1. Calculation of shear forces and bending moments
|
|
- Shona Simpson
- 5 years ago
- Views:
Transcription
1 Lectre 16(18). CALCULATION OF SHEAR FORCE AND BENDING MOMENT FOR BIG ASPECT RATIO WING Plan: 1. Calclation of shear forces and bending oents. Diagra of redced oents. Featres of load calclations for sept ing 4. Check of loading calclation. 1. Calclation of shear forces and bending oents In previos lectre e considered calclation of distribted loads. In this lectre e shall consider calclation of shear force and bending oent b ing span. We consider a ing as a cantilever bea. In beginning fnctions shear force Q d ( ) and bending oent M d ( ) fro the total distribted load q t () are fond b ing span. Fro echanic of aterials sie of shear force is eqal to: q ( )d G n q t ci.5 L t ( )d M ci g Q n, (1) L here G ci - eans eight of i-th cargo, M ci is ass of i-th cargo. As o can see e have different forlas for shear force fro distribted and concentrated forces. Bending oent is eqal: M L Q()d () For this prpose integrals are calclated b tablated a ith trapeoids ethod. Yo st deterine orself signs for Q, M according to sign convention fro echanic of aterials (see fig. 1). Q> M> Fig. 1. Sign conventions for shear force Q and bending oent M. Usall shear forces and bending oents are calclated separatel fro distribted and concentrated forces and then e shold sarie the. 1
2 A calclation schee is given in the tab. 1 for shear force and bending oent fro distribted forces. Table 1 The Q d () shear forces and the М d () bending oent are affected b the q t () distribted load. i Δ i i, q t, Q di Q, di, M, di M, di q t ΔQ d Q d ΔM d M d Δ 9 q t9 ΔQ d9 Q d9 ΔM d9 M d Δ 1 q t1 ΔQ d1 Q d1 ΔM d1 M d q t11 First and second colns are reritten fro table 1 fro previos lectre. In third coln of the table 1 e shold copte distance beteen cross sections i fro i-th cross section p to i+1 cross section in eters b the forla: Δi.5(i1 i)l; Δ 11 =, (i =1, , ). We shold calclate fro tenth cross section here i=1, becase 11 =. The forth coln o shold rerite fro previos table 1 last coln. Reslt of previos table is initial data for those calclations. Integration is begn fro a ing tip of a console as for cantilever bea. This integration is ade b to steps. First step is calclation of increent for shear force. Increent of shear force fro distribted loads Q di is fond as area of trapee so: q q t,i t,i1 Q, Q di i d11 =, (i =1, , ), () Those vales e shold rite don in fifth coln. A second step is calclation of shear force fro distribted loads as area of fnction q t =f(): Q Q Q, Q di di 1 di d11 = ; (i = 1, , ), (4) here Q d11 = is shear force in cross-section nber 11 fro distribted loads in a tip ing. Q d1 - is shear force in cross-section nber 1 fro distribted loads on site beteen 1 and 11 cross-sections and so on. Those vales e shold rite don in the sixth coln. B the sae ethodic e shold calclate bending oent fro distribted loads:
3 , M d11 =, (i =1, 9 1, ), M d11 = ; (i = 1, 9 1, ) (5) here ΔM d11 = - is increent of bending oent in cross-section nber 11 fro distribted loads in tip ing, ΔM d1 - is increent of bending oent in cross-section nber 1 fro distribted loads on site beteen 1 and 11 cross-sections and so on, hich e shold rite don in seventh coln; M d11 = is bending oent in cross-section nber 11 fro distribted loads in tip ing; M d1 - is bending oent in cross-section nber 1 fro distribted loads on site beteen 1 and 11 cross-sections and so on, hich e shold rite don in eighth coln. It also is necessar to reslt shear forces and bending oents affected b P,agr concentrated ass forces (in the sae coordinate sstes that Q d and M d and in the sae scale of diagras). Hoever the sign of these diagras is opposite to sign Q d and M d. On fig. diagra Q c fro concentrated forces is shon (table ) and on fig. is shon M c. To concentrated ass forces o st inclde all aggregates of ing engines, landing gears, fel tanks and so on. Ultiate loads fro aggregates, as for concentrated loads are eqal:, =n G agr,i =n M agr,i g= Q ic (6) here G agr,i is aggregate eight in i-th cross section, M agr,i - is aggregate ass in i-th cross section, i is nber of cross section, g is gravit acceleration. Yo shold copte these vales onl for cross sections ith aggregates, in an cross sections o shold rite don. Calclation schee is given in the tab., hich incldes folloing vales: Q ic =, fro (6) here i - is nber of cross section in hich this nit is placed; in an cross sections Q ic =. Yo shold rite don this vale in forth coln. In table for exaple concentrated force is given onl in cross section i= 9. Yo can rerite colns 1, and fro previos table. Sation of the concentrated cargoes is condcted fro the tip of ing to cross section ith coordinate. In practice there are carr ot nerical integration, procedre consists in the folloing. On the ing tip in the cross section N=11 e have 11. In this forla it takes into accont a cargo is located on i-th site., (i = 1, , ), (7) here Q c11 = is shear force in cross-section nber 11 fro concentrated loads in the tip ing. Q c1 - is shear force in the cross-section nber 1 fro concentrated loads. For exaple e have concentrated load in cross section nber 9. In this case Q c9 - is shear force in cross-section nber 9 fro concentrated loads hich has jp in this crosssection and to vales one previos vale - and ne vale ΔQ c9 and so on. In cross sections ith concentrated load e have jp of shear force and to vales of the. Yo shold rite don this vale in fifth coln. Bending oent fro concentrated loads is received as reslt of integration shear forces fro concentrated loads, integration condct fro the ing tip as for cantilever bea:
4 4 M с Qсd. (8) Integration is carried ot nericall, tablated a b the ethod of trapees. On a tip of a console ing, as it is knon: M t =M t11 =ΔM t11 =. Table The Q ic () shear forces and the М ic () bending oent are affected b concentrated loads. i, Q iс, i Δ i. Q iс M iс, M iс, Q ΔM c с M с Q 7c =Q 9c 8... Q 8c =Q 9c ΔM 8c ΔM 8c =M 8c 9.9 Δ 9 Q 9 Q с 9с =Q 9 с / 1.95 Δ In a cross-section nber i an increent of bending oent is eqal b the ethod of trapees:, M 11c =, (i =1, , ), (9) here ΔM c,11 = - is increent of bending oent in cross-section nber 11 fro concentrated loads ot tip ing. ΔM c,1 - is increent of bending oent in cross-section nber 1 fro concentrated loads in cross section 11 and so on. Bending oent fro concentrated loads is eqal:, M c,11 = ; (i = 1, , ) (1) M c,11 = is bending oent in the cross-section nber 11 fro concentrated loads ot tip ing. M c,1 - is bending oent in cross-section nber 1 fro concentrated loads in cross section 11 and so on. Yo st kno that increent of bending oent fro concentrated force and bending oent fro concentrated force o can calclate for next cross-section ith nber i-1=8 in or exaple see fig. and table. Folding appropriate diagras algebraicall (table ), e shold plot total diagras Q t and M t (on fig. are shon b continos lines). The calclation schee is given in a tab., hich incldes folloing vales: Q di - is shear force fro distribted loads fro table 1; Q ci - is shear force fro concentrated loads fro table ;
5 Q t,i = Q di + Q ci = Q c,i - Q d,i ith accont signs is total shear force; M di - is bending oent fro distribted loads fro table 1; M ci - is bending oent fro concentrated loads fro table ; M t,i = M di + M ci = M di - M ci ith accont signs - is total bending oent. Table Total Q t () shear forces and total М t,i () bending oent are affected b all forces. i Q di, Q ci, Q t,i, M d,i, * M c,i, KN* M t,i, On diagra of shear forces fro concentrated loads and the total shear forces e have discontinos jp in places of application for concentrated forces and have to vales shear force before and after application of concentrated force.. Diagra of redced oents For strength analsis of a ing it is necessar to find position of shear force in cross section. So e plot the diagra of the redced oents that is the oents of shear force rather an a chosen axis. Knoledge of a diagra of redced oents allos finding a point of attack for shear force in ing cross sections. This coordinate is sed at designing and checking calclations. For realiation of calclations e st do a draing of a ing. As an axis of redction it is convenient to choose a straight line taking begin at a point of intersection of a ing leading edge ith an axes of a fselage and perpendiclarl to axes of a fselage (see fig.). On the draing e indicate position of centers of pressre, centers of gravit of a ing cross sections and fel tanks, e shon centers of gravit for concentrated cargoes. Let's consider an cross section ith coordinate. We condct calclation fro a tip of a ing console. In each cross section b the draing e find distances fro the axis of redction to points of the attack for distribted and concentrated forces х a, х W, х f and х c (see fig.5). 5
6 engine fel tank front spar leading edge rredced axis b r b t L / rear spar rear spar q center of gravit q t q a q f Z Q Z Q c Q t Q d Fig.. Diagras of distribted loads and shear forces 6
7 M c Z M tot M d M,, Z M, M, c Z M,t M, d Fig.. Diagras of bending oent M and redced oent M. 7
8 Не удается отобразить связанный рисунок. Возможно, этот файл был перемещен, переименован или удален. Убедит есь, чт о ссылка указывает на правильный файл и верное размещение. Calclation schee for redced oents fro distribted loads Table 4. i Δ i, q a / x a q / x q f / x f i ΔM di M di q a x a q x q f x f ΔM d M d Δ 1 q a1 x a1 q 1 x 1 q f1 x f1 1 ΔM d1 M d1 11 Δ 11 q a11 x a11 q 11 x 11 q f11 x f11 11 We shold plot diagra of distribted redced oent. For this prpose at beginning crrent distribted redced oent in each ing cross section is calclated b the forla: = - q a x a + q x +q f x f (11) A total redced oent M is eqal: M ( )d G n x ( )d g n x, (1) ci ci here x ci is distance fro i-th concentrated cargo p to redced axis. The redced oent is considered like positive if it acts to pitching relative to the redced axis. Integrating the diagra e receive the redced oents M d affected b the distribted loads. A schee of calclation is shon in tab. 4 in hich designations is entered: M di.5( i 1,i ) i, M,d,11 M,d, 11 ; (1), (i = 1, 9..., ). At ing tip e have M, M d1 = M d1. M d 11 d 11 Also it is necessar to copte and to plot the diagra of the redced oents affected b concentrated asses (on fig. it is shon b the light line). Affected b concentrated ass of i-th aggregate increent of oent Δ M,c,i is fond ot b the forla: ΔM,c,i =, r i =M agr,i g r i, (14) ci ci 8
9 here the r i is a distance fro i-th concentrated ass gravit center to redced axis (it is easred on the draing)., is ltiate inertia force b forla (6). This increent e have onl in point here e have aggregates. In an points this increent is eqal ero. Redced oent M.c.i is calclated b the forla: ΔM,c,11 M,c,11 ; M,c,i M,c,i1 ΔM,c,i. (i = 1, 9..., ). (15) In a point ith aggregate e have jp of redced oent (see fig. ). For this table e take M di fro table 4 and total redced oent o shold copte ith accont of signs b the forla: M,t = M,d + M,c (16) A cg of cargo redced axis cp cg cg of fel A Fig. 4. Calclation of redced oents Distance fro the axis of redction to a point of attack of a resltant force X a,i in a cross section ith coordinate eqal to: M ti Х a,i (17) Qti It is necessar coordinate position of shear force in designing cross section fro a leading edge. Distance fro a leading edge p to a point of attack for a resltant force d e take fro the draing. Calclation of the total redced oents is carr ot in the table 5 b the ethod of trapees. It also is necessar to plot the M,t total redced oent diagra (on fig it is shon b a solid line). 9
10 ra x a q a cg of fel cg of ing x f x Fig. 5. Calclation of crrent redced oents Table 5 Calclation schee of redced oent fro concentrated loads and fro all loads. I,.i r i ΔM.c.i M.c.i M,d,i M,t,i * * * * X r, M ra Fig. 6. Calclation of a point of attack for resltant force 1
11 . Featres of load calclations for sept ing For sept ing his longitdinal axis is not perpendiclar axes of a plane, and is rejected back b flight. We dra a straight line taking place throgh.5 chords and e estiate a seep angle b this line for accont of seep back fro a draing of a ing. Frther e calclate an aendent b seep back: Г Г45 45 L c Fig. 7. Calclation settleent seep. We dra a diagra: t f, here circlation of a straight flat ing Г f e calclate for straightened sept ing. With this prpose e dra so-called a straightened sept ing concerning a line hich are taking place throgh.4b() chords that area st be eqal to the area of a sept ing becase approxiatel rigidit axes is placed in this position.4b(). Then Г f e find ot b the techniqe described above for a straight flat ing in vie of aspect ratio and taper for the straightened ing. At frther diagra is dran for the straightened ing, as ell as for straight flat ing. 4. Check of load calclation For check of load calclation an approached calclation of loads and coparison ith earlier received reslts st be carried ot. Fro previos lectre o kno that approxiatel aerodnaic force can be distribted proportionall to chords: 1.5n G 1.5n Mg qa b( ) b( ) (18) S S, ith accont load on stabilier. Sies of ing chords can be calclated b linear interpolation b the forla: 11
12 b b b( ) b r t r (19) Lc here в() is a crrent chord, в r a root chord, b t - a tip chord, L c a length of a ing console, - coordinate of cross section. We cont fel as a concentrated cargo, and then a total distribted loading q t eqal to: n (`1.5G G ) n g( 1.5M M ) p p qt b( ) b( ) () S S here G p eight of a plane, G is a ing eight, M p, M are asses of plane and ing accordingl. Shear force can be calclated b integration fro a ing tip as for a cantilever bea: q d G n q d t ci t l Q gm fn ; (1) ci C S c Centre of gravit b b() b t 1 L c Fig. 6. Circit of approached calclation of loading We st sbstitte q t fro previos lectre: n (G G ) p Q Sc Gcin, () S here S c b( ) d () - is an area of a ing copartent fro considered cross section p to a ing tip. At point =L c in root cross section Q th is eqal to: n ( 1.5G G ) n з Q th Gcin, (4) k 1
13 here n is qantit of concentrated cargoes, G p, G - eight of a plane and eight of a ing, inclding to consoles. Approxiatel bending oent in a cross section is eqal to: Sc M ар n ( (G G )C GciC i ) (5) S i here C i - distance fro a crrent cross-section to a center of gravit of a concentrated cargo, С - distance fro a crrent cross-section to a center of gravit of a ing copartent, hich is eqal: С b( ) bt b( ) bt, as center of gravit for trape. Ths those cargoes hich are located p to section ith coordinate shold be taken into accont onl fro a ing tip. Miscalclation for shear force st be no ore 1% or.1 b forlas: Qta Qth δq.1 Qth here Q ta is vale of shear force fro table, Q th theoretical vale of shear force fro (4). Miscalclation for bending oent st be no ore 1% or.1 b forlas: δm M ta Map M ta.1 here M ta is vale of bending oent fro table, M ap vale of bending oent fro (5). D:\Документы\Users\kir\SA18\T6DesStrnAn\L16(18)ABendMo 1
Boundary layer develops in the flow direction, δ = δ (x) τ
58:68 Trblent Flos Handot: Bondar Laers Differences to Trblent Channel Flo Bondar laer develops in the flo direction, not knon a priori Oter part of the flo consists of interittent trblent/non-trblent
More informationChapter 1: Differential Form of Basic Equations
MEG 74 Energ and Variational Methods in Mechanics I Brendan J. O Toole, Ph.D. Associate Professor of Mechanical Engineering Howard R. Hghes College of Engineering Universit of Nevada Las Vegas TBE B- (7)
More informationGuide for home task CALCULATION OF WING LOADS. National Aerospace University named after N.Ye. Zhukovsky Kharkiv Aviation Institute
National Aerospace University named after N.Ye. Zhukovsky Kharkiv Aviation Institute Guide for home task by course Strength of airplanes and helicopters CALCULATION OF WING LOADS Kharkiv, 2014 Manual is
More informationVerification Analysis of the Gravity Wall
Verification Manal no. Update 0/06 Verification Analysis of the Gravity Wall Progra File Gravity Wall Deo_v_en_0.gtz In this verification anal yo will find hand-ade verification analysis calclations of
More informationAn alternative approach to evaluate the average Nusselt number for mixed boundary layer conditions in parallel flow over an isothermal flat plate
An alternative approach to evalate the average Nsselt nber for ied bondary layer conditions in parallel flo over an isotheral flat plate Viacheslav Stetsyk, Krzysztof J. Kbiak, ande i and John C Chai Abstract
More information5. The Bernoulli Equation
5. The Bernolli Eqation [This material relates predominantly to modles ELP034, ELP035] 5. Work and Energy 5. Bernolli s Eqation 5.3 An example of the se of Bernolli s eqation 5.4 Pressre head, velocity
More information3 2D Elastostatic Problems in Cartesian Coordinates
D lastostatic Problems in Cartesian Coordinates Two dimensional elastostatic problems are discssed in this Chapter, that is, static problems of either plane stress or plane strain. Cartesian coordinates
More informationChapter 8 Deflection. Structural Mechanics 2 Dept of Architecture
Chapter 8 Deflection Structural echanics Dept of rchitecture Outline Deflection diagras and the elastic curve Elastic-bea theory The double integration ethod oent-area theores Conjugate-bea ethod 8- Deflection
More informationMomentum Equation. Necessary because body is not made up of a fixed assembly of particles Its volume is the same however Imaginary
Momentm Eqation Interest in the momentm eqation: Qantification of proplsion rates esign strctres for power generation esign of pipeline systems to withstand forces at bends and other places where the flow
More informationComputational Fluid Dynamics Simulation and Wind Tunnel Testing on Microlight Model
Comptational Flid Dynamics Simlation and Wind Tnnel Testing on Microlight Model Iskandar Shah Bin Ishak Department of Aeronatics and Atomotive, Universiti Teknologi Malaysia T.M. Kit Universiti Teknologi
More informationConcept of Stress at a Point
Washkeic College of Engineering Section : STRONG FORMULATION Concept of Stress at a Point Consider a point ithin an arbitraril loaded deformable bod Define Normal Stress Shear Stress lim A Fn A lim A FS
More informationFormal Methods for Deriving Element Equations
Formal Methods for Deriving Element Eqations And the importance of Shape Fnctions Formal Methods In previos lectres we obtained a bar element s stiffness eqations sing the Direct Method to obtain eact
More informationCS 331: Artificial Intelligence Naïve Bayes. Naïve Bayes
CS 33: Artificial Intelligence Naïe Bayes Thanks to Andrew Moore for soe corse aterial Naïe Bayes A special type of Bayesian network Makes a conditional independence assption Typically sed for classification
More information1 Differential Equations for Solid Mechanics
1 Differential Eqations for Solid Mechanics Simple problems involving homogeneos stress states have been considered so far, wherein the stress is the same throghot the component nder std. An eception to
More informationNumerical Simulation of Three Dimensional Flow in Water Tank of Marine Fish Larvae
Copyright c 27 ICCES ICCES, vol.4, no.1, pp.19-24, 27 Nmerical Simlation of Three Dimensional Flo in Water Tank of Marine Fish Larvae Shigeaki Shiotani 1, Atsshi Hagiara 2 and Yoshitaka Sakakra 3 Smmary
More informationLateral Load Capacity of Piles
Lateral Load Capacity of Piles M. T. DAVSSON, Department of Civil Engineering, University of llinois, Urbana Pile fondations sally find resistance to lateral loads from (a) passive soil resistance on the
More informationExtended Intervened Geometric Distribution
International Jornal of Statistical Distribtions Applications 6; (): 8- http://www.sciencepblishinggrop.co//isda Extended Intervened Geoetric Distribtion C. Satheesh Kar, S. Sreeaari Departent of Statistics,
More informationENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 2 LINEAR IMPULSE AND MOMENTUM
ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D5 TUTORIAL LINEAR IMPULSE AND MOMENTUM On copletion of this ttorial yo shold be able to do the following. State Newton s laws of otion. Define linear
More informationModels to Estimate the Unicast and Multicast Resource Demand for a Bouquet of IP-Transported TV Channels
Models to stiate the Unicast and Mlticast Resorce Deand for a Boqet of IP-Transported TV Channels Z. Avraova, D. De Vleeschawer,, S. Wittevrongel, H. Brneel SMACS Research Grop, Departent of Teleconications
More informationLecture 5. Differential Analysis of Fluid Flow Navier-Stockes equation
Lectre 5 Differential Analsis of Flid Flo Naier-Stockes eqation Differential analsis of Flid Flo The aim: to rodce differential eqation describing the motion of flid in detail Flid Element Kinematics An
More informationConsistent Numerical Model for Wind Buffeting Analysis of Long-Span Bridges
Consistent Nmerical Model for Wind Bffeting Analysis of Long-pan Bridges Dorian JANJIC Technical Director TDV GesmbH Graz, Astria Heinz PIRCHER Director TDV GesmbH Graz, Astria mmary The bffeting analysis
More informationPrandl established a universal velocity profile for flow parallel to the bed given by
EM 0--00 (Part VI) (g) The nderlayers shold be at least three thicknesses of the W 50 stone, bt never less than 0.3 m (Ahrens 98b). The thickness can be calclated sing Eqation VI-5-9 with a coefficient
More informationUNCERTAINTY FOCUSED STRENGTH ANALYSIS MODEL
8th International DAAAM Baltic Conference "INDUSTRIAL ENGINEERING - 19-1 April 01, Tallinn, Estonia UNCERTAINTY FOCUSED STRENGTH ANALYSIS MODEL Põdra, P. & Laaneots, R. Abstract: Strength analysis is a
More information3. Several Random Variables
. Several Random Variables. To Random Variables. Conditional Probabilit--Revisited. Statistical Independence.4 Correlation beteen Random Variables Standardied (or ero mean normalied) random variables.5
More informationTransformation of Orbital Angular Momentum and Spin Angular Momentum
Aerian Jornal of Matheatis and Statistis 6, 65: 3-6 DOI: 593/jajs6653 Transforation of Orbital Anglar Moent and Spin Anglar Moent Md Tarek Hossain *, Md Shah Ala Departent of Physis, Shahjalal Uniersity
More informationMicroscopic Properties of Gases
icroscopic Properties of Gases So far we he seen the gas laws. These came from observations. In this section we want to look at a theory that explains the gas laws: The kinetic theory of gases or The kinetic
More informationSection 7.4: Integration of Rational Functions by Partial Fractions
Section 7.4: Integration of Rational Fnctions by Partial Fractions This is abot as complicated as it gets. The Method of Partial Fractions Ecept for a few very special cases, crrently we have no way to
More information3-D dynamic modeling and simulation of a multidegree of freedom 3-axle rigid truck with trailing arm bogie suspension
University of Wollongong Research Online University of Wollongong Thesis Collection 1954-016 University of Wollongong Thesis Collections 006 3-D dynamic modeling and simlation of a mltidegree of freedom
More informationTechnical Note. ODiSI-B Sensor Strain Gage Factor Uncertainty
Technical Note EN-FY160 Revision November 30, 016 ODiSI-B Sensor Strain Gage Factor Uncertainty Abstract Lna has pdated or strain sensor calibration tool to spport NIST-traceable measrements, to compte
More informationReflections on a mismatched transmission line Reflections.doc (4/1/00) Introduction The transmission line equations are given by
Reflections on a mismatched transmission line Reflections.doc (4/1/00) Introdction The transmission line eqations are given by, I z, t V z t l z t I z, t V z, t c z t (1) (2) Where, c is the per-nit-length
More information1 JAXA Special Pblication JAXA-SP-1-E Small-scale trblence affects flow fields arond a blff body and therefore it governs characteristics of cross-sec
First International Symposim on Fltter and its Application, 1 11 IEXPERIMENTAL STUDY ON TURBULENCE PARTIAL SIMULATION FOR BLUFF BODY Hiroshi Katschi +1 and Hitoshi Yamada + +1 Yokohama National University,
More informationCorrelation of Nuclear Density Results with Core Densities
TRANSPORTATION RESEARCH RECORD 1126 53 Correlation of Nclear Density Reslts ith Core Densities JAMESL. BURATI,JR.,ANDGEORGEB. ELZOGHBI The paper smmaries the findings of a research effort (a) to determine
More informationLecture Notes: Finite Element Analysis, J.E. Akin, Rice University
9. TRUSS ANALYSIS... 1 9.1 PLANAR TRUSS... 1 9. SPACE TRUSS... 11 9.3 SUMMARY... 1 9.4 EXERCISES... 15 9. Trss analysis 9.1 Planar trss: The differential eqation for the eqilibrim of an elastic bar (above)
More informationcalled the potential flow, and function φ is called the velocity potential.
J. Szantr Lectre No. 3 Potential flows 1 If the flid flow is irrotational, i.e. everwhere or almost everwhere in the field of flow there is rot 0 it means that there eists a scalar fnction ϕ,, z), sch
More informationChapter 6 Momentum Transfer in an External Laminar Boundary Layer
6. Similarit Soltions Chapter 6 Momentm Transfer in an Eternal Laminar Bondar Laer Consider a laminar incompressible bondar laer with constant properties. Assme the flow is stead and two-dimensional aligned
More informationNumerical Simulation of Melting Process in Single Screw Extruder with Vibration Force Field
Nerical Silation of Melting Process in Single Screw Extrder with Vibration Force Field Yanhong Feng Jinping Q National Eng. Research Center of Novel Eqipent for Polyer Processing, Soth China University
More informationInertial and gravitational mass in relativistic mechanics
Träge nd schere Masse in der Relativitätsmechanik Ann. Phs. (Leipig) (4) 4 (1913) 856-878. Inertial and gravitational mass in relativistic mechanics B Gnnar Nordstrøm Translated b D. H. Delphenich In several
More informationFREQUENCY DOMAIN FLUTTER SOLUTION TECHNIQUE USING COMPLEX MU-ANALYSIS
7 TH INTERNATIONAL CONGRESS O THE AERONAUTICAL SCIENCES REQUENCY DOMAIN LUTTER SOLUTION TECHNIQUE USING COMPLEX MU-ANALYSIS Yingsong G, Zhichn Yang Northwestern Polytechnical University, Xi an, P. R. China,
More informationUNIT V BOUNDARY LAYER INTRODUCTION
UNIT V BOUNDARY LAYER INTRODUCTION The variation of velocity from zero to free-stream velocity in the direction normal to the bondary takes place in a narrow region in the vicinity of solid bondary. This
More informationStudy on the impulsive pressure of tank oscillating by force towards multiple degrees of freedom
EPJ Web of Conferences 80, 0034 (08) EFM 07 Stdy on the implsive pressre of tank oscillating by force towards mltiple degrees of freedom Shigeyki Hibi,* The ational Defense Academy, Department of Mechanical
More informationModelling by Differential Equations from Properties of Phenomenon to its Investigation
Modelling by Differential Eqations from Properties of Phenomenon to its Investigation V. Kleiza and O. Prvinis Kanas University of Technology, Lithania Abstract The Panevezys camps of Kanas University
More informationDecision Oriented Bayesian Design of Experiments
Decision Oriented Bayesian Design of Experiments Farminder S. Anand*, Jay H. Lee**, Matthew J. Realff*** *School of Chemical & Biomoleclar Engineering Georgia Institte of echnology, Atlanta, GA 3332 USA
More informationSetting The K Value And Polarization Mode Of The Delta Undulator
LCLS-TN-4- Setting The Vale And Polarization Mode Of The Delta Undlator Zachary Wolf, Heinz-Dieter Nhn SLAC September 4, 04 Abstract This note provides the details for setting the longitdinal positions
More informationCHAPTER 4: DYNAMICS: FORCE AND NEWTON S LAWS OF MOTION
CHAPTE 4: DYNAMICS: FOCE AND NEWTON S LAWS OF MOTION 4. NEWTON S SECOND LAW OF MOTION: CONCEPT OF A SYSTEM. A 6.- kg sprinter starts a race ith an acceleration of external force on him? 4. m/s. What is
More informationSubject Code: R13110/R13 I B. Tech I Semester Regular Examinations Jan./Feb ENGINEERING MECHANICS
Set No - 1 I B. Tech I Seester Regular Exainations Jan./Feb. 2015 ENGINEERING MECHANICS (Coon to CE, ME, CSE, PCE, IT, Che E, Aero E, AME, Min E, PE, Metal E) Tie: 3 hours Max. Marks: 70 What is the principle
More informationSECTION 6.7. The Dot Product. Preview Exercises. 754 Chapter 6 Additional Topics in Trigonometry. 7 w u 7 2 =?. 7 v 77w7
754 Chapter 6 Additional Topics in Trigonometry 115. Yo ant to fly yor small plane de north, bt there is a 75-kilometer ind bloing from est to east. a. Find the direction angle for here yo shold head the
More informationCalculations involving a single random variable (SRV)
Calclations involving a single random variable (SRV) Example of Bearing Capacity q φ = 0 µ σ c c = 100kN/m = 50kN/m ndrained shear strength parameters What is the relationship between the Factor of Safety
More informationDepartment of Industrial Engineering Statistical Quality Control presented by Dr. Eng. Abed Schokry
Department of Indstrial Engineering Statistical Qality Control presented by Dr. Eng. Abed Schokry Department of Indstrial Engineering Statistical Qality Control C and U Chart presented by Dr. Eng. Abed
More informationIMPROVED ANALYSIS OF BOLTED SHEAR CONNECTION UNDER ECCENTRIC LOADS
Jornal of Marine Science and Technology, Vol. 5, No. 4, pp. 373-38 (17) 373 DOI: 1.6119/JMST-17-3-1 IMPROVED ANALYSIS OF BOLTED SHEAR ONNETION UNDER EENTRI LOADS Dng-Mya Le 1, heng-yen Liao, hien-hien
More informationarxiv: v1 [cs.sy] 26 Oct 2018
A simple controller for the transition manever of a tail-sitter drone A. Flores, A. Montes de Oca and G. Flores arxiv:8.534v [cs.sy] 26 Oct 28 Abstract This paper presents a controller for the transition
More informationDILUTE GAS-LIQUID FLOWS WITH LIQUID FILMS ON WALLS
Forth International Conference on CFD in the Oil and Gas, Metallrgical & Process Indstries SINTEF / NTNU Trondheim, Noray 6-8 Jne 005 DILUTE GAS-LIQUID FLOWS WITH LIQUID FILMS ON WALLS John MORUD 1 1 SINTEF
More informationFEATURES OF ADJACENT STREAM HYDRODYNAMICS OF THE TWO-PHASE MEDIUM
UDC 6.7 Gravity separation V.I. KRIVOSHCHEKOV, PhD. (Ukraine, Dnepropetrovsk, National Mining University),.A. NOVIKOV (Ukraine, Dnepropetrovsk, Institte of Geotechnical Mechanics named by of N.S. Polyakov
More informationNew MINLP Formulations for Flexibility Analysis for Measured and Unmeasured Uncertain Parameters
Anton A. Kiss, Edwin Zondervan, Richard Lakerveld, Leyla Özkan (Eds.) Proceedings of the 29 th Eropean Syposi on Copter Aided Process Engineering Jne 16 th to 19 th, 219, Eindhoven, The Netherlands. 219
More informationLinear System Theory (Fall 2011): Homework 1. Solutions
Linear System Theory (Fall 20): Homework Soltions De Sep. 29, 20 Exercise (C.T. Chen: Ex.3-8). Consider a linear system with inpt and otpt y. Three experiments are performed on this system sing the inpts
More informationEffects of modifications on the hydraulics of Denil fishways
BOREAL ENVIRONMENT RESEARCH 5: 67 79 ISSN 1239-6095 Helsinki 28 March 2000 2000 Effects of modifications on the hydralics of Denil fishways Riitta Kamla 1) and Jan Bärthel 2) 1) Water Resorces and Environmental
More informationOptimal Control of a Heterogeneous Two Server System with Consideration for Power and Performance
Optimal Control of a Heterogeneos Two Server System with Consideration for Power and Performance by Jiazheng Li A thesis presented to the University of Waterloo in flfilment of the thesis reqirement for
More informationLab Manual for Engrd 202, Virtual Torsion Experiment. Aluminum module
Lab Manal for Engrd 202, Virtal Torsion Experiment Alminm modle Introdction In this modle, o will perform data redction and analsis for circlar cross section alminm samples. B plotting the torqe vs. twist
More informationDiffraction of light due to ultrasonic wave propagation in liquids
Diffraction of light de to ltrasonic wave propagation in liqids Introdction: Acostic waves in liqids case density changes with spacing determined by the freqency and the speed of the sond wave. For ltrasonic
More informationUpper Bounds on the Spanning Ratio of Constrained Theta-Graphs
Upper Bonds on the Spanning Ratio of Constrained Theta-Graphs Prosenjit Bose and André van Renssen School of Compter Science, Carleton University, Ottaa, Canada. jit@scs.carleton.ca, andre@cg.scs.carleton.ca
More information4.4 Moment of a Force About a Line
4.4 Moment of a orce bot a Line 4.4 Moment of a orce bot a Line Eample 1, page 1 of 3 1. orce is applied to the end of gearshift lever DE. Determine the moment of abot shaft. State which wa the lever will
More informationMECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 2 INTERMEDIATE AND SHORT COMPRESSION MEMBERS
MECHANICS O SOIDS COMPRESSION MEMBERS TUTORIA INTERMEDIATE AND SHORT COMPRESSION MEMBERS Yo shold jdge yor progress by completing the self assessment exercises. On completion of this ttorial yo shold be
More informationNumerical Simulation of Density Currents over a Slope under the Condition of Cooling Period in Lake Biwa
Nmerical Simlation of Densit Crrents oer a Slope nder the Condition of Cooling Period in Lake Bia Takashi Hosoda Professor, Department of Urban Management, Koto Uniersit, C1-3-65, Kotodai-Katsra, Nishiko-k,
More informationChapter 3. Preferences and Utility
Chapter 3 Preferences and Utilit Microeconomics stdies how individals make choices; different individals make different choices n important factor in making choices is individal s tastes or preferences
More informationCosmic Microwave Background Radiation. Carl W. Akerlof April 7, 2013
Cosmic Microwave Backgrond Radiation Carl W. Akerlof April 7, 013 Notes: Dry ice sblimation temperatre: Isopropyl alcohol freezing point: LNA operating voltage: 194.65 K 184.65 K 18.0 v he terrestrial
More informationSimulation investigation of the Z-source NPC inverter
octoral school of energy- and geo-technology Janary 5 20, 2007. Kressaare, Estonia Simlation investigation of the Z-sorce NPC inverter Ryszard Strzelecki, Natalia Strzelecka Gdynia Maritime University,
More informationA New Approach to Direct Sequential Simulation that Accounts for the Proportional Effect: Direct Lognormal Simulation
A ew Approach to Direct eqential imlation that Acconts for the Proportional ffect: Direct ognormal imlation John Manchk, Oy eangthong and Clayton Detsch Department of Civil & nvironmental ngineering University
More informationThe Calculation of the Diffraction Integral Using Chebyshev Polynomials
International Jornal of Applied Engineering Research ISSN 97-456 Vole, Nber (7) pp. -9 Research India Pblications. http://www.ripblication.co The Calclation of the Diffraction Integral Using Chebyshev
More informationCopyright Canadian Institute of Steel Construction
Copyright 017 by Canadian Institte of Steel Constrction All rights reserved. This book or any part thereof mst not be reprodced in any form withot the written permission of the pblisher. Third Edition
More informationStudent Book pages
Chapter 7 Review Student Boo pages 390 39 Knowledge. Oscillatory otion is otion that repeats itself at regular intervals. For exaple, a ass oscillating on a spring and a pendulu swinging bac and forth..
More informationIntegration of Basic Functions. Session 7 : 9/23 1
Integration o Basic Fnctions Session 7 : 9/3 Antiderivation Integration Deinition: Taking the antiderivative, or integral, o some nction F(), reslts in the nction () i ()F() Pt simply: i yo take the integral
More informationGeometric Image Manipulation. Lecture #4 Wednesday, January 24, 2018
Geometric Image Maniplation Lectre 4 Wednesda, Janar 4, 08 Programming Assignment Image Maniplation: Contet To start with the obvios, an image is a D arra of piels Piel locations represent points on the
More informationTheoretical Fluid Mechanics Turbulent Flow Velocity Profile By James C.Y. Guo, Professor and P.E. Civil Engineering, U. of Colorado at Denver
Theoretical Flid Mechanics Trblent Flow Velocit Proile B Jaes C.Y. Go, Proessor and P.E. Civil Engineering, U. o Colorado at Denver 1. Concept o Mixing Process in Trblent Flow Far awa ro the solid wall,
More informationHorizontal Distribution of Forces to Individual Shear Walls
Horizontal Distribtion of Fores to ndividal Shear Walls nteration of Shear Walls ith Eah Other n the shon figre the slabs at as horizontal diaphragms etending beteen antilever alls and the are epeted to
More informationElements of Coordinate System Transformations
B Elements of Coordinate System Transformations Coordinate system transformation is a powerfl tool for solving many geometrical and kinematic problems that pertain to the design of gear ctting tools and
More informationLumped-Parameter Model for Foundation on Layer
Missori University of Science and Technology Scholars' Mine International Conferences on Recent Advances in Geotechnical Earthqake Engineering and Soil Dynamics 1991 - Second International Conference on
More informationDetermining of temperature field in a L-shaped domain
Available online at www.pelagiaresearchlibrary.com Advances in Applied Science Research, 0, (:-8 Determining of temperatre field in a L-shaped domain Oigo M. Zongo, Sié Kam, Kalifa Palm, and Alione Oedraogo
More informationBLOOM S TAXONOMY. Following Bloom s Taxonomy to Assess Students
BLOOM S TAXONOMY Topic Following Bloom s Taonomy to Assess Stdents Smmary A handot for stdents to eplain Bloom s taonomy that is sed for item writing and test constrction to test stdents to see if they
More informationElectromagnetics I Exam No. 3 December 1, 2003 Solution
Electroagnetics Ea No. 3 Deceber 1, 2003 Solution Please read the ea carefull. Solve the folloing 4 probles. Each proble is 1/4 of the grade. To receive full credit, ou ust sho all ork. f cannot understand
More informationSareban: Evaluation of Three Common Algorithms for Structure Active Control
Engineering, Technology & Applied Science Research Vol. 7, No. 3, 2017, 1638-1646 1638 Evalation of Three Common Algorithms for Strctre Active Control Mohammad Sareban Department of Civil Engineering Shahrood
More informationDESIGNING FOR LATERAL-TORSIONAL STABILITY IN WOOD MEMBERS
DESIGNING FOR ATERA-TORSIONA STABIITY IN WOOD EBERS American Wood oncil TEHNIA REPORT 4 American Forest & Paper Association The American Wood oncil (AW) is the wood prodcts division of the American Forest
More informationJ.A. BURNS AND B.B. KING redced order controllers sensors/actators. The kernels of these integral representations are called fnctional gains. In [4],
Jornal of Mathematical Systems, Estimation, Control Vol. 8, No. 2, 1998, pp. 1{12 c 1998 Birkhaser-Boston A Note on the Mathematical Modelling of Damped Second Order Systems John A. Brns y Belinda B. King
More informationOPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Final Exam In Class Page 1/16 Fall, 2015
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 1/16 Fall, 2015 Name Closed book; closed notes. Time limit: 120 mintes. An eqation sheet is attached and can be
More informationPhysicsAndMathsTutor.com
. Two smooth niform spheres S and T have eqal radii. The mass of S is 0. kg and the mass of T is 0.6 kg. The spheres are moving on a smooth horizontal plane and collide obliqely. Immediately before the
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA. PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 13 NQF LEVEL 3 OUTCOME 3 - HYDRODYNAMICS
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 3 NQF LEVEL 3 OUTCOME 3 - HYDRODYNAMICS TUTORIAL - PIPE FLOW CONTENT Be able to determine the parameters of pipeline
More informationChapter 3. Systems of Linear Equations: Geometry
Chapter 3 Systems of Linear Equations: Geometry Motiation We ant to think about the algebra in linear algebra (systems of equations and their solution sets) in terms of geometry (points, lines, planes,
More informationSimplified Identification Scheme for Structures on a Flexible Base
Simplified Identification Scheme for Strctres on a Flexible Base L.M. Star California State University, Long Beach G. Mylonais University of Patras, Greece J.P. Stewart University of California, Los Angeles
More informationAE Stability and Control of Aerospace Vehicles
AE 430 - Stability and ontrol of Aerospace Vehicles Static/Dynamic Stability Longitudinal Static Stability Static Stability We begin ith the concept of Equilibrium (Trim). Equilibrium is a state of an
More informationA Cyclic Shear-Volume Coupling and Pore Pressure Model for Sand
Missori University of Science and Technology Scholars' Mine nternational Conferences on Recent Advances in Geotechnical Earthqake Engineering and Soil Dynamics 1991 - Second nternational Conference on
More informationDetermination of the Young's modulus of an aluminium specimen
Maria Teresa Restivo, Faculdade de Engenharia da Universidade do Porto, Portugal, trestivo@fe.up.pt Carlos Sousa, CATIM - Centro de Apoio à Industria Metaloecânica, Porto, Portugal, csousa@cati.pt Noveber,
More informationTwo-media boundary layer on a flat plate
Two-media bondary layer on a flat plate Nikolay Ilyich Klyev, Asgat Gatyatovich Gimadiev, Yriy Alekseevich Krykov Samara State University, Samara,, Rssia Samara State Aerospace University named after academician
More informationECON3120/4120 Mathematics 2, spring 2009
University of Oslo Department of Economics Arne Strøm ECON3/4 Mathematics, spring 9 Problem soltions for Seminar 4, 6 Febrary 9 (For practical reasons some of the soltions may inclde problem parts that
More informationQuadratic forms and a some matrix computations
Linear Algebra or Wireless Conications Lectre: 8 Qadratic ors and a soe atri coptations Ove Edors Departent o Electrical and Inoration echnology Lnd University it Stationary points One diension ( d d =
More informationPart I: How Dense Is It? Fundamental Question: What is matter, and how do we identify it?
Part I: How Dense Is It? Fundaental Question: What is atter, and how do we identify it? 1. What is the definition of atter? 2. What do you think the ter ass per unit volue eans? 3. Do you think that a
More informationCHAPTER 8 ROTORS MOUNTED ON FLEXIBLE BEARINGS
CHAPTER 8 ROTORS MOUNTED ON FLEXIBLE BEARINGS Bearings commonly sed in heavy rotating machine play a significant role in the dynamic ehavior of rotors. Of particlar interest are the hydrodynamic earings,
More informationSTEP Support Programme. STEP III Hyperbolic Functions: Solutions
STEP Spport Programme STEP III Hyperbolic Fnctions: Soltions Start by sing the sbstittion t cosh x. This gives: sinh x cosh a cosh x cosh a sinh x t sinh x dt t dt t + ln t ln t + ln cosh a ln ln cosh
More informationIJSER. =η (3) = 1 INTRODUCTION DESCRIPTION OF THE DRIVE
International Jornal of Scientific & Engineering Research, Volme 5, Isse 4, April-014 8 Low Cost Speed Sensor less PWM Inverter Fed Intion Motor Drive C.Saravanan 1, Dr.M.A.Panneerselvam Sr.Assistant Professor
More informationMotion in an Undulator
WIR SCHAFFEN WISSEN HEUTE FÜR MORGEN Sven Reiche :: SwissFEL Beam Dnamics Grop :: Pal Scherrer Institte Motion in an Undlator CERN Accelerator School FELs and ERLs On-ais Field of Planar Undlator For planar
More informationCurves - Foundation of Free-form Surfaces
Crves - Fondation of Free-form Srfaces Why Not Simply Use a Point Matrix to Represent a Crve? Storage isse and limited resoltion Comptation and transformation Difficlties in calclating the intersections
More informationReduction of over-determined systems of differential equations
Redction of oer-determined systems of differential eqations Maim Zaytse 1) 1, ) and Vyachesla Akkerman 1) Nclear Safety Institte, Rssian Academy of Sciences, Moscow, 115191 Rssia ) Department of Mechanical
More informationLIGHTWEIGHT STRUCTURES in CIVIL ENGINEERING - CONTEMPORARY PROBLEMS
ITERATIOAL SEMIAR Organized by Polish Chapter o International Association or Shell and Spatial Strctres LIGHTWEIGHT STRUCTURES in CIVIL EGIEERIG - COTEMPORARY PROBLEMS STOCHASTIC CORROSIO EFFECTS O RELIABILITY
More information