEEL FRAME-
13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 24 Paper No. 69 DEVEOPENT OF REA-TIE RESIDUA SEISIC CAPACITY EVAUATION SYSTE -INTEGRA ETHOD AND SHAKING TABE TEST WITH
More informationAnalysis of the Magnetomotive Force of a Three-Phase Winding with Concentrated Coils and Different Symmetry Features
Analyss of the Magnetomotve Force of a Three-Phase Wndng wth Concentrated Cols and Dfferent Symmetry Features Deter Gerlng Unversty of Federal Defense Munch, Neubberg, 85579, Germany Emal: Deter.Gerlng@unbw.de
More informationDESIGN OF STEEL PLATE SHEAR WALLS CONSIDERING BOUNDARY FRAME MOMENT RESISTING ACTION. B. Qu 1 and M.Bruneau 2 ABSTRACT
Proceedngs of the 9th U.S. Natonal and 0th Canadan Conference on Earthquake Engneerng Compte Rendu de la 9ème Conférence Natonale Amércane et 0ème Conférence Canadenne de Géne Parassmque July 5-9, 00,
More informationNONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM
Advanced Steel Constructon Vol. 5, No., pp. 59-7 (9) 59 NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM M. Abdel-Jaber, A.A. Al-Qasa,* and M.S. Abdel-Jaber Department of Cvl Engneerng, Faculty
More informationProblem Points Score Total 100
Physcs 450 Solutons of Sample Exam I Problem Ponts Score 1 8 15 3 17 4 0 5 0 Total 100 All wor must be shown n order to receve full credt. Wor must be legble and comprehensble wth answers clearly ndcated.
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Experment-I MODULE VIII LECTURE - 34 ANALYSIS OF VARIANCE IN RANDOM-EFFECTS MODEL AND MIXED-EFFECTS EFFECTS MODEL Dr Shalabh Department of Mathematcs and Statstcs Indan
More informationInfluential Factors Affecting Inherent Deformation during Plate Forming by Line Heating (Report 1)
Transactons of JWRI, Vol.36 (2007), No.1 Influental Factors Affectng Inherent Deformaton durng Plate Formng by Lne Heatng (Report 1) The Effect of Plate Sze and Edge Effect VEGA Adan*, RASHED Sherf**,
More informationMeasurement of the shear modulus of wood by asymmetric four-point bending tests
J Wood Sc (2002) 48:14-19 9 The Japan Wood Research Socety 2002 Hrosh Yoshhara 9 Yoshtaka Kubojma Measurement of the shear modulus of wood by asymmetrc four-pont bendng tests Receved: December 8, 2000
More informationQualitative Interpretation of Load-Settlement Curves of Bored Piles
ENGNEER - Vol. XXXX, No. 4, pp. 61-68,27 The nsttuton of Engneers, Sr Lanka Qualtatve nterpretaton of Load-Settlement Curves of Bored Ples H. S. Thlakasr Abstract: Statc load testng of ples yeld only the
More informationStatistics MINITAB - Lab 2
Statstcs 20080 MINITAB - Lab 2 1. Smple Lnear Regresson In smple lnear regresson we attempt to model a lnear relatonshp between two varables wth a straght lne and make statstcal nferences concernng that
More informationMD. LUTFOR RAHMAN 1 AND KALIPADA SEN 2 Abstract
ISSN 058-71 Bangladesh J. Agrl. Res. 34(3) : 395-401, September 009 PROBLEMS OF USUAL EIGHTED ANALYSIS OF VARIANCE (ANOVA) IN RANDOMIZED BLOCK DESIGN (RBD) ITH MORE THAN ONE OBSERVATIONS PER CELL HEN ERROR
More informationMODEL OF HYDROPNEUMATIC THREE POINT HITCH
ENINEERIN FR RUR DEVEPMENT Jelgava, 3.-4.05.03. MDE F YDRPNEUMTI TREE PINT IT Jans acekls-bertmans, Erks Kronbergs atva Unversty of grculture jans.lacekls@llu.lv, erks.kronbergs@llu.lv bstract. Ths paper
More informationRELIABILITY ASSESSMENT
CHAPTER Rsk Analyss n Engneerng and Economcs RELIABILITY ASSESSMENT A. J. Clark School of Engneerng Department of Cvl and Envronmental Engneerng 4a CHAPMAN HALL/CRC Rsk Analyss for Engneerng Department
More informationSTAT 511 FINAL EXAM NAME Spring 2001
STAT 5 FINAL EXAM NAME Sprng Instructons: Ths s a closed book exam. No notes or books are allowed. ou may use a calculator but you are not allowed to store notes or formulas n the calculator. Please wrte
More informationLecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics
Lecture 16 Chapter 11 Physcs I Energy Dsspaton Lnear Momentum Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Department o Physcs and Appled Physcs IN IN THIS CHAPTER, you wll learn
More informationDESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS
Munch, Germany, 26-30 th June 2016 1 DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS Q.T. Guo 1*, Z.Y. L 1, T. Ohor 1 and J. Takahash 1 1 Department of Systems Innovaton, School
More informationSupplemental Material: Causal Entropic Forces
Supplemental Materal: Causal Entropc Forces A. D. Wssner-Gross 1, 2, and C. E. Freer 3 1 Insttute for Appled Computatonal Scence, Harvard Unversty, Cambrdge, Massachusetts 02138, USA 2 The Meda Laboratory,
More informationPulse Coded Modulation
Pulse Coded Modulaton PCM (Pulse Coded Modulaton) s a voce codng technque defned by the ITU-T G.711 standard and t s used n dgtal telephony to encode the voce sgnal. The frst step n the analog to dgtal
More informationDesign and Optimization of Fuzzy Controller for Inverse Pendulum System Using Genetic Algorithm
Desgn and Optmzaton of Fuzzy Controller for Inverse Pendulum System Usng Genetc Algorthm H. Mehraban A. Ashoor Unversty of Tehran Unversty of Tehran h.mehraban@ece.ut.ac.r a.ashoor@ece.ut.ac.r Abstract:
More informationLINEAR REGRESSION ANALYSIS. MODULE VIII Lecture Indicator Variables
LINEAR REGRESSION ANALYSIS MODULE VIII Lecture - 7 Indcator Varables Dr. Shalabh Department of Maematcs and Statstcs Indan Insttute of Technology Kanpur Indcator varables versus quanttatve explanatory
More information