Chapter 10: Failure. Titanic on April 15, 1912 ISSUES TO ADDRESS. Failure Modes:
|
|
- Γαλήνη Αναγνωστάκης
- 5 χρόνια πριν
- Προβολές:
Transcript
1 Chapter10:Failure ISSUESTOADDRESS FailureModes: 1 LECTURER: PROF. SEUNGTAE CHOI TitaniconApril15, 1912 RMS Titanic was a British passenger liner that sank in the North Atlantic Ocean on 15 April 1912 after colliding with an iceberg during her maiden voyage from Southampton, UK to New York City, US. The sinking of Titanic caused the deaths of 1,502 people in one of the deadliest peacetime maritime disasters in history. ( 2 LECTURER: PROF. SEUNGTAE CHOI
2 10.3DuctileFracture(Rupture) Classificationoffracturebehavior Callister &Rethwisch 9e. AR EL 3 LECTURER: PROF. SEUNGTAE CHOI ModeratelyDuctileFracture(Rupture) Stagesinthecupandconefracture Callister &Rethwisch 9e. Analysisof MetallurgicalFailures 4 LECTURER: PROF. SEUNGTAE CHOI
3 10.4 Brittle Fracture Brittle Fracture I. Transgranular Fracture (Cleavage Fracture) 5 Ǥ ͳͳǥ ǡ Callister & Rethwisch 9e. LECTURER: PROF. SEUNGTAE CHOI II. Intergranular Fracture II. Intergranular Fracture: Ǥ Ǥ ͳǥ ʹǤ Ǥ Ǥ ͳͳǥ ǡ Callister & Rethwisch 9e. 6 LECTURER: PROF. SEUNGTAE CHOI
4 10.5PrincipleofFractureMechanics AnAtomicViewofFracture Bonding energy: E b Pdx x0 Interatomic force-displacement relation: x P Pc sin For small displacements, forcedisplacement relationship is linear: x Pc cx0 PPc kx, where k= E= E c Surface energy: 1 x sin dx 2 0 Es c x s c c 7 LECTURER: PROF. SEUNGTAE CHOI 0 StressConcentrationEffectofFlows StressconcentrationaroundanellipticholebyC.E.Inglis (1913) x a y b b a x 2 MAX a yy (A) b a a a 2 0 a 0 b A a x Theaboveequationshowthatasb 0(theellipsebecomesacrack)astress singularity( ~1/r) developsatthecracktip. 8 LECTURER: PROF. SEUNGTAE CHOI
5 StressAnalysisofCracks ThreeModesofFracture Stressfieldsnearacracktip K m I I KII II KIII III 2 (m) f( ) f( ) f ( ) Amr g ( ) 2r 2r 2r m0 I I II III : stress tensor K : Mode I stress intensity factor K : Mode II stress intensity factor K : Mode III stress intensity factor II III f,f, and f : dimensionless functions of 9 LECTURER: PROF. SEUNGTAE CHOI StressFieldsnearaCrackTip Stressfieldsnearacracktip 1sin 2 sin K I 22 cos 2 1 sin 2 sin 3 2 2r 12 sin 2 cos 3 2 sin 2 2 cos 2 cos K II 22 sin 2 cos 2 cos 3 2 2r 12 cos 2 1 sin 2 sin K sin 2 III 32 2r cos 2 K I: Mode I stress intensity factor K II: Mode II stress intensity factor K III: Mode III stress intensity factor 10 LECTURER: PROF. SEUNGTAE CHOI
6 DesignCriteria Stressapproach : applied stress : ultimate stregth u u Fracturemechanics approach K I K IC KI: stress intensity factor (SIF) calculated value due to loading KIC: fracture toughness material property yy KI 2r r 11 LECTURER: PROF. SEUNGTAE CHOI ExamplesofStressIntensityFactors Acenteredcrackinaninfiniteplate: underuniformuniaxialstress Apennyshapedcrackinaninfinite domain KI a a KI 2 12 LECTURER: PROF. SEUNGTAE CHOI
7 ElasticEnergy Strainenergydensity: u d 0 Internalenergyofadeformablebody: U udv d dv V V 0 Linearelasticmaterials(Hooke slaw): 1 kk or 2 kk E E ( and:lamé constant) Strainenergydensityoflinearelasticmaterials: 1 u d 0 2 Internalenergyoflinearelasticmaterials: V 1 U d dv dv 0 2 V 13 LECTURER: PROF. SEUNGTAE CHOI ConservationofEnergy 14 LECTURER: PROF. SEUNGTAE CHOI
8 EnergyBalanceDuringCrackGrowth Thefirstlawofthermodynamics(Lawofconservationofenergy) W U U E P E P W : Work done by the applied load U : Elastic energy U : Plastic energy : Surface energy Applied traction A A t A t A a 2a a U A A A P E where =U W Thereductionofpotentialenergyisequaltotheenergydissipatedinplastic workandsurfacecreation. Forbrittlematerials,U P 0. 2 A A S 15 LECTURER: PROF. SEUNGTAE CHOI GriffithEnergyBalance Griffith(1920)usedthestressanalysisofInglis (1913)toshow ab a 0 E A E 4aBS 2S A Griffithfracturestress a 2a a f 2E S a 12 B ModifiedGriffithfracturestress f 2E( P S) a 12 P : plastic work per unit area of surface 16 LECTURER: PROF. SEUNGTAE CHOI
9 EnergyReleaseRate Energyreleaserate,G:Ameasureofthe energyavailableforanincrementofcrack extension(irwin,1948) A Itisalsocalledthecrackextensionforceor thecrackdrivingforce. FromtheGriffithenergybalance,thecrack extensionoccurswheng reachesacritical value,i.e., 2 a c 2 S, A E A whereg c isameasureofthefracture toughnessofthematerial. 17 LECTURER: PROF. SEUNGTAE CHOI 10.6FractureToughnessTesting Standard:ASTME399,D5045 Specimen:CompactTension(CT) Calculation K PQ fx BW IC 1/ 2 K IC :Fracturetoughness P Q :Criticalload f(x)= 8.34 atx= atx= atx=0.55 x=a/w,(0.45<x<0.55) K IC B, a 2.5 yield 2 18 LECTURER: PROF. SEUNGTAE CHOI
10 PlasticEffectonCrackTip Yielding zone size: r y 1 K I 2 y 2 Plastic zone size ry rp r 2 1 K I rp 2r y for plane stress y 2 1 K I rp 2r y for plane strain 3 y Ductile fracture : sufficient plastic deformation before fracture Brittle fracture : small plastic deformation before fracture 19 LECTURER: PROF. SEUNGTAE CHOI 3DAspectsofPlasticZone 20 LECTURER: PROF. SEUNGTAE CHOI
11 VariationofK C withspecimenthickness K C Plane stress Transition region Plane strain K IC Specimen thickness 21 LECTURER: PROF. SEUNGTAE CHOI FractureToughnessRanges K IC (MPam 0.5 ) Callister&Rethwisch 9e. ASMHandbook FractureMechanics ofceramics Ceram.Eng.Sci.Proc. 22 LECTURER: PROF. SEUNGTAE CHOI
12 ImpactTesting Impactloading: final height Callister&Rethwisch 9e. TheStructureandPropertiesof MaterialsMechanicalBehavior initial height 23 LECTURER: PROF. SEUNGTAE CHOI InfluenceofTemperatureonImpactEnergy DuctiletoBrittleTransitionTemperature(DBTT)... T y E Callister&Rethwisch 9e. 24 LECTURER: PROF. SEUNGTAE CHOI
13 LibertyShipduringWorldWarII 25 LECTURER: PROF. SEUNGTAE CHOI LibertyShipduringWorldWarII JohnP.Gaines EmpireDuke 26 LECTURER: PROF. SEUNGTAE CHOI
14 Patterning by Controlled Cracking K. H. Nam, I. H. Park, & S. H. Ko, Patterning by controlled cracking, Nature, Vol. 485, pp , LECTURER: PROF. SEUNGTAE CHOI Fragmentation of Ice in the Arctic Ocean 28 LECTURER: PROF. SEUNGTAE CHOI
15 10.7CyclicStressesFatigue Fatigue=failureunderappliedcyclicstress. Callister&Rethwisch 9e. Stressvarieswithtime. Keypoints:Fatigue... Callister&Rethwisch 9e. 29 LECTURER: PROF. SEUNGTAE CHOI 10.8TheSNCurve Fatiguelimit,S fat : Forsomematerials, S fat Callister&Rethwisch 9e. Callister&Rethwisch 9e. 30 LECTURER: PROF. SEUNGTAE CHOI
16 10.9CrackInitiationandPropagation RateofFatigueCrackGrowth:Crackgrowsincrementally da dn ( K ) m ~ a Failedrotatingshaft Callister&Rethwisch 9e. UnderstandingHowComponentsFail 31 LECTURER: PROF. SEUNGTAE CHOI 10.10FactorsThatAffectFatigueLife 1.Imposecompressivesurfacestresses (tosuppresssurfacecracksfromgrowing) Callister&Rethwisch 9e. m m m bad bad better better Callister &Rethwisch 9e. 32 LECTURER: PROF. SEUNGTAE CHOI
17 10.12GeneralizedCreepBehavior Creepphenomenon:Time dependentandpermanent deformationofmaterialswhen subjectedtoconstantloador stress. e t et) 33 LECTURER: PROF. SEUNGTAE CHOI CreepFractureMechanism Schematicdrawingofthreefracturemechanismsinahightemperaturecreep regime [Abe et al., Creep-Resistant Steels, 2008] 34 LECTURER: PROF. SEUNGTAE CHOI
18 10.13StressandTemperatureEffects Occursatelevatedtemperature,T>0.4T m (ink) tertiary secondary primary elastic Callister&Rethwisch 9e. 35 LECTURER: PROF. SEUNGTAE CHOI SecondaryCreep Strainrateisconstantatagiven(T,s) StrainrateincreaseswithincreasingT, Stress(MPa) n Q c s K2 exp RT Steadystatecreeprate(%/1000hr) e s 427C 538 C 649 C Callister&Rethwisch 4e. Metals Handbook:PropertiesandSelection: StainlessSteels,ToolMaterials,and SpecialPurposeMetals 36 LECTURER: PROF. SEUNGTAE CHOI
19 ArrheniusEquation TheArrheniusequation(SvanteArrhenius,1889) E a k Aexp RT or E B k Aexp kbt k T A E a R E B k B 37 LECTURER: PROF. SEUNGTAE CHOI 10.14DataExtrapolationMethods TheLarson Millerparameterisameansofpredictingthelifetimeofmaterial vs.timeandtemperatureusingacorrelativeapproachbasedonthearrhenius rateequation. LarsenMillerparameterP LM isusedtorepresentcreepstressrupturedata. n Qc s K2 exp RT l Qc A exp t RT l Qc ln lna t RT Qc TB lnt where R A B ln l P LM T C log t r 38 LECTURER: PROF. SEUNGTAE CHOI
20 PredictionofCreepRuptureLifetime T s t r T (20 logt r ) P LM Tt r Callister&Rethwisch 9e. Trans.ASME74 ( 1073K)(20 logt ) t r r 3 24x10 39 LECTURER: PROF. SEUNGTAE CHOI SUMMARY Engineeringmaterialsnotasstrongaspredictedbytheory Flawsactasstressconcentratorsthatcausefailureatstresseslowerthan theoreticalvalues. Sharpcornersproducelargestressconcentrationsandprematurefailure. FailuretypedependsonTand: 40 LECTURER: PROF. SEUNGTAE CHOI
MECHANICAL PROPERTIES OF MATERIALS
MECHANICAL PROPERTIES OF MATERIALS! Simple Tension Test! The Stress-Strain Diagram! Stress-Strain Behavior of Ductile and Brittle Materials! Hooke s Law! Strain Energy! Poisson s Ratio! The Shear Stress-Strain
Διαβάστε περισσότεραChapter 8: Mechanical Properties of Metals
Chapter8:MechanicalPropertiesofMetals ISSUESTOADDRESS 1 LECTURER: PRO. SEUNGTAE CHOI 8.1Introduction Mechanicalbehaviorofamaterialreflectsitsresponseordeformationin relationtoanappliedloadorforce. Keymechanicaldesignproperties:stiffness,strength,hardness,ductilityand
Διαβάστε περισσότερα(Mechanical Properties)
109101 Engineering Materials (Mechanical Properties-I) 1 (Mechanical Properties) Sheet Metal Drawing / (- Deformation) () 3 Force -Elastic deformation -Plastic deformation -Fracture Fracture 4 Mode of
Διαβάστε περισσότεραDr. D. Dinev, Department of Structural Mechanics, UACEG
Lecture 4 Material behavior: Constitutive equations Field of the game Print version Lecture on Theory of lasticity and Plasticity of Dr. D. Dinev, Department of Structural Mechanics, UACG 4.1 Contents
Διαβάστε περισσότεραINDEX. Introduction (ch 1) Theoretical strength (ch 2) Ductile/brittle (ch 2) Energy balance (ch 4) Stress concentrations (ch 6)
INDEX Introduction (ch 1) Theoretical strength (ch 2) Ductile/brittle (ch 2) Energy balance (ch 4) Stress concentrations (ch 6) () April 30, 2018 1 / 52 back to index INTRODUCTION Introduction () 3 / 52
Διαβάστε περισσότεραHomework 8 Model Solution Section
MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx
Διαβάστε περισσότεραIntroduction to Theory of. Elasticity. Kengo Nakajima Summer
Introduction to Theor of lasticit Summer Kengo Nakajima Technical & Scientific Computing I (48-7) Seminar on Computer Science (48-4) elast Theor of lasticit Target Stress Governing quations elast 3 Theor
Διαβάστε περισσότεραECE Spring Prof. David R. Jackson ECE Dept. Notes 2
ECE 634 Spring 6 Prof. David R. Jackson ECE Dept. Notes Fields in a Source-Free Region Example: Radiation from an aperture y PEC E t x Aperture Assume the following choice of vector potentials: A F = =
Διαβάστε περισσότεραAquinas College. Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET
Aquinas College Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical
Διαβάστε περισσότεραΑπόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.
Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action
Διαβάστε περισσότεραDiscontinuous Hermite Collocation and Diagonally Implicit RK3 for a Brain Tumour Invasion Model
1 Discontinuous Hermite Collocation and Diagonally Implicit RK3 for a Brain Tumour Invasion Model John E. Athanasakis Applied Mathematics & Computers Laboratory Technical University of Crete Chania 73100,
Διαβάστε περισσότεραConstitutive Equation for Plastic Behavior of Hydrostatic Pressure Dependent Polymers
1/5 Constitutive Equation for Plastic Behavior of Hydrostatic Pressure Deendent Polymers by Yukio SANOMURA Hydrostatic ressure deendence in mechanical behavior of olymers is studied for the constitutive
Διαβάστε περισσότεραAluminum Electrolytic Capacitors
Aluminum Electrolytic Capacitors Snap-In, Mini., 105 C, High Ripple APS TS-NH ECE-S (G) Series: TS-NH Features Long life: 105 C 2,000 hours; high ripple current handling ability Wide CV value range (47
Διαβάστε περισσότεραAnswers - Worksheet A ALGEBRA PMT. 1 a = 7 b = 11 c = 1 3. e = 0.1 f = 0.3 g = 2 h = 10 i = 3 j = d = k = 3 1. = 1 or 0.5 l =
C ALGEBRA Answers - Worksheet A a 7 b c d e 0. f 0. g h 0 i j k 6 8 or 0. l or 8 a 7 b 0 c 7 d 6 e f g 6 h 8 8 i 6 j k 6 l a 9 b c d 9 7 e 00 0 f 8 9 a b 7 7 c 6 d 9 e 6 6 f 6 8 g 9 h 0 0 i j 6 7 7 k 9
Διαβάστε περισσότεραMock Exam 7. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q2 (a) (1 + kx) n 1M + 1A = (1) =
Mock Eam 7 Mock Eam 7 Section A. Reference: HKDSE Math M 0 Q (a) ( + k) n nn ( )( k) + nk ( ) + + nn ( ) k + nk + + + A nk... () nn ( ) k... () From (), k...() n Substituting () into (), nn ( ) n 76n 76n
Διαβάστε περισσότεραAluminum Electrolytic Capacitors (Large Can Type)
Aluminum Electrolytic Capacitors (Large Can Type) Snap-In, 85 C TS-U ECE-S (U) Series: TS-U Features General purpose Wide CV value range (33 ~ 47,000 µf/16 4V) Various case sizes Top vent construction
Διαβάστε περισσότεραWritten Examination. Antennas and Propagation (AA ) April 26, 2017.
Written Examination Antennas and Propagation (AA. 6-7) April 6, 7. Problem ( points) Let us consider a wire antenna as in Fig. characterized by a z-oriented linear filamentary current I(z) = I cos(kz)ẑ
Διαβάστε περισσότεραCH-4 Plane problems in linear isotropic elasticity
CH-4 Plane problems in linear isotropic elasticity HUMBERT Laurent laurent.humbert@epfl.ch laurent.humbert@ecp.fr Thursday, march 18th 010 Thursday, march 5th 010 1 4.1 ntroduction Framework : linear isotropic
Διαβάστε περισσότεραChapter 7 Transformations of Stress and Strain
Chapter 7 Transformations of Stress and Strain INTRODUCTION Transformation of Plane Stress Mohr s Circle for Plane Stress Application of Mohr s Circle to 3D Analsis 90 60 60 0 0 50 90 Introduction 7-1
Διαβάστε περισσότεραwave energy Superposition of linear plane progressive waves Marine Hydrodynamics Lecture Oblique Plane Waves:
3.0 Marine Hydrodynamics, Fall 004 Lecture 0 Copyriht c 004 MIT - Department of Ocean Enineerin, All rihts reserved. 3.0 - Marine Hydrodynamics Lecture 0 Free-surface waves: wave enery linear superposition,
Διαβάστε περισσότεραDETERMINATION OF DYNAMIC CHARACTERISTICS OF A 2DOF SYSTEM. by Zoran VARGA, Ms.C.E.
DETERMINATION OF DYNAMIC CHARACTERISTICS OF A 2DOF SYSTEM by Zoran VARGA, Ms.C.E. Euro-Apex B.V. 1990-2012 All Rights Reserved. The 2 DOF System Symbols m 1 =3m [kg] m 2 =8m m=10 [kg] l=2 [m] E=210000
Διαβάστε περισσότεραEXPERIMENTAL AND NUMERICAL STUDY OF A STEEL-TO-COMPOSITE ADHESIVE JOINT UNDER BENDING MOMENTS
NATIONAL TECHNICAL UNIVERSITY OF ATHENS SCHOOL OF NAVAL ARCHITECTURE AND ARINE ENGINEERING SHIPBUILDING TECHNOLOGY LABORATORY EXPERIENTAL AND NUERICAL STUDY OF A STEEL-TO-COPOSITE ADHESIVE JOINT UNDER
Διαβάστε περισσότεραContents. Preface... xv Acknowledgments... xix About the Authors... xxi Nomenclature... xxiii
Preface... xv Acknowledgments... xix About the Authors... xxi Nomenclature... xxiii Chapter 1: Road Load Analysis Techniques in Automotive Engineering... 1 Xiaobo Yang, Peijun Xu Introduction... 1 Fundamentals
Διαβάστε περισσότερα1. (a) (5 points) Find the unit tangent and unit normal vectors T and N to the curve. r(t) = 3cost, 4t, 3sint
1. a) 5 points) Find the unit tangent and unit normal vectors T and N to the curve at the point P, π, rt) cost, t, sint ). b) 5 points) Find curvature of the curve at the point P. Solution: a) r t) sint,,
Διαβάστε περισσότεραUniversity of Waterloo. ME Mechanical Design 1. Partial notes Part 1
University of Waterloo Department of Mechanical Engineering ME 3 - Mechanical Design 1 Partial notes Part 1 G. Glinka Fall 005 1 Forces and stresses Stresses and Stress Tensor Two basic types of forces
Διαβάστε περισσότεραLecture 21: Scattering and FGR
ECE-656: Fall 009 Lecture : Scattering and FGR Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA Review: characteristic times τ ( p), (, ) == S p p
Διαβάστε περισσότεραMacromechanics of a Laminate. Textbook: Mechanics of Composite Materials Author: Autar Kaw
Macromechanics of a Laminate Tetboo: Mechanics of Composite Materials Author: Autar Kaw Figure 4.1 Fiber Direction θ z CHAPTER OJECTIVES Understand the code for laminate stacing sequence Develop relationships
Διαβάστε περισσότεραHOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
Διαβάστε περισσότεραΤο σχέδιο της μέσης τομής πλοίου
ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΤΜΗΜΑ ΝΑΥΠΗΓΩΝ ΜΗΧΑΝΙΚΩΝ ΜΕΤΑΠΤΥΧΙΑΚΟ ΠΡΟΓΡΑΜΜΑ ΣΠΟΥΔΩΝ Το σχέδιο της μέσης τομής πλοίου Α. Θεοδουλίδης Σχέδιο Μέσης Τομής Αποτελεί ένα από τα βασικώτερα κατασκευαστικά σχέδια του πλοίου.
Διαβάστε περισσότεραkatoh@kuraka.co.jp okaken@kuraka.co.jp mineot@fukuoka-u.ac.jp 4 35 3 Normalized stress σ/g 25 2 15 1 5 Breaking test Theory 1 2 Shear tests Failure tests Compressive tests 1 2 3 4 5 6 Fig.1. Relation between
Διαβάστε περισσότεραb. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!
MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.
Διαβάστε περισσότερα6.4 Superposition of Linear Plane Progressive Waves
.0 - Marine Hydrodynamics, Spring 005 Lecture.0 - Marine Hydrodynamics Lecture 6.4 Superposition of Linear Plane Progressive Waves. Oblique Plane Waves z v k k k z v k = ( k, k z ) θ (Looking up the y-ais
Διαβάστε περισσότεραStrain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
Διαβάστε περισσότεραLifting Entry 2. Basic planar dynamics of motion, again Yet another equilibrium glide Hypersonic phugoid motion MARYLAND U N I V E R S I T Y O F
ifting Entry Basic planar dynamics of motion, again Yet another equilibrium glide Hypersonic phugoid motion MARYAN 1 010 avid. Akin - All rights reserved http://spacecraft.ssl.umd.edu ifting Atmospheric
Διαβάστε περισσότεραSolution to Review Problems for Midterm III
Solution to Review Problems for Mierm III Mierm III: Friday, November 19 in class Topics:.8-.11, 4.1,4. 1. Find the derivative of the following functions and simplify your answers. (a) x(ln(4x)) +ln(5
Διαβάστε περισσότεραGraded Refractive-Index
Graded Refractive-Index Common Devices Methodologies for Graded Refractive Index Methodologies: Ray Optics WKB Multilayer Modelling Solution requires: some knowledge of index profile n 2 x Ray Optics for
Διαβάστε περισσότεραCHAPTER 70 DOUBLE AND TRIPLE INTEGRALS. 2 is integrated with respect to x between x = 2 and x = 4, with y regarded as a constant
CHAPTER 7 DOUBLE AND TRIPLE INTEGRALS EXERCISE 78 Page 755. Evaluate: dxd y. is integrated with respect to x between x = and x =, with y regarded as a constant dx= [ x] = [ 8 ] = [ ] ( ) ( ) d x d y =
Διαβάστε περισσότεραADVANCED STRUCTURAL MECHANICS
VSB TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING ADVANCED STRUCTURAL MECHANICS Lecture 1 Jiří Brožovský Office: LP H 406/3 Phone: 597 321 321 E-mail: jiri.brozovsky@vsb.cz WWW: http://fast10.vsb.cz/brozovsky/
Διαβάστε περισσότεραΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΣΥΓΚΡΙΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΓΚΡΑΤΗΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΟΡΙΣΜΕΝΩΝ ΠΡΟΚΑΤΑΣΚΕΥΑΣΜΕΝΩΝ ΣΥΝΔΕΣΜΩΝ ΑΚΡΙΒΕΙΑΣ
Διαβάστε περισσότεραMatrices and Determinants
Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z
Διαβάστε περισσότεραMao KURUMATANI, Tatsuya YUMOTO, Kenjiro TERADA, Takashi KYOYA and Mitsuyoshi AKIYAMA
応用力学論文集 Vol.3, pp.33-3 ( 年 8 月 ) Vol. 3 8 土木学会 Study for evaluating fracture-toughness in quasi-brittle materials based on the energy valance of structures Mao KURUMATANI, Tatsuya YUMOTO, Kenjiro TERADA,
Διαβάστε περισσότεραSwirl diffusers, Variable swirl diffusers Swirl diffusers
, Variable swirl diffusers Swirl diffuser OD-9 Square or round front mask Square or radial deflector arrangement Plastic deflectors Possible volume control damper in spigot Foam sealing on the flange St
Διαβάστε περισσότεραFourier Analysis of Waves
Exercises for the Feynman Lectures on Physics by Richard Feynman, Et Al. Chapter 36 Fourier Analysis of Waves Detailed Work by James Pate Williams, Jr. BA, BS, MSwE, PhD From Exercises for the Feynman
Διαβάστε περισσότεραLifting Entry (continued)
ifting Entry (continued) Basic planar dynamics of motion, again Yet another equilibrium glide Hypersonic phugoid motion Planar state equations MARYAN 1 01 avid. Akin - All rights reserved http://spacecraft.ssl.umd.edu
Διαβάστε περισσότερα+85 C Snap-Mount Aluminum Electrolytic Capacitors. High Voltage Lead free Leads Rugged Design. -40 C to +85 C
+85 C Snap-Mount Capacitors FEATURES High ripple Current Ratings Large Case Size Selection Extended Life High Voltage Lead free Leads Rugged Design SPECIFICATIONS Tolerance ±20% at 120Hz, 20 C Operating
Διαβάστε περισσότερα5.0 DESIGN CALCULATIONS
5.0 DESIGN CALCULATIONS Load Data Reference Drawing No. 2-87-010-80926 Foundation loading for steel chimney 1-00-281-53214 Boiler foundation plan sketch : Figure 1 Quantity Unit Dia of Stack, d 6.00 m
Διαβάστε περισσότεραΜηχανουργική Τεχνολογία & Εργαστήριο Ι
Μηχανουργική Τεχνολογία & Εργαστήριο Ι Mechanics in Deforming Processes - Διεργασίες Διαμόρφωσης Καθηγητής Χρυσολούρης Γεώργιος Τμήμα Μηχανολόγων & Αεροναυπηγών Μηχανικών Mechanics in deforming processes
Διαβάστε περισσότεραr r t r r t t r t P s r t r P s r s r r rs tr t r r t s ss r P s s t r t t tr r r t t r t r r t t s r t rr t Ü rs t 3 r r r 3 rträ 3 röÿ r t
r t t r t ts r3 s r r t r r t t r t P s r t r P s r s r P s r 1 s r rs tr t r r t s ss r P s s t r t t tr r 2s s r t t r t r r t t s r t rr t Ü rs t 3 r t r 3 s3 Ü rs t 3 r r r 3 rträ 3 röÿ r t r r r rs
Διαβάστε περισσότεραReview Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) sin - 11π 1 1) + - + - - ) sin 11π 1 ) ( -
Διαβάστε περισσότεραSection 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
Διαβάστε περισσότεραDuPont Suva 95 Refrigerant
Technical Information T-95 ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 95 Refrigerant (R-508B) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered
Διαβάστε περισσότεραInverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------
Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin
Διαβάστε περισσότεραMechanical Behaviour of Materials Chapter 5 Plasticity Theory
Mechanical Behaviour of Materials Chapter 5 Plasticity Theory Dr.-Ing. 郭瑞昭 Yield criteria Question: For what combinations of loads will the cylinder begin to yield plastically? The criteria for deciding
Διαβάστε περισσότεραSampling Basics (1B) Young Won Lim 9/21/13
Sampling Basics (1B) Copyright (c) 2009-2013 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any
Διαβάστε περισσότεραSurface Mount Multilayer Chip Capacitors for Commodity Solutions
Surface Mount Multilayer Chip Capacitors for Commodity Solutions Below tables are test procedures and requirements unless specified in detail datasheet. 1) Visual and mechanical 2) Capacitance 3) Q/DF
Διαβάστε περισσότεραDuPont Suva. DuPont. Thermodynamic Properties of. Refrigerant (R-410A) Technical Information. refrigerants T-410A ENG
Technical Information T-410A ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 410A Refrigerant (R-410A) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered
Διαβάστε περισσότεραRadio détection des rayons cosmiques d ultra-haute énergie : mise en oeuvre et analyse des données d un réseau de stations autonomes.
Radio détection des rayons cosmiques d ultra-haute énergie : mise en oeuvre et analyse des données d un réseau de stations autonomes. Diego Torres Machado To cite this version: Diego Torres Machado. Radio
Διαβάστε περισσότεραω α β χ φ() γ Γ θ θ Ξ Μ ν ν ρ σ σ σ σ σ σ τ ω ω ω µ υ ρ α Coefficient of friction Coefficient of friction 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 0.90 0.80 0.70 0.60 0.50 0.40 0.30
Διαβάστε περισσότεραCONSULTING Engineering Calculation Sheet
E N G I N E E R S Consulting Engineers jxxx 1 Structure Design - EQ Load Definition and EQ Effects v20 EQ Response Spectra in Direction X, Y, Z X-Dir Y-Dir Z-Dir Fundamental period of building, T 1 5.00
Διαβάστε περισσότεραRectangular Polar Parametric
Harold s Precalculus Rectangular Polar Parametric Cheat Sheet 15 October 2017 Point Line Rectangular Polar Parametric f(x) = y (x, y) (a, b) Slope-Intercept Form: y = mx + b Point-Slope Form: y y 0 = m
Διαβάστε περισσότεραD Alembert s Solution to the Wave Equation
D Alembert s Solution to the Wave Equation MATH 467 Partial Differential Equations J. Robert Buchanan Department of Mathematics Fall 2018 Objectives In this lesson we will learn: a change of variable technique
Διαβάστε περισσότεραE T E L. E e E s G LT. M x, M y, M xy M H N H N x, N y, N xy. S ijkl. V v V crit
A c,a f,a m E c.e f,e m E e E s G f,g m L M x, M y, M xy M H N H N x, N y, N xy P c,p f,p m Q S S ijkl T T V V v V crit W h k t c,t f,t m u 0 v c,v f,v m w c,w f,w m cross-sectional area of composite,fiber
Διαβάστε περισσότερα3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
Διαβάστε περισσότεραP AND P. P : actual probability. P : risk neutral probability. Realtionship: mutual absolute continuity P P. For example:
(B t, S (t) t P AND P,..., S (p) t ): securities P : actual probability P : risk neutral probability Realtionship: mutual absolute continuity P P For example: P : ds t = µ t S t dt + σ t S t dw t P : ds
Διαβάστε περισσότεραAssalamu `alaikum wr. wb.
LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump
Διαβάστε περισσότεραExercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.
Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given
Διαβάστε περισσότεραElectronic Supplementary Information (ESI)
Electronic Supplementary Material (ESI) for RSC Advances. This journal is The Royal Society of Chemistry 2016 Electronic Supplementary Information (ESI) Cyclopentadienyl iron dicarbonyl (CpFe(CO) 2 ) derivatives
Διαβάστε περισσότεραGF GF 3 1,2) KP PP KP Photo 1 GF PP GF PP 3) KP ULultra-light 2.KP 2.1KP KP Fig. 1 PET GF PP 4) 2.2KP KP GF 2 3 KP Olefin film Stampable sheet
JFE No. 4 20045 p 82 Composite Material for Automotive Headliners Expandable Stampable Sheet with Light Weight and High Stiffness A JFE SUZU JFE HA KP 50 mass 30 UL 800 g/m 2 7.2 N/mm Abstract: KP-Sheet
Διαβάστε περισσότεραTRIAXIAL TEST, CORPS OF ENGINEERS FORMAT
TRIAXIAL TEST, CORPS OF ENGINEERS FORMAT .5 C, φ, deg Tan(φ) Total.7 2.2 Effective.98 8.33 Shear,.5.5.5 2 2.5 3 Total Normal, Effective Normal, Deviator,.5.25.75.5.25 2.5 5 7.5 Axial Strain, % Type of
Διαβάστε περισσότεραUsing the Jacobian- free Newton- Krylov method to solve the sea- ice momentum equa<on
Using the Jacobian- free Newton- Krylov method to solve the sea- ice momentum equa
Διαβάστε περισσότεραA Bonus-Malus System as a Markov Set-Chain. Małgorzata Niemiec Warsaw School of Economics Institute of Econometrics
A Bonus-Malus System as a Markov Set-Chain Małgorzata Niemiec Warsaw School of Economics Institute of Econometrics Contents 1. Markov set-chain 2. Model of bonus-malus system 3. Example 4. Conclusions
Διαβάστε περισσότεραChapter 2. Stress, Principal Stresses, Strain Energy
Chapter Stress, Principal Stresses, Strain nergy Traction vector, stress tensor z z σz τ zy ΔA ΔF A ΔA ΔF x ΔF z ΔF y y τ zx τ xz τxy σx τ yx τ yz σy y A x x F i j k is the traction force acting on the
Διαβάστε περισσότεραSPECIAL FUNCTIONS and POLYNOMIALS
SPECIAL FUNCTIONS and POLYNOMIALS Gerard t Hooft Stefan Nobbenhuis Institute for Theoretical Physics Utrecht University, Leuvenlaan 4 3584 CC Utrecht, the Netherlands and Spinoza Institute Postbox 8.195
Διαβάστε περισσότεραNotations. Primary definition. Specific values. General characteristics. Series representations. Traditional name. Traditional notation
Pi Notations Traditional name Π Traditional notation Π Mathematica StandardForm notation Pi Primary definition.3... Π Specific values.3.3.. Π 3.5965358979338663383795889769399375589795937866868998683853
Διαβάστε περισσότεραBoundary-Layer Flow over a Flat Plate Approximate Method
Bounar-aer lo oer a lat Plate Approimate Metho Transition Turbulent aminar The momentum balance on a control olume o the bounar laer leas to the olloing equation: + () The approimate metho o bounar laer
Διαβάστε περισσότερα: Monte Carlo EM 313, Louis (1982) EM, EM Newton-Raphson, /. EM, 2 Monte Carlo EM Newton-Raphson, Monte Carlo EM, Monte Carlo EM, /. 3, Monte Carlo EM
2008 6 Chinese Journal of Applied Probability and Statistics Vol.24 No.3 Jun. 2008 Monte Carlo EM 1,2 ( 1,, 200241; 2,, 310018) EM, E,,. Monte Carlo EM, EM E Monte Carlo,. EM, Monte Carlo EM,,,,. Newton-Raphson.
Διαβάστε περισσότεραΜΔΛΔΣΖ ΔΝΓΟΣΡΑΥΤΝΖ Δ ΥΑΛΤΒΔ ΘΔΡΜΖ ΔΛΑΖ
ΔΘΝΗΚΟ ΜΔΣΟΒΗΟ ΠΟΛΤΣΔΥΝΔΗΟ ΔΙΑΣΜΗΜΑΣΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΣΑΠΣΤΥΙΑΚΩΝ ΠΟΤΔΩΝ (Δ.Π.Μ..): "ΔΠΗΣΖΜΖ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΛΗΚΧΝ" ΜΔΛΔΣΖ ΔΝΓΟΣΡΑΥΤΝΖ Δ ΥΑΛΤΒΔ ΘΔΡΜΖ ΔΛΑΖ ΜΕΣΑΠΣΤΥΙΑΚΗ ΕΡΓΑΙΑ ΕΔΡΒΑ ΑΗΜΗΛΗΑΝΟ Διπλωματούτος
Διαβάστε περισσότερα4.4 Superposition of Linear Plane Progressive Waves
.0 Marine Hydrodynamics, Fall 08 Lecture 6 Copyright c 08 MIT - Department of Mechanical Engineering, All rights reserved..0 - Marine Hydrodynamics Lecture 6 4.4 Superposition of Linear Plane Progressive
Διαβάστε περισσότεραE62-TAB AC Series Features
NEW! E62-TAB AC Series Features Perfect for non-sinusoidal voltages and pulsed s. Housed in a hermetically sealed aluminum can which is filled with environmentally friendly plant oil as standard. The integrated
Διαβάστε περισσότεραSpherical Coordinates
Spherical Coordinates MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Spherical Coordinates Another means of locating points in three-dimensional space is known as the spherical
Διαβάστε περισσότερα20/01/ of 8 TOW SSD v3. C 2.78AC Σ Cumul. A*C. Tc 1 =A14+1 =B14+1 =C14+1 =D14+1 =E14+1 =F14+1 =G14+1 =H14+1 =I14+1 =J14+1 =K14+1
20/01/2014 1 of 8 TOW SSD v3 Location Project a =IF(Design_Storm>0,VL b =IF(Design_Storm>0,VL c =IF(Design_Storm>0,VL Designed By Checked By Date Date Comment Min Tc 15 LOCATION From To MH or CBMH STA.
Διαβάστε περισσότεραFRACTURE MECHANICS. Piet Schreurs. Eindhoven University of Technology Department of Mechanical Engineering Materials Technology September 5, 2013
FRACTURE MECHANICS Piet Schreurs Eindhoven University of Technology Department of Mechanical Engineering Materials Technology September 5, 2013 INDEX back to index () 1 / 303 Introduction Fracture mechanisms
Διαβάστε περισσότεραGrey Cast Irons. Technical Data
Grey Cast Irons Standard Material designation Grey Cast Irons BS EN 1561 EN-GJL-200 EN-GJL-250 EN-GJL-300 EN-GJL-350-1997 (EN-JL1030) (EN-JL1040) (EN-JL1050) (EN-JL1060) Characteristic SI unit Tensile
Διαβάστε περισσότεραSMD Transient Voltage Suppressors
SMD Transient Suppressors Feature Full range from 0 to 22 series. form 4 to 60V RMS ; 5.5 to 85Vdc High surge current ability Bidirectional clamping, high energy Fast response time
Διαβάστε περισσότεραTechnical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)]
d Suva refrigerants Technical Information T-9100SI Thermodynamic Properties of Suva 9100 Refrigerant [R-410A (50/50)] Thermodynamic Properties of Suva 9100 Refrigerant SI Units New tables of the thermodynamic
Διαβάστε περισσότεραDifferential equations
Differential equations Differential equations: An equation inoling one dependent ariable and its deriaties w. r. t one or more independent ariables is called a differential equation. Order of differential
Διαβάστε περισσότεραL p approach to free boundary problems of the Navier-Stokes equation
L p approach to free boundary problems of the Navier-Stokes equation e-mail address: yshibata@waseda.jp 28 4 1 e-mail address: ssshimi@ipc.shizuoka.ac.jp Ω R n (n 2) v Ω. Ω,,,, perturbed infinite layer,
Διαβάστε περισσότεραOscillatory Gap Damping
Oscillatory Gap Damping Find the damping due to the linear motion of a viscous gas in in a gap with an oscillating size: ) Find the motion in a gap due to an oscillating external force; ) Recast the solution
Διαβάστε περισσότεραRECIPROCATING COMPRESSOR CALCULATION SHEET ISOTHERMAL COMPRESSION Gas properties, flowrate and conditions. Compressor Calculation Sheet
RECIPRCATING CMPRESSR CALCULATIN SHEET ISTHERMAL CMPRESSIN Gas properties, flowrate and conditions 1 Gas name Air Item or symbol Quantity Unit Item or symbol Quantity Unit Formula 2 Suction pressure, ps
Διαβάστε περισσότεραDurbin-Levinson recursive method
Durbin-Levinson recursive method A recursive method for computing ϕ n is useful because it avoids inverting large matrices; when new data are acquired, one can update predictions, instead of starting again
Διαβάστε περισσότεραΕυθύμης ΛΕΚΚΑΣ 1. 3 o Πανελλήνιο Συνέδριο Αντισεισμικής Μηχανικής & Τεχνικής Σεισμολογίας 5 7 Νοεμβρίου, 2008 Άρθρο 2109
3 o Πανελλήνιο Συνέδριο Αντισεισμικής Μηχανικής & Τεχνικής Σεισμολογίας 5 7 Νοεμβρίου, 2008 Άρθρο 2109 Σεισμός Wenchuan (Mw 7.9, 12 Μαΐου 2008) Sichuan, Κίνα. Γεωτεκτονικό Καθεστώς και Μακρο-κατανομή των
Διαβάστε περισσότεραSecond Order Partial Differential Equations
Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y
Διαβάστε περισσότεραCycloaddition of Homochiral Dihydroimidazoles: A 1,3-Dipolar Cycloaddition Route to Optically Active Pyrrolo[1,2-a]imidazoles
X-Ray crystallographic data tables for paper: Supplementary Material (ESI) for Organic & Biomolecular Chemistry Cycloaddition of Homochiral Dihydroimidazoles: A 1,3-Dipolar Cycloaddition Route to Optically
Διαβάστε περισσότεραChapter 6: Systems of Linear Differential. be continuous functions on the interval
Chapter 6: Systems of Linear Differential Equations Let a (t), a 2 (t),..., a nn (t), b (t), b 2 (t),..., b n (t) be continuous functions on the interval I. The system of n first-order differential equations
Διαβάστε περισσότεραΜΗΧΑΝΙΚΕΣ ΙΔΙΟΤΗΤΕΣ ΤΩΝ ΜΕΤΑΛΛΩΝ II
ΜΗΧΑΝΙΚΕΣ ΙΔΙΟΤΗΤΕΣ ΤΩΝ ΜΕΤΑΛΛΩΝ II 4.3 ΟΛΚΙΜΟΤΗΤΑ (DUCTILITY) Ολκιμότητα - μέτρο του βαθμού πλαστικής παραμόρφωσης στο σημείο θραύσης στένωση, λαιμός (necking) θραύση όλκιμου υλικού (ductile material)
Διαβάστε περισσότεραTUBO LED T8 LLUMOR PROLED 25W 150CM
PHOTOMETRIC TEST REPORT Luminaire Property Luminaire: Report NO.: Test NO.: Lamp: LLUMOR-PL-T8-25W 6000K Sum Lumens: 3473.92 lm Number of Lamps: 1 Diameter: 0mm Length: 1500mm Photometric Type: Type C
Διαβάστε περισσότεραIV. ANHANG 179. Anhang 178
Anhang 178 IV. ANHANG 179 1. Röntgenstrukturanalysen (Tabellen) 179 1.1. Diastereomer A (Diplomarbeit) 179 1.2. Diastereomer B (Diplomarbeit) 186 1.3. Aldoladdukt 5A 193 1.4. Aldoladdukt 13A 200 1.5. Aldoladdukt
Διαβάστε περισσότερα1. If log x 2 y 2 = a, then dy / dx = x 2 + y 2 1] xy 2] y / x. 3] x / y 4] none of these
1. If log x 2 y 2 = a, then dy / dx = x 2 + y 2 1] xy 2] y / x 3] x / y 4] none of these 1. If log x 2 y 2 = a, then x 2 + y 2 Solution : Take y /x = k y = k x dy/dx = k dy/dx = y / x Answer : 2] y / x
Διαβάστε περισσότερα2 4 5
f Æ 2 4 5 6 e D S. 7 8 9 : H ; BhL Ä,giU W? i?t ),giu 2 b 6 6 6 6 6 6 6 6 6 f < 43 3 3 2 2 2 44 45 46 w wã4 w wã4 BhL Ä,giU W? i?t ),giu 2 e D S ^ 2 M^ e D S ^ M^ Figure 1 US GDP and Exports, 1980-1994
Διαβάστε περισσότεραThermistor (NTC /PTC)
ISO/TS16949 ISO 9001 ISO14001 2015 Thermistor (NTC /PTC) GNTC (Chip in Glass Thermistor) SMD NTC Thermistor SMD PTC Thermistor Radial type Thermistor Bare Chip Thermistor (Gold & silver Electrode) 9B-51L,
Διαβάστε περισσότερα