Overview. Overview Page 1 of 8
|
|
- Marvin Dickerson
- 6 years ago
- Views:
Transcription
1 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIORNIA DECEMBER 2001 COMPOSITE BEAM DESIGN AISC-LRD93 Tecnical Noe Compac and Noncompac Requiemens Tis Tecnical Noe descibes o e pogam cecks e AISC-LRD93 specificaion equiemens fo compac and noncompac beams. Te basic compac and noncompac equiemens cecked ae in AISC-LRD93 specificaion Cape B, Table B5.1. Te pogam cecks e id-o-ickness aios of e beam compession flange, beam eb, and, if i exiss and is in compession, e cove plae. Wen a singl smmeic beam is designed fo noncomposie beavio, i is also cecked fo laeal osional buckling equiemens. Ovevie Te pogam classifies beam secions as eie compac, noncompac o slende. I cecks e compac and noncompac secion equiemens a eac design locaion along e beam fo eac design load combinaion sepaael. A beam secion ma be classified diffeenl fo diffeen design load combinaions. o example, a beam ma be classified as compac fo design load combinaion A and as noncompac fo design load combinaion B. To easons a a beam ma be classified diffeenl fo diffeen design load cases ae:! Te compac secion equiemens fo beam ebs depend on e axial load in e beam. Diffeen design load combinaions ma poduce diffeen axial loads in e beam. Tis is onl an issue en beam axial loads ae specified o be consideed in e composie beam analsis and design.! Te compession flange ma be diffeen fo diffeen design load combinaions. If e sizes of e op and boom flanges ae no e same, classificaion of e secion ma depend on ic flange is deemined o be e compession flange. A eac design locaion, fo eac design load combinaion, e pogam fis cecks a beam secion fo e compac secion equiemens fo e compession flange, eb, cove plae (if applicable) and laeal osional buckling (if Ovevie Page 1 of 8
2 Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens applicable) descibed eein. If e beam secion mees all of ose equiemens, i is classified as compac fo a design load combinaion. If e beam secion does no mee all of e compac secion equiemens, i is cecked fo e noncompac equiemens fo e flanges, eb, cove plae (if applicable) and laeal osional buckling (if applicable) descibed eein. If e beam secion mees all of ose equiemens, i is classified as noncompac fo a design load combinaion. If e beam secion does no mee all of e noncompac secion equiemens, i is classified as slende fo a design load combinaion and e pogam does no conside i fo composie beam design. Limiing Wid-o-Tickness Raios fo langes Tis secion descibes e limiing id-o-ickness aios consideed b e pogam fo beam compession flanges. Te id-o-ickness aio fo flanges is denoed b/, and is equal o b f /2 f fo I-saped secions and b f / f fo cannel secions. Compac Secion Limis fo langes o compac secions, e id-o-ickness aio fo e compession flange is limied o a indicaed b Equaion 1. b 65, fo compac secions Eqn. 1 f ee f is e specified ield sess of e flange consideed. Equaion 1 applies o bo olled secions seleced fom e pogam's daabase and o use-defined secions. Noncompac Secion Limis fo langes I-Saped Rolled Beams and Cannels o noncompac I-saped olled beams and cannels, e id-o-ickness aio fo e compession flange is limied o a indicaed b Equaion 2. b 141, fo noncompac secions Eqn ee is e specified ield sess of e beam o cannel. Limiing Wid-o-Tickness Raios fo langes Page 2 of 8
3 Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens Use-Defined and Hbid Beams o noncompac use-defined and bid beams, e id-o-ickness aio fo e compession flange is limied o a indicaed b Equaion 3. b 162, fo noncompac secions Eqn. 3 f k c ee f is e ield sess of e compession flange and, k c = 4 bu no less an 0.35 k c Eqn. 4 Limiing Wid-o-Tickness Raios fo Webs Tis secion descibes e limiing id-o-ickness aios consideed b e pogam fo beam ebs. Compac Secion Limis fo Webs Wen cecking a beam eb fo compac secion equiemens, e id-oickness aio used is /. Te equaion used fo cecking e compac secion limis in e eb depends on e magniude of e axial compession sess aio, (P u / φ b P ) in e beam. Wen calculaing e axial compession sess aio, e folloing o ules ae used:! Te pogam akes P as A s fo olled secions and b f-op f-op f-op + + b f-bo f-bo f-bo fo use-defined secions.! Te pogam uses φ b = 0.85 if a plasic sess disibuion is used fo momen and φ b = 0.9 if an elasic sess disibuion is used fo momen.! Te pogam compues e axial compession sess aio (P u / φ b P ) based on e aea of e seel beam alone no including e cove plae, even if i exiss, and no including e concee slab. Wen (P u / φ b P ) 0.125, Equaion 5a defines e compac secion limi fo ebs. Wen (P u / φ b P ) > 0.125, Equaion 5b defines e compac secion limi fo ebs. Limiing Wid-o-Tickness Raios fo Webs Page 3 of 8
4 Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens P P 1 u u, en P φ b φbp Eqn. 5a 191 P u , P φb Pu en > φ P b Eqn. 5b In Equaions 5a and 5b, e value of used is e lages of e values fo e beam flanges and e eb. If ee is no axial foce, o if ee is axial ension onl (i.e., no axial compessive foce), onl Equaion 5a applies. Noncompac Secion Limis fo Webs Wen cecking a beam eb of a beam fo noncompac secion equiemens, e id-o-ickness aio cecked is /. Te noncompac secion limis depend on ee e flanges of e beam ae of equal o unequal size. Beams i Equal Sized langes Equaion 6 defines e noncompac secion limi fo ebs in beams i equal sized flanges P 1 φ b P u Eqn. 6 In Equaion 6, e value of used is e lages of e values fo e beam flanges and e eb. Beams i Unequal Sized langes Equaion 7 defines e noncompac secion limi fo ebs in beams i unequal sized flanges Limiing Wid-o-Tickness Raios fo Webs Page 4 of 8
5 Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens ee, c c 0.74P 1 φ b P 3 2 u, Eqn. 7 In Equaion 7, e value of used is e lages of e values fo e beam flanges and e eb. Equaion 7 is Equaion A-B5-1 in e AISC-LRD93 specificaion. Limiing Wid-o-Tickness Raios fo Cove Plaes Te id-o-ickness cecks made fo e cove plae depend on e id of e cove plae compaed o e id of e beam boom flange. igue 1 illusaes e condiions consideed. In Case A of e figue, e id of e cove plae is less an o equal o e id of e beam boom flange. In a case, e id-o-ickness aio is aken as b 1 / cp, and i is cecked as a flange cove plae. In Case B of igue 1, e id of e cove plae is geae an e id of e beam boom flange. To condiions ae cecked in a case. Te fis condiion is e same as a son in Case A, ee e id-o-ickness aio is aken as b 1 / cp and is cecked as a flange cove plae. Te second condiion cecked in Case B akes b 2 / cp as e id-o-ickness aio and cecks i as a plae pojecing fom a beam. Tis second condiion is onl cecked fo e noncompac equiemens; i is no cecked fo compac equiemens. Compac Secion Limis fo Cove Plaes o bo cases A and B son in igue 1, e cove plae is cecked fo compac secion equiemens as son in Equaion 8. b1 190 Eqn. 8 cp cp ee b 1 is defined in igue 1. Limiing Wid-o-Tickness Raios fo Cove Plaes Page 5 of 8
6 Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens Beam Beam Cove plae b 1 cp b 2 b 1 b 2 cp Cove plae Case A Case B igue 1: Condiions Consideed Wen Cecking Wid-o-Tickness Raios of Cove Plaes Noncompac Secion Limis fo Cove Plaes Te cecks made fo noncompac secion equiemens depend on ee e id of e cove plae is less an o equal o a of e boom flange of e beam, Case A in igue 1, o geae an a of e boom flange of e beam, Case B in igue 1. Cove Plae Wid Beam Boom lange Wid Wen e cove plae id is less an o equal o e id of e beam boom flange, Equaion 9 applies fo e noncompac ceck fo e cove plae. b1 238 Eqn. 9 cp cp Te em b 1 in Equaion 9 is defined in igue 1. Limiing Wid-o-Tickness Raios fo Cove Plaes Page 6 of 8
7 Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens Cove Plae Wid > Beam Boom lange Wid Wen e cove plae id exceeds e id of e beam boom flange, bo Equaions 9 and 10 appl fo e noncompac ceck fo e cove plae. b 2 95 Eqn. 10 cp cp Te em b 2 in Equaion 10 is defined in igue 1. Laeal Tosional Buckling Wen a singl smmeic beam is designed fo noncomposie beavio, i is cecked fo laeal osional buckling equiemens. If e singl smmeic beam is unsoed, is ceck occus fo an consucion design load case. I also occus fo beams a ave negaive bending a ae no specified o conside e composie acion povided b e slab eba. inall, e ceck occus fo an singl smmeic beam specified o be noncomposie. Wen evieing fo laeal osional buckling equiemens, e value of L b / c is cecked. L b is e laeall unbaced leng of beam; a is, e leng beeen poins a ae baced agains laeal displacemen of e compession flange. Te em c is adius of gaion of e compession flange abou e -axis. Compac Limis fo Laeal Tosional Buckling Te compac secion limi fo laeal osional buckling is given in Equaion 11. Lb 300 Eqn. 11 c f In Equaion 11 e em f is e ield sess of e compession flange. Noncompac Limis fo Laeal Tosional Buckling Te noncompac secion limi fo laeal osional buckling is given in Equaion 12. * L b L b Eqn. 12 c c Laeal Tosional Buckling Page 7 of 8
8 Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens * ee L b is e value of L b fo ic M c, as defined b Equaions 13a oug 13c, is equal o M, as defined b Equaions 14a and 14b. Te fomula fo M c given in Equaions 13a oug 13c is aken fom AISC- LRD93 Table A-1.1, foonoe (e). Te value of C b is aken as 1 as specified in e Table. ee, M B 1 c = ( 57000)( 1) L b I J B B2 + B 2 1 Eqn. 13a I c I = Eqn. 13b I L b J B 2 2 I c I c 25 1 I J L = Eqn. 13c b Te fomula fo M given in Equaions 14a and 14b is aken fom AISC- LRD93 Table A-1.1. M = S S Eqn. 14a L xc f x ee, L = smalle of ( ) and Eqn. 14b f In Equaion 14a, f is e ield sess of e ension flange. In Equaion 14b, f is e ield sess of e compession flange. Te oe ems ae defined in e noaion in Tecnical Noe Geneal and Noaion Composie Beam Design AISC-LRD93. Laeal Tosional Buckling Page 8 of 8
General. Eqn. 1. where, F b-bbf = Allowable bending stress at the bottom of the beam bottom flange, ksi.
COMPUERS AND SRUCURES, INC., BERKELEY, CALIORNIA DECEMBER 2001 COMPOSIE BEAM DESIGN AISC-ASD89 echnical Note Allowale Bending Stesses Geneal his echnical Note descies how the pogam detemines the allowale
More informationMECHANICS OF MATERIALS Poisson s Ratio
Fouh diion MCHANICS OF MATRIALS Poisson s Raio Bee Johnson DeWolf Fo a slende ba subjeced o aial loading: 0 The elongaion in he -diecion is accompanied b a conacion in he ohe diecions. Assuming ha he maeial
More informationPressure Vessels Thin and Thick-Walled Stress Analysis
Pessue Vessels Thin and Thick-Walled Sess Analysis y James Doane, PhD, PE Conens 1.0 Couse Oveview... 3.0 Thin-Walled Pessue Vessels... 3.1 Inoducion... 3. Sesses in Cylindical Conaines... 4..1 Hoop Sess...
More informationCombined 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 informationThis Technical Note describes how the program calculates the moment capacity of a noncomposite steel beam, including a cover plate, if applicable.
COPUTERS AND STRUCTURES, INC., BERKEEY, CAIORNIA DECEBER 001 COPOSITE BEA DESIGN AISC-RD93 Techical te This Techical te descibes how the ogam calculates the momet caacit of a ocomosite steel beam, icludig
More informationOrthotropic Materials
Kapiel 2 Ohoopic Maeials 2. Elasic Sain maix Elasic sains ae elaed o sesses by Hooke's law, as saed below. The sesssain elaionship is in each maeial poin fomulaed in he local caesian coodinae sysem. ε
More informationBUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES
Guide fo Buckling and Ulimae Sengh Assessmen fo Offshoe Sucues GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES APRIL 4 (Updaed Augus 18 see nex page) Ameican Bueau of Shipping
More informationSections 3.1 and 3.4 Exponential Functions (Growth and Decay)
Secions 3.1 and 3.4 Eponenial Funcions (Gowh and Decay) Chape 3. Secions 1 and 4 Page 1 of 5 Wha Would You Rahe Have... $1million, o double you money evey day fo 31 days saing wih 1cen? Day Cens Day Cens
More informationHeat Conduction Problem in a Thick Circular Plate and its Thermal Stresses due to Ramp Type Heating
ISSN(Online): 319-8753 ISSN (Pin): 347-671 Inenaional Jounal of Innovaive Reseac in Science, Engineeing and Tecnology (An ISO 397: 7 Ceified Oganiaion) Vol 4, Issue 1, Decembe 15 Hea Concion Poblem in
More informationChapter Finite Difference Method for Ordinary Differential Equations
Chape 8.7 Finie Diffeence Mehod fo Odinay Diffeenial Eqaions Afe eading his chape, yo shold be able o. Undesand wha he finie diffeence mehod is and how o se i o solve poblems. Wha is he finie diffeence
More informationAdditional Exercises for Chapter What is the slope-intercept form of the equation of the line given by 3x + 5y + 2 = 0?
ddiional Eercises for Caper 5 bou Lines, Slopes, and Tangen Lines 39. Find an equaion for e line roug e wo poins (, 7) and (5, ). 4. Wa is e slope-inercep form of e equaion of e line given by 3 + 5y +
More informationDepartment of Chemical Engineering University of Tennessee Prof. David Keffer. Course Lecture Notes SIXTEEN
D. Keffe - ChE 40: Hea Tansfe and Fluid Flow Deamen of Chemical Enee Uniesi of Tennessee Pof. Daid Keffe Couse Lecue Noes SIXTEEN SECTION.6 DIFFERENTIL EQUTIONS OF CONTINUITY SECTION.7 DIFFERENTIL EQUTIONS
More informationMade by AAT Date June Checked by JEK Date June Revised by JBL/MEB Date April 2006
Job No. RSU658 See 1 of 7 Rev B Kemiinie, oo P.O.Box 185, FN VTT, Finland Teleone: + 58 9 561 Fax: + 58 9 56 7 Job Tile Subjec Clien Sainle Seel Valoriaion Projec Deign xamle Deign of a wo-an raezoidal
More informationCONSIDERATIONS REGARDING THE OPTIMUM DESIGN OF PRESTRESSED ELEMENTS
Bullein of e Transilvania Universiy of Braşov CIBv 5 Vol. 8 (57) Special Issue No. - 5 CONSIDERTIONS REGRDING THE OPTIU DESIGN OF PRESTRESSED ELEENTS D. PRECUPNU C. PRECUPNU bsrac: Engineering educaion
More informationPHYS PRACTICE EXAM 2
PHYS 1800 PRACTICE EXAM Pa I Muliple Choice Quesions [ ps each] Diecions: Cicle he one alenaive ha bes complees he saemen o answes he quesion. Unless ohewise saed, assume ideal condiions (no ai esisance,
More informationLecture 18: Kinetics of Phase Growth in a Two-component System: general kinetics analysis based on the dilute-solution approximation
Lecue 8: Kineics of Phase Gowh in a Two-componen Sysem: geneal kineics analysis based on he dilue-soluion appoximaion Today s opics: In he las Lecues, we leaned hee diffeen ways o descibe he diffusion
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 informationComputer Propagation Analysis Tools
Compue Popagaion Analysis Tools. Compue Popagaion Analysis Tools Inoducion By now you ae pobably geing he idea ha pedicing eceived signal sengh is a eally impoan as in he design of a wieless communicaion
More informationWORK POWER AND ENERGY Consevaive foce a) A foce is said o be consevaive if he wok done by i is independen of pah followed by he body b) Wok done by a consevaive foce fo a closed pah is zeo c) Wok done
More informationConstant Acceleration
Objecive Consan Acceleraion To deermine he acceleraion of objecs moving along a sraigh line wih consan acceleraion. Inroducion The posiion y of a paricle moving along a sraigh line wih a consan acceleraion
More informationPseudosteady-State Flow Relations for a Radial System from Department of Petroleum Engineering Course Notes (1997)
Pseudoseady-Sae Flow Relaions fo a Radial Sysem fom Deamen of Peoleum Engineeing Couse Noes (1997) (Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem) (Deivaion of he Pseudoseady-Sae Flow
More informationProbabilistic Models. CS 188: Artificial Intelligence Fall Independence. Example: Independence. Example: Independence? Conditional Independence
C 188: Aificial Inelligence Fall 2007 obabilisic Models A pobabilisic model is a join disibuion ove a se of vaiables Lecue 15: Bayes Nes 10/18/2007 Given a join disibuion, we can eason abou unobseved vaiables
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES In igid body kinemaics, we use he elaionships govening he displacemen, velociy and acceleaion, bu mus also accoun fo he oaional moion of he body. Descipion of he moion of igid
More informationseventeen steel construction: columns & tension members ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: ORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS Co-Ten Steel Sculptue By Richad Sea Museum of Moden At ot Woth, TX (AISC - Steel Stuctues of the Eveyday) SUMMER 2014 lectue seventeen
More informationCircular Motion. Radians. One revolution is equivalent to which is also equivalent to 2π radians. Therefore we can.
1 Cicula Moion Radians One evoluion is equivalen o 360 0 which is also equivalen o 2π adians. Theefoe we can say ha 360 = 2π adians, 180 = π adians, 90 = π 2 adians. Hence 1 adian = 360 2π Convesions Rule
More informationCHEMISTRY 047 STUDY PACKAGE
CHEMISTRY 047 STUDY PACKAGE Tis maerial is inended as a review of skills you once learned. PREPARING TO WRITE THE ASSESSMENT VIU/CAP/D:\Users\carpenem\AppDaa\Local\Microsof\Windows\Temporary Inerne Files\Conen.Oulook\JTXREBLD\Cemisry
More informationPhysics 201 Lecture 18
Phsics 0 ectue 8 ectue 8 Goals: Define and anale toque ntoduce the coss poduct Relate otational dnamics to toque Discuss wok and wok eneg theoem with espect to otational motion Specif olling motion (cente
More informationComparison between the Discrete and Continuous Time Models
Comparison beween e Discree and Coninuous Time Models D. Sulsky June 21, 2012 1 Discree o Coninuous Recall e discree ime model Î = AIS Ŝ = S Î. Tese equaions ell us ow e populaion canges from one day o
More informationME311 Machine Design
ME311 Machine Desin Lectue 7: Columns W Donfeld 6Oct17 Faifield Univesit School of Enineein Column Bucklin We have aad discussed axiall loaded bas. Fo a shot ba, the stess /A, and the defction is L/AE.
More informationNUMERICAL SIMULATION FOR NONLINEAR STATIC & DYNAMIC STRUCTURAL ANALYSIS
Join Inenaional Confeence on Compuing and Decision Making in Civil and Building Engineeing June 14-16, 26 - Monéal, Canada NUMERICAL SIMULATION FOR NONLINEAR STATIC & DYNAMIC STRUCTURAL ANALYSIS ABSTRACT
More informationMathematics Paper- II
R Prerna Tower, Road No -, Conracors Area, Bisupur, Jamsedpur - 8, Tel - (65789, www.prernaclasses.com Maemaics Paper- II Jee Advance PART III - MATHEMATICS SECTION - : (One or more opions correc Type
More information02. MOTION. Questions and Answers
CLASS-09 02. MOTION Quesions and Answers PHYSICAL SCIENCE 1. Se moves a a consan speed in a consan direcion.. Reprase e same senence in fewer words using conceps relaed o moion. Se moves wi uniform velociy.
More informationWater Tunnel Experiment MAE 171A/175A. Objective:
Wate Tunnel Expeiment MAE 7A/75A Objective: Measuement of te Dag Coefficient of a Cylinde Measuement Tecniques Pessue Distibution on Cylinde Dag fom Momentum Loss Measued in Wake it lase Dopple Velocimety
More informationEN221 - Fall HW # 7 Solutions
EN221 - Fall2008 - HW # 7 Soluions Pof. Vivek Shenoy 1.) Show ha he fomulae φ v ( φ + φ L)v (1) u v ( u + u L)v (2) can be pu ino he alenaive foms φ φ v v + φv na (3) u u v v + u(v n)a (4) (a) Using v
More information, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t
Lecue 6: Fiis Tansmission Equaion and Rada Range Equaion (Fiis equaion. Maximum ange of a wieless link. Rada coss secion. Rada equaion. Maximum ange of a ada. 1. Fiis ansmission equaion Fiis ansmission
More informationBENDING OF BEAM. Compressed layer. Elongated. layer. Un-strained. layer. NA= Neutral Axis. Compression. Unchanged. Elongation. Two Dimensional View
BNDING OF BA Compessed laye N Compession longation Un-stained laye Unchanged longated laye NA Neutal Axis Two Dimensional View A When a beam is loaded unde pue moment, it can be shown that the beam will
More informationIB 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 informationANALYSIS OF REINFORCED CONCRETE BUILDINGS IN FIRE
ANALYSIS OF REINFORCED CONCRETE BUILDINGS IN FIRE Dr Zhaohui Huang Universiy of Sheffield 6 May 2005 1 VULCAN layered slab elemens: connecion o beam elemens Plae Elemen Slab nodes y x Reference Plane h
More informationTHE CATCH PROCESS (continued)
THE CATCH PROCESS (coninued) In our previous derivaion of e relaionsip beween CPUE and fis abundance we assumed a all e fising unis and all e fis were spaially omogeneous. Now we explore wa appens wen
More informationMECHANICS OF MATERIALS Poisson s Ratio
Poisson s Raio For a slender bar subjeced o axial loading: ε x x y 0 The elongaion in he x-direcion i is accompanied by a conracion in he oher direcions. Assuming ha he maerial is isoropic (no direcional
More informationSTUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE WEIBULL DISTRIBUTION
Inenaional Jounal of Science, Technology & Managemen Volume No 04, Special Issue No. 0, Mach 205 ISSN (online): 2394-537 STUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE
More informationLecture 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 informationThe sudden release of a large amount of energy E into a background fluid of density
10 Poin explosion The sudden elease of a lage amoun of enegy E ino a backgound fluid of densiy ceaes a song explosion, chaaceized by a song shock wave (a blas wave ) emanaing fom he poin whee he enegy
More information7 Wave Equation in Higher Dimensions
7 Wave Equaion in Highe Dimensions We now conside he iniial-value poblem fo he wave equaion in n dimensions, u c u x R n u(x, φ(x u (x, ψ(x whee u n i u x i x i. (7. 7. Mehod of Spheical Means Ref: Evans,
More informationDESIGN 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 informationStability of an ideal (flat) plate. = k. critical stresses σ* (or N*) take the. Thereof infinitely many solutions: Critical stresses are given as:
. Buckling of plaes Linear and nonlinear heor of uckling, uckling under direc sresses (class secions), uckling under shear, local loading and Eurocode approach. Saili of an ideal (fla) plae various loading
More informationCH.7. PLANE LINEAR ELASTICITY. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.7. PLANE LINEAR ELASTICITY Coninuum Mechanics Course (MMC) - ETSECCPB - UPC Overview Plane Linear Elasici Theor Plane Sress Simplifing Hpohesis Srain Field Consiuive Equaion Displacemen Field The Linear
More informationMATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH
Fundamenal Jounal of Mahemaical Phsics Vol 3 Issue 013 Pages 55-6 Published online a hp://wwwfdincom/ MATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH Univesias
More information2CO8 Advanced design of steel and composite structures Lectures: Machacek (M), Netusil (N), Wald (W), Ungureanu (U)
CO8 Advanced design of seel and composie srucures Lecures: Machacek (M), Neusil (N), Wald (W), Ungureanu (U) 1 (M) Global analysis. Torsion of seel members (M) Buil-up seel members 3 (M) aigue 4 (M) Laeral-orsional
More informationCS537. Numerical Analysis
CS57 Numerical Analsis Lecure Numerical Soluion o Ordinar Dierenial Equaions Proessor Jun Zang Deparmen o Compuer Science Universi o enuck Leingon, Y 4006 0046 April 5, 00 Wa is ODE An Ordinar Dierenial
More informationWhat Ties Return Volatilities to Price Valuations and Fundamentals? On-Line Appendix
Wha Ties Reurn Volailiies o Price Valuaions and Fundamenals? On-Line Appendix Alexander David Haskayne School of Business, Universiy of Calgary Piero Veronesi Universiy of Chicago Booh School of Business,
More informationTwo-dimensional Effects on the CSR Interaction Forces for an Energy-Chirped Bunch. Rui Li, J. Bisognano, R. Legg, and R. Bosch
Two-dimensional Effecs on he CS Ineacion Foces fo an Enegy-Chiped Bunch ui Li, J. Bisognano,. Legg, and. Bosch Ouline 1. Inoducion 2. Pevious 1D and 2D esuls fo Effecive CS Foce 3. Bunch Disibuion Vaiaion
More information4. Torsion Open and closed cross sections, simple St. Venant and warping torsion, interaction of bending and torsion, Eurocode approach.
4. orsion Open and closed cross secions, simple S. enan and arping orsion, ineracion of bending and orsion, Eurocode approach. Common is elasic soluion (nonlinear plasic analysis e.g. Srelbickaja) Eurocode
More informationû s L u t 0 s a ; i.e., û s 0
Te Hille-Yosida Teorem We ave seen a wen e absrac IVP is uniquely solvable en e soluion operaor defines a semigroup of bounded operaors. We ave no ye discussed e condiions under wic e IVP is uniquely solvable.
More informationMolecular Evolution and Phylogeny. Based on: Durbin et al Chapter 8
Molecula Evoluion and hylogeny Baed on: Dubin e al Chape 8. hylogeneic Tee umpion banch inenal node leaf Topology T : bifucaing Leave - N Inenal node N+ N- Lengh { i } fo each banch hylogeneic ee Topology
More informationr P + '% 2 r v(r) End pressures P 1 (high) and P 2 (low) P 1 , which must be independent of z, so # dz dz = P 2 " P 1 = " #P L L,
Lecue 36 Pipe Flow and Low-eynolds numbe hydodynamics 36.1 eading fo Lecues 34-35: PKT Chape 12. Will y fo Monday?: new daa shee and daf fomula shee fo final exam. Ou saing poin fo hydodynamics ae wo equaions:
More informationTRANSILVANIA UNIVERSITY OF BRASOV MECHANICAL ENGINEERING FACULTY DEPARTMENT OF MECHANICAL ENGINEERING ONLY FOR STUDENTS
TNSILVNI UNIVSITY OF BSOV CHNICL NGINING FCULTY DPTNT OF CHNICL NGINING Couse 9 Cuved as 9.. Intoduction The eams with plane o spatial cuved longitudinal axes ae called cuved as. Thee ae consideed two
More informationNumerical solution of fuzzy differential equations by Milne s predictor-corrector method and the dependency problem
Applied Maemaics and Sciences: An Inenaional Jounal (MaSJ ) Vol. No. Augus 04 Numeical soluion o uzz dieenial equaions b Milne s pedico-coeco meod and e dependenc poblem Kanagaajan K Indakuma S Muukuma
More informationV.sin. AIM: Investigate the projectile motion of a rigid body. INTRODUCTION:
EXPERIMENT 5: PROJECTILE MOTION: AIM: Invesigae e projecile moion of a rigid body. INTRODUCTION: Projecile moion is defined as e moion of a mass from op o e ground in verical line, or combined parabolic
More informationMEEN 617 Handout #11 MODAL ANALYSIS OF MDOF Systems with VISCOUS DAMPING
MEEN 67 Handou # MODAL ANALYSIS OF MDOF Sysems wih VISCOS DAMPING ^ Symmeic Moion of a n-dof linea sysem is descibed by he second ode diffeenial equaions M+C+K=F whee () and F () ae n ows vecos of displacemens
More informationPSAT/NMSQT PRACTICE ANSWER SHEET SECTION 3 EXAMPLES OF INCOMPLETE MARKS COMPLETE MARK B C D B C D B C D B C D B C D 13 A B C D B C D 11 A B C D B C D
PSTNMSQT PRCTICE NSWER SHEET COMPLETE MRK EXMPLES OF INCOMPLETE MRKS I i recommended a you ue a No pencil I i very imporan a you fill in e enire circle darkly and compleely If you cange your repone, erae
More informationCS 188: Artificial Intelligence Fall Probabilistic Models
CS 188: Aificial Inelligence Fall 2007 Lecue 15: Bayes Nes 10/18/2007 Dan Klein UC Bekeley Pobabilisic Models A pobabilisic model is a join disibuion ove a se of vaiables Given a join disibuion, we can
More informationPHYS GENERAL RELATIVITY AND COSMOLOGY PROBLEM SET 7 - SOLUTIONS
PHYS 54 - GENERAL RELATIVITY AND COSMOLOGY - 07 - PROBLEM SET 7 - SOLUTIONS TA: Jeome Quinin Mach, 07 Noe ha houghou hee oluion, we wok in uni whee c, and we chooe he meic ignaue (,,, ) a ou convenion..
More informationÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s
MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN
More information2015 Practice Test #1
Pracice Te # Preliminary SATNaional Meri Scolarip Qualifying Te IMPORTANT REMINDERS A No. pencil i required for e e. Do no ue a mecanical pencil or pen. Saring any queion wi anyone i a violaion of Te Securiy
More informationDesign Beam Flexural Reinforcement
COPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEBER 2001 CONCRETE FRAE DESIGN ACI-318-99 Technical Note This Technical Note describes how this program completes beam design when the ACI 318-99
More informationThe plastic moment capacity of a composite cross-section is calculated in the program on the following basis (BS 4.4.2):
COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA SEPTEMBER 2002 COMPOSITE BEAM DESIGN BS 5950-90 Technical Note Composite Plastic Moment Capacity for Positive Bending This Technical Note describes
More informationRepresenting Knowledge. CS 188: Artificial Intelligence Fall Properties of BNs. Independence? Reachability (the Bayes Ball) Example
C 188: Aificial Inelligence Fall 2007 epesening Knowledge ecue 17: ayes Nes III 10/25/2007 an Klein UC ekeley Popeies of Ns Independence? ayes nes: pecify complex join disibuions using simple local condiional
More informationLecture 5. Chapter 3. Electromagnetic Theory, Photons, and Light
Lecue 5 Chape 3 lecomagneic Theo, Phoons, and Ligh Gauss s Gauss s Faada s Ampèe- Mawell s + Loen foce: S C ds ds S C F dl dl q Mawell equaions d d qv A q A J ds ds In mae fields ae defined hough ineacion
More informationSteel members come in a wide variety of shapes; the properties of the cross section are needed for analysis and design. (Bob Scott/Getty Images)
Seel memers come in a wide varie of sapes; e properies of e cross secion are needed for analsis and design. (Bo Sco/Ge Images) 01 engage Learning. All Rigs Reserved. Ma no e scanned, copied or duplicaed,
More informationCSE590B Lecture 4 More about P 1
SE590 Lece 4 Moe abo P 1 Tansfoming Tansfomaions James. linn Jimlinn.om h://coses.cs.washingon.ed/coses/cse590b/13a/ Peviosly On SE590b Tansfomaions M M w w w w w The ncion w w w w w w 0 w w 0 w 0 w The
More informationSee the solution to Prob Ans. Since. (2E t + 2E c )ch - a. (s max ) t. (s max ) c = 2E c. 2E c. (s max ) c = 3M bh 2E t + 2E c. 2E t. h c.
*6 108. The beam has a ectangula coss section and is subjected to a bending moment. f the mateial fom which it is made has a diffeent modulus of elasticity fo tension and compession as shown, detemine
More informationThermal-Fluids I. Chapter 17 Steady heat conduction. Dr. Primal Fernando Ph: (850)
emal-fluids I Capte 7 Steady eat conduction D. Pimal Fenando pimal@eng.fsu.edu P: (850 40-633 Steady eat conduction Hee we conside one dimensional steady eat conduction. We conside eat tansfe in a plane
More informationLecture 17: Kinetics of Phase Growth in a Two-component System:
Lecue 17: Kineics of Phase Gowh in a Two-componen Sysem: descipion of diffusion flux acoss he α/ ineface Today s opics Majo asks of oday s Lecue: how o deive he diffusion flux of aoms. Once an incipien
More informationDESIGN OF BEAMS FOR MOMENTS
CHAPTER Stuctual Steel Design RFD ethod Thid Edition DESIGN OF BEAS FOR OENTS A. J. Clak School of Engineeing Deatment of Civil and Envionmental Engineeing Pat II Stuctual Steel Design and Analysis 9 FA
More informationThe Production of Polarization
Physics 36: Waves Lecue 13 3/31/211 The Poducion of Polaizaion Today we will alk abou he poducion of polaized ligh. We aleady inoduced he concep of he polaizaion of ligh, a ansvese EM wave. To biefly eview
More information( ) ( ) Last Time. 3-D particle in box: summary. Modified Bohr model. 3-dimensional Hydrogen atom. Orbital magnetic dipole moment
Last Time 3-dimensional quantum states and wave functions Couse evaluations Tuesday, Dec. 9 in class Deceasing paticle size Quantum dots paticle in box) Optional exta class: eview of mateial since Exam
More informationSecond-Order Differential Equations
WWW Problems and Soluions 3.1 Chaper 3 Second-Order Differenial Equaions Secion 3.1 Springs: Linear and Nonlinear Models www m Problem 3. (NonlinearSprings). A bod of mass m is aached o a wall b means
More informationWind Tunnel Experiment MAE 171A/175A. Objective:
Wind Tunnel Exeiment MAE 7A/75A Objective: Measue te Aeodynamic Foces and Moments of a Clak Y-4 Aifoil Unde Subsonic Flo Conditions Measuement Tecniques Pessue Distibution on Aifoil Dag fom Momentum Loss
More informationME 210 Applied Mathematics for Mechanical Engineers
Tangent and Ac Length of a Cuve The tangent to a cuve C at a point A on it is defined as the limiting position of the staight line L though A and B, as B appoaches A along the cuve as illustated in the
More informationToday - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations
Today - Lecue 13 Today s lecue coninue wih oaions, oque, Noe ha chapes 11, 1, 13 all inole oaions slide 1 eiew Roaions Chapes 11 & 1 Viewed fom aboe (+z) Roaional, o angula elociy, gies angenial elociy
More informationStatic equilibrium requires a balance of forces and a balance of moments.
Static Equilibium Static equilibium equies a balance of foces and a balance of moments. ΣF 0 ΣF 0 ΣF 0 ΣM 0 ΣM 0 ΣM 0 Eample 1: painte stands on a ladde that leans against the wall of a house at an angle
More informationConstruction Figure 10.1: Jaw clutches
CHAPTER TEN FRICTION CLUTCHES The wod clutch is a geneic tem descibing any one wide vaiety of devices that is capable of causing a machine o mechanism to become engaged o disengaged. Clutches ae of thee
More informationVariance and Covariance Processes
Vaiance and Covaiance Pocesses Pakash Balachandan Depamen of Mahemaics Duke Univesiy May 26, 2008 These noes ae based on Due s Sochasic Calculus, Revuz and Yo s Coninuous Maingales and Bownian Moion, Kaazas
More informationEx: An object is released from rest. Find the proportion of its displacements during the first and second seconds. y. g= 9.8 m/s 2
FREELY FALLING OBJECTS Free fall Acceleraion If e only force on an objec is is wei, e objec is said o be freely fallin, reardless of e direcion of moion. All freely fallin objecs (eay or li) ae e same
More informationGeneral Non-Arbitrage Model. I. Partial Differential Equation for Pricing A. Traded Underlying Security
1 Geneal Non-Abiage Model I. Paial Diffeenial Equaion fo Picing A. aded Undelying Secuiy 1. Dynamics of he Asse Given by: a. ds = µ (S, )d + σ (S, )dz b. he asse can be eihe a sock, o a cuency, an index,
More informationCity of Ottumwa. Sewer System
Ciy of Oumwa Sewe Sysem Fxisin ġ Sewe Sysem SANTARY SEWER SYSTEM 787, 329 L. F. ( 49. miles) of known Gaviy Saniay Sewe 2, 893 known Saniay Sewe Manholes 50, 9 L.F. ( 9. 5 miles) of known Foce Main Saniay
More informationCapacitance Extraction. Classification (orthogonal to 3D/2D)
Capacitance Etaction n Intoduction n Table lookup metod n Fomula-based metod n Numeical metod Classification otogonal to D/D n Numeical metod accuate an geometic stuctues etemel epensive n Fomula-based
More informationGCSE: Volumes and Surface Area
GCSE: Volumes and Suface Aea D J Fost (jfost@tiffin.kingston.sc.uk) www.dfostmats.com GCSE Revision Pack Refeence:, 1, 1, 1, 1i, 1ii, 18 Last modified: 1 st August 01 GCSE Specification. Know and use fomulae
More informationFundamental Vehicle Loads & Their Estimation
Fundaenal Vehicle Loads & Thei Esiaion The silified loads can only be alied in he eliinay design sage when he absence of es o siulaion daa They should always be qualified and udaed as oe infoaion becoes
More informationMotion along a Straight Line
chaper 2 Moion along a Sraigh Line verage speed and average velociy (Secion 2.2) 1. Velociy versus speed Cone in he ebook: fer Eample 2. Insananeous velociy and insananeous acceleraion (Secions 2.3, 2.4)
More informationAt 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 information1 1 + x 2 dx. tan 1 (2) = ] ] x 3. Solution: Recall that the given integral is improper because. x 3. 1 x 3. dx = lim dx.
. Use Simpson s rule wih n 4 o esimae an () +. Soluion: Since we are using 4 seps, 4 Thus we have [ ( ) f() + 4f + f() + 4f 3 [ + 4 4 6 5 + + 4 4 3 + ] 5 [ + 6 6 5 + + 6 3 + ]. 5. Our funcion is f() +.
More informationProcess model for the design of bent 3-dimensional free-form geometries for the three-roll-push-bending process
Available online a www.sciencediec.com Pocedia CIRP 7 (213 ) 24 245 Foy Sixh CIRP Confeence on Manufacuing Sysems 213 Pocess model fo he design of ben 3-dimensional fee-fom geomeies fo he hee-oll-push-bending
More informationElastic-Plastic Deformation of a Rotating Solid Disk of Exponentially Varying Thickness and Exponentially Varying Density
Poceedings of he Inenaional MuliConfeence of Enginees Compue Scieniss 6 Vol II, IMECS 6, Mach 6-8, 6, Hong Kong Elasic-Plasic Defomaion of a Roaing Solid Dis of Exponenially Vaying hicness Exponenially
More informationRight-handed screw dislocation in an isotropic solid
Dislocation Mechanics Elastic Popeties of Isolated Dislocations Ou study of dislocations to this point has focused on thei geomety and thei ole in accommodating plastic defomation though thei motion. We
More information[ ] 0. = (2) = a q dimensional vector of observable instrumental variables that are in the information set m constituents of u
Genealized Mehods of Momens he genealized mehod momens (GMM) appoach of Hansen (98) can be hough of a geneal pocedue fo esing economics and financial models. he GMM is especially appopiae fo models ha
More informationInfluence 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 informationOur main purpose in this section is to undertake an examination of the stock
3. Caial gains ax and e sock rice volailiy Our main urose in is secion is o underake an examinaion of e sock rice volailiy by considering ow e raional seculaor s olding canges afer e ax rae on caial gains
More informationBuckling of a structure means failure due to excessive displacements (loss of structural stiffness), and/or
Buckling Buckling of a rucure mean failure due o exceive diplacemen (lo of rucural iffne), and/or lo of abiliy of an equilibrium configuraion of he rucure The rule of humb i ha buckling i conidered a mode
More information