3543.181 Simulation of a cementitious beam exposed to calcium leaching and mechanical loading.. 3603.187 Numerical simulation of a concrete beam affected by alkali-silica reaction: Result
Trang 1XXXII List of Figures
3.78 Load history with various rest periods [150] 192
3.79 Behaviour of the longitudinal strain at Smax/Smin = 0.675/0.10 192
3.80 Related longitudinal strain at Smax/Smin = 0.675/0.10 193
3.81 Correlation between the fatigue strain and the residual stiffness subjected to different sequences of cyclic loading 194
3.82 Steps of exposure and measuring during CDF/CIF test [731] 195
3.83 Example relationship between RDM and relative moisture uptake - concrete type 2 [610] 195
3.84 Internal damage due to freeze-thaw cycles at several depths of the specimen (left), Moisture uptake vs number of freeze-thaw cycles (right) 197
3.85 Test devices and definitions 199
3.86 Cyclic flow rule (I) 200
3.87 Cyclic flow rule (II) 201
3.88 Intensity of accumulation in drained cyclic element tests on soils (I) 202
3.89 Intensity of accumulation in drained cyclic element tests on soils (II) 204
3.90 Influence of the grain size distribution curve on Dacc 205
3.91 Undrained cyclic tests 206
3.92 Effect of cycles atσ=0 207
3.93 Application of headed shear studs in composite bridges 208
3.94 Load-deflection behaviour of headed shear studs embedded in solid concrete slabs under static loading 209
3.95 Fatigue strength curve for cyclic loaded headed shear studs according [685] 210
3.96 Safety concept to determine the lifetime of composite structures subjected to high cycle loading 211
3.97 Tests with multiple blocks of loading 213
3.98 Tests to compare the effect of the mode control - force control vs displacement control - and the effect of low temperature 215
3.99 Duration of the crack initiation phase and crack growth velocity due to very low cyclic loads [685] 216
3.100 Details of the push-out test specimen 216
3.101 Servo hydraulic actuators 217
3.102 Position of transducers 218
3.103 Development of plastic slip over the fatigue life in series S1 - S4 220
3.104 Decrease of static strength vs lifetime due to high cycle loading 221
3.105 Test programme and loading parameters of the composite beam tests VT1 and VT2 226
3.106 Details of test beam VT1 228
3.107 Details of test beam VT2 229
Trang 2List of Figures XXXIII
3.108 Test setup of test beams VT1 and VT2 230
3.109 Electric circuit to detect complete shear failure of headed studs 231
3.110 Change of initial deflections due to cyclic loading 234
3.111 Load-deflection behaviour of test beams VT1 and VT2 in the static tests after cyclic loading 234
3.112 Experimental determination of the reduced static strength of the steel section near midspan after high cycle pre-loading 235
3.113 Slip along the interfaces of steel and concrete after first loading and after cyclic loading 236
3.114 Crack lengths at the stud feet after the cyclic loading phase -Preparation stages for examination purposes 237
3.115 Representation of different failure surfaces in the principal strain space 239
3.116 Stress-strain diagrams for uniaxial compressive and tensile loading obtained from the damage model by Mazars 240
3.117 Anisotropic damage model by [604]: Illustration of the failure surface in the principal stress space, see eq (3.29) 242
3.118 Definition of a local coordinate system and decomposition of the traction vectort= into the normal part t n and the tangential part t m 243
3.119 Anisotropic elastoplastic damage model by [534]: Influence of the scalar coupling parameter β on the stress-strain diagram 246
3.120 Yield conditions 247
3.121 Stress-strain relation of concrete 249
3.122 Discrete representation of cracks: Traction separation law of the formatt=t( u ) across the crack surface 253
3.123 Strong Discontinuity Approach: Additive decomposition of the displacement field u(equation (3.84)) 254
3.124 Strong Discontinuity Approach: Strain field resulting from the displacement field u(x) = ¯u(x) + ˆu(x) 254
3.125 Model-based concept for life time assessment of metallic structures 257
3.126 Numerical and experimental data for (a) material softening and (b) ratcheting effect 259
3.127 Low Cycle Fatigue in metals: Numerical and experimental results for cyclically loaded round notched bar 260
3.128 Low Cycle Fatigue in metals: Damage accumulation and predicted damage in a cyclically loaded round notched bar 261
3.129 S-N -approach 263
3.130 Degradation of compressive strength and sequence effects 263
3.131 Evaluation of the approach for sequence effects 264
3.132 Rheological element 265
3.133 Fatigue strain evolution 267
3.134 Split of fatigue strains 268
Trang 3XXXIV List of Figures
3.135 Evaluation of the split variable βfat 2683.136 Kinked crack and its equivalent elliptical crack 2773.137 Growth of the circular crack and its equivalent elliptical
crack 2793.138 Order of the considered sequential loading 2803.139 Evolution of the geometry and the orientations of the
equivalent elliptical crack 2813.140 Evolution of the stiffness components in the principle
directions 2823.141 Specimen geometry and different mesh patterns 2833.142 Load-cycle curves for different mesh patterns 2843.143 Chemo-mechanical damage of porous materials within the
Theory of Mixtures 295
3.144 Conductivity of the pore fluid D0 and macroscopic
conductivity of non-reactive porous media φD0 2993.145 Chemical equilibrium function by G´erard [307, 308] and
Delagrave et al.[232] 3023.146 Microstructure, constituents and volume fractions of concrete
as a partially saturated porous media 303
u r − 1 and of their dependence on the liquid saturation s l 3123.148 Theoretical model for the prediction of the mean value of the
ultimate shear resistance according [684] 3173.149 Result of the statistical analysis of the results of 101 statically
loaded push-out tests according to EN 1990 [16] 3223.150 Comparison of the result of the statistical analysis with the
rules in current German and European standards 3243.151 Preparation stages for examination purposes 3243.152 Failure modes A and B 3253.153 Weld collar - Close-up view of the crack shown in Figure
3.152 3263.154 Correlation between reduced static strength and damage at
the stud feet based on the fatigue fracture area 3273.155 Correlation between reduced static strength and damage at
the stud feet based on crack lengths 3283.156 Comparison of fatigue test results with the prediction in
Eurocode 4 3293.157 Model for the prediction of the fatigue life of a headed shear
stud in a push-out test 3313.158 (a) Reduced static strength over lifetime, (b) Comparison of
the reduced static strength 3313.159 Load-slip curve of headed shear studs - load deflection
behaviour 3323.160 Effect of high-cycle loading on the load-slip behaviour 3333.161 Elastic stiffness and accumulated plastic slip 334
Trang 4List of Figures XXXV
3.162 Relationship between crack velocity, crack propagation and
reduction of static strength 3353.163 Fatigue strength and lifetime of cyclic loaded shear studs 3363.164 Comparison between the test results with the lifetime
prediction 3383.165 Damage accumulation considering the load sequence effects 3393.166 Damage accumulation in the case of multiple block loading
tests with decreasing peak loads 3403.167 Comparison between the test results with the results of the
lifetime prediction 3403.168 Ductility after high cycle loading 3413.169 Comparison between test results and finite element
calculations 3423.170 Comparison between test results and finite element
calculations 3433.171 Test series S9 - Effect of control mode - Effect of low
temperature 3453.172 Failure surface of the improved material model CONCRETE 3473.173 Comparison between the results of numerical simulations and
test results 3483.174 Test beam VT1 - Effect of high cycle loading on load bearing
capacity 3483.175 Cyclic behaviour of test beam VT1 3503.176 Test beam VT2 - Effect of high cycle loading - Typical crack
formation 3513.177 Geometry of a tunnel lining subjected to cyclic hygral and
thermal loading 352
3.178 Evolution of the crack width w of a tunnel lining subjected
to cyclic hygral and thermal loading 352
3.179 Scalar damage measure d at the crown of a tunnel lining
subjected to cyclic hygral and thermal loading 353
3.180 Liquid saturation S lat the crown of a tunnel lining subjected
to cyclic hygral and thermal loading 3543.181 Simulation of a cementitious beam exposed to calcium
leaching and mechanical loading 355
3.182 Temporal evolution of the vertical displacement u s of the
cementitious beam and prediction of the collapse 3553.183 Chemo-mechanical analysis of a concrete panel: Conditions 3563.184 Chemo-mechanical analysis of a concrete panel: Results I 3583.185 Chemo-mechanical analysis of a concrete panel: Results II 3593.186 Numerical simulation of a concrete beam affected by
alkali-silica reaction: Conditions 3603.187 Numerical simulation of a concrete beam affected by
alkali-silica reaction: Results I 361
Trang 5XXXVI List of Figures
3.188 Numerical simulation of a concrete beam affected by
alkali-silica reaction: Results II 3623.189 Numerical simulation of a concrete beam affected by
alkali-silica reaction: Results III 3633.190 Low Cycle Fatigue Model: (a) Spherical pressure vessel, (b)
Vertical displacement-time plot of the El Centro earthquake 3633.191 Low Cycle Fatigue Model: (a) Damage accumulation
(El Centro earthquake), (b) Temporal evolution of the
maximal void volume fraction f 364
4.1 Overview of the methodological implementation of lifetime
oriented design concepts 3664.2 Numerical modeling and general multiphysics problem 3754.3 Modeling and numerical analysis of multiphysics problems 3764.4 Illustration of isotropic Lagrange shape functions 3814.5 Illustration of anisotropic Lagrange shape functions 3824.6 Computation of generalized element tensors of multiphysics
p-finite elements 387
4.7 Sinusoidial loading of a truss member and rel error of
internal energy plotted over the number of dof 3884.8 Modified Legendre-polynomials 3904.9 Comparison of high order shape function concepts 3914.10 Comparison of the structure of element vectors and matrices
for the Legendre- and Lagrange-concept 3924.11 3D-p-element: definition and numbering of element vertices
(N i ), edges (E i ) and faces (F i) 3934.12 3D-p-shape functions: nodal, edge, face and internal modes
for different polynomial degrees 3954.13 Structure types, corresponding classical finite element models
and 3D-p finite element models with spatially anisotropic
approximations 3964.14 Hygro-thermo-mechanical loading of a structural segment,
Fieldwise anisotropic discretization using the p-FEM 398
4.15 Discretization of the standard structures (truss, slab, shell)
into an infinite numbers of elements 3994.16 Relative reduction of system nodes/dof for different
structures 4024.17 Strategy for solving non-linear vector equationri(u) =r 4044.18 Control of load factor and Newton-Raphson iteration 4044.19 Algorithmic set-up of the load controlled Newton-Raphson
scheme 4064.20 Illustration of arc-length methods and predictor step
calculation 4074.21 Algorithmic set-up of the arc-length controlled
scheme 410
Trang 6List of Figures XXXVII
4.22 Design of Newmark type time integration schemes 413
4.23 Illustration of Newmark and generalized mid-point approximations 414
4.24 Algorithmic set-up of Newmark-α schemes including error controlled adaptive time stepping 417
4.25 Galerkintime integration schemes 418
4.26 Algorithmic set-up of discontinuous and continuous Galerkintime integration schemes 423
4.27 Modular concept for multiphysics finite element programs 425
4.28 Example geometry and warping-based error criterion 432
4.29 Two-element example with two hanging nodes 434
4.30 Beam 1: Geometry and boundary conditions 435
4.31 Beam 1: Load-displacement curve fortolerr = 10−5 andcrit1 (variousnGP) 435
4.32 Beam 1: Different states of mesh refinement (Q1SPs/o, 16El.), contours: accumulated plastic strain 436
4.33 Beam 1: Load-displacement curve and number of elements fortolerr = 10−7 andcrit1 (various nGP0) 437
4.34 Beam 1: Load-displacement curve and number of elements for different tolerances andcrit2 (Q1SPs/o, nGP0 = 16) 438
4.35 Beam 2: Load-displacement curve and number of elements for different tolerances andcrit2 (Q1SPs/o, nGP = 16) 438
4.36 Beam 2: Different states of mesh refinement (Q1SPs/o, 16 El.), contours: accumulated plastic strain 439
4.37 Plate 1: Geometry and boundary conditions 440
4.38 Plate 1: Load-displacement curve and number of elements for different tolerances andcrit2 (Q1SPs, nGP = 8) 440
4.39 Plate 1: Load-displacement curve for different tolerances and crit2 (Q1SPs, nGP = 8) 441
4.40 Plate 1: Different states of mesh refinement (Q1SPs/o, 16 El.), contours: accumulated plastic strain 441
4.41 Plate 1: Load-displacement curve and number of elements for different load steps and crit2 (Q1SPs/o, nGP = 8, tolerr = 0.01) 442
4.42 Plate 1: Load-displacement curve and number of elements for different load steps and crit2 (Q1SPs, nGP = 8, tolerr = 0.0001) 442
4.43 Illustration of h- and p-method error estimates and indicators 443
4.44 Algorithmic set-up for the error controlled adaptive time integration by Newmark-α schemes 447
4.45 Algorithmic set-up for the error controlled adaptive time integration by Newmark-α or p-Galerkin methods and h-method error estimates/indicators 447
Trang 7XXXVIII List of Figures
4.46 Algorithmic set-up for the error controlled adaptive time
integration by p-Galerkin methods and p-method error
estimates/indicators 448
4.47 Function to be approximated 450
4.48 Approximation of equation (4.147) 451
4.49 Normal and tangential vector 452
4.50 Four crack tip functions 453
4.51 Crack with one kink 454
4.52 Crack after mapping 456
4.53 Multiple kinked crack 456
4.54 Multiple kinked crack after the first mapping 457
4.55 Pointxand mirrored point ˆx 458
4.56 Strain ε from equation (4.173) for the integral (4.175) 462
4.57 Number of integration points used in the numerical integration of (4.174) 462
4.58 Strain ε from equation (4.173) for the integral (4.177) 463
4.59 Number of integration points used in the numerical integration of (4.176) 463
4.60 Strain ε from equation (4.173) for the integral (4.179) 465
4.61 Number of integration points used in the numerical integration of (4.178) 465
4.62 Strain ε from equation (4.173) for the integral (4.181) 466
4.63 Number of integration points used in the numerical integration of (4.180) 466
4.64 Strain ε from equation (4.173) for the integral (4.183) 467
4.65 Number of integration points used in the numerical integration of (4.182) 467
4.66 Strain ε from equation (4.173) for the integral (4.185) 468
4.67 Number of integration points used in the numerical integration of (4.184) 468
4.68 Tension test configuration 469
4.69 Displacements u x for the deformed system using bilinear shape functions 470
4.70 Displacements u x for the deformed system, left: using bi-quadratic shape functions, right: using quadratic hierarchical shape functions 470
4.71 Differences of displacements inside the 1st blending element 471
4.72 Differences of displacements inside the 2nd blending element 471
4.73 Differences of displacements inside the 3rd blending element 472
4.74 Differences of displacements inside the 4th blending element 472
4.75 Differences of displacements inside the 5th blending element 473
4.76 Numerical integration in the context of X-FEM: Subdivision of the continuum element into six sub-tetrahedrons 475
4.77 Separation of a sub-tetrahedron by a plane crack segment 475
4.78 C0-crack plane evolution 476
Trang 8List of Figures XXXIX
4.79 Definition of the crack plane by pointPand normal vectorn 477
4.80 Constant strain triangular element cut by means of a planar internal boundary ∂sΩ; see [745] 481
4.81 Enhanced discontinuous displacement field ru (Hs− ϕ): (a) bi-linear approximation (2 nodes in Ω+); (b) bi-quadratic approximation (1 node in Ω+) 482
4.82 Numerical study of a notched concrete beam: dimensions (in [cm]) and material parameters 486
4.83 Numerical study of a notched concrete beam using the proposed multiple crack concept and the rotating crack approach 488
4.84 Sketch for the computation of the SIF for a kinking crack with r → 0 491
4.85 Schematic figure for the calculation of the SIF with constant radius for kinking cracks 491
4.86 Sketch of K II (left) and|K II | (right) depending on the angle θ for a three point bending test 492
4.87 Energy function Πtot for a three point bending test 493
4.88 Crack simulation of a double notched slab: System, material data and finite element mesh 494
4.89 Crack simulation of a double notched slab: Visualization of the crack topology by the φ = 0-level set 495
4.90 Crack simulation of a double notched slab: Comparison of crack topology and of load-displacement curves 495
4.91 Bumerical investigation of crack propagation of an anchor pull-out test: System and finite element mesh (N E = 996) 496
4.92 Numerical investigation of crack propagation of an anchor pull-out test: Crack topology and displacement u3 in pull-out direction 497
4.93 Numerical investigation of crack propagation of an anchor pull-out test: Stress σ33 at the beginning and the end of the crack process 497
4.94 Numerical investigation of crack propagation of an anchor pull-out test: Load-displacement curve 498
4.95 Concept for the efficient simulation of dynamic, partially damaged structures 501
4.96 Decomposition of the structure 507
4.97 Geometry and loading 513
4.98 Exploded view of the bridge 514
4.99 Damage evolution in the largest two hangers 515
4.100 Displacement in X2-direction in point B 516
4.101 Mean relative displacement-based error in point B 516
4.102 Comparison of a pure implicit and an explicit calculation of accumulation 518
Trang 9XL List of Figures
4.103 General definition of the failure domain depending on
scattering resistance (R) and stress (S) values 529
4.104 Standardization of an exemplary 2D joint distribution function for a subsequent FORM/SORM analysis 532
4.105 Comparison of Latin Hypercube Sampling and Monte-Carlo Simulation 536
4.106 Parallel execution of stochastically independent DC-MCS of fatigue analyses on a distributed memory architecture [824] 545
4.107 Parallel software framework 561
4.108 Experimental setup 562
4.109 Damage equipment 563
4.110 Singular values 564
4.111 1’st eigenfrequency and mode shape 564
4.112 2’nd eigenfrequency and mode shape 565
4.113 3’rd eigenfrequency and mode shape 565
4.114 4’th eigenfrequency and mode shape 566
4.115 Cut modelling 566
4.116 Optimization topology 570
4.117 The new 3-series convertible 573
4.118 3-series convertible with battery 574
4.119 Battery as vibration absorber 574
4.120 FE model of the shaker test arrangement 575
4.121 Measured acceleration data for the y-direction 576
4.122 Power spectral density function of the resulting von Mises stress for the elements of Figure 4.119, load direction y 577
4.123 Dirlik distribution function of the stress amplitudes 579
4.124 Typical stress picture for load in y-direction (Time History Analysis) 581
4.125 Expected life time in arbitrary time units for the Time History calculation (acceleration load in y-direction) 582
4.126 Hygro-mechanically loaded concrete shell structure: System geometry and material data 584
4.127 Hygro-mechanically loaded concrete shell structure: Hygral boundary conditions of the inner and outer surface of the shell 584
4.128 Hygro-mechanically loaded concrete shell structure: Finite element mesh of the numerical analysis 585
4.129 Hygro-mechanically loaded concrete shell structure: Deformation and stresses due to dead load 586
4.130 Hygro-mechanically loaded concrete shell structure: Distribution of the saturation S l 587
4.131 Hygro-mechanically loaded concrete shell structure: Damage evolution at the support area 588
4.132 Hygro-mechanically loaded concrete shell structure: Damage zone and accelerated transport process in the area of cracks 588
Trang 10List of Figures XLI
4.133 Hygro-mechanically loaded concrete shell structure:
Distribution of saturation S l and damage variable d across
the shell thickness (I) 5894.134 Hygro-mechanically loaded concrete shell structure:
Distribution of saturation S l and damage variable d across
the shell thickness (II) 5904.135 Calcium leaching of a cementitious bar and a cementitious
beam: Geometry, FE mesh and chemical loading history 5914.136 Calcium leaching of a cementitious bar: Numerical results
obtained from the cG(1) method 5934.137 Calcium leaching of a cementitious bar: Numerical results
and time integration error obtained from adaptive Newmark
integration 5954.138 Calcium leaching of a cementitious bar: Time histories
c(t, X1)/c0 obtained from dG(p)-integration (t [108s],
X1[mm]) 5964.139 Calcium leaching of a cementitious bar: Time histories
c(t, X1)/c0 obtained from cG(p)-integration (t [108s],
X1[mm]) 5974.140 Calcium leaching of a cementitious bar: Spatial local and
global error estimates for Newmark time integrations 5984.141 Calcium leaching of a cementitious bar: Logarithm of error
estimates e Δt/5 for dG-methods with different time steps Δt 599
4.142 Calcium leaching of a cementitious bar: Logarithm of error
estimates e p/p+1 for dG-methods with different time steps Δt 600
4.143 Calcium leaching of a cementitious bar: Logarithm of error
estimates e p/p+1 and e Δt/5 for cG-methods with different
time steps Δt 601
4.144 Calcium leaching of a cementitious bar: Average relative
errors of the Newmark method and Galerkin methods 6034.145 Calcium leaching of a cementitious beam: Numerical results
obtained from cG(1) 6044.146 Calcium leaching of a cementitious beam: Investigation of
the oscillations in the results of cG(1)- and cG(2)-solutions 6054.147 Calcium leaching of a cementitious beam: Investigation of
the robustness of the cG(1)-solution for small T c 6064.148 Pictures of damaged road bridge in M¨unster (Germany) and
correspondent FE models 6074.149 Refined FE models of a connecting plate and the
correspondent welding 6084.150 Effective stress values of a connecting plate under a constant
rod deflection 6104.151 Representative surface of partial damage values for varying
wind and initial displacements at the critical tie rod 611
Trang 11XLII List of Figures
4.152 Time-dependent evolution of the failure probability of critical
material points in the welding region and the bulk material 612
4.153 Optimization model 613
4.154 Optimization results 614
4.155 The road bridge at H¨unxe (Germany) shortly before its deconstruction in 2006 616
4.156 Location of prestressing tendons and crack pattern observed on the bridges main girders 617
4.157 Location of drilling cores 618
4.158 Comparison of stress-strain curves between bridge concrete and laboratory concretes with different strengths [193] 620
4.159 LM-micrograph of in-situ concrete 621
4.160 Total longitudinal (left) and fatigue strain (right) at Smax 622
4.161 Correlation between fatigue strain and the residual stiffness for Smax/Smin= 0.675/0.10 623
4.162 Three dimensional Finite Element model of the road bridge at H¨unxe 624
4.163 Applied corrosion model 626
4.164 Modified S-N curves for steel and fatigue damage evolution function 627
4.165 Higher order statistical moments 628
4.166 Validation of input data 628
4.167 Evolution of compressive strength and histogram of concrete strength 629
4.168 Random field dependency on correlation length and eigenvalues used for reconstruction of correlation matrix 632
4.169 Load deflection diagram and time deflection diagram 3D 633
4.170 Load deflection curves and lifetime distribution and estimation 633
4.171 State space model 636
4.172 Impulse excitation in laboratory 639
4.173 Comparison between measured signals and signals from identified model 639
4.174 Cantilever bending beam used for experiments in laboratory 641
4.175 Drawing from the cantilever bending beam with the location of saw cut 641
4.176 Markov parameters for damage detection 642
4.177 Bridge near H¨unxe / Germany (span: 62.5m) 643
4.178 System modification: hanger cut through 643
4.179 Torsional mode from reference system and after cut hanger 644
4.180 Recalculation of a centrifuge model test of Helm et al [365] 646
4.181 Parametric studies of shallow strip foundations under cyclic loading 647
4.182 FE calculations with stochastically fluctuating void ratio 648
Trang 12List of Figures XLIII
4.183 FE calculation of vibratory compaction and bridge
settlements 6494.184 Calculation of pore water pressure accumulation due to
earthquake loading 6504.185 FE calculation of a geogrid-reinforced embankment 6514.186 FE calculation of a monopile foundation of an offshore wind
power plant 6515.1 Reinforced concrete column under fatigue loading 6545.2 Load-carrying-capacity and response surface method 6545.3 Time-dependent hazard function and time-dependent
reliability 6555.4 Multi-level system approach followed during the lifetime
analysis of the arched steel bridge [826] 6565.5 Multi-scale modeling and analysis of fatigue-related
structural problems 6575.6 Comparison of resulting time-dependent failure probabilities
of the researched connection plate 658
Trang 13List of Tables
2.1 Conversion of the wind data of the observation station at the
airport of Hannover into data for the building location 20
2.2 Determination of a reduced characteristic suction force on the fa¸cade element after Figure 2.8 24
2.3 Statistical parameters of the traffic records of Auxerre (1986) 49
2.4 Relation between gross weight of the heavy vehicles and the axle weights of the lorries of types 1 to 4 in % (mean values and standard deviation) 50
2.5 Distance of axles in [m] of the different types of vehicles (mean values and standard deviation) 50
2.6 Statistical parameters of the corrected static traffic records of Auxerre (1986) 53
2.7 Different cross-sections and traffic types for the random generations 55
2.8 Traffic data of different locations and characteristic values of gross and axle weight [720] 60
2.9 Different design situations and corresponding return periods and fractiles 60
2.10 Factors Ψ for the determination of the representative values for serviceability limit states acc to [9] 63
2.11 Traffic categories acc to Eurocode 1-2 66
2.12 Statistical parameters of the traffic records at highway A61 (2004) 75
2.13 Relation between gross weight of the heavy vehicles and the axle weights of the lorries of types 1 to 5 (mean values) 76
2.14 Readings: winter 05/06 and winter 06/07; field station Meißen 102
3.1 Classification of pore sizes in concrete according to [724] 151
3.2 Influences on the degree of chemical attack 152
3.3 Changes of concrete properties due to cyclic loading 185
Trang 14XLVI List of Tables
3.4 Crack characteristics at certain number of cycles
Smax/Smin= 0.675/0.10 191
3.5 Correlation between frost suction and internal damage due
to freeze-thaw testing 1973.6 Summary of the single level tests 2133.7 Summary of the tests with multiple blocks of loading 2143.8 Mean values of material properties of concrete according to
EN 206-1 [12] 2183.9 Mean values of material properties of steel members 2193.10 Average test results per stud 2193.11 Loading parameters and results of the tests with two blocks
of loading (series S5) 2223.12 Loading parameters and results of the tests with four blocks
of loading (series S6) 2223.13 Average test results per stud in series S9 2233.14 Measured mean values of the peak load and the load range
at discrete number of load cycles in tests S9 4 2233.15 Loading parameters and block lengths in tests S9 5 2243.16 Average test results per stud in series S11 and S13 2253.17 Mean values of material properties of concrete according to
EN 206-1 [12] 2313.18 Mean values of material properties of steel members 2323.19 Main test results of beams VT1 and VT2 2333.20 Parameter of the elasto-plastic micropore damage model for
20MnMoNi55 2603.21 Low Cycle Fatigue in metals: Number of load cycles until
failure obtained 2613.22 Characteristics of the applied sequential loading 2813.23 Summary of the functions, material constants and reference
quantities of the high-cycle model 3143.24 Summary of the statically loaded push-out tests with decisive
criterion “failure of the concrete” (tests 1 - 27) 3193.25 Summary of the statically loaded push-out tests with decisive
criterion “failure of the concrete” (tests 28 - 58) 3203.26 Summary of the statically loaded push-out tests with decisive
criterion “shear failure of the stud” 3213.27 Result of the statistical analysis according EN 1990, Annex
D [16] 3233.28 Mean values of the crack length a h(see Figure 3.155) in test
series S11 and S13 3374.1 Multi-dimensional Lagrange shape functions 3824.2 Total number of geometric entities (vertices, edges, faces) of
the discretizations with an infinite number of elements 3994.3 Convergence criteria of iterative solution methods 405
Trang 15List of Tables XLVII
4.4 Comparison of iteration methods 406
4.5 Constraints and load factor increments of selected arc-length methods 409
4.6 Error indicators for Newmark type time integration schemes for non-linear second order initial value problems 445
4.7 Error indicators for Newmark type time integration schemes for non-linear first order initial value problems 446
4.8 Equivalent square sections 514
4.9 Modal Assurance Criterion 569
4.10 Gauss-Newton (c p /c d =800/1smm) 571
4.11 Gauss-Newton iteration (c p /c d =1400/1mm) 571
4.12 Results for an early design proposal 582
4.13 Standard parameter set [307, 454, 457] 592
4.14 Calcium leaching of a cementitious bar: Average relative errors of the Newmark method, discontinuous Galerkin methods and continuous Galerkin methods 602
4.15 Type of random variables (RV) included in the reliability problem used to describe the scatter of wind load parameters as well as material properties 609
4.16 Comparison of resulting runtime values analyzing the connecting plate 615
4.17 Dynamic elastic moduli Edyn (mean) and their standard deviations (SD) of the concrete after a service life of 50 years 619
4.18 Relevant mechanical concrete properties Estat, u and fc (mean values) as well as their standard deviations (SD) after a service life of 50 years 619
4.19 Number of elements of structural members 624
4.20 Determination of compressive strength at time of construction 629
4.21 Concrete strength grades according to German standards 630
4.22 Summary of the results of the FE calculations of strip foundations under cyclic loading 647