ALLOWABLE STRESS DESIGN FLOWCHART FOR AISC MANUAL OF STEEL CONSTRUCTION, NINTH EDITION APPENDIX B BEARING STIFFENERS AND TRANSVERSE STIFFENERS DESIGN

Size: px
Start display at page:

Download "ALLOWABLE STRESS DESIGN FLOWCHART FOR AISC MANUAL OF STEEL CONSTRUCTION, NINTH EDITION APPENDIX B BEARING STIFFENERS AND TRANSVERSE STIFFENERS DESIGN"

Transcription

1 ALLOWABLE TRE DEIGN LOWCHART OR AIC MANUAL O TEEL CONTRUCTION, NINTH EDITION APPENDIX B BEARING TIENER AND TRANVERE TIENER DEIGN HEN-YEH CHEN, PH.D. Aug, 1995 All Righs Reserve. No pr o his ook my e reprouce or commercil purpose, in ny orm or y ny mens, ihou permission in riing rom he uhor.

2 DICLAIMER AND COPYRIGHT NOTICE The uhor mkes no rrny o ny kin, expresse or implie, ih regr o ny ex, he lgorihms n he progrm conine in his ook. The uhor shll no e relile in ny even or incienl or consequenil mges in connecion ih, or rising ou o, he urnishing, perormnce, or use o his ex, lgorihms n progrms. You my isriue his ocumenion or eucionl purpose, provie h none o he ex in his ocumenion hs een moiie or elee. This inclues, u no limie o, cover pge, isclimer n copyrigh noice n ll remining pges. or commercil usge o his ocumenion, he reer shoul conc he uhor irecly or eils. I you use ny inormion in his ocumenion, you nee o reer o his ocumenion, or he olloing reerence -Y. Chen, Decemer 1997, Using Geneic Algorihms or he Opiml Design o rucurl ysems, Disserion or Docor o Philosophy, Deprmen o Civil Engineering, Arizon e Universiy.

3 BEARING TIENER iuions When Bering ieners Are Require (ee igure AD01.em) 1. P I N > 0. 15, n 0. 4 yc, pir o sieners shoul e provie opposie o ension lnge, o preven Locl lnge Bening. I (K1-) n (K1-) re sisie, n R is in compression, sieners mus e provie o preven Locl We Yieling. I (K1-4) n (K1-5) re sisie, n R is in compression, sieners mus e provie such h k ' >, o preven We Crippling (igure AD04.em). 4. When R is on one lnge, n (K1-6) n (K1-7) re sisie, n R is in compression, sieners mus e provie such h k ' > o preven iesy We Buckling (igure AD04.em) yc 5. When R is on oh lnge, n ( k) >, siener or pir o siener shoul e provie opposie o he P compression lnge, such h k ' >, o preven compression Buckling o he We 6. I he ousie ce o he lnge is connece o noher em or ering momen, (K1-9) mus e sisie, u i is NOT necessry o exen k ', such h k ' >. (ee igure AD0.em)

4 pecil requiremen or Designing Bering ieners (igure AD01.em, AD0.em) 1. or coniions,, 4, 5, 6 ove, (J8-1) mus e sisie. or coniions, 4, 5 ove, [pec K1.8] mus e sisie. or coniions 1, 5, 6, he olloing coniions mus e sisie. 1 1 * or + (Wih o he Momen Connecion Ple). 1 1 c. ieners ele o e o he column shoul e size o crry he orce (in he siener) cuse y unlnce momens Oher Equions or Bering ieners (Menione Aove) (K1-) hen R, (K1-) hen R <, (K1-4) hen R, R > 0.66 y ( N + 5k) R > 0.66 y ( N +.5k ) R > N N (K1-5) hen R <, R > 4 1+ here is yieling sress o em e y y y

5 (K1-6) c c 6800 hen <., n he lnge is gins roion n R > l h l (K1-7) c c 6800 hen < 1. 7, n he lnge is NOT gins roion n R > 0.4 l h l. = k, l =unrce lengh o lnge c c c. I he lnge is gins roion n., or he lnge is NOT gins roion n 1. 7, hen l l coniion 4 nee no e checke. (K1-1) & (K1-8) yc column yieling sress 5 I he orce is ue o e n live lo only P = (orce elivere y he lnge or momen connecion) (J8-1) I he orce is ue o e n live lo in conjuncion ih in or erhquke R ' 0.9 y P (AIC , Tex 675) 4 = (orce elivere y he lnge or momen connecion)

6 [pec K 1.8] (K1-9) hen hen A s R + m P, ih k l = 0. 75h (igure AD05.em) R < m= 1 R m= 5 yc ys ( + 5k) A s = ' ys =iener yieling sress

7 TRANVERE TIENER iuions When Trnsverse ieners Are Require (igure AD0.em) h When > 60 n 1.. >, sieners re require, such h v 60 h h * v v here v n <. 0 h * v = v h (5-1)

8 M N ' ' R R * k' k Bering ieners Ousie o he lnge connece o noher em or ering momen igure AD01.em igure AD0.em

9 h We her Yieling Trnsverse iener igure AD0.em Brce Brce We Crippling iesy We Buckling igure AD04.em

10 ieners m We lnge [pec K1.8] Minimum Are Requiremen or Bering ieners igure AD05.em

MTH 146 Class 11 Notes

MTH 146 Class 11 Notes 8.- Are of Surfce of Revoluion MTH 6 Clss Noes Suppose we wish o revolve curve C round n is nd find he surfce re of he resuling solid. Suppose f( ) is nonnegive funcion wih coninuous firs derivive on he

More information

twenty seven masonry construction: beams & columns Masonry Design Masonry Beam & Wall Design Masonry Design

twenty seven masonry construction: beams & columns Masonry Design Masonry Beam & Wall Design Masonry Design ELEENTS O ARCHITECTURAL STRUCTURES: OR, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SRING 017 lecure weny even monry conrucion: em & column onry Conrucion 1 www.heegle.com S009n onry Deign onry Snr Join Commiee

More information

PHYSICS 1210 Exam 1 University of Wyoming 14 February points

PHYSICS 1210 Exam 1 University of Wyoming 14 February points PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry 2013 150 poins This es is open-noe nd closed-book. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher

More information

Solutions to assignment 3

Solutions to assignment 3 D Sruure n Algorihm FR 6. Informik Sner, Telikeplli WS 03/04 hp://www.mpi-.mpg.e/~ner/oure/lg03/inex.hml Soluion o ignmen 3 Exerie Arirge i he ue of irepnie in urreny exhnge re o rnform one uni of urreny

More information

( ) ( ) ( ) ( ) ( ) ( y )

( ) ( ) ( ) ( ) ( ) ( y ) 8. Lengh of Plne Curve The mos fmous heorem in ll of mhemics is he Pyhgoren Theorem. I s formulion s he disnce formul is used o find he lenghs of line segmens in he coordine plne. In his secion you ll

More information

CS3510 Design & Analysis of Algorithms Fall 2017 Section A. Test 3 Solutions. Instructor: Richard Peng In class, Wednesday, Nov 15, 2017

CS3510 Design & Analysis of Algorithms Fall 2017 Section A. Test 3 Solutions. Instructor: Richard Peng In class, Wednesday, Nov 15, 2017 Uer ID (NOT he 9 igi numer): gurell4 CS351 Deign & Anlyi of Algorihm Fll 17 Seion A Te 3 Soluion Inruor: Rihr Peng In l, Weney, Nov 15, 17 Do no open hi quiz ookle unil you re iree o o o. Re ll he inruion

More information

Average & instantaneous velocity and acceleration Motion with constant acceleration

Average & instantaneous velocity and acceleration Motion with constant acceleration Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission

More information

e t dt e t dt = lim e t dt T (1 e T ) = 1

e t dt e t dt = lim e t dt T (1 e T ) = 1 Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie

More information

Flow Networks Alon Efrat Slides courtesy of Charles Leiserson with small changes by Carola Wenk. Flow networks. Flow networks CS 445

Flow Networks Alon Efrat Slides courtesy of Charles Leiserson with small changes by Carola Wenk. Flow networks. Flow networks CS 445 CS 445 Flow Nework lon Efr Slide corey of Chrle Leieron wih mll chnge by Crol Wenk Flow nework Definiion. flow nework i direced grph G = (V, E) wih wo diingihed erice: orce nd ink. Ech edge (, ) E h nonnegie

More information

PARABOLA. moves such that PM. = e (constant > 0) (eccentricity) then locus of P is called a conic. or conic section.

PARABOLA. moves such that PM. = e (constant > 0) (eccentricity) then locus of P is called a conic. or conic section. wwwskshieducioncom PARABOLA Le S be given fixed poin (focus) nd le l be given fixed line (Direcrix) Le SP nd PM be he disnce of vrible poin P o he focus nd direcrix respecively nd P SP moves such h PM

More information

Bipartite Matching. Matching. Bipartite Matching. Maxflow Formulation

Bipartite Matching. Matching. Bipartite Matching. Maxflow Formulation Mching Inpu: undireced grph G = (V, E). Biprie Mching Inpu: undireced, biprie grph G = (, E).. Mching Ern Myr, Hrld äcke Biprie Mching Inpu: undireced, biprie grph G = (, E). Mflow Formulion Inpu: undireced,

More information

September 20 Homework Solutions

September 20 Homework Solutions College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum

More information

M r. d 2. R t a M. Structural Mechanics Section. Exam CT5141 Theory of Elasticity Friday 31 October 2003, 9:00 12:00 hours. Problem 1 (3 points)

M r. d 2. R t a M. Structural Mechanics Section. Exam CT5141 Theory of Elasticity Friday 31 October 2003, 9:00 12:00 hours. Problem 1 (3 points) Delf Universiy of Technology Fculy of Civil Engineering nd Geosciences Srucurl echnics Secion Wrie your nme nd sudy numer he op righ-hnd of your work. Exm CT5 Theory of Elsiciy Fridy Ocoer 00, 9:00 :00

More information

Properties of Logarithms. Solving Exponential and Logarithmic Equations. Properties of Logarithms. Properties of Logarithms. ( x)

Properties of Logarithms. Solving Exponential and Logarithmic Equations. Properties of Logarithms. Properties of Logarithms. ( x) Properies of Logrihms Solving Eponenil nd Logrihmic Equions Properies of Logrihms Produc Rule ( ) log mn = log m + log n ( ) log = log + log Properies of Logrihms Quoien Rule log m = logm logn n log7 =

More information

SOME USEFUL MATHEMATICS

SOME USEFUL MATHEMATICS SOME USEFU MAHEMAICS SOME USEFU MAHEMAICS I is esy o mesure n preic he behvior of n elecricl circui h conins only c volges n currens. However, mos useful elecricl signls h crry informion vry wih ime. Since

More information

CSC 373: Algorithm Design and Analysis Lecture 9

CSC 373: Algorithm Design and Analysis Lecture 9 CSC 373: Algorihm Deign n Anlyi Leure 9 Alln Boroin Jnury 28, 2013 1 / 16 Leure 9: Announemen n Ouline Announemen Prolem e 1 ue hi Friy. Term Te 1 will e hel nex Mony, Fe in he uoril. Two nnounemen o follow

More information

Homework 2 Solutions

Homework 2 Solutions Mah 308 Differenial Equaions Fall 2002 & 2. See he las page. Hoework 2 Soluions 3a). Newon s secon law of oion says ha a = F, an we know a =, so we have = F. One par of he force is graviy, g. However,

More information

An object moving with speed v around a point at distance r, has an angular velocity. m/s m

An object moving with speed v around a point at distance r, has an angular velocity. m/s m Roion The mosphere roes wih he erh n moions wihin he mosphere clerly follow cure phs (cyclones, nicyclones, hurricnes, ornoes ec.) We nee o epress roion quniiely. For soli objec or ny mss h oes no isor

More information

f t f a f x dx By Lin McMullin f x dx= f b f a. 2

f t f a f x dx By Lin McMullin f x dx= f b f a. 2 Accumulion: Thoughs On () By Lin McMullin f f f d = + The gols of he AP* Clculus progrm include he semen, Sudens should undersnd he definie inegrl s he ne ccumulion of chnge. 1 The Topicl Ouline includes

More information

N H. be the number of living fish outside area H, and let C be the cumulative catch of fish. The behavior of N H

N H. be the number of living fish outside area H, and let C be the cumulative catch of fish. The behavior of N H ALTRNATV MODLS FOR CPU AND ABUNDANC Fishing is funamenally a localize process. Tha is, fishing gear operaing in a paricular geographic area canno cach fish ha are no in ha area. Here we will evelop wo

More information

ANALYSIS OF SECTION. Behaviour of Beam in Bending

ANALYSIS OF SECTION. Behaviour of Beam in Bending ANALYSIS OF SECTION Behaviour o Beam in Bening Conier a imply upporte eam ujecte to graually increaing loa. The loa caue the eam to en an eert a ening moment a hown in igure elow. The top urace o the eam

More information

Flow networks. Flow Networks. A flow on a network. Flow networks. The maximum-flow problem. Introduction to Algorithms, Lecture 22 December 5, 2001

Flow networks. Flow Networks. A flow on a network. Flow networks. The maximum-flow problem. Introduction to Algorithms, Lecture 22 December 5, 2001 CS 545 Flow Nework lon Efra Slide courey of Charle Leieron wih mall change by Carola Wenk Flow nework Definiion. flow nework i a direced graph G = (V, E) wih wo diinguihed verice: a ource and a ink. Each

More information

Example 1. Examples for walls are available on our Web page: Columns

Example 1. Examples for walls are available on our Web page:   Columns Portlan Cement Association Page 1 o 9 Te ollowing examples illustrate te esign metos presente in te article Timesaving Design Ais or Reinorce Concrete, Part 3: an Walls, by Davi A. Fanella, wic appeare

More information

And I Saw a New Heaven

And I Saw a New Heaven n I Sw New Heven NTHEM For Choir (STB) n Orgn John Kilprik 2008 John Kilprik This work my freely uplie, performe n reore. Copies shoul no sol exep o over prining oss. rev: 06/03/2010 prin: 02/07/2013 2

More information

Location is relative. Coordinate Systems. Which of the following can be described with vectors??

Location is relative. Coordinate Systems. Which of the following can be described with vectors?? Locion is relive Coordine Sysems The posiion o hing is sed relive o noher hing (rel or virul) review o he physicl sis h governs mhemicl represenions Reerence oec mus e deined Disnce mus e nown Direcion

More information

Algorithms and Data Structures 2011/12 Week 9 Solutions (Tues 15th - Fri 18th Nov)

Algorithms and Data Structures 2011/12 Week 9 Solutions (Tues 15th - Fri 18th Nov) Algorihm and Daa Srucure 2011/ Week Soluion (Tue 15h - Fri 18h No) 1. Queion: e are gien 11/16 / 15/20 8/13 0/ 1/ / 11/1 / / To queion: (a) Find a pair of ube X, Y V uch ha f(x, Y) = f(v X, Y). (b) Find

More information

MIXED BOUNDARY VALUE PROBLEM FOR A QUARTER-PLANE WITH A ROBIN CONDITION

MIXED BOUNDARY VALUE PROBLEM FOR A QUARTER-PLANE WITH A ROBIN CONDITION Jornal o Science, Ilamic Repblic o Iran 3: 65-69 Naional Cener For Scieniic Reearch, ISSN 6-4 MIXED OUNDRY VLUE PROLEM FOR QURTER-PLNE WITH ROIN CONDITION ghili * Deparmen o Mahemaic, Facl o Science, Gilan

More information

And I Saw a New Heaven

And I Saw a New Heaven n Sw New Heven NTHEM For Choir (STB) n Orgn John Kilprik (VERSON FOR KEYBORD) 2008 John Kilprik This work my freely uplie, performe n reore. Copies shoul sol exep o over prining oss. rev: 23/08/2010 prin:

More information

More on Magnetically C Coupled Coils and Ideal Transformers

More on Magnetically C Coupled Coils and Ideal Transformers Appenix ore on gneiclly C Couple Coils Iel Trnsformers C. Equivlen Circuis for gneiclly Couple Coils A imes, i is convenien o moel mgneiclly couple coils wih n equivlen circui h oes no involve mgneic coupling.

More information

Version 001 test-1 swinney (57010) 1. is constant at m/s.

Version 001 test-1 swinney (57010) 1. is constant at m/s. Version 001 es-1 swinne (57010) 1 This prin-ou should hve 20 quesions. Muliple-choice quesions m coninue on he nex column or pge find ll choices before nswering. CubeUniVec1x76 001 10.0 poins Acubeis1.4fee

More information

DC Miniature Solenoids KLM Varioline

DC Miniature Solenoids KLM Varioline DC Miniure Solenoi KLM Vrioline DC Miniure Solenoi Type KLM Deign: Single roke olenoi pulling n puhing, oule roke n invere roke ype. Snr: Zinc ple (opionl: pine / nickel ple) Fixing: Cenrl or flnge mouning.

More information

Characteristic Function for the Truncated Triangular Distribution., Myron Katzoff and Rahul A. Parsa

Characteristic Function for the Truncated Triangular Distribution., Myron Katzoff and Rahul A. Parsa Secion on Survey Reserch Mehos JSM 009 Chrcerisic Funcion for he Trunce Tringulr Disriuion Jy J. Kim 1 1, Myron Kzoff n Rhul A. Prs 1 Nionl Cener for Helh Sisics, 11Toleo Ro, Hysville, MD. 078 College

More information

DESIGN OF TENSION MEMBERS

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

More information

Transformations. Ordered set of numbers: (1,2,3,4) Example: (x,y,z) coordinates of pt in space. Vectors

Transformations. Ordered set of numbers: (1,2,3,4) Example: (x,y,z) coordinates of pt in space. Vectors Trnformion Ordered e of number:,,,4 Emple:,,z coordine of p in pce. Vecor If, n i i, K, n, i uni ecor Vecor ddiion +w, +, +, + V+w w Sclr roduc,, Inner do roduc α w. w +,.,. The inner produc i SCLR!. w,.,

More information

P441 Analytical Mechanics - I. Coupled Oscillators. c Alex R. Dzierba

P441 Analytical Mechanics - I. Coupled Oscillators. c Alex R. Dzierba Lecure 3 Mondy - Deceber 5, 005 Wrien or ls upded: Deceber 3, 005 P44 Anlyicl Mechnics - I oupled Oscillors c Alex R. Dzierb oupled oscillors - rix echnique In Figure we show n exple of wo coupled oscillors,

More information

Longitudinal Strength Standard. S11 (cont) S11

Longitudinal Strength Standard. S11 (cont) S11 (1989) (Rev.1 199) (Rev. Nov 001) (Rev. June 00) (Rev.4 July 004) (Rev.5 Jn 006) (Rev.6 My 0) Longiudinl Srengh Sndrd.1 Applicion This requiremen pplies only o seel ships of lengh 90 m nd greer in unresriced

More information

Physics Notes - Ch. 2 Motion in One Dimension

Physics Notes - Ch. 2 Motion in One Dimension Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,

More information

A LOG IS AN EXPONENT.

A LOG IS AN EXPONENT. Ojeives: n nlze nd inerpre he ehvior of rihmi funions, inluding end ehvior nd smpoes. n solve rihmi equions nlill nd grphill. n grph rihmi funions. n deermine he domin nd rnge of rihmi funions. n deermine

More information

Jonathan Turner Exam 2-10/28/03

Jonathan Turner Exam 2-10/28/03 CS Algorihm n Progrm Prolm Exm Soluion S Soluion Jonhn Turnr Exm //. ( poin) In h Fioni hp ruur, u wn vrx u n i prn v u ing u v i v h lry lo hil in i l m hil o om ohr vrx. Suppo w hng hi, o h ing u i prorm

More information

Physics 240: Worksheet 16 Name

Physics 240: Worksheet 16 Name Phyic 4: Workhee 16 Nae Non-unifor circular oion Each of hee proble involve non-unifor circular oion wih a conan α. (1) Obain each of he equaion of oion for non-unifor circular oion under a conan acceleraion,

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

How to Prove the Riemann Hypothesis Author: Fayez Fok Al Adeh.

How to Prove the Riemann Hypothesis Author: Fayez Fok Al Adeh. How o Prove he Riemnn Hohesis Auhor: Fez Fok Al Adeh. Presiden of he Srin Cosmologicl Socie P.O.Bo,387,Dmscus,Sri Tels:963--77679,735 Emil:hf@scs-ne.org Commens: 3 ges Subj-Clss: Funcionl nlsis, comle

More information

Temperature Rise of the Earth

Temperature Rise of the Earth Avilble online www.sciencedirec.com ScienceDirec Procedi - Socil nd Behviorl Scien ce s 88 ( 2013 ) 220 224 Socil nd Behviorl Sciences Symposium, 4 h Inernionl Science, Socil Science, Engineering nd Energy

More information

ME 141. Engineering Mechanics

ME 141. Engineering Mechanics ME 141 Engineeing Mechnics Lecue 13: Kinemics of igid bodies hmd Shhedi Shkil Lecue, ep. of Mechnicl Engg, UET E-mil: sshkil@me.bue.c.bd, shkil6791@gmil.com Websie: eche.bue.c.bd/sshkil Couesy: Veco Mechnics

More information

Section P.1 Notes Page 1 Section P.1 Precalculus and Trigonometry Review

Section P.1 Notes Page 1 Section P.1 Precalculus and Trigonometry Review Secion P Noe Pge Secion P Preclculu nd Trigonomer Review ALGEBRA AND PRECALCULUS Eponen Lw: Emple: 8 Emple: Emple: Emple: b b Emple: 9 EXAMPLE: Simplif: nd wrie wi poiive eponen Fir I will flip e frcion

More information

ECE Microwave Engineering. Fall Prof. David R. Jackson Dept. of ECE. Notes 10. Waveguides Part 7: Transverse Equivalent Network (TEN)

ECE Microwave Engineering. Fall Prof. David R. Jackson Dept. of ECE. Notes 10. Waveguides Part 7: Transverse Equivalent Network (TEN) EE 537-635 Microwve Engineering Fll 7 Prof. Dvid R. Jcson Dep. of EE Noes Wveguides Pr 7: Trnsverse Equivlen Newor (N) Wveguide Trnsmission Line Model Our gol is o come up wih rnsmission line model for

More information

FM Applications of Integration 1.Centroid of Area

FM Applications of Integration 1.Centroid of Area FM Applicions of Inegrion.Cenroid of Are The cenroid of ody is is geomeric cenre. For n ojec mde of uniform meril, he cenroid coincides wih he poin which he ody cn e suppored in perfecly lnced se ie, is

More information

The solution is often represented as a vector: 2xI + 4X2 + 2X3 + 4X4 + 2X5 = 4 2xI + 4X2 + 3X3 + 3X4 + 3X5 = 4. 3xI + 6X2 + 6X3 + 3X4 + 6X5 = 6.

The solution is often represented as a vector: 2xI + 4X2 + 2X3 + 4X4 + 2X5 = 4 2xI + 4X2 + 3X3 + 3X4 + 3X5 = 4. 3xI + 6X2 + 6X3 + 3X4 + 6X5 = 6. [~ o o :- o o ill] i 1. Mrices, Vecors, nd Guss-Jordn Eliminion 1 x y = = - z= The soluion is ofen represened s vecor: n his exmple, he process of eliminion works very smoohly. We cn elimine ll enries

More information

Contraction Mapping Principle Approach to Differential Equations

Contraction Mapping Principle Approach to Differential Equations epl Journl of Science echnology 0 (009) 49-53 Conrcion pping Principle pproch o Differenil Equions Bishnu P. Dhungn Deprmen of hemics, hendr Rn Cmpus ribhuvn Universiy, Khmu epl bsrc Using n eension of

More information

Addition & Subtraction of Polynomials

Addition & Subtraction of Polynomials Addiion & Sucion of Polynomil Addiion of Polynomil: Adding wo o moe olynomil i imly me of dding like em. The following ocedue hould e ued o dd olynomil 1. Remove enhee if hee e enhee. Add imil em. Wie

More information

Theme 6 Shearing stress in bending

Theme 6 Shearing stress in bending Elasici and plasici Theme 6 Shearing sress in bending Basic relaionships and condiions o soluions Shearing sress in chosen cross-secions Dimension o members in shear Shear lux and shear cenre Composie

More information

This UR does not apply to CSR Bulk Carriers and Oil Tankers or to container ships to which UR S11A is applicable.

This UR does not apply to CSR Bulk Carriers and Oil Tankers or to container ships to which UR S11A is applicable. (1989) (Rev.1 199) (Rev. Nov 001) (Rev. June 00) (Rev.4 July 004) (Rev.5 Jn 006) (Rev.6 My 0) (Rev.7 Nov 0) (Rev.8 June 015) Longiudinl Srengh Sndrd.1 Applicion This requiremen pplies only o seel ships

More information

Lecture 2: Network Flow. c 14

Lecture 2: Network Flow. c 14 Comp 260: Avne Algorihms Tufs Universiy, Spring 2016 Prof. Lenore Cowen Srie: Alexner LeNil Leure 2: Nework Flow 1 Flow Neworks s 16 12 13 10 4 20 14 4 Imgine some nework of pipes whih rry wer, represene

More information

Released Assessment Questions, 2017 QUESTIONS

Released Assessment Questions, 2017 QUESTIONS Relese Assessmen Quesions, 17 QUESTIONS Gre 9 Assessmen of Mhemis Aemi Re he insruions elow. Along wih his ookle, mke sure ou hve he Answer Bookle n he Formul Shee. You m use n spe in his ook for rough

More information

Graduate Algorithms CS F-18 Flow Networks

Graduate Algorithms CS F-18 Flow Networks Grue Algorihm CS673-2016F-18 Flow Nework Dvi Glle Deprmen of Compuer Siene Univeriy of Sn Frnio 18-0: Flow Nework Diree Grph G Eh ege weigh i piy Amoun of wer/eon h n flow hrough pipe, for inne Single

More information

Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals

Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals Sud. Univ. Beş-Bolyi Mh. 6(5, No. 3, 355 366 Hermie-Hdmrd-Fejér ype inequliies for convex funcions vi frcionl inegrls İmd İşcn Asrc. In his pper, firsly we hve eslished Hermie Hdmrd-Fejér inequliy for

More information

Maximum Flow. Flow Graph

Maximum Flow. Flow Graph Mximum Flow Chper 26 Flow Grph A ommon enrio i o ue grph o repreen flow nework nd ue i o nwer queion ou meril flow Flow i he re h meril move hrough he nework Eh direed edge i ondui for he meril wih ome

More information

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218 Chper Moion long srigh line 9/9/05 Physics 8 Gols for Chper How o describe srigh line moion in erms of displcemen nd erge elociy. The mening of insnneous elociy nd speed. Aerge elociy/insnneous elociy

More information

ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 2

ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 2 ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER Seion Eerise -: Coninuiy of he uiliy funion Le λ ( ) be he monooni uiliy funion defined in he proof of eisene of uiliy funion If his funion is oninuous y hen

More information

ARCH 614 Note Set 5 S2012abn. Moments & Supports

ARCH 614 Note Set 5 S2012abn. Moments & Supports RCH 614 Note Set 5 S2012abn Moments & Supports Notation: = perpenicular istance to a force from a point = name for force vectors or magnitue of a force, as is P, Q, R x = force component in the x irection

More information

Admin MAX FLOW APPLICATIONS. Flow graph/networks. Flow constraints 4/30/13. CS lunch today Grading. in-flow = out-flow for every vertex (except s, t)

Admin MAX FLOW APPLICATIONS. Flow graph/networks. Flow constraints 4/30/13. CS lunch today Grading. in-flow = out-flow for every vertex (except s, t) /0/ dmin lunch oday rading MX LOW PPLIION 0, pring avid Kauchak low graph/nework low nework direced, weighed graph (V, ) poiive edge weigh indicaing he capaciy (generally, aume ineger) conain a ingle ource

More information

Mathcad Lecture #4 In-class Worksheet Vectors and Matrices 1 (Basics)

Mathcad Lecture #4 In-class Worksheet Vectors and Matrices 1 (Basics) Mh Lr # In-l Workh Vor n Mri (Bi) h n o hi lr, o hol l o: r mri n or in Mh i mri prorm i mri mh oprion ol m o linr qion ing mri mh. Cring Mri Thr r rl o r mri. Th "Inr Mri" Wino (M) B K Poin Rr o

More information

The Covenant Renewed. Family Journal Page. creation; He tells us in the Bible.)

The Covenant Renewed. Family Journal Page. creation; He tells us in the Bible.) i ell orie o go ih he picure. L, up ng i gro ve el ur Pren, ho phoo picure; u oher ell ee hey (T l. chi u b o on hi pge y ur ki kn pl. (We ee Hi i H b o b o kn e hem orie.) Compre h o ho creion; He ell

More information

CALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION

CALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION Avilble online hp://scik.org Eng. Mh. Le. 15, 15:4 ISSN: 49-9337 CALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION PANDEY, C. P. 1, RAKESH MOHAN AND BHAIRAW NATH TRIPATHI 3 1 Deprmen o Mhemics, Ajy

More information

0 for t < 0 1 for t > 0

0 for t < 0 1 for t > 0 8.0 Sep nd del funcions Auhor: Jeremy Orloff The uni Sep Funcion We define he uni sep funcion by u() = 0 for < 0 for > 0 I is clled he uni sep funcion becuse i kes uni sep = 0. I is someimes clled he Heviside

More information

3.3 Internal Stress. Cauchy s Concept of Stress

3.3 Internal Stress. Cauchy s Concept of Stress INTERNL TRE 3.3 Inernal ress The idea of sress considered in 3.1 is no difficul o concepualise since objecs ineracing wih oher objecs are encounered all around us. more difficul concep is he idea of forces

More information

Physics Worksheet Lesson 4: Linear Motion Section: Name:

Physics Worksheet Lesson 4: Linear Motion Section: Name: Physics Workshee Lesson 4: Liner Moion Secion: Nme: 1. Relie Moion:. All moion is. b. is n rbirry coorine sysem wih reference o which he posiion or moion of somehing is escribe or physicl lws re formule.

More information

Soviet Rail Network, 1955

Soviet Rail Network, 1955 7.1 Nework Flow Sovie Rail Nework, 19 Reerence: On he hiory o he ranporaion and maximum low problem. lexander Schrijver in Mah Programming, 91: 3, 00. (See Exernal Link ) Maximum Flow and Minimum Cu Max

More information

A LIMIT-POINT CRITERION FOR A SECOND-ORDER LINEAR DIFFERENTIAL OPERATOR IAN KNOWLES

A LIMIT-POINT CRITERION FOR A SECOND-ORDER LINEAR DIFFERENTIAL OPERATOR IAN KNOWLES A LIMIT-POINT CRITERION FOR A SECOND-ORDER LINEAR DIFFERENTIAL OPERATOR j IAN KNOWLES 1. Inroducion Consider he forml differenil operor T defined by el, (1) where he funcion q{) is rel-vlued nd loclly

More information

How to prove the Riemann Hypothesis

How to prove the Riemann Hypothesis Scholrs Journl of Phsics, Mhemics nd Sisics Sch. J. Phs. Mh. S. 5; (B:5-6 Scholrs Acdemic nd Scienific Publishers (SAS Publishers (An Inernionl Publisher for Acdemic nd Scienific Resources *Corresonding

More information

Relation between Fourier Series and Transform

Relation between Fourier Series and Transform EE 37-3 8 Ch. II: Inro. o Sinls Lcur 5 Dr. Wih Abu-Al-Su Rlion bwn ourir Sris n Trnsform Th ourir Trnsform T is riv from h finiion of h ourir Sris S. Consir, for xmpl, h prioic complx sinl To wih prio

More information

Some Inequalities variations on a common theme Lecture I, UL 2007

Some Inequalities variations on a common theme Lecture I, UL 2007 Some Inequliies vriions on common heme Lecure I, UL 2007 Finbrr Hollnd, Deprmen of Mhemics, Universiy College Cork, fhollnd@uccie; July 2, 2007 Three Problems Problem Assume i, b i, c i, i =, 2, 3 re rel

More information

Chapter 10. Simple Harmonic Motion and Elasticity. Goals for Chapter 10

Chapter 10. Simple Harmonic Motion and Elasticity. Goals for Chapter 10 Chper 0 Siple Hronic Moion nd Elsiciy Gols or Chper 0 o ollow periodic oion o sudy o siple hronic oion. o sole equions o siple hronic oion. o use he pendulu s prooypicl syse undergoing siple hronic oion.

More information

Page 1 o 13 1. The brighes sar in he nigh sky is α Canis Majoris, also known as Sirius. I lies 8.8 ligh-years away. Express his disance in meers. ( ligh-year is he disance coered by ligh in one year. Ligh

More information

Homework Solution - Set 5 Due: Friday 10/03/08

Homework Solution - Set 5 Due: Friday 10/03/08 CE 96 Introduction to the Theory of Computtion ll 2008 Homework olution - et 5 Due: ridy 10/0/08 1. Textook, Pge 86, Exercise 1.21. () 1 2 Add new strt stte nd finl stte. Mke originl finl stte non-finl.

More information

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 36 3 1!!!!!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!" 1 1 3 3 1. 401331. 610000 3. 610000!!!!!!", ( ),,,,,,, ; ; ; ; ; TE973.6 A 100106 (010) 0300104 0 D /m; β

More information

H SERIES. Algebra Basics. Algebra Basics. Solutions. Curriculum Ready.

H SERIES. Algebra Basics. Algebra Basics. Solutions. Curriculum Ready. Alger Bsis H SERIES Alger Bsis Curriulum Rey www.mthletis.om Copyright 009 P Lerning. All rights reserve. First eition printe 009 in Austrli. A tlogue reor for this ook is ville from P Lerning Lt. ISBN

More information

Computer-Aided Analysis of Electronic Circuits Course Notes 3

Computer-Aided Analysis of Electronic Circuits Course Notes 3 Gheorghe Asachi Technical Universiy of Iasi Faculy of Elecronics, Telecommunicaions and Informaion Technologies Compuer-Aided Analysis of Elecronic Circuis Course Noes 3 Bachelor: Telecommunicaion Technologies

More information

June Further Pure Mathematics FP2 Mark Scheme

June Further Pure Mathematics FP2 Mark Scheme Jne 75 Frher Pre Mheis FP Mrk Shee. e e e e 5 e e 7 M: Siplify o for qri in e ( e )(e 7) e, e 7 M: Solve er qri. ln or ln ln 7 B M A M A A () Mrks. () Using ( e ) or eqiv. o fin e or e: ( = n = ) M A e

More information

twenty four masonry construction: beams & columns Office Hours Masonry Beam & Wall Design Masonry Design Masonry Standards Joint Committee

twenty four masonry construction: beams & columns Office Hours Masonry Beam & Wall Design Masonry Design Masonry Standards Joint Committee ARCHITECTURAL STRUCTURES: FOR, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUER 013 lecure weny our Oice Hour link o poed chedule onry conrucion: e & colun www.u.edu onry Conrucion 1 Lecure 4 Archiecurl Srucure

More information

Type SEK 105 ºC Radial Leaded Aluminum Electrolytic Capacitors

Type SEK 105 ºC Radial Leaded Aluminum Electrolytic Capacitors Type SEK 5 ºC Raial Leae luminum Elecrolyic Capaciors Long Life, luminum Elecrolyic Specificaions Type SEK is a raial leae aluminum elecrolyic capacior wih a +5 º C, long life raing. The volumeic efficien

More information

LAPLACE TRANSFORMS. 1. Basic transforms

LAPLACE TRANSFORMS. 1. Basic transforms LAPLACE TRANSFORMS. Bic rnform In hi coure, Lplce Trnform will be inroduced nd heir properie exmined; ble of common rnform will be buil up; nd rnform will be ued o olve ome dierenil equion by rnforming

More information

Theme 8 Stability and buckling of members

Theme 8 Stability and buckling of members Elsticity nd plsticity Theme 8 Stility nd uckling o memers Euler s solution o stility o n xilly compressed stright elstic memer Deprtment o Structurl Mechnics culty o Civil Engineering, VSB - Technicl

More information

AN ANALYTICAL TOOL TO PREDICT LOAD DISTRIBUTION OF MULTI-BOLT SINGLE-LAP THICK LAMINATE JOINTS

AN ANALYTICAL TOOL TO PREDICT LOAD DISTRIBUTION OF MULTI-BOLT SINGLE-LAP THICK LAMINATE JOINTS 8 TH INTERNATIONAL CONERENCE ON COMOITE MATERIAL AN ANALYTICAL TOOL TO REDICT LOAD DITRIBUTION O MULTI-BOLT INGLE-LA THIC LAMINATE JOINT Longqun Liu*, Ying Mo, Rn Wei chool of Aeronuics nd Asronuics, hnghi

More information

ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX.

ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX. ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX. MEHMET ZEKI SARIKAYA?, ERHAN. SET, AND M. EMIN OZDEMIR Asrc. In his noe, we oin new some ineuliies

More information

Network Flows: Introduction & Maximum Flow

Network Flows: Introduction & Maximum Flow CSC 373 - lgorihm Deign, nalyi, and Complexiy Summer 2016 Lalla Mouaadid Nework Flow: Inroducion & Maximum Flow We now urn our aenion o anoher powerful algorihmic echnique: Local Search. In a local earch

More information

Crash course in interpretting NMR spectra for lab. NMR = the workhorse of characterization tools reveals connectivity & alkyl chains

Crash course in interpretting NMR spectra for lab. NMR = the workhorse of characterization tools reveals connectivity & alkyl chains EM 222 secion 01 rash course in inerpreing NM specra for lab NM = he workhorse of characerizaion ools reveals conneciviy & chains For a basic overview of NM (o help inerpre specra): - rea hese summary

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

Mathematics 805 Final Examination Answers

Mathematics 805 Final Examination Answers . 5 poins Se he Weiersrss M-es. Mhemics 85 Finl Eminion Answers Answer: Suppose h A R, nd f n : A R. Suppose furher h f n M n for ll A, nd h Mn converges. Then f n converges uniformly on A.. 5 poins Se

More information

Research Article New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals

Research Article New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals Hindwi Pulishing orporion Inernionl Journl of Anlysis, Aricle ID 35394, 8 pges hp://d.doi.org/0.55/04/35394 Reserch Aricle New Generl Inegrl Inequliies for Lipschizin Funcions vi Hdmrd Frcionl Inegrls

More information

Seminar 5 Sustainability

Seminar 5 Sustainability Seminar 5 Susainabiliy Soluions Quesion : Hyperbolic Discouning -. Suppose a faher inheris a family forune of 0 million NOK an he wans o use some of i for himself (o be precise, he share ) bu also o beques

More information

BUCKLING OF FRP BEAMS AND COLUMNS

BUCKLING OF FRP BEAMS AND COLUMNS BUCKLIG OF FRP BEMS D COLUMS Lásló Kollár n Ákos Spkás Bupes Universi o Technolog n Economics, Deprmens o Mechnics, Merils n Srucures BSTRCT The pper presens he sbili nlsis o hin lle n close oss secion

More information

The Forming Theory and Computer Simulation of the Rotary Cutting Tools with Helical Teeth and Complex Surfaces

The Forming Theory and Computer Simulation of the Rotary Cutting Tools with Helical Teeth and Complex Surfaces Compuer nd Informion Siene The Forming Theory nd Compuer Simulion of he Rory Cuing Tools wih Helil Teeh nd Comple Surfes Hurn Liu Deprmen of Mehnil Engineering Zhejing Universiy of Siene nd Tehnology Hngzhou

More information

Physics 218 Exam 1. with Solutions Fall 2010, Sections Part 1 (15) Part 2 (20) Part 3 (20) Part 4 (20) Bonus (5)

Physics 218 Exam 1. with Solutions Fall 2010, Sections Part 1 (15) Part 2 (20) Part 3 (20) Part 4 (20) Bonus (5) Physics 18 Exam 1 wih Soluions Fall 1, Secions 51-54 Fill ou he informaion below bu o no open he exam unil insruce o o so! Name Signaure Suen ID E-mail Secion # ules of he exam: 1. You have he full class

More information

3 Motion with constant acceleration: Linear and projectile motion

3 Motion with constant acceleration: Linear and projectile motion 3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr

More information

Mathematical Notation Math Calculus & Analytic Geometry I

Mathematical Notation Math Calculus & Analytic Geometry I Mthemticl Nottio Mth - Clculus & Alytic Geometry I Nme : Use Wor or WorPerect to recrete the ollowig ocumets. Ech rticle is worth poits c e prite give to the istructor or emile to the istructor t jmes@richl.eu.

More information

rank Additionally system of equation only independent atfect Gawp (A) possible ( Alb ) easily process form rang A. Proposition with Definition

rank Additionally system of equation only independent atfect Gawp (A) possible ( Alb ) easily process form rang A. Proposition with Definition Defiion nexivnol numer ler dependen rows mrix sid row Gwp elimion mehod does no fec h numer end process i possile esily red rng fc for mrix form der zz rn rnk wih m dcussion i holds rr o Proposiion ler

More information

1.B Appendix to Chapter 1

1.B Appendix to Chapter 1 Secon.B.B Append o Chper.B. The Ordnr Clcl Here re led ome mporn concep rom he ordnr clcl. The Dervve Conder ncon o one ndependen vrble. The dervve o dened b d d lm lm.b. where he ncremen n de o n ncremen

More information

STRUNET CONCRETE DESIGN AIDS

STRUNET CONCRETE DESIGN AIDS Introtion to Conrete Bem Deign Flow Chrt The onrete em eign low hrt re the ollowing jet: For retnglr em with given imenion: Anlzing the em etion to etere it moment trength n th eining the em etion to e

More information

Coefficient Inequalities for Certain Subclasses. of Analytic Functions

Coefficient Inequalities for Certain Subclasses. of Analytic Functions I. Jourl o Mh. Alysis, Vol., 00, o. 6, 77-78 Coeiie Iequliies or Ceri Sulsses o Alyi Fuios T. Rm Reddy d * R.. Shrm Deprme o Mhemis, Kkiy Uiversiy Wrgl 506009, Adhr Prdesh, Idi reddyr@yhoo.om, *rshrm_005@yhoo.o.i

More information