Bridge deck modelling and design process for bridges


 Avice Bradford
 2 years ago
 Views:
Transcription
1 EURussia Regulatory Dialogue Construction Sector Subgroup 1 Bridge deck modelling and design process for bridges Application to a composite twingirder bridge according to Eurocode 4 Laurence Davaine PhD, Bridge structural engineer, INGEROP, Paris, France
2 General design process of a bridge 2 1. Global analysis a. Calculate the internal forces and moments according to Eurocode s principles b. By modelling the bridge deck (geometry and stiffness to represent its actual behaviour in the best way) c. And by applying the load cases 2. Section and member analysis a. Stress limitations at ULS and SLS b. Concrete crack width control c. Stability (plate or member buckling) d. Connection at the steel concrete interface e. Fatigue
3 Steel concrete composite bridges 3 The twingirder composite bridge represents a large majority of the new road and railway bridges built in France: Usual span length: 40 m < L < 80 m Deck width up to 22 m (2 x 2 highway lanes) with connected crossgirders Setra Competitive solution Simple design Quick construction process Reliable structure Setra
4 Global analysis of a composite bridge deck 4 1. Bridge deck modelling Geometry and bridge structural behaviour Effective width (shear lag effect) Modular ratios (concrete creep) Crosssectional mechanical properties 2. Apply the loads Construction phases Concrete shrinkage Transversal traffic load distribution between main girders 3. Global cracked analysis according to EN Determination of the cracked zones around internal supports Results from the global analysis
5 Twingirder bridge modelling 5 C3 G P2 y z x P1 C0 simply supported bar element model halfbridge crosssection represented by its centre of gravity G (neutral fibre) structural steel alone, or composite, mechanical properties according to the construction phases of the bridge slab
6 Shear lag in composite bridges 6 b slab b eff,slab x Concrete slab in EN Same effective s width b eff at SLS and ULS Steel flange in EN Used for the bottom flange of a boxgirder bridge Different effective s width at SLS and ULS b eff,flange b flange
7 Effective slab width in Eurocode 4 7 Equivalent span length L e L e is the approximate distance between points of zero bending moment. Global analysis (determining internal forces and moments) : effective width constant for each span (equal to the value at midspan) for simplification Section analysis (calculation of stresses) : effective width linearly variable on both sides of the vertical supports over a length L i /4
8 Shear lag in the concrete slab according to Eurocode 4 xy 8 b eff xx,max Nonuniform transverse distribution of the longitudinal stresses xx xx be1 b e 2 Le equivalent span length b 0 b m b m b ei Le 8 b i b 0 2 b mm b b0 eff b ei i
9 Shear lag in the concrete slab according to Eurocode 4 9 C0 P1 P2 C3 60 m 80 m 60 m L e (m) 0.85 x 60 = x 80 = x 60 = x (60+80) = x (60+80) = 35 L e (m) b e1 (m) b e2 (m) b eff (m) Inspan 1 and Inspan Internal supports P1 and P The concrete slab is fully effective (no reduction) because, for each steel main girder, its width (6 m) is small compared to the span length (60 m or 80 m).
10 Mechanical properties of the composite crosssections Uncracked behaviour (midspan regions: M c,ed > 0) 10 b eff Reinforcement neglected (in compression) y Gc y G y Ga G c G G a elastic neutral axis Ac A A a n Ay A y A n y c G a Ga Gc y a a ( G Ga ) c c G Gc I I A y y I A y n Cracked behaviour (support regions: M c,ed < 0) n = E a / E c is the modular ratio between elasticity moduli. b eff E a = E s = N/mm² G s y Gs y G y Ga G G a elastic neutral axis A A A a s Ay G Aa yga As ygs 2 I I A ( y y ) I A y y 2 a a G Ga s s G Gs I s 0
11 Concrete creep effect : modular ratios 11 Shortterm loading (no creep): Longterm loading (creep to be considered): E a with E cm f cm 10 Ecm n n L n 1 0 L t t t t 0 is the creep coefficient according to EN 1992 with : t = age of concrete at the considered design date during the bridge life t 0 = age of concrete when the considered loading is applied to the bridge L depends on the load case: Permanent loads Shrinkage Imposed deformations
12 Creep coefficient according to EN 1992 t t 0, fcm, RH, h0,t 0 12 End of construction All loading cases are applied to the bridge model using the shortterm mechanical properties (n 0 ). Design life of the bridge Shortterm loading : n 0 Longterm loading : n L
13 Worked example: modular ratios 1 st 16 th t = 0 Phase 1 3 Phase t = 66 t = 80 t = 110 Time (in days) Phase Mean value of the ages of concrete segments : t phases days used for all concreting phases (simplification of EN19942). t,t 1 0 t days days,t days t days,t 3 0 n n L,1 0 1 n n L,2 0 2 n n L,3 0 3 Note : t 0 = 1 day when shrinkage is applied to a concrete segment.,t nl,4 n
14 Worked example: modular ratios 14 Shortterm loading : Ea n0 6.2 E cm Longterm loading (permanent loads, shrinkage, imposed deformations) : Load case L t 0 (days) t = 0 n L Concrete slab segment (selfweight) Settlement Shrinkage Bridge equipments (safety barriers, road pavement, )
15 Global analysis of a composite bridge deck 1. Bridge deck modelling Geometry and global bridge behaviour Effective width (shear lag effect) Modular ratios (concrete creep) Crosssectional mechanical properties Apply the loads Construction phases Concrete shrinkage Transversal traffic load distribution between main girders 3. Global cracked analysis according to EN Determination of the cracked zones around internal supports Results from the global analysis
16 Applied loads for the road bridge example 16 Permanent loads (taking creep into account if relevant) G max, G min S Self weight: structural steel concrete (by segments in a selected order) non structural equipments (safety barriers, pavement, ) Shrinkage (drying, autogenous and thermal shrinkage strains) EN1991 part 11 EN1992 part 11 EN1994 part 2 P Prestressing by imposed deformations (for instance, jacking on internal supports) Variable loads (no creep effect) T k Temperature effects EN1991 part 15 UDL, TS Road traffic EN1991 part 2 FLM3 Fatigue load model (for instance, the equivalent lorry FLM3) EN1991 part 2
17 Construction slab stages 17 imposed concreting order to reduce the concrete tension around internal supports For the example, 16 concreting phases (12.5 m long slab segment) C0 P1 P2 C3 Setra Setra
18 Construction slab stages 18 During the 10 th concreting phase, the load case is the selfweight of the 10 th concrete segment m 50 m 24 m C0 P1 P2 C3 () Mechanical properties of the composite uncracked crosssection Mechanical properties of the structural steel alone crosssection In the crosssection (), the stress distribution should take into account the construction history. M a,ed M c,ed M M M Ed a,ed c,ed + =
19 Effects of shrinkage in a composite bridge 19 cs Ncs E ccs.b chc N cs h c + e.n.a. z cs Free shrinkage strain applied on concrete slab only (no steel concrete interaction) Shrinkage strain applied on the composite section (after steel concrete interaction) 1 Autoequilibrated stress diagram in every section and an imposed rotation due to the bending moment M iso = N cs z cs : e.n.a. bc  + z  steel 1 N N. csz cs cs E n A I concrete c cs Ncs A Ncs z cs. z I. z
20 Effects of shrinkage in a composite bridge Curvature in an isostatic bridge due to the imposed deformations : L M iso M iso P1 vx P2 3 Compatibility of deformations to be considered in an hyperstatic bridge : v P3 0 P1 P3 L1 2 L P2 M hyper Effects of shrinkage 1+2 = isostatic (or primary) effects 3 = hyperstatic (or secondary) effects
21 Shrinkage and cracked global analysis Concrete in tension Cracked zone 21 Isostatic effects neglected in cracked zones for calculating hyperstatic effects Miso Miso M iso M iso SLS combinations ULS combinations iso + hyper effects hyper (if class 1) hyper iso + hyper hyper Hyper (if class 1) M hyper M hyper
22 Thermal gradient from Eurocode 1 Part 15 could be neglected if all crosssections are in Class 1 or 2 3 options: have to be chosen in the National Annex Non linear gradients : 2 Linear gradients : 0.6h 400 mm 16 C 5 C 4 C 8 C +15 C 18 C 3 Difference +/ 10 C : +/ 10 C
23 Transversal distribution of live load between the two girders 23 Influence line of the support reaction on girder no. 1 1 a F e a 0 Bridge axle Girder no.1 (modelled) e / 2 e / 2 girder no. 2 R1 F1 a e R 2 a F e No warping stress calculations and slab torsional stiffness neglected
24 Application to the traffic load model LM Conventional traffic lanes positioning Safety barrier 1 m 0.5 m Lane no.1 Lane no.2 Lane no.3 Residual area 3 m 3 m 3 m 2 m Safety barrier Bridge axis Girder no.1 (modelled) girder no m 3.5 m 3.5 m 2.5 m
25 Application to the traffic load model LM Tandem System TS Bridge axis 1 TS 2 = 200 kn/axle TS 1 = 300 kn/axle TS 3 = 100 kn/axle 0 R1 0.5 m 1 m 2 m R2 Influence line of the support reaction on girder no. 1 Support reaction on each main girder : R 1 = kn R 2 = kn
26 Application to the traffic load model LM Uniform Design Load UDL Bridge axis Load on lane no.1 : 9 kn/m² x 3 m = 27 kn/ml 1 Load on lane no.2 : 2.5 kn/m² x 3 m = 7.5 kn/ml LANE 1 LANE 2 LANE 3 Load on lane no.3 : 2.5 kn/m² x 3 m = 7.5 kn/ml R1 R2 0.5 m 1 m 2 m 0 Transverse distribution line Support reaction for each main girder : R 1 = kn/ml R 2 = 6.64 kn/ml
27 Application to the traffic load model LM1 4. Bending Moment (MN.m) for UDL and TS 27
28 Combinations of actions 28 For every permanent design situation, two limit states of the bridge should be considered : Serviceability Limit States (SLS) Quasi permanent SLS G max + G min + S + P T k Frequent SLS G max + G min + S + P TS UDL T k G max + G min + S + P T k Characteristic SLS G max + G min + S + P + (TS+UDL) T k G max + G min + S + P + Q lk TS UDL T k G max + G min + S + P + T k TS UDL Ultime Limite State (ULS) other than fatigue 1.35 G max + G min + S + P (TS + UDL) (0.6 T k ) 1.35 G max + G min + S + P Q lk (0.75 TS UDL) (0.6 T k ) 1.35 G max + G min + S + P T k (0.75 TS UDL)
29 Global analysis of a composite bridge deck Bridge deck modelling Geometry and global bridge behaviour Effective width (shear lag effect) Modular ratios (concrete creep) Crosssectional mechanical properties 2. Apply the loads Construction phases Concrete shrinkage Transversal traffic load distribution between main girders 3. Global cracked analysis according to EN Determination of the cracked zones around internal supports Results from the global analysis
30 Classification of crosssections (EC3) 30 M Cl.1 M pl M el Cl.3 Cl.2 Cl > 6 / el F M = F L / 4
31 Classification of crosssections CLASS 1 sections which can form a plastic hinge with the rotation capacity required for a global plastic analysis Not for bridges Except accidental design situation 31 CLASS 2 sections which can develop M pl,rd with limited rotation capacity CLASS 3 sections which can develop M el,rd CL. 1 CL.3/4 COMPOSITE BRIDGES Nonuniform section (except for small spans)
32 Actual behaviour of a composite bridge 32 When performing the elastic global analysis, two aspects of the nonlinear behaviour are indirectly considered. F Cracking of concrete 1 M Yielding 2 M pl,rd M at midspan with increase of F M el,rd Class 1
33 Cracked global analysis 1 33 Determination of the stresses c in the extreme fibre of the concrete slab under SLS characteristic combination according to a noncracked global analysis In sections where c <  2 f ctm, the concrete is assumed to be cracked and its resistance is neglected EI 1 EI 2 EI1 EI 1 = uncracked composite inertia (structural steel + concrete in compression) EI 2 = cracked composite inertia (structural steel + reinforcement)! No iteration is needed!
34 Cracked global analysis 1 Simplified method usable if :  no prestressing by imposed deformation  L min /L max > (L EI 1 + L 2 ) 2 34 A s L 1 L 2 EI 1 A c = 0 In the cracked zones EI 2 : the resistance of the concrete in tension is neglected the resistance of the reinforcement is taken into account
35 Stresses in concrete slab (N/mm²) Characteristic SLS combination Worked example: Cracked zones around internal supports 35 Stresses calculated including the construction phasing and the uncracked composite behaviour Cracked 14 4 zones 5 for the 6 global analysis f ctm 6.4 N/mm 215 x = 35.0 m x = 76.0 m x = m x = m Cracked zone for P % 19.5 % Cracked zone for P % 20.0 %
36 Yielding 2 Yielding at midspan induces bending redistribution which should be considered if : 36 Class 1 or 2 crosssection at midspan (and M Ed > M el,rd ) Class 3 or 4 near intermediate support L min /L max < 0.6 L max L min Class 1 or 2 Class 3 or 4 Elastic linear analysis with an additional verification for the crosssections in sagging bending zone (M>0) : M Ed < 0.9 M pl,rd or Non linear global analysis (Finite Elements for instance)
37 Global analysis  Synthesis To calculate the internal forces and moments for the ULS combination of actions 37 elastic global analysis (except for accidental loads) cracking of the concrete slab shear lag (in the concrete slab : L e /8 constant value for each span) neglecting plate buckling (except for an effective p area of an element 0.5 * gross area) To calculate the internal forces and moments for the SLS combinations of actions as for ULS To calculate the longitudinal shear per unit length (SLS and ULS) at the steelconcrete interface Cracked global analysis, elastic and linear Always uncracked section analysis
38 Bending moment (MN.m) Results for the twingirder bridge example 38 SLS and ULS bending moment distribution M Ed (= M a,ed + M c,ed ) Characteristic SLS Fundamental ULS
39 Shear forces (MN) Results for the twingirder bridge example 39 SLS and ULS shear force distribution V Ed Characteristic SLS Fundamental ULS
40 Results for the twingirder bridge example 40 ULS stresses (N/mm²) Fondamental along ULS the  Flanges steel (extreme flanges, fiber) calculated  Without concrete without resistance concrete resistance
41 41 The results from the global analysis will be used for :  the bridge deck crosssection analysis,  the abutments and piers check,  the foundation calculations,  Thank you for your attention!
Composite bridge design (EN19942) Bridge modelling and structural analysis
EUROCODES Bridges: Background and applications Dissemination of information for training Vienna, 46 October 2010 1 Composite bridge design (EN19942) Bridge modelling and structural analysis Laurence
More informationJob No. Sheet No. Rev. CONSULTING Engineering Calculation Sheet. Member Design  Steel Composite Beam XX 22/09/2016
CONSULTING Engineering Calculation Sheet jxxx 1 Member Design  Steel Composite Beam XX Introduction Chd. 1 Grade 50 more common than Grade 43 because composite beam stiffness often 3 to 4 times non composite
More informationŽILINSKÁ UNIVERZITA V ŽILINE. Fakulta stavebná BRIDGES. Examples. Jozef GOCÁL
ŽILINSKÁ UNIVERZITA V ŽILINE Fakulta stavebná BRIDGES Examples Joz GOCÁL Ž I L I N A 2 0 0 8 ŽILINSKÁ UNIVERZITA V ŽILINE, Stavebná fakulta BRIDGES, Examples Podľa prednášok a návodu na cvičenia preložil
More informationDesign of reinforced concrete sections according to EN and EN
Design of reinforced concrete sections according to EN 199211 and EN 19922 Validation Examples Brno, 21.10.2010 IDEA RS s.r.o. South Moravian Innovation Centre, U Vodarny 2a, 616 00 BRNO tel.: +420511
More informationSTEEL BUILDINGS IN EUROPE. MultiStorey Steel Buildings Part 10: Technical Software Specification for Composite Beams
STEEL BUILDINGS IN EUROPE MultiStorey Steel Buildings Part 10: Technical Software Specification for Composite Beams MultiStorey Steel Buildings Part 10: Technical Software Specification for Composite
More informationCOMBRI DESIGN MANUAL Part I: Application of Eurocode rules
COMBRI DESIGN MANUAL Part I: Application of Eurocode rules A project carried out with a financial grant from the Research Fund for Coal and Steel (RFCS) of the European Community. COMBRI DESIGN MANUAL
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 crosssection 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 informationIntroduction to The Design Example and EN Basis of Design
EUROCODES Bridges: Background and applications St Petersburg April 2011 1 Introduction to The Design Example and EN 1990  Basis of Design Professor Steve Denton Engineering Director, Parsons Brinckerhoff
More informationRoadway Grade = m, amsl HWM = Roadway grade dictates elevation of superstructure and not minimum free board requirement.
Example on Design of Slab Bridge Design Data and Specifications Chapter 5 SUPERSTRUCTURES Superstructure consists of 10m slab, 36m box girder and 10m Tgirder all simply supported. Only the design of Slab
More informationDesign of AAC wall panel according to EN 12602
Design of wall panel according to EN 160 Example 3: Wall panel with wind load 1.1 Issue Design of a wall panel at an industrial building Materials with a compressive strength 3,5, density class 500, welded
More informationStructural Steelwork Eurocodes Development of A Transnational Approach
Structural Steelwork Eurocodes Development of A Transnational Approach Course: Eurocode Module 7 : Worked Examples Lecture 0 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic Loads
More informationSTRUCTURAL ANALYSIS CHAPTER 2. Introduction
CHAPTER 2 STRUCTURAL ANALYSIS Introduction The primary purpose of structural analysis is to establish the distribution of internal forces and moments over the whole part of a structure and to identify
More informationInfluence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes
October 2014 Influence of residual stresses in the structural behavior of Abstract tubular columns and arches Nuno Rocha Cima Gomes Instituto Superior Técnico, Universidade de Lisboa, Portugal Contact:
More informationDesign of Beams (Unit  8)
Design of Beams (Unit  8) Contents Introduction Beam types Lateral stability of beams Factors affecting lateral stability Behaviour of simple and built  up beams in bending (Without vertical stiffeners)
More informationC C JTS 16:00 17:30. Lebet
24 1 27 ()16001730 C C JTS 21 ( ) 16:0017:30 Lebet SGST // Branson Bridge, Martigny, 2006 LéopoldSédarSenghor Bridge, Nantes (F), 2009 Taulhac Bridge, PuyenVelay (F), 2012 Langensand Bridge Lucerne,
More informationFundamentals of Structural Design Part of Steel Structures
Fundamentals of Structural Design Part of Steel Structures Civil Engineering for Bachelors 133FSTD Teacher: Zdeněk Sokol Office number: B619 1 Syllabus of lectures 1. Introduction, history of steel structures,
More informationSERVICEABILITY LIMIT STATE DESIGN
CHAPTER 11 SERVICEABILITY LIMIT STATE DESIGN Article 49. Cracking Limit State 49.1 General considerations In the case of verifications relating to Cracking Limit State, the effects of actions comprise
More informationSeismic design of bridges
NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY FOR EARTHQUAKE ENGINEERING Seismic design of bridges Lecture 3 Ioannis N. Psycharis Capacity design Purpose To design structures of ductile behaviour
More informationPLATE GIRDERS II. Load. Web plate Welds A Longitudinal elevation. Fig. 1 A typical Plate Girder
16 PLATE GIRDERS II 1.0 INTRODUCTION This chapter describes the current practice for the design of plate girders adopting meaningful simplifications of the equations derived in the chapter on Plate Girders
More informationPrestressed concrete = Precompression concrete Precompression stresses is applied at the place when tensile stress occur Concrete weak in tension
Prestressed concrete = Precompression concrete Precompression stresses is applied at the place when tensile stress occur Concrete weak in tension but strong in compression Steel tendon is first stressed
More informationLongitudinal strength standard
(1989) (Rev. 1 199) (Rev. Nov. 001) Longitudinal strength standard.1 Application This requirement applies only to steel ships of length 90 m and greater in unrestricted service. For ships having one or
More informationCHAPTER 4. Design of R C Beams
CHAPTER 4 Design of R C Beams Learning Objectives Identify the data, formulae and procedures for design of R C beams Design simplysupported and continuous R C beams by integrating the following processes
More informationCHAPTER 4. Stresses in Beams
CHAPTER 4 Stresses in Beams Problem 1. A rolled steel joint (RSJ) of section has top and bottom flanges 150 mm 5 mm and web of size 00 mm 1 mm. t is used as a simply supported beam over a span of 4 m
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 postyield behaviour in one or more degrees of freedom. Hinges only
More information9.5 Compression Members
9.5 Compression Members This section covers the following topics. Introduction Analysis Development of Interaction Diagram Effect of Prestressing Force 9.5.1 Introduction Prestressing is meaningful when
More informationUniversity of Sheffield. Department of Civil Structural Engineering. Member checks  Rafter 44.6
Member checks  Rafter 34 6.4Haunch (UB 457 x 191 x 89) The depth of a haunch is usually made approximately twice depth of the basic rafter sections, as it is the normal practice to use a UB cutting of
More informationSeminar Bridge Design with Eurocodes
Seminar Bridge Design with Eurocodes JRC Ispra, 12 October 2012 1 EURussia Regulatory Dialogue: Construction Sector Subgroup Seminar Bridge Design with Eurocodes JRCIspra, 12 October 2012 Organized
More informationAppendix J. Example of Proposed Changes
Appendix J Example of Proposed Changes J.1 Introduction The proposed changes are illustrated with reference to a 200ft, single span, Washington DOT WF bridge girder with debonded strands and no skew.
More informationMade by SMH Date Aug Checked by NRB Date Dec Revised by MEB Date April 2006
Job No. OSM 4 Sheet 1 of 8 Rev B Telephone: (0144) 45 Fax: (0144) 944 Made b SMH Date Aug 001 Checked b NRB Date Dec 001 Revised b MEB Date April 00 DESIGN EXAMPLE 9  BEAM WITH UNRESTRAINED COMPRESSION
More informationStructural Steelwork Eurocodes Development of A Transnational Approach
Structural Steelwork Eurocodes Development of A Transnational Approach Course: Eurocode 3 Module 7 : Worked Examples Lecture 20 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic
More informationServiceability Limit States
Serviceability Limit States www.eurocode2.info 1 Outline Crack control and limitations Crack width calculations Crack width calculation example Crack width calculation problem Restraint cracking Deflection
More information1. ARRANGEMENT. a. Frame A1P3. 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 P3P6
Page 3 Page 4 Substructure Design. ARRANGEMENT a. Frame AP3 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 P3P6 L = 25 m H 3 = 8.39 m L 2 = 3 m H 4 = 8.5 m L
More information= = = 1,000 1,000 1,250. g M0 g M1 g M2 = = = 1,100 1,100 1,250 [ ] 1 0,000 8,000 HE 140 B 0,0. [m] Permanent Permanent Variable Variable Variable
Project Job name Part Author Date Steel Products and Solutions Standard 29.01.2018 Standard EN 199311, EN 199314/Czech Rep.. Factors for steel structures Section capacity Section resistance when checking
More informationAPPENDIX D SUMMARY OF EXISTING SIMPLIFIED METHODS
APPENDIX D SUMMARY OF EXISTING SIMPLIFIED METHODS D1 An extensive literature search revealed many methods for the calculation of live load distribution factors. This appendix will discuss, in detail,
More informationCE5510 Advanced Structural Concrete Design  Design & Detailing of Openings in RC Flexural Members
CE5510 Advanced Structural Concrete Design  Design & Detailing Openings in RC Flexural Members Assoc Pr Tan Kiang Hwee Department Civil Engineering National In this lecture DEPARTMENT OF CIVIL ENGINEERING
More informationFire resistance assessment of composite steelconcrete structures
Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 Fire resistance assessment of composite steelconcrete structures Basic design methods Worked examples CAJOT
More informationSoftware Verification
PROGRAM NAME: SAFE 014 EXAMPLE 16 racked Slab Analysis RAKED ANALYSIS METHOD The moment curvature diagram shown in Figure 161 depicts a plot of the uncracked and cracked conditions, 1 State 1, and, State,
More informationEUROCODE EN SEISMIC DESIGN OF BRIDGES
Brussels, 1820 February 2008 Dissemination of information workshop 1 EUROCODE EN19982 SEISMIC DESIGN OF BRIDGES Basil Kolias Basic Requirements Brussels, 1820 February 2008 Dissemination of information
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS PART A (2 MARKS)
More informationMoment redistribution of continuous composite Igirders with high strength steel
Moment redistribution of continuous composite Igirders with high strength steel * Hyun Sung Joo, 1) Jiho Moon, 2) IkHyun sung, 3) HakEun Lee 4) 1), 2), 4) School of Civil, Environmental and Architectural
More informationQUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS
QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,
More informationSoftware Verification
EXAMPLE 16 racked Slab Analysis RAKED ANALYSIS METHOD The moment curvature diagram shown in Figure 161 depicts a plot of the uncracked and cracked conditions, Ψ 1 State 1, and, Ψ State, for a reinforced
More informationPERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR  VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK
PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR  VALLAM  613 403  THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310
More informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or builtin beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported
More informationName :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CENEW)/SEM3/CE301/ SOLID MECHANICS
Name :. Roll No. :..... Invigilator s Signature :.. 2011 SOLID MECHANICS Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are required to give their answers
More informationTHE EC3 CLASSIFICATION OF JOINTS AND ALTERNATIVE PROPOSALS
EUROSTEEL 2002, Coimbra, 1920 September 2002, p.987996 THE EC3 CLASSIFICATION OF JOINTS AND ALTERNATIVE PROPOSALS Fernando C. T. Gomes 1 ABSTRACT The Eurocode 3 proposes a classification of beamtocolumn
More informationSERVICEABILITY OF BEAMS AND ONEWAY SLABS
CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach  Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONEWAY SLABS A. J. Clark School of Engineering Department of Civil
More information1C8 Advanced design of steel structures. prepared by Josef Machacek
1C8 Advanced design of steel structures prepared b Josef achacek List of lessons 1) Lateraltorsional instabilit of beams. ) Buckling of plates. 3) Thinwalled steel members. 4) Torsion of members. 5)
More information3. Stability of builtup members in compression
3. Stability of builtup members in compression 3.1 Definitions Buildup members, made out by coupling two or more simple profiles for obtaining stronger and stiffer section are very common in steel structures,
More informationFeasibility of dynamic test methods in classification of damaged bridges
Feasibility of dynamic test methods in classification of damaged bridges Flavio Galanti, PhD, MSc., Felieke van Duin, MSc. TNO Built Environment and Geosciences, P.O. Box 49, 26 AA, Delft, The Netherlands.
More informationDelhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:
Serial : IG1_CE_G_Concrete Structures_100818 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Email: info@madeeasy.in Ph: 011451461 CLASS TEST 01819 CIVIL ENGINEERING
More informationModule 6. Approximate Methods for Indeterminate Structural Analysis. Version 2 CE IIT, Kharagpur
Module 6 Approximate Methods for Indeterminate Structural Analysis Lesson 35 Indeterminate Trusses and Industrial rames Instructional Objectives: After reading this chapter the student will be able to
More informationKarbala University College of Engineering Department of Civil Eng. Lecturer: Dr. Jawad T. Abodi
Chapter 05 Structural Steel Design According to the AISC Manual 13 th Edition Analysis and Design of Beams By Dr. Jawad Talib AlNasrawi University of Karbala Department of Civil Engineering 71 Introduction
More information93. Structural response
93. Structural response in fire František Wald Czech Technical University in Prague Objectives of the lecture The mechanical load in the fire design Response of the structure exposed to fire Levels of
More informationA.2 AASHTO Type IV, LRFD Specifications
A.2 AASHTO Type IV, LRFD Specifications A.2.1 INTRODUCTION A.2.2 DESIGN PARAMETERS 1'5.0" Detailed example showing sample calculations for design of typical Interior AASHTO Type IV prestressed concrete
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 informationBasis of Design, a case study building
Basis of Design, a case study building Luís Simões da Silva Department of Civil Engineering University of Coimbra Contents Definitions and basis of design Global analysis Structural modeling Structural
More informationRigid Pavement Mechanics. Curling Stresses
Rigid Pavement Mechanics Curling Stresses Major Distress Conditions Cracking Bottomup transverse cracks Topdown transverse cracks Longitudinal cracks Corner breaks Punchouts (CRCP) 2 Major Distress Conditions
More informationMechanics of Structure
S.Y. Diploma : Sem. III [CE/CS/CR/CV] Mechanics of Structure Time: Hrs.] Prelim Question Paper Solution [Marks : 70 Q.1(a) Attempt any SIX of the following. [1] Q.1(a) Define moment of Inertia. State MI
More informationStructural Analysis I Chapter 4  Torsion TORSION
ORSION orsional stress results from the action of torsional or twisting moments acting about the longitudinal axis of a shaft. he effect of the application of a torsional moment, combined with appropriate
More informationUNIT I Thin plate theory, Structural Instability:
UNIT I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and inplane loading Thin plates having
More informationC6 Advanced design of steel structures
C6 Advanced design of steel structures prepared b Josef achacek List of lessons 1) Lateraltorsional instabilit of beams. ) Buckling of plates. 3) Thinwalled steel members. 4) Torsion of members. 5) Fatigue
More informationAvailable online at ScienceDirect. Procedia Engineering 172 (2017 )
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 172 (2017 ) 1093 1101 Modern Building Materials, Structures and Techniques, MBMST 2016 Iterative Methods of BeamStructure Analysis
More informationDesign of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
5.10 Examples 5.10.1 Analysis of effective section under compression To illustrate the evaluation of reduced section properties of a section under axial compression. Section: 00 x 80 x 5 x 4.0 mm Using
More information7 Vlasov torsion theory
7 Vlasov torsion theory P.C.J. Hoogenboom, October 006 Restrained Warping The typical torsion stresses according to De Saint Venant only occur if warping can take place freely (Fig. 1). In engineering
More informationServiceability Deflection calculation
Chp6:Lecture Goals Serviceability Deflection calculation Deflection example Structural Design Profession is concerned with: Limit States Philosophy: Strength Limit State (safetyfracture, fatigue, overturning
More informationCIV100 Mechanics. Module 5: Internal Forces and Design. by: Jinyue Zhang. By the end of this Module you should be able to:
CIV100 Mechanics Module 5: Internal Forces and Design by: Jinyue Zhang Module Objective By the end of this Module you should be able to: Find internal forces of any structural members Understand how Shear
More informationEurocode Training EN : Reinforced Concrete
Eurocode Training EN 199211: Reinforced Concrete Eurocode Training EN 199211 All information in this document is subject to modification without prior notice. No part of this manual may be reproduced,
More informationFINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NONLINEAR VARYING WEB DEPTH
Journal of Engineering Science and Technology Vol. 12, No. 11 (2017) 28392854 School of Engineering, Taylor s University FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NONLINEAR VARYING
More informationQUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A
DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State
More informationCurved Steel Igirder Bridge LFD Guide Specifications (with 2003 Edition) C. C. Fu, Ph.D., P.E. The BEST Center University of Maryland October 2003
Curved Steel Igirder Bridge LFD Guide Specifications (with 2003 Edition) C. C. Fu, Ph.D., P.E. The BEST Center University of Maryland October 2003 Guide Specifications (19932002) 2.3 LOADS 2.4 LOAD COMBINATIONS
More informationExample 2.2 [Ribbed slab design]
Example 2.2 [Ribbed slab design] A typical floor system of a lecture hall is to be designed as a ribbed slab. The joists which are spaced at 400mm are supported by girders. The overall depth of the slab
More informationDESIGN OF STAIRCASE. Dr. Izni Syahrizal bin Ibrahim. Faculty of Civil Engineering Universiti Teknologi Malaysia
DESIGN OF STAIRCASE Dr. Izni Syahrizal bin Ibrahim Faculty of Civil Engineering Universiti Teknologi Malaysia Email: iznisyahrizal@utm.my Introduction T N T G N G R h Flight Span, L Landing T = Thread
More informationRedistribution of force concentrations in reinforced concrete cantilever slab using 3D nonlinear FE analyses
y x m y m y Linear elastic isotropic Linear elastic orthotropic Plastic Redistribution of force concentrations in reinforced concrete cantilever slab using 3D nonlinear FE analyses x Master of Science
More informationInfluence of cracked inertia and momentcurvature curve idealization on pushover analysis
Influence of cracked inertia and momentcurvature curve idealization on pushover analysis Vivier Aurélie, Sekkat Dayae, Montens Serge Systra, 3 avenue du Coq, 75009 Paris SUMMARY: The pushover analysis
More informationPractical Design to Eurocode 2
Practical Design to Eurocode 2 The webinar will start at 12.30 (Any questions beforehand? use Questions on the GoTo Control Panel) Course Outline Lecture Date Speaker Title 1 21 Sep Jenny Burridge Introduction,
More information7.3 Design of members subjected to combined forces
7.3 Design of members subjected to combined forces 7.3.1 General In the previous chapters of Draft IS: 800 LSM version, we have stipulated the codal provisions for determining the stress distribution in
More informationA METHOD OF LOAD INCREMENTS FOR THE DETERMINATION OF SECONDORDER LIMIT LOAD AND COLLAPSE SAFETY OF REINFORCED CONCRETE FRAMED STRUCTURES
A METHOD OF LOAD INCREMENTS FOR THE DETERMINATION OF SECONDORDER LIMIT LOAD AND COLLAPSE SAFETY OF REINFORCED CONCRETE FRAMED STRUCTURES Konuralp Girgin (Ph.D. Thesis, Institute of Science and Technology,
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 informationDownloaded from Downloaded from / 1
PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION2002 LEVEL : B. E. (Civil) SUBJECT: BEG256CI, Strength of Material Full Marks: 80 TIME: 03:00 hrs Pass marks: 32 Candidates are required to give their
More informationPart 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1.
NAME CM 3505 Fall 06 Test 2 Part 1 is to be completed without notes, beam tables or a calculator. Part 2 is to be completed after turning in Part 1. DO NOT turn Part 2 over until you have completed and
More informationSeismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design
Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Elmer E. Marx, Alaska Department of Transportation and Public Facilities Michael Keever, California Department
More informationMechanics of Solids notes
Mechanics of Solids notes 1 UNIT II Pure Bending Loading restrictions: As we are aware of the fact internal reactions developed on any crosssection of a beam may consists of a resultant normal force,
More informationDEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8  PART 3 PROVISIONS
DEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8  PART 3 PROVISIONS Konstantinos CHRISTIDIS 1, Emmanouil VOUGIOUKAS 2 and Konstantinos TREZOS 3 ABSTRACT
More information3.5 Reinforced Concrete Section Properties
CHAPER 3: Reinforced Concrete Slabs and Beams 3.5 Reinforced Concrete Section Properties Description his application calculates gross section moment of inertia neglecting reinforcement, moment of inertia
More informationStandardisation of UHPC in Germany
Standardisation of UHPC in Germany Part II: Development of Design Rules, University of Siegen Prof. Dr.Ing. Ekkehard Fehling, University of Kassel 1 Overvie Introduction: Work of the Task Group Design
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 informationSIMPLIFIED METHOD FOR PREDICTING DEFORMATIONS OF RC FRAMES DURING FIRE EXPOSURE
SIMPLIFIED METHOD FOR PREDICTING DEFORMATIONS OF RC FRAMES DURING FIRE EXPOSURE M.A. Youssef a, S.F. ElFitiany a a Western University, Faculty of Engineering, London, Ontario, Canada Abstract Structural
More informationFlexure: Behavior and Nominal Strength of Beam Sections
4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kipin.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015
More informationEurocode 3 for Dummies The Opportunities and Traps
Eurocode 3 for Dummies The Opportunities and Traps a brief guide on element design to EC3 Tim McCarthy Email tim.mccarthy@umist.ac.uk Slides available on the web http://www2.umist.ac.uk/construction/staff/
More informationCivil Engineering Design (1) Analysis and Design of Slabs 2006/7
Civil Engineering Design (1) Analysis and Design of Slabs 006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Elastic Methods... 3 1.1 Introduction... 3 1. Grillage Analysis... 4 1.3 Finite Element
More informationEAS 664/4 Principle Structural Design
UNIVERSITI SAINS MALAYSIA 1 st. Semester Examination 2004/2005 Academic Session October 2004 EAS 664/4 Principle Structural Design Time : 3 hours Instruction to candidates: 1. Ensure that this paper contains
More informationNUMERICAL EVALUATION OF THE ROTATIONAL CAPACITY OF STEEL BEAMS AT ELEVATED TEMPERATURES
8 th GRACM International Congress on Computational Mechanics Volos, 12 July 15 July 2015 NUMERICAL EVALUATION OF THE ROTATIONAL CAPACITY OF STEEL BEAMS AT ELEVATED TEMPERATURES Savvas Akritidis, Daphne
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 XX and YY of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine
More informationSlenderness Effects for Concrete Columns in Sway Frame  Moment Magnification Method (CSA A )
Slenderness Effects for Concrete Columns in Sway Frame  Moment Magnification Method (CSA A23.394) Slender Concrete Column Design in Sway Frame Buildings Evaluate slenderness effect for columns in a
More informationJob No. Sheet 1 of 7 Rev A. Made by ER/EM Date Feb Checked by HB Date March 2006
Job No. Sheet of 7 Rev A Design Example Design of a lipped channel in a Made by ER/EM Date Feb 006 Checked by HB Date March 006 DESIGN EXAMPLE DESIGN OF A LIPPED CHANNEL IN AN EXPOSED FLOOR Design a simply
More informationFigure 21: Stresses under axisymmetric circular loading
. Stresses in Pavements.1. Stresses in Fleible Pavements.1.1. Stresses in Homogeneous Mass Boussinesq formulated models for the stresses inside an elastic halfspace due to a concentrated load applied
More informationAPPENDIX 1 MODEL CALCULATION OF VARIOUS CODES
163 APPENDIX 1 MODEL CALCULATION OF VARIOUS CODES A1.1 DESIGN AS PER NORTH AMERICAN SPECIFICATION OF COLD FORMED STEEL (AISI S100: 2007) 1. Based on Initiation of Yielding: Effective yield moment, M n
More informationMS Excel Toolkit: Design of steelconcrete composite columns in accordance with EN
MS Excel Toolkit: Design of steelconcrete composite columns in accordance with EN 199411 Guilherme de Azevedo Guedes Lebre Dissertation in Civil Engineering, Master Degree Instituto Superior Técnico,
More informationSabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in
Sabah Shawkat Cabinet of Structural Engineering 17 3.6 Shear walls Walls carrying vertical loads should be designed as columns. Basically walls are designed in the same manner as columns, but there are
More information