Uncertainty modelling using software FReET
|
|
- Ami Gilmore
- 5 years ago
- Views:
Transcription
1 Uncertainty modelling using software FReET D. Novak, M. Vorechovsky, R. Rusina Brno University of Technology Brno, Czech Republic 1/30
2 Outline Introduction Methods and main features Software FReET Selected applications Probabilistic analyses of concrete structures Statistical size effect studies Identification of computational model parameters 2/18 2/25 2/30
3 Methods and main features Small-sample simulation of Monte Carlo type Imposing statistical correlation Sensitivity analysis Reliability analysis 2/18 12/25 3/30
4 Latin hypercube sampling The range (0; 1) of PDF Φ(Y i ) of each random variable Y i is divided into N non-overlapping intervals of equal probability 1/N (McKay et al Iman & Conover 1980, Iman & Shortencarier 1984). The centroids are selected randomly based on random permutations of integers. Every interval of each variable is used only once during the simulation process. variable simulation 2/18 13/25 4/30
5 LHS: Step 1 - simulation x i, k Sim ( ) b = N x f x dx a Huntington & Lyrintzis (1998) Mean value: accurately Stand. deviation: significant improvement 2/18 14/25 5/23
6 LHS: Step 2 imposing statistical correlation simulation variable x 1 y 1 z 1 x 2 y 2 z 2 x 3 y 3 z 3 x 4 y 4 z 4 x 5 y 5 z 5 x 6 y 6 z 6 x 7 y 7 z 7 x 8 y 8 z 8 x NSim y NSim z NSim Simulated annealing: Probability to escape from local minima Cooling - decreasing of system excitation Boltzmann PDF, energetic analogy r kb ( ) P E e E T 2/18 15/25 6/30
7 LHS: Step 2 imposing statistical correlation variable x 1 y 1 z 1 x 2 y 2 z 2 x 3 y 3 z 3 x 4 y 4 z 4 simulation x 5 y 5 z 5 x 6 y 6 z 6 x 7 y 7 z 7 x 8 y 8 z 8 x NSim y NSim z NSim 2/18 16/25 7/30
8 Sensitivity analysis Nonparametric rank-order correlation between input variables ane output response variable Kendall tau Spearman ( q,p ), j = 1,2, K N τi = τ ji j, r s = ( n 1)( n + 1) Robust - uses only orders Additional result of LHS simulation, no extra effort Bigger correlation coefficient = high sensitivity Relative measure of sensitivity (-1, 1) 6 i= 1 1 n n d 2 i INPUT x 1,1 x 1,N INPUT q 1,1 q 1,N OUTPUT R 1 R, N OUTPUT p 1 p N 2/18 17/25 8/30
9 Reliability analysis Simplified rough estimates, as constrained by extremally small number of simulations (10-100)! Cornell safety index Curve fitting FORM, importance sampling response surface 2/18 18/25 9/30
10 FREET Probabilistic techniques Crude Monte Carlo simulation Latin Hypercube Sampling (3 types) First Order Reliability Method (FORM) Curve fitting Simulated Annealing Bayesian updating Response/Limit state function Closed form (direct) using implemented Equation Editor (simple problems) Numerical (indirect) using user-defined DLL function prepared practically in..any programming language (C++, Fortran, Delphi, etc.) General interface to third-parties software using user-defined *.BAT or *.EXE 2/18 23/25 10/30
11 FREET Stochastic model (inputs) Friendly Graphical User Environment (GUE) 30 probability distribution functions (PDF), mostly 2-parametric, some 3-parametric, two 4-parametric (Beta PDF and normal PDF with Weibullian left tail) Unified description of random variables optionally by statistical moments or parameters or a combination of moments and parameters PDF calculator Statistical correlation (also weighting option) Categories and comparative values for PDFs Basic random variables visualization, including statistical correlation in both Cartesian and parallel coordinates 2/18 23/25 11/30
12 FREET Stochastic model 2/18 23/25 12/30
13 FREET Correlation, simulation 2/18 23/25 13/30
14 FREET Assessment 2/18 23/25 14/30
15 Software tools: SARA Studio Probabilistic software FReET + Software for nonlinear fracture mechanics analysis ATENA 2/18 21/25 15/30
16 ATENA Well-balanced approach for practical applications of advanced FEM in civil engineering Numerical core state-of-art background User friendly Graphical user environment visualization + interaction 2/18 22/25 16/30
17 Material models for concrete: ATENA software Numerical core advanced nonlinear material models concrete in tension tensile cracks post-peak behavior smeared crack approach crack band method fracture energy fixed or rotated cracks crack localization size-effect is captured 2/18 20/25 17/30
18 Software tools: SARA Studio 2/18 24/25 18/30
19 Probabilistis analyses of concrete structures Coll de Isarco viaduct 30 Safety index β CoV = 0.15 CoV = 0.12 CoV = 0.10 CoV = CoV = 0.05 Eurocode Design Load Line Load [kn/m] 2/18 9/25 19/30
20 Probabilistis analyses of concrete structures Coll de Isarco viaduct Random variable description Symbol Units Mean value COV Distribution type Reference Concrete grade B500 6 Modulus of elasticity Ec GPa Lognormal Poisson's ratio µ Lognormal Estimation 6 Tensile strength ft MPa Weibull 6,7 Compressive strength fc MPa Lognormal 8 Specific fracture energy Gf N/m Weibull 6 Uniaxial compressive strain ε c Lognormal Reduction of strength cred Rectangular Estimation Critical comp displacement wd m Lognormal Estimation Specific material weight ρ MN/m Normal Prestressing strands 10 Modulus of elasticity Es GPa Lognormal 10 Yield stress fy MPa Lognormal 9 Prestressing force F MN Normal Area of strands As m Normal 2/18 9/25 20/30
21 Probabilistis analyses of concrete structures soil structure interaction Stability of concrete tunnel tube in complicated geological conditions Influence of spatial variability of Young modulus and material constants of Drucker-Prager criterion (based on cohesion and angle of internal friction) Analyzed part 50 x 60m, diametr of tunnel 11m, wall thickness 0.5m Plain strain state, 5000 finite elements 5.657E E E E E E E E E E E E E-01 2/18 9/25 21/30
22 Statistical size effect studies Malpasset dam (failed 1959) Calculation for different sizes, microplane M4 model Bažant, Vořechovský, Novák - Icossar /18 9/25 22/30
23 Statistical size effect studies 2/18 9/25 23/30
24 Statistical size effect studies Shear failure, verification of design formulas BN100 BN50 BN25 BN12 Nominal strength [kn/m2] Experiments Statistical simulation ACI Eurocode 2 Collins Bažant Size (depth of beam) [m] 2/18 9/25 24/30
25 Identification of computational model parameters Structural response Material model parameters Stochastic calculation (LHS) training set for calibration of synaptic weights and biases 2/18 9/25 25/30
26 Identification of computational model parameters shear wall test Variable Symb ol Unit Mean value COV Modulus of elasticity E GPa Tensile strength ft MPa Compressive strength fc MPa Fracture energy GF N/m Compressive strain εc Max. comp. displacement Bilinear diagram of steel for smeared reinforcement wd m x1 m fx1 kn x2 m fx2 kn /18 9/25 26/30
27 Identification of computational model parameters 2/18 9/25 27/30
28 Identification of computational model parameters Horizontal force [kn] S2 Experiment ATENA 6 parameters identified ATENA 10 parameters identified Horizontal displacement [mm] DLNNET 6 par. 10 par. E [MPa] 29,9 33,0 f t [MPa] 2,47 2,47 f c [MPa] 34,51 35,3 G f [MN/m] 75,0 77,85 e c [-] 2,51E-03 2,57E-03 w d [m] 3,00E-03 3,10E-03 x 1 2,72E-03 2,74E-03 fx 1 566,9 570,7 x 2 1,50E-02 1,47E-02 fx ,8 2/18 9/25 28/30
29 Conclusions FREET - software for statistical, sensitivity and reliability analysis Suitable for analysis of computationally intensive problems (eg. continuum mechanics, FEM) Software development: 1) Stand alone module - definition of reliability problem (user-defined response/limit state function) 2) Integration with software ATENA - nonlinear fracture mechanics of reinforced concrete structures (Červenka Consulting) 2/18 25/25 29/30
30 Thank You for Your attention! 2/30
Stochastická nelineárn. rní analýza betonových konstrukcí: : spolehlivost, vliv velikosti, inverzní analýza
Stochastická nelineárn rní analýza betonových konstrukcí: : spolehlivost, vliv velikosti, inverzní analýza Drahomír Novák Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University
More informationVeveri 331/95, Brno, Czech Republic
Advanced Materials Research Online: 2014-06-24 ISSN: 1662-8985, Vol. 969, pp 298-301 doi:10.4028/www.scientific.net/amr.969.298 2014 Trans Tech Publications, Switzerland Probabilistic Simulation of the
More informationINVERSE RELIABILITY ANALYSIS IN STRUCTURAL DESIGN
INVERSE RELIABILITY ANALYSIS IN STRUCTURAL DESIGN David Lehký, Drahomír Novák Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech Republic.6.0 ISUME
More informationDetermination of statistical material parameters of concrete using fracture test and inverse analysis based on FraMePID-3PB tool
Determination of statistical material parameters of concrete using fracture test and inverse analysis based on FraMePID-3PB tool David Lehký, Zbyněk Keršner, Drahomír Novák Brno University of Technology,
More informationStatistical Analysis of Stresses in Rigid Pavement
Statistical Analysis of Stresses in Rigid Pavement Aleš Florian, Lenka Ševelová, and Rudolf Hela Abstract Complex statistical analysis of stresses in concrete slab of the real type of rigid pavement is
More informationAbstract. 1 Introduction
Contact analysis for the modelling of anchors in concrete structures H. Walter*, L. Baillet** & M. Brunet* *Laboratoire de Mecanique des Solides **Laboratoire de Mecanique des Contacts-CNRS UMR 5514 Institut
More informationRELIABLITY OF CURVED TIMBER BEAM EXPOSED TO FIRE
Applications of Structural Fire Engineering, 15-16 October 2015, Dubrovnik, Croatia RELIABLITY OF CURVED TIMBER BEAM EXPOSED TO FIRE Robert Pečenko, Tomaž Hozjan, Goran Turk University of Ljubljana, Faculty
More informationSimulation of random fields for stochastic finite element analysis
Simulation of random fields for stochastic finite element analysis M. Vořechovský Faculty of Civil Engineering, Brno University of Technology, Brno, Czech Republic D. Novák Faculty of Civil Engineering,
More informationHowever, reliability analysis is not limited to calculation of the probability of failure.
Probabilistic Analysis probabilistic analysis methods, including the first and second-order reliability methods, Monte Carlo simulation, Importance sampling, Latin Hypercube sampling, and stochastic expansions
More informationSHEAR RESISTANCE BETWEEN CONCRETE-CONCRETE SURFACES
, DOI: 10.2478/sjce-2013-0018 M. KOVAČOVIC SHEAR RESISTANCE BETWEEN CONCRETE-CONCRETE SURFACES Marek KOVAČOVIC Email: marek.kovacovic@gmail.com Research field: composite structures Address: Department
More informationNonlocal model for size effect in quasibrittle failure based on extreme value statistics
Structural Safety and Reliability, Corotis et al. (eds), 2001 Swets & Zeitinger, ISBN 90 5809 197 X Nonlocal model for size effect in quasibrittle failure based on extreme value statistics Z.P. Bažant
More informationProbability of failure estimation of current reinforced structures using the Latin Hypercube Sampling
Probability of failure estimation of current reinforced structures using the Latin Hypercube Sampling J. Delgado*, M. de Azeredo^, R. Delgado^ ' Viana do Castelo Polytechnic Institute, Portugal *Departement
More informationUniversity of Sheffield The development of finite elements for 3D structural analysis in fire
The development of finite elements for 3D structural analysis in fire Chaoming Yu, I. W. Burgess, Z. Huang, R. J. Plank Department of Civil and Structural Engineering StiFF 05/09/2006 3D composite structures
More informationOptimization as a tool for the inverse identification of parameters of nonlinear material models
Optimization as a tool for the inverse identification of parameters of nonlinear material models FILIP HOKES, JIRI KALA, ONDREJ KRNAVEK Institute of Structural Mechanics Brno University of Technology,
More informationEntrance exam Master Course
- 1 - Guidelines for completion of test: On each page, fill in your name and your application code Each question has four answers while only one answer is correct. o Marked correct answer means 4 points
More informationReliability Analysis of a Tunnel Design with RELY
Reliability Analysis of a Tunnel Design with RELY W.Betz, I. Papaioannou, M. Eckl, H. Heidkamp, D.Straub Reliability-based structural design Eurocode 0 partial safety factors probabilistic techniques decrease
More informationMEZNÍ STAVY TRVANLIVOSTI MODELOVÁNÍ A ROZMĚR ČASU
MEZNÍ STAVY TRVANLIVOSTI MODELOVÁNÍ A ROZMĚR ČASU LIMIT STATES FOR DURABILITY DESIGN MODELLING AND THE TIME FORMAT Dita Matesová 1, Florentina Pernica 2, Břetislav Teplý 3 Abstract Durability limit states
More informationDiscrete Element Modelling of a Reinforced Concrete Structure
Discrete Element Modelling of a Reinforced Concrete Structure S. Hentz, L. Daudeville, F.-V. Donzé Laboratoire Sols, Solides, Structures, Domaine Universitaire, BP 38041 Grenoble Cedex 9 France sebastian.hentz@inpg.fr
More informationCALCULATION OF A SHEET PILE WALL RELIABILITY INDEX IN ULTIMATE AND SERVICEABILITY LIMIT STATES
Studia Geotechnica et Mechanica, Vol. XXXII, No. 2, 2010 CALCULATION OF A SHEET PILE WALL RELIABILITY INDEX IN ULTIMATE AND SERVICEABILITY LIMIT STATES JERZY BAUER Institute of Mining, Wrocław University
More informationAnálisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas
San Miguel de Tucuman, Argentina September 14 th, 2011 Seminary on Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas Antonio Caggiano 1, Guillermo Etse 2, Enzo
More informationNUMERICAL SIMULATIONS OF CORNERS IN RC FRAMES USING STRUT-AND-TIE METHOD AND CDP MODEL
Numerical simulations of corners in RC frames using Strut-and-Tie Method and CDP model XIII International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XIII E. Oñate, D.R.J.
More informationUNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich
UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST
More informationVORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS
The 4 th World Conference on Earthquake Engineering October -7, 008, Beijing, China VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS K.
More informationSENSITIVITY ANALYSIS OF LATERAL BUCKLING STABILITY PROBLEMS OF HOT-ROLLED STEEL BEAMS
2005/2 PAGES 9 14 RECEIVED 18.10.2004 ACCEPTED 18.4.2005 Z. KALA, J. KALA SENSITIVITY ANALYSIS OF LATERAL BUCKLING STABILITY PROBLEMS OF HOT-ROLLED STEEL BEAMS ABSTRACT Doc. Ing. Zdeněk KALA, PhD. Brno
More informationReliability analysis of slender reinforced concrete column using probabilistic SBRA method
Proceedings of the third international conference ISBN 978-80-7395-096-5 "Reliability, safety and diagnostics of transport structures and means 2008" University of Pardubice, Czech Republic, 25-26 September
More informationSoftware Verification
EXAMPLE 16 racked Slab Analysis RAKED ANALYSIS METHOD The moment curvature diagram shown in Figure 16-1 depicts a plot of the uncracked and cracked conditions, Ψ 1 State 1, and, Ψ State, for a reinforced
More informationDynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models
Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models I. Rhee, K.J. Willam, B.P. Shing, University of Colorado at Boulder ABSTRACT: This paper examines the global
More informationSensitivity and Reliability Analysis of Nonlinear Frame Structures
Sensitivity and Reliability Analysis of Nonlinear Frame Structures Michael H. Scott Associate Professor School of Civil and Construction Engineering Applied Mathematics and Computation Seminar April 8,
More informationParametric analysis and torsion design charts for axially restrained RC beams
Structural Engineering and Mechanics, Vol. 55, No. 1 (2015) 1-27 DOI: http://dx.doi.org/10.12989/sem.2015.55.1.001 1 Parametric analysis and torsion design charts for axially restrained RC beams Luís F.A.
More informationS. Freitag, B. T. Cao, J. Ninić & G. Meschke
SFB 837 Interaction Modeling Mechanized Tunneling S Freitag, B T Cao, J Ninić & G Meschke Institute for Structural Mechanics Ruhr University Bochum 1 Content 1 Motivation 2 Process-oriented FE model for
More informationMODIFIED MONTE CARLO WITH LATIN HYPERCUBE METHOD
MODIFIED MONTE CARLO WITH LATIN HYPERCUBE METHOD Latin hypercube sampling (LHS) was introduced by McKay, Conover and Beckman as a solution to increase the efficiency of computer simulations. This technique
More informationBE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS)
BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)
More informationSoftware Verification
PROGRAM NAME: SAFE 014 EXAMPLE 16 racked Slab Analysis RAKED ANALYSIS METHOD The moment curvature diagram shown in Figure 16-1 depicts a plot of the uncracked and cracked conditions, 1 State 1, and, State,
More informationCracking in Quasi-Brittle Materials Using Isotropic Damage Mechanics
Cracking in Quasi-Brittle Materials Using Isotropic Damage Mechanics Tobias Gasch *1 and Anders Ansell 1 1 KTH Royal Institute of Technology, Department of Civil and Architectural Engineering *Corresponding
More informationRELIABILITY ASSESSMENT OF EXISTING STRUCTURES
1. Introduction RELIABILITY ASSESSMENT OF EXISTING STRUCTURES EN Eurocodes, presently being implemented into the system of national standards nearly in the whole Europe, are particularly intended for the
More informationInteraction Diagram Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements
Interaction Diagram Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements Interaction Diagram - Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements Investigate the capacity for the irregular
More informationStochastic fracture mechanics and size effect
Institute of Structural Mechanics Stochastic fracture mechanics and size effect by Miroslav Vořechovský A dissertation submitted in partial fulfillment of the requirements for the degree Doctor of Philosophy
More informationEQUIVALENT FRACTURE ENERGY CONCEPT FOR DYNAMIC RESPONSE ANALYSIS OF PROTOTYPE RC GIRDERS
EQUIVALENT FRACTURE ENERGY CONCEPT FOR DYNAMIC RESPONSE ANALYSIS OF PROTOTYPE RC GIRDERS Abdul Qadir Bhatti 1, Norimitsu Kishi 2 and Khaliq U Rehman Shad 3 1 Assistant Professor, Dept. of Structural Engineering,
More informationEnergetic statistical size effect simulated by SFEM with stratified sampling and crack band model
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2007; 71:1297 1320 Published online 15 February 2007 in Wiley InterScience (www.interscience.wiley.com)..1986 Energetic
More informationNORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.
NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric
More informationCivil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7
Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Introduction... 3 1.1 Background... 3 1.2 Failure Modes... 5 1.3 Design Aspects...
More informationStability Analysis of a Geometrically Imperfect Structure using a Random Field Model
Stabilit Analsis of a Geometricall Imperfect Structure using a Random Field Model JAN VALEŠ, ZDENĚK KALA Department of Structural Mechanics Brno Universit of Technolog, Facult of Civil Engineering Veveří
More informationDYNAMIC ANALYSIS OF PILES IN SAND BASED ON SOIL-PILE INTERACTION
October 1-17,, Beijing, China DYNAMIC ANALYSIS OF PILES IN SAND BASED ON SOIL-PILE INTERACTION Mohammad M. Ahmadi 1 and Mahdi Ehsani 1 Assistant Professor, Dept. of Civil Engineering, Geotechnical Group,
More informationBasic Energy Principles in Stiffness Analysis
Basic Energy Principles in Stiffness Analysis Stress-Strain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting
More informationMechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationAnalysis of the horizontal bearing capacity of a single pile
Engineering manual No. 16 Updated: 07/2018 Analysis of the horizontal bearing capacity of a single pile Program: Soubor: Pile Demo_manual_16.gpi The objective of this engineering manual is to explain how
More informationINTRODUCTION TO STRAIN
SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,
More informationVerification of a Micropile Foundation
Engineering manual No. 36 Update 02/2018 Verification of a Micropile Foundation Program: File: Pile Group Demo_manual_en_36.gsp The objective of this engineering manual is to explain the application of
More informationD : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown.
D : SOLID MECHANICS Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having
More informationStress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress
More informationChapter. Materials. 1.1 Notations Used in This Chapter
Chapter 1 Materials 1.1 Notations Used in This Chapter A Area of concrete cross-section C s Constant depending on the type of curing C t Creep coefficient (C t = ε sp /ε i ) C u Ultimate creep coefficient
More informationCHAPTER 4: BENDING OF BEAMS
(74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are
More informationReliability of sheet pile walls and the influence of corrosion structural reliability analysis with finite elements
Risk, Reliability and Societal Safety Aven & Vinnem (eds) 2007 Taylor & Francis Group, London, ISBN 978-0-415-44786-7 Reliability of sheet pile walls and the influence of corrosion structural reliability
More informationIDE 110 Mechanics of Materials Spring 2006 Final Examination FOR GRADING ONLY
Spring 2006 Final Examination STUDENT S NAME (please print) STUDENT S SIGNATURE STUDENT NUMBER IDE 110 CLASS SECTION INSTRUCTOR S NAME Do not turn this page until instructed to start. Write your name on
More informationPredicting Failure of Multiangle Composite Laminates
Predicting Failure of Multiangle Composite Laminates Preliminary discussion (not in textbook): Micromechanics failure analyses vs Macromechanics failure analyses Fiber Architecture of Some Common Composite
More informationand F NAME: ME rd Sample Final Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points)
ME 270 3 rd Sample inal Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points) IND: In your own words, please state Newton s Laws: 1 st Law = 2 nd Law = 3 rd Law = PROBLEM
More informationEDEM DISCRETIZATION (Phase II) Normal Direction Structure Idealization Tangential Direction Pore spring Contact spring SPRING TYPES Inner edge Inner d
Institute of Industrial Science, University of Tokyo Bulletin of ERS, No. 48 (5) A TWO-PHASE SIMPLIFIED COLLAPSE ANALYSIS OF RC BUILDINGS PHASE : SPRING NETWORK PHASE Shanthanu RAJASEKHARAN, Muneyoshi
More information6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS
6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS Blondet et al. [25] carried out a cyclic test on an adobe wall to reproduce its seismic response and damage pattern under in-plane loads. The displacement
More informationHaulage Drift Stability Analysis- A Sensitivity Approach
Haulage Drift Stability Analysis- A Sensitivity Approach W. Abdellah University of Assiut, Assiut, Egypt ABSTRACT Haulage drifts are the primary access to the mining blocks of an ore body in a multi-level
More informationStructural reliability analysis of rotor blades in ultimate loading
EWEA 2011 Brussels, Belgium: Europe s Premier Wind Energy Event Structural reliability analysis of rotor blades in ultimate loading K. C. Bacharoudis 1, D. J. Lekou 2, T. P. Philippidis 1 1. University
More informationUsing Probabilistic Analysis with Finite Element Modeling of High Temperature Geothermal Well Casings
Using Probabilistic Analysis with Finite Element Modeling of High Temperature Geothermal Well Casings Gunnar Skúlason Kaldal, Magnús Þór Jónsson, Halldór Pálsson, and Sigrún Nanna Karlsdóttir Faculty of
More informationCRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES
S. Kakay et al. Int. J. Comp. Meth. and Exp. Meas. Vol. 5 No. (017) 116 14 CRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES SAMDAR KAKAY DANIEL BÅRDSEN
More informationAvailable online at ScienceDirect. Procedia Engineering 161 (2016 )
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 161 (2016 ) 892 897 World Multidisciplinary Civil Engineering-Architecture-Urban Planning Symposium 2016, WMCAUS 2016 Parameter
More information3D Finite Element analysis of stud anchors with large head and embedment depth
3D Finite Element analysis of stud anchors with large head and embedment depth G. Periškić, J. Ožbolt & R. Eligehausen Institute for Construction Materials, University of Stuttgart, Stuttgart, Germany
More informationε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram
CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case
More informationFinite Element Modelling with Plastic Hinges
01/02/2016 Marco Donà Finite Element Modelling with Plastic Hinges 1 Plastic hinge approach A plastic hinge represents a concentrated post-yield behaviour in one or more degrees of freedom. Hinges only
More informationPrediction of Reliability Index and Probability of Failure for Reinforced Concrete Beam Subjected To Flexure
Prediction of Reliability Index and Probability of Failure for Reinforced Concrete Beam Subjected To Flexure Salma Taj 1, Karthik B.M. 1, Mamatha N.R. 1, Rakesh J. 1, Goutham D.R. 2 1 UG Students, Dept.
More informationSimplified procedures for calculation of instantaneous and long-term deflections of reinforced concrete beams
Simplified procedures for calculation of instantaneous and long-term deflections of reinforced concrete beams José Milton de Araújo 1 Department of Materials and Construction, University of Rio Grande
More informationMECE 3321 MECHANICS OF SOLIDS CHAPTER 3
MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.
More informationMechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002
student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity
More informationPre-stressed concrete = Pre-compression concrete Pre-compression stresses is applied at the place when tensile stress occur Concrete weak in tension
Pre-stressed concrete = Pre-compression concrete Pre-compression stresses is applied at the place when tensile stress occur Concrete weak in tension but strong in compression Steel tendon is first stressed
More information5 ADVANCED FRACTURE MODELS
Essentially, all models are wrong, but some are useful George E.P. Box, (Box and Draper, 1987) 5 ADVANCED FRACTURE MODELS In the previous chapter it was shown that the MOR parameter cannot be relied upon
More informationEngineering Science OUTCOME 1 - TUTORIAL 4 COLUMNS
Unit 2: Unit code: QCF Level: Credit value: 15 Engineering Science L/601/10 OUTCOME 1 - TUTORIAL COLUMNS 1. Be able to determine the behavioural characteristics of elements of static engineering systems
More informationApproximation of complex nonlinear functions by means of neural networks
Approximation of complex nonlinear functions by means of neural networks Thomas Most Abstract In this paper the applicability of neural networks for the approximation of several nonlinear problems is investigated.
More informationChapter Objectives. Design a beam to resist both bendingand shear loads
Chapter Objectives Design a beam to resist both bendingand shear loads A Bridge Deck under Bending Action Castellated Beams Post-tensioned Concrete Beam Lateral Distortion of a Beam Due to Lateral Load
More informationPROCEDURE OF STATISTICAL SIZE EFFECT PREDICTION FOR CRACK INITIATION PROBLEMS
ICF II (11 th Int. Conf. on Fracture) Turin, March 20-25, 2005 Paper 40-6-1, pp. 1-6 PROCEDURE OF STATISTICAL SIZE EFFECT PREDICTION FOR CRACK INITIATION PROBLEMS M. VORECHOVSKY I, Z.P. BAZANT 2 and D.
More informationExperimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives
Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives Mark Oliver October 19, 2016 Adhesives and Sealants Council Fall Convention contact@veryst.com www.veryst.com Outline
More informationMicroplane Model formulation ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary
Microplane Model formulation 2010 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary Table of Content Engineering relevance Theory Material model input in ANSYS Difference with current concrete
More informationRecent Developments in the Area of Probabilistic Design of Timer Structures Köhler, J.; Sørensen, John Dalsgaard
Aalborg Universitet Recent Developments in the Area of Probabilistic Design of Timer Structures Köhler, J.; Sørensen, John Dalsgaard Published in: ICASP10 : Applications of Statistics and Probability in
More information1. ARRANGEMENT. a. Frame A1-P3. L 1 = 20 m H = 5.23 m L 2 = 20 m H 1 = 8.29 m L 3 = 20 m H 2 = 8.29 m H 3 = 8.39 m. b. Frame P3-P6
Page 3 Page 4 Substructure Design. ARRANGEMENT a. Frame A-P3 L = 20 m H = 5.23 m L 2 = 20 m H = 8.29 m L 3 = 20 m H 2 = 8.29 m H 3 = 8.39 m b. Frame P3-P6 L = 25 m H 3 = 8.39 m L 2 = 3 m H 4 = 8.5 m L
More informationChapter 4-b Axially Loaded Members
CIVL 222 STRENGTH OF MATERIALS Chapter 4-b Axially Loaded Members AXIAL LOADED MEMBERS Today s Objectives: Students will be able to: a) Determine the elastic deformation of axially loaded member b) Apply
More informationThe University of Melbourne Engineering Mechanics
The University of Melbourne 436-291 Engineering Mechanics Tutorial Four Poisson s Ratio and Axial Loading Part A (Introductory) 1. (Problem 9-22 from Hibbeler - Statics and Mechanics of Materials) A short
More informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More informationDesign issues of thermal induced effects and temperature dependent material properties in Abaqus
Materials Characterisation VII 343 Design issues of thermal induced effects and temperature dependent material properties in Abaqus I. Both 1, F. Wald 1 & R. Zaharia 2 1 Department of Steel and Timber
More informationStructural reliability analysis of deep excavations
Timo Schweckendiek, TU Delft, Wim Courage, TNO Built Environment and Geosciences Introduction The Finite Element Method is nowadays widely used in structural design, both for the Servicebility Limit State
More informationALGORITHM FOR NON-PROPORTIONAL LOADING IN SEQUENTIALLY LINEAR ANALYSIS
9th International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-9 Chenjie Yu, P.C.J. Hoogenboom and J.G. Rots DOI 10.21012/FC9.288 ALGORITHM FOR NON-PROPORTIONAL LOADING
More informationLOAD CARRYING BEHAVIOR OF PRESTRESSED BOLTED STEEL FLANGES CONSIDERING RANDOM GEOMETRICAL IMPERFECTIONS
8 th ASCESpecialtyConferenceonProbabilisticMechanicsandStructuralReliability PMC2000-185 LOAD CARRYING BEHAVIOR OF PRESTRESSED BOLTED STEEL FLANGES CONSIDERING RANDOM GEOMETRICAL IMPERFECTIONS C. Bucher
More informationMulti-scale approach of the mechanical behavior of RC structures Application to nuclear plant containment buildings
Multi-scale approach of the mechanical behavior of RC structures Application to nuclear plant containment buildings Martin DAVID June 19, 2012 1 Industrial context EDF is responsible for numerous reinforced
More informationPractice Final Examination. Please initial the statement below to show that you have read it
EN175: Advanced Mechanics of Solids Practice Final Examination School of Engineering Brown University NAME: General Instructions No collaboration of any kind is permitted on this examination. You may use
More informationCIVIL DEPARTMENT MECHANICS OF STRUCTURES- ASSIGNMENT NO 1. Brach: CE YEAR:
MECHANICS OF STRUCTURES- ASSIGNMENT NO 1 SEMESTER: V 1) Find the least moment of Inertia about the centroidal axes X-X and Y-Y of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine
More informationSPECIFIC VERIFICATION Chapter 5
As = 736624/(0.5*413.69) = 3562 mm 2 (ADAPT 3569 mm 2, B29, C6) Data Block 27 - Compressive Stresses The initial compressive strength, f ci, is the strength entered in the Material/Concrete input screen.
More informationClayey sand (SC)
Pile Bearing Capacity Analysis / Verification Input data Project Task : PROJECT: "NEW STEAM BOILER U-5190 Part : A-1 Descript. : The objective of this Analysis is the Pile allowable bearing Capacity Analysis
More informationANALYSIS OF GATE 2018*(Memory Based) Mechanical Engineering
ANALYSIS OF GATE 2018*(Memory Based) Mechanical ME Industrial 4% General Aptitude 15% Mathematics 14% Mechanics 4% Manufacturing 14% Mechanics of Materials 14% Thermodynamics 10% Heat Transfer 2% Fluid
More informationModule 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur
Module 11 Design of Joints for Special Loading Version ME, IIT Kharagpur Lesson Design of Eccentrically Loaded Welded Joints Version ME, IIT Kharagpur Instructional Objectives: At the end of this lesson,
More informationMECHANICS OF MATERIALS Sample Problem 4.2
Sample Problem 4. SOLUTON: Based on the cross section geometry, calculate the location of the section centroid and moment of inertia. ya ( + Y Ad ) A A cast-iron machine part is acted upon by a kn-m couple.
More informationEvaluation of conformity criteria for reinforcing steel properties
IASSAR Safety, Reliability, Risk, Resilience and Sustainability of Structures and Infrastructure 12th Int. Conf. on Structural Safety and Reliability, Vienna, Austria, 6 10 August 2017 Christian Bucher,
More informationPROBABILISTIC FRAGILITY ANALYSIS OF COHESIVE CRACK MODELS
9th International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-9 V. Saouma, J. Bolander, and E. Landis (Eds) DOI.22/FC9.46 PROBABILISTIC FRAGILITY ANALYSIS OF COHESIVE CRACK
More informationTHE BEHAVIOUR OF REINFORCED CONCRETE AS DEPICTED IN FINITE ELEMENT ANALYSIS.
THE BEHAVIOUR OF REINFORCED CONCRETE AS DEPICTED IN FINITE ELEMENT ANALYSIS. THE CASE OF A TERRACE UNIT. John N Karadelis 1. INTRODUCTION. Aim to replicate the behaviour of reinforced concrete in a multi-scale
More information1.050: Beam Elasticity (HW#9)
1050: Beam Elasticity (HW#9) MIT 1050 (Engineering Mechanics I) Fall 2007 Instructor: Markus J BUEHER Due: November 14, 2007 Team Building and Team Work: We strongly encourage you to form Homework teams
More informationNumerical modeling of standard rock mechanics laboratory tests using a finite/discrete element approach
Numerical modeling of standard rock mechanics laboratory tests using a finite/discrete element approach S. Stefanizzi GEODATA SpA, Turin, Italy G. Barla Department of Structural and Geotechnical Engineering,
More information