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1. Webinar Purpose

2. Introduction to midas FEA

3. Reference Material

4. Analysis Details

5. Results

6. Conclusion

7. Future Research Possibilities

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• Analyse different anchorage solutions using advanced nonlinear numerical models

• Compare stress distribution to theoretical models

• Check crack distribution

• Compare crack distribution considering:• High Strength Concrete(C90/105) vs. UHPFRC (G2TM)

• Plain concrete vs. Reinforced concrete

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• midas FEA is state of the art software which defines a new paradigm for advanced nonlinear and detail analysis for civil and structural engineering applications;

• It is specialized for refined method analysis, which is required by design codes for complex geometry;

• Able to perform local analysis for elements and obtain in-depth and highly accurate calculations that are essential for projects that require refined method analyses.

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01. Linear Static Analysis

• Multiple Load Cases & Combinations

• Output Control (Data, Node, Element)

• Result Coordinate System

• Extensive Element Library

• Equation Solvers• Direct Solvers

• Multi-frontal Sparse Gaussian Solver

• Skyline Solver

• Iterative Solvers• PCG, GMR (Unsymmetric)

• Construction Stage Analysis• Material Nonlinearity

• Restart

02. Nonlinear Static Analysis

• Material Nonlinearity• von Mises, Tresca, Mohr-Coulomb,

• Drucker-Prager, Rankine,

• User Supplied Material

• Geometric Nonlinearity• Total Lagrangian

• Co-rotational

• Iteration Method• Full Newton-Raphson

• Modified Newton-Raphson

• Arc-Length Method

• Initial Stiffness

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03. Reinforcement Analysis

• Reinforcements• Embedded Bar

• Embedded Grid

• Various Mother Elements (Solid, Plate, Axisymmetric, etc.)

• Prestress (Pre-tensioned & Post-tensioned)

• Material Nonlinearity

• Geometric Nonlinearity

04. Crack Analysis

• Total Strain Crack• Fixed & Rotating Crack Model

• Discrete Drack Model• Interface Nonlinearity

• Results• Crack Pattern

• Element Status(Crack, Plasticity)

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05. Eigenvalue Analysis

• Modal Analysis• Lanczos Method

• Subspace Iteration

• Sturm-Sequence Check

• Include Rigid Body Modes

• Modal Participation Factors

• Linear Buckling Analysis• Critical Load Factors

• Buckling Modes

• Load Combinations & Factors

06. Dynamic Analysis

• Transient / Frequency Response• Direct Integration

• Mode Superposition

• Time Forcing Function DB

• Time Varying Loads

• Ground Acceleration

• Time History Plot / Graph

• Spectrum Response• SRSS, CQC, ABS

• Design Spectrum DB

• Seismic Data Generator

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07. Interface Nonlinear Analysis

• Interface Elements

• Point, Line, Plane

• Pile (Solid-Line)

• Interface Models

• Rigid

• Coulomb Friction

• Discrete Cracking

• Crack Dilatancy

• Bond-Slip

• Combined CSC

08. Contact Analysis

• Contact Type

• Weld Contact, General Contact

• Behaviors

• Material Nonlinearity

• Geometry Nonlinearity

• Result

• Displacement

• Stress

• Contact force

09. Fatigue Analysis

• Methods and Parameters

• S-N Method (Stress-Life)

• Load / Stress History

• Rainflow Counting

• Mean Stress Corrections

• Stress Concentration Factor

• Modifying Factors

• Results

• Cycles to Failure

• Damage estimation

10. Heat of Hydration Analysis

• Heat Transfer

• Steady-State / Transient

• Heat Generation

• Conduction

• Convection

• Pipe Cooling

• Concrete Behavior

• Creep / Shrinkage

• Compressive Strength

• Design Codes (JCI, JSCE, etc.)

11. Heat Transfer/Stress Analysis

• Steady-State & Transient

• Conduction, Convection

• Heat Flux

• Heat Flow

• Temperature Gradient Display

12. CFD Analysis

• CFD Models• Turbulence Models

• Compressible/ Incompressible Flow

• Inviscid Flow

• Unsteady Flow

• Discretization Scheme• 2nd-order (Spatial)

• Dual time stepping (Temporal)

• Boundary Conditions

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• EUROCODE 2

• CIRIA: A guide to the design of anchor blocks for post-tensioned concrete members

• Structural Implications of Ultra-High Performance Fibre-Reinforced Concrete in Bridge Design, Ana Spasojević (2008)

• Ultra High Performance Fibre-Reinforced Concretes: Interim Recommendations, AFGC-SETRA (2002)

• Testing and analysing innovative design of UHPFRC anchor blocks for post-tensioning tendons, F. Toutlemonde, J.-C. Renaud & L. Lauvin

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Geometry

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Material Properties

• S355

• Plastic material constitutive model: von Mises

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Geometry Material Properties

• Two separate cases:• High Strength Concrete: C90/105

• Ultra High Performance Fiber Reinforced Concrete: Ductal G2TM

• In both cases the Total Strain Crack constitutive model will be used

• For each type of concrete two cases will be considered:• Plain concrete

• Reinforced (only bursting reinforcement modelled)

C90/105

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• Smeared crack model

• Fixed crack model: the axes of cracks remain unchanged once the crack axes are defined

• Rotating crack model: the directions of the cracks are assumed to continuously rotate depending on the changes in the axes of principle strains

• Secant stiffness: suitable for finding excellent and stable solutions to analyses of reinforced concrete structures, which widely develop cracks

• Tangent stiffness: very appropriate for analyses of local cracking or crack propagation

C90/105

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• In cracked concrete, large tensilestrains perpendicular to the principal compressive direction reduce the concrete compressive strength

• The compressive strengths is dependent on the lateral damage variables

• Accounts for increase in strength given by lateral confinement

• The increased ductility of confined concrete is modelled by a linear adoption of the descending branch of the Thorenfeldt curve

C90/105

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• Hordijk Model

• Expresses tension softening behaviour of concrete

• Results in a crack stress equal to zero at ultimate crack strain

• Thorenfeldt Model

Mechanical characteristics at 28 days

Characteristic compressive strength f_ck 150.00 MPa

Characteristic limit of elasticity under tension f_ctk,el 8.00 MPa

Characteristic maximal post-cracking stress f_ctfk = σ_(0,3) 6.10 MPa

Mean Young’s modulus E_cm 53000.00 MPa

Poisson’s ratio 0.20

Other characteristics

Density 24 to 25 kN/m^3

Thermal expansion coefficient at 28 days 11.00 μm/m/°C

Autogenous shrinkage from 0 to 90 days ≤0.5 mm/m

Drying shrinkage from 0 to 90 days ≤0.3 mm/m

Creep coefficient 1.00

Durability characteristics

Water porosity at 90 days 1.5 to 2.5 %

Oxygen permeability at 28 days (at 20°C) ≤6*10^(-19) m^2

Chloride ions diffusion coefficient ≤0.5*10^(-12) m^2*s^(-1)

Mercury porosity at 90 jours 3 to 5 %

Carbonation thickness (natural and accelerated conditions) ≤0.1 mm

Resistance to freeze / thaw cycles (severe conditions – 300 cycles) 100.00 %

Resistance to spalling (de-icing salts - 56 cycles) ≤10 g/m^2

Resistance to hydraulic abrasion (CNR coefficient) 1.00

Impact resistance (CNR print testing) 65.00

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Ductal G2TM

Compression curve Tension curve

StrainStress [MPa]

StrainStress [MPa]

0 0 0 0

f_cd -0.00169811 -90 f_ctfk/K 6.39E-05 3.388889

ε_u,pic 6.80E-04 3.388889

K_local 1.8 ε_lim 5.25E-03 0

Ductal G2TM

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Tension curve Compression curve

B500C

• Two reinforcement spirals• Spiral 1 Diameter: 200mm

• Spiral 2 Diameter: 250mm

• Bar diameter: 10mm

• As per CIRIA:• Spiral diameter ≥ anchorage(2ypo)+50mm

• Distributed in region [0.2yo, 2yo]

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• Prestress load applied as pressure on top of bearing plate

• Total prestress load: 30strands x 180kN = 5400kN

• γP,unfav = 1.2 as per 2.4.2.2 of EC2

• Self weight applied using automated self weight function

• Supports applied as full restraints of nodes at the bottom of the anchorage block

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Stress distribution, CIRIA

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σ1 – max tension σ3 – max compression

σ1

C90/105 no reinforcement

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C90/105 with reinforcement

UHPFRC no reinforcement UHPFRC with reinforcement

0.85Pt

σ3

C90/105 no reinforcement

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C90/105 with reinforcement

UHPFRC no reinforcement UHPFRC with reinforcement

0.85Pt

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C90/105 no reinforcement

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C90/105 with reinforcement

UHPFRC no reinforcement UHPFRC with reinforcement

0.85Pt 0.95Pt

C90/105 no reinforcement

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C90/105 with reinforcement

UHPFRC no reinforcement UHPFRC with reinforcement

0.85Pt 0.95Pt

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0.20Pt 0.40Pt 0.60Pt 0.80Pt 1.00Pt

C90/105 no reinforcement

UHPFRC no reinforcement

0.95Pt

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0.20Pt 0.40Pt 0.60Pt 0.80Pt 1.00Pt

C90/105 with reinforcement

UHPFRC with reinforcement

UHPRFC no reinforcement

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-100

-80

-60

-40

-20

0

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-2.00E-03 -1.00E-03 0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 5.00E-03 6.00E-03

Stress [MPa]

Strain [mm/mm]

Stress-Strain Diagram G2TM

G2TM

Elem. 102925 (Max Stress, Strain)

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C90/105 reinforcement Stress C90/105 reinforcement Strain

UHPFRC reinforcement Stress UHPFRC reinforcement Strain

• Bursting reinforcement has a very beneficial effect for HSC

• The reinforcement has little to no effect on the crack distribution for UHPFRC

• UHPFRC shows a more even distribution of stresses compared to HSC

• The fibers have a very beneficial effect on crack distribution, helping to keep the crack dimensions limited

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• Check theoretical models against tests on UHPFRC samples

• Improve calibration of models from tests on UHPFRC samples

• Implement UHPFRC models and databases as standard for finite element software

• Better implementation of UHPFRC into current design standards, as current codes tend to be ultra conservative

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Contact us at:

uksupport@midasuser.com

+44 (0)207 559 1389

Visit our website at:

uk.midasuser.com

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