Suvremene metode proracuna
Transcript of Suvremene metode proracuna
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Suvremeni postupciproračuna konstrukcija
Povijest i razvoj računala
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Prvo računalo – ABAK ili ABAKUS 3000 godina prije Krista
♦ Ploča s utorima u kojima su oblutci podsjeća nas na vrijeme kad su kamenčići (calculus) korišteni za računanje
♦ Kina (Babilon?) – okvir s napetim žicama i nanizanim kuglicama.
Jednostavni računski strojevi
Jedna od prvih naprava bila je kineski abakus kojom su se već u trećem mileniju p.n.e. učinkovito obavljale operacije zbrajanja i oduzimanja.
Abacus (kineski Abak), najstariji "kompjutor" na svijetu preživio je sve do danas. Svi proračuni potrebni za izradu prve kineske atomske bombe obavljeni su na njemu.
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Johan Napier♦ Škotski matematičar
Johan Napier (NEPER)[Nejpjer] – napravio logaritamske tablice (1617).
♦ Kopirao je svoje tablice na šipke od slonovače i mehaničkim pomicanjem šipki dobivao je željeni umnožak. Iz te je naprave kroz generacije proizašlo logaritamsko računalo
Babbageov diferencijalni stroj.
Charles Babbage -1833. godine
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Elektronska programibilna računala
Amerikanci John Mauchly i Presper Eckert konstruirali su 1946. godine ENIAC (Electronic Numerical Integrator and Calculator), prvo računalo na temelju elektronskih cijevi.
Računalo ENIAC bilo je pravi elektronski kolos: težak oko 30 tona, imao je 18000 elektronskih cijevi, smješten u dvorani površine 1500 m2.
Nedostaci:
♦mala memorija i
♦nije bio programibilan.
Godine 1948. pojavljuju se tranzistori. U odnosu na elektronsku cijev tranzistor se manje grijao i bio pouzdaniji u radu. To je dovelo do smanjivanja dimenzija računala, njihove stabilnosti u radu i jeftinije izrade.
Čip (chip) – pločica u kojoj je smješteno (integrirano) na stotine tranzistora.
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1970. Intel proizvodi prvi mikroprocesor 1973. prvo osobno računalo (Xerox Altos)1977. Apple II računalo. 1981. IBM proizveo PC Junior računalo.
Operativni sustavi
1. Windows XP 86.80% 2. Windows 2000 6.09% 3. Windows 98 2.68% 4. Macintosh 2.32% 5. Windows ME 1.09% 6. Linux 0.36% 7. Windows NT 0.24% 8. Macintosh Power PC 0.15%
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Programski jezici
Kompjutor može izvršiti samo mali broj veomajednostavnih operacija. Na primjer, oduzimanje, množenje i dijeljenje svodi na operacijezbrajanja i pomi-canja znamenki.
Kompjutor "razumije" i može izvršiti samoinstrukcije strojnog jezika.
Generacije jezika za programiranje
S razvojem kompjutora usavršavao se i jezikza komuniciranje (programiranje), pa razlikujemo četiri generacije:
1. strojni jezici,
2. simbolički (asemblerski) jezici,
3. jezici za programiranje visoke razine,
4. jezici četvrte generacije (jezici krajnjihkorisnika).
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Strojni jezik00100100 01011111 00100010 0101111100110010 01000000 01001110 11111010 00000000 00000110 00001000 00101001 00000000 00000000 00000000 0000000101100111 0000001011010100 0101000101010100 0100100101010001 11001001 11111111 1111001000111110 1000001001001110 11010010
Simbolički (asemblerski) jezik SUMMODDS MOVE.L (A7)+,A2
MOVE.L (A7)+,A1MOVE.W (A7)+,D2CLR.W D2JMP COUNT
LOOP BTST 0,1(A1)BEQ.S NEXTADD.W (A1),D2
NEXT ADDQ.W #2,A1COUNT DBF D1,LOOP
MOVE.W D2,-(A7)JMP (A2)
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Treća generacija: viši programski jezici
FORTRAN, ALGOL, COBOL, PL/1, Ada, LISP, PROLOG BASIC, LOGO, Pascal (Delphi), C (C++)
Treća generacija: viši programski jezici
TO ZBROJIMAKE “A READMAKE “B READMAKE “Z :A+:BPR :ZEND
INPUT AINPUT BZ=A+BPRINT ZEND
program zbroji;var a, b: integer;begin
readln (a);readln (b);z:=a+b;
writeln (z);end.
#include <stdio.h>void main () {int a,b,c;
scanf ("%d,%d",&a, &b);z=a+b;printf ("%d", z);
}
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Jezici četvrte generacije
•upitni jezici za bazu podataka (SQL, Asi, GIS,…)• jezici za podršku u odlučivanju (visiCalc, Multiplan, …)• generatori programa (Mapper, Focus, …)• jezici za programiranje vrlo visoke razine (AME, NOMAD, …)
Objektno orijentirani programiProgrameri programe sastavljaju od već gotovih dijelova - objekata.
Visual BASIC, Visual C++, Delphi
Jezični prevoditeljiPrevode program u strojni jezik
Tijekom svakog izvođenja interpreteri prevode svakunaredbu izvornog programa u strojni (binarni) oblik.
Kompajleri izvorni program prevode u strojni oblik u posebnom postupku prevođenja (kompajliranja). Prevođenjem izvornog programa dobit ćemo datotekuobjektnog kôda (object code). Povezivanjem objektnogkôda s već postojećim bibliotekama nastaje izvršniprogram (EXEcutable program).
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Ekstenzije datotekaARJ Robert Jung ARJ compressed archive
AVI Microsoft Video for Windows movie
BAS BASIC code
BAT Batch file
BMP Windows or OS/2 bitmap
CSV Comma-separated values file
DOC Microsoft Word document
DOT Microsoft Word document Template
DWG AutoCAD drawing, or older Generic CADD drawing format
DXF Drawing Interchange (eXchange) format
EMF Enhanced Windows Metafile
EXE Executable file (program)
GIF CompuServe bitmap
JPEG JPEG ("Joint Picture Expert Group") compressed bitmap
JPG JPEG compressed bitmap
MP3 MPEG Audio Layer 3 (AC3) file
MPEG MPEG ("Motion-PEG") animation
Ekstenzije datoteka
PCX ZSoft PC Paintbrush bitmapPDF Adobe Acrobat Portable Document Format PNG Portable Network Graphics bitmapPPS Microsoft PowerPoint slide showPPT Microsoft PowerPoint presentationTIF Tag Image File Format (TIFF) bitmapTIFF Tag Image File Format (TIFF) bitmapWMF Windows MetafileWRL Virtual Reality modelXLS Microsoft Excel worksheetZIP Zip file Compressed archive
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Umjetna inteligencija
UUmjetna inteligencija je znanstveno područje koje se bavi razvojem računarskih tehnika za rješavanje zadaćapovezanih s ljudskom inteligencijom.
IInteligencija je sposobnost stjecanja i korištenja znanjau cilju indukcije novog.
Očituje se u moći komunikacije, učenja i zaključivanja.
UUz inteligenciju se vezuju pojmovi kao što sukreativnost, intuicija, znanje, razmišljanje ...
Umjetna inteligencija
Osnovne pravce razvoja čine:1. ekspertni sustavi, (medicina, industrija,
prirodni govor, prevođenje)2. neuronske mreže, (umjetni vid u robotici,
biomedicini, analizi materijala)3. fuzzy logika (matematika, upravljanje
procesima) i4. genetski algoritmi (konstruiranje, oblikovanje,
optimizacija).
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Umjetna inteligencija
Može li računalo misliti?
• nije li računalo stroj koji radi samo s nulama ijedinicama ?
• ako računalo može misliti, onda je inteligencijanešto mehaničko pa čovjek nije ništa bolji odstroja ?
• neće li stoga strojevi preuzeti čovjeku primat ?
•.... itd.
Ekspretni sustavi
Pravila:
Pr 1. AKO m TADA p b, c, d
Pr 2. AKO g ILI m TADA r
Pr 3. AKO f TADA g
Pr 4. AKO f I e TADA m
Pr 5. AKO a I d TADA f
Pr 6. AKO b TADA a
Pr 7. AKO b I c I d TADA e
IF .... THEN
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Neuronske mreže
60 ulaza 6 skrivenih 2 izlaza
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Trenirana mreža-prepoznavanje govoraMarko
Maja
0.01
0.99
0.99
0.01
Šiber
Rapidografi
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Proračun prije primjene računala:
Ulagao se velik napor na teoretska i eksperimentalna istraživanja novih metoda proračuna relativno niske složenosti.
Proračun danas• primjena računala u analizi konstrukcija,• razvoj novih “kompjutorskih” metoda proračuna, • dominaciju MKE (FEM),• istraživanje znanja/vještine pod nazivom ¨Numeričko
modeliranje¨,• inženjer usmjerava svoju energiju na razumjevanje
fizikalnog ponašanja konstrukcije,• mogućnost analiza i najsloženijih konstrukcija bez
nužnog znanja kompliciranih matematičkih teorija
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Akashi-Kaikyo Bridge 1990m
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Messina bridge
Messina bridge
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Messina bridge
Osnovna ideja MKE
Promatrana domena, kao kontinuum s beskonačno mnogo stupnjeva slobode, zamjenjuje se diskretnim modelom međusobno povezanih konačnih elemenata, s konačnim brojem stupnjeva slobode.
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Izbor nepoznanica u čvorovima
Nepoznanice u čvorovima: 1 1 2 2, , ,v vϕ ϕ gdje su:
1 21 2
,dv dvdx dx
ϕ ϕ = =
Izbor funkcije pomaka
Izbor funkcije pomaka ( ) 2 3
1 2 3 41v x x x xα α α α= ⋅ + ⋅ + ⋅ + ⋅ Kut zaokreta dan je izrazom:
2
2 3 42 3dv x xdx
ϕ α α α= = + ⋅ ⋅ + ⋅ ⋅
a zakrivljenost:
2
3 42 2 6d v xdx
α α− = − ⋅ − ⋅ ⋅
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Osnovna jednadžba konačnog elementa
2 2
21
d vx F M dxdx
δδ
= − ⋅ ⋅
∫
Osnovna jednadžba konačnog elementa izvodi se koristeći principo minimumu energije.
"Pri svakom zadanom virtualnom (mogućem) pomaku konačnogelementa, prirast rada vanjskih sila na zadanim pomacima čvorovajednak je prirastu rada unutarnjih sila na odgovarajućimdeformacijama".
[ ] [ ] [ ]F K q= ⋅
U matričnom obliku: [ ]K -matrica krutosti konačnog elementa,
[ ]F -vektor čvornih sila,
[ ]q - vektor čvornih pomaka.
Model
• Model mora simulirati stvarno ponašanje konstrukcije,• Sva pojednostavljenja moraju biti na strani sigurnosti
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Model ljuska - SHELL
SHELL = PLOČA + MEMBRANA= PLATE + MEMB
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Štapni (linijski) modeli
Plošni modeli
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Brick elementi
Model pločastog mosta.Kombinacija plošnih i linijskih elemenata
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+PROG ASE
HEAD
NMAT 1 MEMB 1 1
SYST PROB THII ITER 30
GRP 0 FACS 1E-10
HIGH 0 0 PR1 7 PTPR 0.2
LC 1 DLZ 1 TITL ''
NL 481 WZ -6
END
+PROG ASE urs:4
HEAD
SYST PLC 1 STOR YES
END
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Dimenzioniranje
• Granična stanja• Proračun pukotina• Proračun progiba• Proračun naprezanja
U program je ugrađen jedan od propisaEC2, DIN1045, DIN4227, PBAB, ACI...
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DABP
Software:ABAQUS - Non-Linear F.E. Analysis Aprop - Determine section properties of shapes or composites Adapt Software Systems - Prestressed/Reinforced Concrete Design & Analysis. ADINA - Non Linear F.E. Analysis AFE Software Ltd - Masonry arch design software ALGOR - General Purpose F.E. Alashki - Impressive concrete design programs ANSYS/ CivilFEMATIR Engineering Software - Home of STRAP - F.E. Modeling Software CADRE Pro and CADRE Lite - 3D and 2D Beam Analysis CADS - Analysis and design software Cbeam2002 - Solve statically indeterminate beam structures Cobras - Concrete Bridge Assessment Program - Yield Line Analysis Department of Civil and Mechanical Engineering, United States Military Academy - Free Utilities! Design Data - Structural steel design and detailing Dr.techn.OlavOlsen a.s - Advanced concrete design tools DTColumn - Interaction diagrams for round concrete columnsFree! EDI-SACS - Nonlinear analysis software DIANA - Finite element program EngineeringSpreadsheets.co.uk - Excel programs for structural design Ensoft - LPile and more FastFrame - Windows 95, 98 & NT Two-Dimensional frame analysis programFree! Finite Element Home Page - Comprehensive Links Page for Commercial and Public Domain F.E. Software FELT - Public Domain F.E. Software GT STRUDL, Structural Analysis and Design Software for Civil Engineers GT STRUDL - from SC Solutions GRAPE - 3D Beam/Truss Finite Element Program Grasp - Windows truss and frame analysis HEAT - Non Linear F.E. software for early age crack control IDARC - Nonlinear structural analysis of concrete behavior. University at BuffaloFree! IES - Integrated Engineering Software - FEA and Other Structural Utilities LARSA - Linear and nonlinear FEA program LIMCON - Steel connection design LISA MECHANIC - 2D and 3D frames, plates, and solid elements; statics and dynamics. 1300 node version is Free! Losch Engineering Corporation - Wall and prestressed beam design software The Mechanical Engineering Zone - Java apps for beam analysis and more Free! Microstran - General structural analysis MLS - Non Linear F.E. software for Multi Layer Systems MOISTURE - Non Linear F.E. software for combined moisture and stress simulations MSTower - Tower and mast design Multiframe - Three dimensional structural analysis and design software system MSC Software - Home of NASTRAN and many other programs NONLIN - Nonlinear Dynamic Time History Analysis of Single Degree of Freedom Systems Free! Oasys GSA - Static and dynamic analysis of frame and 2D finite element models OpenSEES - Software framework for seismic structural analysis Free! PCA - Concrete design programs PCStruct - 2D Structural Analysis for MS Windows Pikaso Software - Reinforced concrete utilities. PROKON - FE Software and more. RISA Technologies - FE Software Research Engineers Inc. - Home of STAAD, STRUCT.ect, STARDYNE, CIVILSOFT Response 2000 - Calculates strength and ductility of reinforced concrete cross-sections subjected to shear, moment, and axial load ROBOT 97 - Very graphical F.E. analysis software. SAFI - 2D and 3D finite element analysis SCALE - All sorts of structural utilities CSI - SAP 2000, General Purpose Analysis and Design
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Predprocesor
Postprocesor
PROCESOR (Solver)
DirectX
OpenGL
DirectX (DirectDraw, DirectSound, Direct3D, DirectPlay, DirectInput)
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BRIDG97
STAAD III
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Nemetschek
Nemetschek
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Allplan
Supported steel design codes:
•AISC - 1989 ASD*. •AISC - 1993 LRFD*. •BS5950 - 1990. •BS5950 - 2000*. •CSA-S16.1 - M94. •Eurocode 3 - 1992. •GBL 17 - 1988*. •IS800 - 1984*. •SABS0162 - 1984 (allowable stress design). •SABS0162 - 1993 (limit state design).
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Supported concrete design codes:
•ACI 318-95*. •BS 8110 - 1997. •CP 65 - 1999. •CSA-A23.3-94. •Eurocode 2 - 1992. •SABS 0100 - 1992.
Supported timber design codes:
•BS 5268 - 1991 (allowable stress design). •SABS 0163 - 1989 (allowable stress design).
Supported units of measurement:
•Imperial. •Metric.
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TOWER
Tower
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ANSYS
SCADDS/RC-Beam Drafter
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PROKON
Potporni zid
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Potporni zid
Potporni zid
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Čelik - detalji
Temelj
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Temelj
Temelj
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Stup
Stup
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Stup
Stup
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Stup
FEMAP
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FASTRAK
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SismiCAD
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BEAMD
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BEAMD
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ROBOT
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•Unlimited number of spans •T, L R cross sections •Precast/Prefab •Bending, shear torsion •Unlimited number of load cases and combinations •Change of inertia within a span •Preliminary sizing •Design based on ACI 318-99, EC2, DIN, BAEL •Skipping loads •Bending and shear envelop diagrams •Rectangular and circular holes •3D view of every single rebar •Graphical interaction with every single bar for editing •Automatic detailing drawing fully customizable •Generates dxf files •Graphical and tabular Word report •Price estimation •Friendly user interface •Fully interfaced with Robot Millenium and Robot Concrete Building system •American and metric units
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Aspalathos
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ArmaCAD
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ArmaCAD
ArmaCAD
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SofiCAD
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ADINA
ADINA- protok krvi
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ADINA-generator brick elemenata
ADINA2-D Multi-body Contact Example solved using Explicit Time Integration
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ADINA
SAP 2000
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SAP 2000
SAP 2000
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DIANA
Ceste
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Vodovod i kanalizacija
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Dinamički proračunProračun vlastitih frekvencija i vlastitih vektora
Nelinearni proračun• Geometrijska nelinearnost• Materijalna nelinearnost
Utjecaj reoloških značajki gradivaSpecijalni programi (prednapinjanje)
Predprocesori i postprocesori
Most preko rijeke Krke
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Dinamičko opterećenje
Dinamičko opterećenje
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a
b
Kopplung
Ebene der Knotenpunkte
Exzentrizität
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Lamelirani nosač
Progib i naprezanjaKatz+Bellmann, 85764 Oberschleißheim, Bruckmannring 6, Tel:089/315-878-0GRAF 1997 28.01.99
-5.00 0.00 5.00 10.00
-35.00
X
Y
Z VERSCHOBENE STRUKTUR AUS LASTFALL 1 UEBERHOEHUNG 25.0
-5.00 0.00 5.00 10.00
-35.00
HAUPTMEMBRANKRAEFTE LF 1 1 CM = 2000. kN/m
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Naponi
-6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00
-34.00
-35.00
-36.00
-37.00
-38.00
6.62
-3.96-2.77
9.85
-10.01
9.12
-9.54
8.46
-9.08
7.07
-7.45
7.66
-8.35
Strut – tie modeli
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Strut – tie model
Strut – tie model
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Strut – tie modeli
Strut – tie model
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Strut – tie model
Optimizacija
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Optimizacija
Optimizacija
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Određivanje strut–tie modela - konzola
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Određivanje strut–tie modela - luk
Visokostjeni nosač
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Određivanje strut–tie
modela
Materijalna i geometrijska nelinearnost.
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Materijalna i geometrijska nelinearnost.Poprečni i uzdužni presjek stupa.
POPRECNI PRESJEK STUPA
UZDUŽNI PRESJEK
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Teorija II reda
Mom
ent s
avija
nja
(kN
m)
Pom
aci (
mm
)
Arm
atur
a (c
m2)
Teorija I redaK
ruto
st E
I (%
)
Kru
tost
EI (
%)
Pom
aci (
mm
)
Arm
atur
a (c
m2)
Mom
ent s
avija
nja
(kN
m)
Promjena koeficijenata αd, αs i αm s obzirom na vitkost za uporabno naprezanje od -12MPa.
1
1.5
2
2.5
3
3.5
0 50 100 150 200 250
Vitkost
Pomak
Armatura
Moment
α
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Dijagrami interakcije za različite vitkosti, za ω =0,25-1,5
-1,3
-1,1
-0,9
-0,7
-0,5
-0,3
-0,1
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40
µSd
ν Sd
As1=ω(fcd/fyd)bh As2=β As1
β =1 ω=0,25 d1/h=d2/h=0,1 RA 400/500
Momentni dijagram za element armiran u gornjoj i donjoj zoni.
L
L
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Momentni dijagram za element armiran samo u donjoj zoni
L
L
pukotine pukotine
Momentni dijagram za element armiran samo u gornjoj zoni
L
L
pukotine
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Momentni dijagrami u ovisnosti o nosivosti presjeka
L
L
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Usmjerenost pukotina
Naprezanje u armaturi
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Pukotine nakon puzanjai skupljanja betona
Plastik
Glas
Glas
Schichtdicken ti
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Panel i stringer elementi
Panel elementi
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Primjer
Statički model
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3 koraka proračuna
Rezultati proračuna
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Armatura
Nelinearni proračun
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Pukotine - SLS
Deformacije ULS
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Stringer
ATENA
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Atena
Preraspodjela naprezanja uslijed dugotrajnih djelovanja
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Naprezanja i deformacije
Naprezanja i deformacije.
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Naprezanja i deformacije u trenutku: To
Naprezanja i deformacije u trenutku: Too
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STUPOVIStupovi su elementi opterećeni uzdužnom silom i
momentom savijanja.
Određivanje dimenzija stupa:Ac ≥ Nsd/(0,75·fcd) za nisku duktilnost LAc ≥ Nsd/(0,65·fcd) za srednju duktilnost MAc ≥ Nsd/(0,55·fcd) za visoku duktilnost H
bmin = 20 cm (14 cm za montažni stup)bmin = 25 cm (Ako preuzima sile potresa )
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Dijagram interakcije
Duktilnost presjeka
yϕ uϕ
u
y
DUKTILNOST ϕϕ
=
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Shaking table
Kontrola vibracija
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PRORAČUN UNUTARNJIH SILA U AB KONSTRUKCIJ AMA IZLOŽENIH DUGOTRAJNOM OPTEREĆENJU
Momentni dijagram dvije montažne proste grede.
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Vremenom se pojavljuje dodatni moment ∆M(t)uslijed reoloških deformacija na drugom statičkom sustavu.
Superpozicijom dolazimo do momenta od vlastite težine u nekom trenutku vremena.
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Momentni dijagram Mt se vremenom mjenja od Mo prema Mk
Dvije prednapete montažne proste grede
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Ukupna deformacija betona sastoji se od tri dijela:
1. elastične deformacije c,elε ,
2. deformacije puzanja ( )cc tε i
3. deformacije skupljanja ( )cs tε .
Veze naprezanja i deformacija analiziraju se:
♦ numeričkim rješavanjem sistema integralnih jednadžbi (integralne veze) ili
♦ svođenjem integralne veze na jednostavnije algebarske veze (algebarske veze).
Integralna veza:
( ) ( ) ( )( ) ( )( )
( ) ( )0 00 0
0 ,28
,11 , , ∂
= + + + ⋅ + ∂ ∫t
c cc cs
c c cto
t t tt t t d t t
E E t Eσ σ τ ϕ
ε ϕ τ ετ
Algebarski veza po Trostu: ( ) ( ) ( )( ) ( ) ( )( ) ( )( ) ( ) ccs00cc00ccc Ett,t1ttt,t1ttE ⋅ε+ϕ⋅χ+σ−σ+ϕ+⋅σ=ε⋅
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PRIMJER 1kontinuirani nosač preko 2 polja
izveden u dvije faze
Problem je odreditinepoznati moment ∆M(t)
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Momentni dijagram u nekom trenutku vrem ena: ( ) ( )0 0= + − ⋅k MM t M M M α
gdje je: 0M -moment od sume f aza građenja; (montažnih stanja) kM -moment na konačnom sustavu Koeficijent Mα prema Trostu iznosi:
1=
+ ⋅Mϕ
αχ ϕ
Koeficijent Mα prema rješenju Dischingerove diferencijalne jednadžbe: 1 −= −M e ϕα
Faze građenja
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Izvedba luka
Faze građenja
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PREDNAPETI PRILAZNI DIO MOSTA PREKORIJEKE DUBROVAČKE
Faze izvedbe grede
GRADIVA:beton MB 50armatura RA 500/550kabeli 1570/1770zaštitni sloj betona 5 cm
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Most Dubrovnik.
Gradjevinski Fakultet * Kaciceva 26 * 41000 ZagrebGEOS (V10.11-99) 7.12.2002
Koranske mlinicekabeli u hrptu 10
M 1 : 283
0.00 10.00 20.00 30.00 40.00 50.00 60.00 m
23601
0.00
24
5.00
24501
5.00
25
10.00
25401
10.00
26
15.00
26301
15.00
27
20.00
27201
20.00
28
25.00
28101
25.00
29
28.75
29111
28.75
30
30.50
30112
30.50
31
32.25
31102
32.25
32
36.00
32202
36.00
33
41.00
33302
41.00
34
46.00
34402
46.00
35
51.00
35502
51.00
36
56.00
36602
56.00
37
61.00
2.452
-0.096
1.977
-0.093
1.977
-0.093
1.527
-0.086
1.527
-0.086
1.129
-0.073
1.129
-0.073
0.808
-0.055
0.808
-0.055
0.590
-0.032
0.590
-0.032
0.509
-0.011
0.509
-0.011
0.500
-0.000
0.500
0.000
0.509
0.011
0.509
0.011
0.590
0.032
0.590
0.032
0.808
0.055
0.808
0.055
1.129
0.073
1.129
0.073
1.527
0.086
1.527
0.086
1.977
0.093
1.977
0.093
2.452
0.096
37 37
37 H 37 H
VERTICAL- Height factor: 2.0 Geometry-No: 37* * Tube axis
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Gradjevinski Fakultet * Kaciceva 26 * 41000 ZagrebGEOS (V10.11-99) 7.12.2002
Koranske mlinicekabeli u hrptu 10
M 1 : 346
-10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 m
601 501 401 301 201 101 111112 102 202 302 402 502 602
0.00
5.00
5.00
10.00
10.00
15.00
15.00
20.00
20.00
25.00
25.00
28.75
28.75
30.50
30.50
32.25
32.25
36.00
36.00
41.00
41.00
46.00
46.00
51.00
51.00
56.00
56.00
61.00
0.874
2195.4
0.879
2208.2
0.879
2208.2
0.890
2234.8
0.890
2234.8
0.903
2268.7
0.903
2268.7
0.913
2292.1
0.913
2292.1
0.924
2319.6
0.924
2319.6
0.931
2338.6
0.931
2338.6
0.953
2391.8
0.953
2391.8
0.957
2402.7
0.957
2402.7
0.982
2466.3
0.982
2466.3
0.993
2492.8
0.993
2492.8
0.996
2501.0
0.996
2501.0
0.986
2477.1
0.986
2477.1
0.973
2442.8
0.973
2442.8
0.962
2415.3
0.874
0.962
1.000
2510.5
1.0391.000
Stress Forces- Height factor: 20.0 Group-No: 37
Poprečni presjeci s rasporedom kabela
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Linijski model za proračun konstrukcije u uzdužnom smjeru.
Razdioba napona po širinipoprečnog presjeka.
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Poprečni presjek mosta Kamačnik
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Kraj