Corso di Laurea Magistrale in Ingegneria Civile ...

UNIVERSITA DEGLI STUDI DI PERUGIA

Facoltà di Ingegneria

RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN

Lehrstuhl Für Baustatik Und Baudynamik

Corso di Laurea Magistrale in Ingegneria Civile

Investigation of AAC vertical panels walls with the FE method based on a damage plasticity material model

Student

Supervisors

Francesca Taddei

Dr.-Ing.Christoph Butenweg Prof.-Ing. Marco Mezzi Dipl.-Ing. Jin Park

Academic Year 2008-2009

Abstract Nonlinear simulations for structures have been widely investigated in recent years. However, for new materials and new structural systems additional models need to be provided, to understand their behavior during a seismic event. In the thesis on hand, based on a concrete damage plasticity material code available in ABAQUS[7], three-dimensional models are proposed for unreinforced and reinforced walls of vertical AAC panels, to simulate the shear loads flow and the failure modes. The shear effects lead to both premature stiffness and strength degradation of the material and consequently of the overall structural system, therefore it is very important to deeply consider every aspect, especially beyond the elastic range. The attention is focused on a ten unreinforced vertical panels shear wall (Shear Wall Specimen 2 model) and on a four vertical panels reinforced shear wall (Shear Wall Specimen 15a model). For the latter, two different solution are developed: in the first the reinforcement is directly embedded inside the AAC mesh elements, while in the second grouted cores are taken in account around the rebar locations. Different material models (concrete, grout and rebar steel) are directly defined through their constitutive laws to provide a better simulation for in shear wall under complicated stress conditions and stress histories. The quasi-static loading condition has been simulated using both static and dynamic implicit analysis, switching from the former to the latter at the nonlinearities occurrence. The simulations results show that the AAC shear wall models can correctly represent the load-displacement responses and the sequences of the cracking formation and propagation. With the concrete damage plasticity model for the AAC, the cycle behavior and the damage accumulation of shear wall can be satisfactorily modeled, which is very important for the performance-based design of structures under disaster loads. Further researches are recommended in order to improve the results and to investigate different combinations of applied axial load, aspect ratios and reinforcement details.

List of Contents

List of Contents List of Tables.................................................................................................................... IV List of Figures ................................................................................................................. VII 1 Introduction .................................................................................................................... 1 1.1

Objective of the thesis ........................................................................................ 7

1.2

Organization of the thesis .................................................................................. 9

1.3

The autoclaved aerated concrete ..................................................................... 11

2 Evaluation and synthesis of available data ................................................................... 16 2.1

Sources of available data ................................................................................. 16

2.2

Available Data on Mechanical Properties of Materials ...................................... 17

2.2.1 Mechanical Properties of AAC ..................................................................... 17 2.2.2 Mechanical properties of the grout material.................................................. 24 2.2.3 Bonds properties .......................................................................................... 26 2.2.4 Stress-strain behavior of reinforcement ........................................................ 33 2.2.5 Summary of available data on mechanical properties of materials ............... 35 2.3

Evaluation and Synthesis of Available Data on Shear Wall Tests .................... 37

2.3.1 Summary of details of shear wall specimens ................................................ 37 2.3.2 Modeled shear wall specimens .................................................................... 39 3 Modeling of Mechanical Properties of Materials and Bonds.......................................... 52 3.1

ABAQUS Material Library ................................................................................ 52

3.2

The concrete damaged plasticity model ........................................................... 52

3.2.1 Description ................................................................................................... 53 3.2.2 Usage .......................................................................................................... 58 3.2.3 Calibration .................................................................................................... 60 3.3

Material model for AAC .................................................................................... 61

3.3.1 Compressive behavior of the AAC material model ....................................... 61 3.3.2 Tensile behavior of the AAC material model ................................................ 65 3.3.3 Cyclic behavior of the AAC material model .................................................. 69

List of Contents

3.4

Grout material model ....................................................................................... 77

3.4.1 Compressive behavior of grout material model ............................................ 77 3.4.2 Stress-strain relationship of grout material model......................................... 79 3.5

Bond modeling: contact interaction analysis..................................................... 80

3.5.1 ABAQUS contact properties overview .......................................................... 80 3.5.2 Shear bond between AAC and thin-bed mortar model ................................. 87 3.5.3 Shear bond between AAC and grout model ................................................. 95 3.5.4 Bedding mortar bond model ....................................................................... 100 4 Modeling of AAC-Ytong Shear Walls .......................................................................... 101 4.1

Introduction .................................................................................................... 101

4.2

Analysis procedure ........................................................................................ 101

4.2.1 Implicit dynamic analysis ............................................................................ 102 4.2.2 Frequency analysis .................................................................................... 103 4.3

Process for the Non-linear Analysis of AAC Shear Walls ............................... 104

4.4

Shear Wall Specimen 2 model ....................................................................... 106

4.4.1

Shear Wall Specimen 2 model pre-processing ........................................... 106

4.4.2 Shear Wall Specimen 2 model frequency analysis ..................................... 108 4.4.3 Shear Wall Specimen 2 model analysis and results ................................... 110 4.5

Shear Wall Specimen 15a model ................................................................... 125

4.5.1 Shear Wall Specimen 15a model pre-processing ....................................... 125 4.5.2 Shear Wall Specimen 15a model frequency analysis ................................. 129 4.5.3 Shear Wall Specimen 15a model analysis and results ............................... 130 5 Significance of Results ............................................................................................... 146 5.1

Significance of results for Shear Wall Specimen 2 model............................... 146

5.1.1 Behavior modes for Shear Wall Specimen 2 model.................................... 146 5.1.2 Hysteretic behavior for Shear Wall Specimen 2 model ............................... 149 5.2

Significance of results for Shear Wall Specimen 15a model........................... 154

5.2.1 Behavior modes for Shear Wall Specimen 15a model................................ 154

List of Contents

5.2.2 Hysteretic behavior for Shear Wall Specimen 15a models ......................... 158 5.3

Notes about the behavior factor .................................................................... 162

6 Summary and conclusions ......................................................................................... 164 References.................................................................................................................... 175

List of Tables

List of Tables Table 2.2-1 Summary of results for compressive strength and density [3] ....................... 17 Table 2.2-2 Summary of Ytong results for compressive strength and density.................. 18 Table 2.2-3 Typical characteristics of AAC in different strength classes [4] ..................... 18 Table 2.2-4 Modulus of elasticity for test from UAB and UT Austin [4] ............................. 19 Table 2.2-5 Results of splitting tensile strength tests performed (UT Austin)0 ................. 21 Table 2.2-6 Results of splitting tensile strength tests performed (UAB)[6] ....................... 21 Table 2.2-7 Modulus of rupture for “Method 1” [4] ........................................................... 22 Table 2.2-8 Modulus of rupture: “Method 2” [4] ............................................................... 22 Table 2.2-9 Modulus of rupture to splitting tensile strength ratios [4] ............................... 23 Table 2.2-10 Modulus of rupture for the Ytong samples .................................................. 23 Table 2.2-11 Summary of results for compressive strength of grout cores ...................... 24 Table 2.2-12 Results for the material Ytong-mortar M10-type A ...................................... 25 Table 2.2-13 Dimensions of direct-shear specimens [3] .................................................. 27 Table 2.2-14 Summary of results from direct-shear tests (thin-bed mortar ) [3] ............... 29 Table 2.2-15 Results for additional direct-shear tests (thin-bed mortar) [4] ...................... 30 Table 2.2-16 Summary of results from direct-shear tests (grout) [5] ................................ 30 Table 2.2-17 Summary of results from direct-shear (grout and thin-bed mortar) [3] ......... 31 Table 2.2-18 Summary table of the available data........................................................... 36 Table 2.3-1 Tests details for each AAC shear wall specimen [11] ................................... 38 Table 2.3-2 Geometrical details for each shear wall specimen [11] ................................. 38 Table 2.3-3 Details of axial load applied to each shear wall specimen [11] ..................... 39 Table 2.3-4 Load points, max. load and drift ratios for Shear Wall Specimen 2 [5] .......... 42 Table 2.3-5 Description of major events for Shear Wall Specimen 2 [3] .......................... 43 Table 2.3-6 Stiffness, strength and horizontal displacement ratios for the sheardominated specimens ............................................................................................ 46 Table 2.3-7 Load points, max. load and drift ratios for Shear Wall Specimen 15a [5] ...... 48

IV

List of Tables

Table 2.3-8 Description of major events for Shear Wall Specimen 15a [3] ...................... 49 Table 2.3-9 Stiffness ratios and horiz. displ. for the Shear Wall Specimen 15a [3] .......... 51 Table 3.3-1 Loading history for the uniaxial compressive test ......................................... 62 Table 3.3-2 AAC Material Model Data for elasticity, flow potential and yield surface ....... 63 Table 3.3-3 AAC Material Model Data for compressive behavior ..................................... 63 Table 3.3-4 Loading history for the three-points-load bending test .................................. 66 Table 3.3-5 AAC Material Model Data for tensile behavior .............................................. 67 Table 3.3-6 Loading history for the cycling tensile test .................................................... 70 Table 3.3-7 Damage Parameters Definition..................................................................... 71 Table 3.3-8 Loading history for the cycling compressive test........................................... 74 Table 3.4-1 Extracted data from the grout compressive test............................................ 78 Table 3.4-2 Grout material model data for elasticity, flow potential and yield surface ...... 79 Table 3.5-1 Thin-bed joint interaction properties and contact controls ............................. 93 Table 3.5-3 Grout joint interaction properties and contact controls .................................. 98 Table 3.5-4 Bedding Mortar joint interaction properties ................................................. 100 Table 4.4-1 Parts geometrical features for Shear Wall Specimen 2[3] model ................ 108 Table 4.4-2 Natural frequencies of the Shear Wall Specimen 2 model .......................... 109 Table 4.5-1 Parts geometrical features for Shear Wall Specimen 15a[3] models .......... 125 Table 4.5-2Table 4.5-2 Holed panels details for Shear Wall Specimen 15a[3] models .. 126 Table 4.5-3 Natural frequencies of the Shear Wall Specimen 15a model ...................... 130 Table 5.1-1 Maximum base shear and drift ratio for Shear Wall Specimen 2 model ...... 147 Table 5.1-2 Maximum base shear and max drift ratio comparison between simulation and experiment for Shear Wall Specimen 2 model .............................. 148 Table 5.2-1 Maximum base shear and drift ratio for Shear Wall Specimen 15a model .. 155 Table 5.2-2 Base shear and max drift ratio comparison between simulated and experimental data for Shear Wall Specimen 15a model ....................................... 156

V

List of Tables

Table 5.2-3 Stiffness ratios and horizontal displacement for the Shear Wall Specimen 15a[3] models ...................................................................................... 161 Table 5.3-1 Types of construction and behavior factors according to ............................ 163

VI

List of Figures

List of Figures Figure 1.3-1 Exterior wall section for multiple stories with vertical reinforcement [4] ........ 12 Figure 1.3-2 Ring beam and joint detail [4] ...................................................................... 13 Figure 1.3-3 Ytong building realization in progress .......................................................... 13 Figure 2.2-1 Compressive stress versus strain for Ytong shipment 2.0 ........................... 20 Figure 2.2-2 Set up for modulus of rupture test for “Method 1” [4] ................................... 22 Figure 2.2-3 Set up for modulus of rupture test for “Method 2” [4] ................................... 23 Figure 2.2-4 Compressive stress versus strain for grout cores (Babb AAC) [3] ............... 26 Figure 2.2-5 Views of direct-shear specimens (grout) [3]................................................. 27 Figure 2.2-6 Views of direct-shear specimens (thin-bed mortar) [3]................................. 27 Figure 2.2-7 Views of direct-shear specimens (thin-bed mortar and grout) [3] ................. 27 Figure 2.2-8 Force vs. displacement for direct-shear tests (thin-bed mortar) [3] .............. 29 Figure 2.2-9 Force vs. displacement for direct-shear tests (grout) [3] .............................. 31 Figure 2.2-10 Force vs. displ. for direct-shear tests (grout/thin-bed mortar) 0................. 32 Figure 2.2-11 Reinforcement behavior (#5, REBAR1) in shear walls [4].......................... 34 Figure 2.2-12 Reinforcement behavior (#4, REBAR2) in the two-story assemblage 0 ..... 34 Figure 2.3-1 Flexural (a), web-shear (b) and flexure-shear cracking (c), diagonal cracks and crushing of the diagonal strut (d), sliding shear (e) ............................... 40 Figure 2.3-2 Layout of Shear Wall Specimen 2 [11] ........................................................ 41 Figure 2.3-3 Actual loading history for Shear Wall Specimen 2 [5] .................................. 42 Figure 2.3-4 Actual tip displacement history for Shear Wall Specimen 2 [5] .................... 42 Figure 2.3-5 Load-displacement relationship for Shear Wall Specimen 2 [5] ................... 45 Figure 2.3-6 Layout of Shear Wall Specimen 15a [11] .................................................... 47 Figure 2.3-7 Plan view of Shear Wall Specimen 15a [11] ................................................ 47 Figure 2.3-8 Actual loading history for Shear Wall Specimen 15a [5] .............................. 48 Figure 2.3-9 Actual tip displacement history for Shear Wall Specimen 15a [5] ................ 48 Figure 2.3-10 Load-displacement relationship for Shear Wall Specimen 15a [5] ............. 50

VII

List of Figures

Figure 3.2-1Response of concrete to uniaxial loading in tension (a) and compression (b)[1] ...................................................................................................................... 55 Figure 3.2-2 Effect of the compression stiffness recovery parameter wc ......................... 56 Figure 3.2-3 Yield surface in plane stress ....................................................................... 58 Figure 3.2-4 Postfailure stress-cracking strain (a) vs. stress-displacement (b) curves ..... 59 Figure 3.2-5 Definition of the compressive inelastic (or crushing) strain .......................... 60 Figure 3.3-1 Plot of extracted data from the Ytong compressive tests ............................. 62 Thereafter, deformation is controlled following the loading history shown in ................... 62 Figure 3.3-2 Set up for the uniaxial compressive test ...................................................... 62 Figure 3.3-3 Stress- strain curves for the compressive test simulation ........................... 64 Figure 3.3-4 Set up for the splitting tension simulation test.............................................. 66 Figure 3.3-5 Post-Failure Tensile stress- cracking strain curve ....................................... 68 Figure 3.3-6 Top Face pressure vs. Tensile stress for the bending test simulation .......... 68 Figure 3.3-7 Tensile stress and strain vs. step number in cycling conditions ................... 72 Figure 3.3-8 Tensile stress-strain curve in cycling conditions .......................................... 73 Figure 3.3-9 Crack Visualization...................................................................................... 74 Figure 3.3-10 Compressive stress and strain vs. step number in cycling conditions ........ 75 Figure 3.3-11 Compressive stress-strain curve in cycling conditions ............................... 75 Figure 3.3-12 Stress and strains vs. step number ........................................................... 76 Figure 3.3-13 Stress vs. strain curve for a tension to compression cycle ......................... 77 Figure 3.4-1 Plot of extracted data from the grout compressive test ................................ 78 Table 3.4-3 Stress-strain data for Grout material model .................................................. 79 Figure 3.5-1 Contact and interaction discretization [1] ..................................................... 81 Figure 3.5-2 Default pressure-overclosure relationship [1] .............................................. 82 Figure 3.5-3 Pressure-overclosure relationship with possible negative pressure transmission (cohesion) and/or overclosure[1] ....................................................... 82 Figure 3.5-4 Slip regions with a limit on the critical shear stress [1] ................................. 83

VIII

List of Figures

Figure 3.5-5 Slip vs. shear traction for sticking and slipping friction [1] ............................ 84 Figure 3.5-6 Typical traction-separation response [1] ...................................................... 86 Figure 3.5-7 Extracted experimental data for the thin-bed contact................................... 88 Figure 3.5-8 Initial condition and loading layout for direct shear test ............................... 89 Figure 3.5-9 Loading history for the direct shear test (thin-bed joint) ............................... 90 Figure 3.5-10 Interpretation of experimental data for the thin-bed joint ............................ 90 Figure 3.5-11 Surfaces Pairing for the interaction setup .................................................. 92 Figure 3.5-12 Direct-shear test simulation results (thin-bed joint) .................................... 94 Figure 3.5-13 Shear stress distribution in the cohesive (a) and frictional (b) range .......... 95 Figure 3.5-14 Extracted experimental data for the grout-AAC contact ............................. 95 Figure 3.5-15 Direct shear test for the grout-AAC bond ................................................... 96 Table 3.5-2 Loading history for the direct shear test (grout joint) ..................................... 96 Figure 3.5-16 Comparison of direct-shear tests results and model curve (grout joint) ..... 99 Figure 3.5-17 Distribution of the shear stress (grout joint) ............................................... 99 Figure 4.3-1 Flow chart of the iterative analysis of the AAC-Ytong shear walls ............. 105 Figure 4.4-1 Unmeshed and Meshed Shear Wall Specimen 2[3] model ........................ 106 Figure 4.4-2 Initial conditions representations for Shear Wall Specimen 2[3] model ...... 107 Figure 4.4-3 First mode of Shear Wall Specimen 2 model, medium and fine mesh ....... 109 Figure 4.4-4 Displacement history for Shear Wall Specimen 2 model ........................... 110 Figure 4.4-5 Base Shear history .................................................................................... 111 Figure 4.4-6 (Step-24, 5a) : Contact tensile stress transfer between panels for Shear Wall Specimen 2 model ....................................................................................... 113 Figure 4.4-7 (Step-21, 5a) Contact status at the beginning of the center line wall failure for Shear Wall Specimen 2 model ............................................................. 114 Figure 4.4-8 (Step-24, 5a) Contact Status at an advanced stage of the center line wall failure for Shear Wall Specimen 2 model ...................................................... 114

IX

List of Figures

Figure 4.4-9 (Step-24, 5a) Bedding mortar crack and uplift of the tensile toe of the wall for Shear Wall Specimen 2 model ................................................................. 115 Figure 4.4-10 (Step-29, 5b) Contact status at a sliding stage of several panels joints Shear Wall Specimen 2 model ............................................................................. 116 Figure 4.4-11 (Step-31, 5b) Contact Status during at advanced sliding stage for Shear Wall Specimen 2 model ............................................................................. 116 Figure 4.4-12 (Step-5, 1a) : Stress distribution at the peak applied displacement for the first cycle Shear Wall Specimen 2 model ....................................................... 117 Figure 4.4-13 (Step-13, 3a) : Stress distribution at the peak applied displacement for the third cycle Shear Wall Specimen 2 model ...................................................... 118 Figure 4.4-14 (Step-24, 5a): Stress distribution at the peak applied displacement for the fifth cycle Shear Wall Specimen 2 model ....................................................... 118 Figure 4.4-15 (Step-32, 5b): First tensile crack in the Shear Wall Specimen 2 model.... 119 Figure 4.4-16 Occurrence of the first diagonal crack formation in the simulation (a) and in the experiment (b) for Shear Wall Specimen 2 [3] ..................................... 120 Figure 4.4-17 (Step-33, 5b): Second tensile crack for Shear Wall Specimen 2 model ... 121 Figure 4.4-18 (Step-33, 5b): Stress distribution at the peak applied displacement for the fifth cycle for Shear Wall Specimen 2 model .................................................. 121 Figure 4.4-19 (Step-41, 6b): Additional tensile cracks occurred in Shear Wall Specimen 2 model ............................................................................................... 122 Figure 4.4-20 Stiffness degradation variable, unloading from -9 mm (a) to 0 mm (b) of displacement for Shear Wall Specimen 2 model .............................................. 123 Figure 4.4-21 State of cracks (principle strains) at various loading stages for Shear Wall Specimen 2 model ....................................................................................... 124 Figure 4.5-1 Assemblage layout for Shear Wall Specimen 15a[3] Model-1(a) and Model-2(b) ........................................................................................................... 126 Figure 4.5-2 Sets of reinforced elements in Shear Wall Specimen 15a Model-1 ........... 127

X

List of Figures

Figure 4.5-3 Stress-strain relationship for reinforcement model (#5, REBAR1) ............. 128 Figure 4.5-4 Initial conditions representations for Shear Wall Specimen 15a model ...... 129 Figure 4.5-5 First mode of vibration of Shear Wall Specimen 15a[3] ............................. 129 Figure 4.5-6 Displacement history for Shear Wall Specimen 15a models...................... 131 Figure 4.5-7 Base Shear history for Shear Wall Specimen 15a models......................... 131 Figure 4.5-8 (Step-15, 3b) Tensile failure in the bedding mortar joint for the Shear Wall Specimen 15a Model-1(a) and Model-2(b) ................................................... 134 Figure 4.5-9 (Step-25, 6b) Distribution of the vertical stresses at a base shear of 76 KN for the Shear Wall Specimen 15a Model-1 ..................................................... 136 Figure 4.5-10 (Step-21; 5a) Formation of the first flexural crack in the Shear Wall Specimen 15a Model-2 ........................................................................................ 137 Figure 4.5-11 (Step-21; 5a) Distribution of the vertical stresses in the Shear Wall Specimen 15a Model-2 ........................................................................................ 138 Figure 4.5-12 (Step-29; 6a) Formation of the crushing failure in the compressive zone of the Shear Wall Specimen 15a[3] Model-1 ................................................ 139 Figure 4.5-13 (Step-29; 7b) First crack in the Shear Wall Specimen 15a Model-1 ......... 141 Figure 4.5-14 (Step-29; 7b) Vertical stress distribution in the Shear Wall Specimen 15a[3] Model-1 ..................................................................................................... 141 Figure 4.5-15 (Step-29; 7b) State of cracks (max. principle strain) of Shear Wall Specimen 15a Model-1 at various loading stages ................................................ 142 Figure 4.5-16 (Step-29; 7b) Contact pressure transer in the Shear Wall Specimen 15a Model-1 ......................................................................................................... 143 Figure 4.5-17 Tensile stress in the rebar ....................................................................... 144 Figure 4.5-18 Tensile strain comparison between the reinforced (a) and the unreinforced (b) case for Shear Wall Specimen 15a Model-1 ............................... 145 Figure 5.1-1 Ratio of the maximum model base shear values (Fm) to the maximum experimental base shear values (Fe) for each cycle ............................................. 149

XI

List of Figures

Figure 5.1-2 Ratio of the maximum model drift ratios (Dm) to the maximum experimental drift ratios (De) for each cycle .......................................................... 149 Figure 5.1-3 Initial tangent and backbone stiffnesses for Shear Wall Specimen 2[3] model ................................................................................................................... 150 Figure 5.1-4 Secant stiffnesses after cracking for Shear Wall Specimen 2[3] model ..... 150 Figure 5.1-5Unloading stiffnesses after cracking for Shear Wall Specimen 2[3] model ................................................................................................................... 151 Figure 5.1-6 Maximum load after cracking in the south and north directions for Shear Wall Specimen 2 model ....................................................................................... 152 Table 5.1-3 Stiffness, strength and horizontal displacement ratios comparison for Shear Wall Specimen 2 model ............................................................................. 152 Figure 5.1-7 Load-drift ratio relationship for Shear Wall Specimen 2 model .................. 153 Figure 5.1-8 Load-drift ratio comparison between simulated and experimental data for Shear Wall Specimen 2 model ........................................................................ 154 Figure 5.2-1 Ratio of the max. model base shear values (Fm) to the max. exp. base shear values (Fe) for Model-1 (a) and Model-2 (b) ................................................ 157 Figure 5.2-2 Ratio of the maximum model drift ratios (Dm) to the maximum experimental drift ratios (De) for Model-1 (a) and Model-2 (b) ............................... 158 Figure 5.2-3 Initial tangent and backbone stiffnesses for Shear Wall Specimen 15a models ................................................................................................................. 159 Figure 5.2-4 Secant stiffnesses after cracking for Shear Wall Specimen 15a[3] Model-1 ................................................................................................................ 160 Figure 5.2-5 Load-drift ratio relationship for Shear Wall Specimen 15a[3] Model-1 ....... 161 Figure 5.2-6 Load-drift ratio comparison between simulated and experimental data for Shear Wall Specimen 2 model ........................................................................ 162

XII

1 Introduction

1 Introduction The current design conception is grounded on the observation that the structures, during a seismic event, are charged in the dynamic range and the loads intensity can turn incompatible with the standard elastic behavior of materials. Depending on the energy dissipation capability, a structural systems classification has been defined in order to overcome traditional design limits and to predict the anelastic seismic response. The general condition which governs a seismic project is: Capacity > Demand

where the “capacity” is the structural answer and it results from the “sum” of the local mechanical resistances of the structural element sections. On the other hand the “demand” is the loading input and , focusing on the seismic case, it is strictly correlated to the system inelastic behavior. Energetically, an earthquake forwards an incoming energy Ei to the construction and it is converted into work done by the base shear force to conduct the solicitations to the foundations. This energy and is absorbed as kinetic energy Ek of the masses, as elastic potential energy Ee of the structures due to elastic deformation, as gradually dissipated energy Ed. The dissipating energy, in turn, has a viscous nature component Ex, attributable to the elastic phase, and an hysteretic component Eh, attributable to the plastic phase.

Ek

Ex

Ee

Eh

Ei

Therefore the energy consumed for deformation is given by the sum of the elastic and hysteretic contributes. The kinetic and elastic components are totally returnable, while viscous and the hysteretic factors are progressively dissipated. In the theoretical assumption of dissipative effects absence, the input energy Ei, transferred into the overall structure, tends to increase during the whole attack, except at most in few short time interval in which the oscillation occurs in phase 1

1 Introduction

contrast, and the accumulation would produce oscillations which become greater and greater. In fact, there are dissipative phenomena such as the viscous behavior, which would allow the facility to not exceed the elastic limit for small earthquakes, and inelasticity and hysteresis, which are followed by permanently deformations. The capability to dissipate energy during a major seismic event is taken into account with the structure factor q, which depends on the structural configuration, ductility class required, and the geometrical regularity of the building. Various categories of structural systems are defined depending on the mode of redistribution of vertical and horizontal actions and in order to classify a building, it is important to determine the stress distribution in the elements that compose it. When a structural system is not easily classifiable, specific and detailed studies are needed to characterize the response to actions, through laboratory tests and numerical simulations. In recent years, the computational approach has seen an increasing employment, especially in the case of new materials and new manufacturing technologies, which has led to new structural system as the AAC-Ytong material applications. Engineers routinely have access to highly capable finite element analysis software and more and more structures are being analyzed regarding their behavior during a seismic event. Among the structural elements and systems, the shear wall is commonly employed to resist lateral loads and it is a key component which plays a major role to ensure stability of the shear building system. Therefore an accurate mathematical model for shear wall structure needs to be proficient to capture all the aspects of the lateral load response and it should also be computationally efficient. Furthermore, when the structure enters the inelastic range, the simplified linear methods cannot be used and other types of analysis need to be computed for taking into account the degradation of the hysteretic behavior. The constitutive models can be represented in different ways among which the most generic type is multi-linear. This model is used to reproduce complex behaviors and can emphasize a gradual transition from elastic to the plastic phase to follow in greater detail the progression of yielding and plastic strain.

2

1 Introduction

The “pushover” analysis are a simplified procedure for the global representation of the inelastic response of a complex system without solving the equations with a direct integration. Applying a system of “quasi-static” horizontal forces to the inelastic model of n degrees of freedom, the seismic action is simulated through small increments and the information is summarized in a force-displacement curve of a one degree of freedom system. Alternatively, using a spectrum-compatible acceleration history at the foot of the model, the response can be calculated by numerical integration, similarly to the “pushover” case, including

the dynamic terms and the dissipative hysteretic

behavior of the parties. The described process is called “time-history” nonlinear analysis. The use of nonlinear analysis methods need to implement very complex numerical models to describe the development of collapse mechanisms and predict the ultimate response. If the seismic action is repeated a certain number of times with alternate direction , it causes a combination of gradual degradation phenomena, referred to as “plastic fatigue”, which is associated with the resistance decay of the sections. In order to resist to a seismic event, for a structure is required that both the plastic deformation and the resistance remain effective for a minimum number of oscillations. It is therefore important to assess the effects of degradation by experimental evidence, applying a “quasi-static” cyclic action process. The evidence of the test allows to derive the nonlinear behavior of individual elements, the skills associated to the dissipative hysteresis and the gradual resistance decay due to repeated large deformations imposed. The data obtained can be used to calibrate numerical models of structural elements when is necessary to take into account the dissipative effects and inelastic deformations[2].

3

1 Introduction

…

La concezione progettuale attuale è basata sull’osservazione che le strutture, durante un evento sismico, sono sollecitate in campo dinamico e l’ intensità delle azioni può raggiungere livelli incompatibili con il normale comportamento elastico dei materiali. In funzione della capacità di dissipare energia, una classificazione dei sistemi strutturali

è stata

stabilita per scavalcare i tradizionali limiti di progetto e valutare la risposta sismica nel campo anelastico. La generica condizione che governa un progetto sismico è

capacità > domanda dove la capacità è la risposta della struttura e deriva dalla “somma” delle resistenze meccaniche locali delle sezioni degli elementi strutturali. Mentre la domanda è l’input sollecitante e, nel caso sismico, è strettamente correlata al comportamento inelastico del sistema. Dal punto di vista energetico, un terremoto trasmette alla costruzione un energia di ingresso Ei, trasformata in lavoro compiuto dalla forza di taglio alla base per condurre la sollecitazione alle fondazioni. Questa energia Ei viene assorbita come energia cinetica Ek delle masse, come energia potenziale elastica Ee delle strutture dovuta alle deformazioni elastiche, come energia dissipata progressivamente Ed. L’energia dissipata ha a sua volta una componente di natura viscosa Ex, attribuibile alla fase elastica, e da quella isteretica Eh, attribuibile alla fase plastica. Riassumendo si ha la seguente relazione:

Ek

Ex

Ee

Eh

Ei

Quindi l’energia consumata per deformazioni strutturali è data dalla somma dell’energia elastica ed isteretica , sono restituibili le componenti cinetica ed elastica, sono progressivamente dissipate quella viscosa e quella isteretica. Nell’ipotesi teorica di assenza di effetti dissipativi, l’energia Ei immessa complessivamente nella costruzione in entrambe le forme tende ad aumentare per tutta la durante dell’attacco, tranne al più in qualche breve intervallo di tempo in cui l’oscillazione avviene in controfase e l’accumulo produrrebbe oscillazioni sempre più ampie . Nella realtà esistono i fenomeni dissipativi: il comportamento viscoso, che permetterebbe alla struttura

4

1 Introduction

di non superare il limite elastico, per piccoli eventi sismici, quelli anelastici ed isteretici, ai quali seguono deformazioni permanenti. La capacità di dissipare energia, durante un forte evento sismico, con conseguenti deformazioni anelastiche, è tenuta in conto globalmente dal fattore di struttura q, che dipende dalla configurazione strutturale, dalla classe duttilità richiesta e dalla regolarità della costruzione. Diverse categorie di sistemi strutturali sono definiti a partire dalla modalità di resistenza alle azioni verticali ed orizzontali e per assegnare un’ etichetta ad ogni edificio, occorre stabilire la distribuzione delle sollecitazioni negli elementi che lo compongono. Quando un sistema strutturale non rientra nelle categorie a disposizione, specifici ed approfonditi studi sono necessari per caratterizzare la risposta alle azioni, tramite prove di laboratorio e simulazioni numeriche che permettano di valutare il coefficiente di struttura. Quando la struttura risponde in campo anelastico, i metodi lineari semplificati non possono essere usati, e si ricorre ad altri tipi di analisi che tengono conto della degradazione del comportamento isteretico. I legami costitutivi possono essere rappresentati in modi diversi fra i quali il più generico è quello di tipo multilineare. Questo modello è utilizzato per riprodurre comportamenti complessi e consente di mettere in evidenza un passaggio graduale dalla fase elastica a quella plastica per seguire con maggiore dettaglio la progressione della plasticizzazione. Le analisi “pushover” costituiscono un procedimento per la rappresentazione globale semplificata della risposta anelastica di un sistema complesso evitando di risolvere le equazioni del moto tramite integrazione diretta. Applicando un sistema di forze orizzontali crescenti in modo “quasi-statico” al modello anelastico di n gradi di libertà, l’azione sismica è simulata per piccoli incrementi e le informazioni vengono riassunte in una curva forza-spostamento di un sistema ad un grado di libertà. In alternativa, applicando un’assegnata storia di accelerazioni spettro-compatibili al piede del modello, la risposta può essere calcolata mediante integrazione per via numerica in modo analogo al caso “pushover”, comprendendo però anche i termini dinamici ed il comportamento isteretico dissipativo delle parti in cui si prevedono fenomeni inelastici. Il procedimento prende così il nome di analisi non lineare mediante “time-history”. L’impiego di metodi di analisi non lineari richiede l’adozione di modelli numerici alquanto complessi per descrivere lo sviluppo dei meccanismi di collasso e prevedere le condizioni estreme di risposta.

5

1 Introduction

Nel caso sismico le azioni si ripetono un certo numero di volte con verso alternato provocando un complesso di fenomeni di progressivo degrado, indicato come “fatica plastica”, associato al decadimento della resistenza delle sezioni. Affinché una struttura sia capace di opporsi ad un attacco sismico è richiesto che la resistenza e la deformabilità plastica rimangano efficaci per un certo numero di oscillazioni. E importante quindi valutare gli effetti di degrado mediante prove sperimentali, applicando la azioni cicliche sollecitanti mediante procedimenti “quasi statici”, che consentono di ricavare così il comportamento non lineare di singoli elementi, le capacità dissipative associate all’isteresi ed i progressivi decadimenti delle resistenze dovuti al ripetersi di grandi deformazioni imposte. I dati ottenuti possono essere usati per calibrare modelli numerici degli elementi strutturali qualora si voglia tener in conto gli effetti dissipativi e le deformazioni anelastiche [2]. …

6

1 Introduction

1.1 Objective of the thesis In this study, two types of shear wall model have been developed, specific constitutive curve for the AAC(aerated autoclaved concrete) material has been employed and a computational algorithm has been utilized. The investigation focuses on the development of effective and suitable modeling of both unreinforced and reinforced vertical panels shear assemblage. The modeling includes physical and constitutive representations: geometry and layout of the shear wall specimens were reproduced, in conjunction with interactions between elements and boundary conditions for the load applications; constitutive law for different materials are used to account for the concrete and grout nonlinearities, due to crushing, cracking and plastic yielding of concrete, for the steel reinforcement, assumed to have a bilinear behavior with strain hardening. Based on the above physical and material modeling two finite element codes have been developed during the course of this study: a three dimensional finite element of a ten unreinforced vertical panels shear wall (Shear Wall Specimen 2 [3] model) and a three dimensional finite element of a four vertical panels reinforced shear wall (Shear Wall Specimen 15a [3] model) The FE models, presented in the thesis in hand, have the purpose to give a reliable analytical tool for improve the knowledge about the overall response of AAC-Ytong shear walls, to understand the load flow and the failure modes due to lateral actions, especially in case of seismic events. They are suitable to study the correlation between the hysteretic behavior of the material and of the entire structural system. The material on focus, has very different properties than those of normal concrete and it is crucial to investigate and propose a modified constitutive law suitable for representing his specific behavior, especially in the plastic range The models represent a good basis for a parametric study of geometrical aspect ratios, constructive details and load application types, to extract further seismic design provisions and suggestions, especially concerning the ductility properties.

7

1 Introduction

…

Nel presente lavoro di tesi sono sviluppate due tipologie di modello per pareti di taglio, basate su una specifica legge costitutiva per il materiale trattato (“areated autoclaved concrete”) e su algoritmi computazionali implementati attraverso il programma di calcolo ABAQUS [1]. L’indagine concentra l’ attenzione nello sviluppo di modelli adeguatamente calibrati per pareti di pannelli verticali armati e non. La modellazione include una rappresentazione fisica e costitutiva delle pareti di taglio: la geometria ed il layout sono riprodotti in combinazione con l’ interazione degli elementi assemblati e le condizioni al contorno per l’ applicazione dei carichi. Sulla base di test sui materiali coinvolti, leggi costitutive multilineari sono definite per il cemento areato, per la malta e per l’acciaio, in modo da considerarne tutti gli aspetti, specialmente in campo non lineare. Due codici agli elementi finiti sono generati e calibrati al fine di simulare test quasi-statici eseguiti presso l’Università del Texas (UT): i modelli rappresentano rispettivamente una parete non armata di dieci pannelli verticali ed una parete armata composta da quattro pannelli verticali confinati da due colonne di blocchi in AAC. Consistentemente con le fonti dei dati sperimentali, con i nomi “Shear Wall Specimen 2 model” e “Shear Wall Specimen 15a model” si fa riferimento al primo e al secondo modello rispettivamente. Lo scopo della tesi in questione è quello di fornire un affidabile strumento analitico per lo studio e l’indagine del comportamento delle pareti di taglio in cemento areato, con approfondimento sulla tipologia “Ytong”. Attraverso l’utilizzo dei modelli numerici presentati è possibile approfondire la conoscenza dei meccanismi di trasferimento dei carichi e dei modi di rottura dovuti alle azioni laterali, focalizzando sul caso di eventi sismici. È possibile investigare la correlazione tra comportamento isteretico del materiale e quello dell’ intero sistema strutturale. Il materiale in questione ha proprietà meccaniche e fisiche differenti dal cemento standard, perciò è di importanza cruciale comprendere le conseguenze in campo strutturale di tali particolarità. I modelli agli elementi finiti costituiscono una base per l’analisi parametrica dei sistemi strutturali di parete di taglio a pannelli verticali: permettono infatti di valutare l’ influenza della geometria, dei dettagli costruttivi e delle condizioni al contorno, e di proporre quindi ulteriori miglioramenti e disposizioni progettuali. …

8

1 Introduction

1.2 Organization of the thesis This thesis describes an investigation of two types of vertical panels shear walls based on the FE method using a concrete damage plasticity material model for the autoclaved aerated concrete (AAC). In the second chapter available data from previous tests on materials, steel, and on shear walls are collected and evaluated in order to choose reference values for the implementation of the analysis. The materials involved in the modeling of shear walls are AAC-Ytong, grout cores and rebars steel. Also a properties summary for the bonds between the walls components are elaborated and presented in the second chapter. In the third chapter the heart of the problem is entered: the choice of material model for the AAC is discussed, based on information previously assessed. Every aspect of the material is carefully analyzed and reproduced through the options of the “concrete damage plasticity " model available in ABAQUS[1]. Similarly, also for the other materials different models, able to reproduce their main features, are generated. Furthermore, a detailed investigation of the bond properties is carried out and three main contact interactions are defined: the modeling of connection between different elements are considered a very important aspect and it proved to retain all the peculiarities of the actual behavior. In the forth chapter the shear-dominated wall and the flexure-dominated wall are modeled by an unreinforced and a reinforced assemblage respectively, in which different aspect ratios and details are adopted to include the main features of the two specimens. In the fifth chapter the significance of results is analyzed comparing the computed hysteretic behaviors with the experimental responses in the damages range. The summary, major conclusions and recommendations for future research are presented in the sixth chapter.

9

1 Introduction

…

Il presente lavoro, come precedentemente accennato, descrive un’ indagine di due tipi di pareti di taglio a pannelli verticali per mezzo del metodo degli elementi finiti, basato su un modello “damage-plasticity” per il materiale analizzato (AAC). Nel secondo capitolo i dati ottenuti da precedenti test sui materiali e sui campioni di pareti sono raccolti ed analizzati al fine di stabilire valori di riferimento per l’ implementazione delle analisi. I materiali usati nella modellazione delle pareti di taglio sono AAC, in particolare la tipologia Ytong, la malta e l’acciaio per le barre d’armatura. Trattandosi di pannelli prefabbricati assemblati, una valutazione dei risultati dei test sulle proprietà dei giunti tra gli elementi è stata necessaria ed i valori di riferimento sono riassunti nel capitolo secondo. Il terzo capitolo è incentrato sul nocciolo del problema, costituito dalla scelta del modello per il materiale AAC, operata sulla base delle informazioni precedentemente valutate. Ogni aspetto del materiale è dettagliatamente analizzato e riprodotto attraverso le proprietà del modello “concrete damage plasticity” disponibile in ABAQUS [1]. Allo stesso modo anche gli altri materiali impiegati sono analizzati e modellati per coglierne le caratteristiche principali. Successivamente sono studiate le proprietà dei giunti attraverso un’indagine dettagliata eseguita su tre principali tipologie di contatto. La modellazione della connessione tra i diversi componenti è considerata un aspetto molto importante ed ha permesso di carpire le caratteristiche principali del comportamento reale dei contatti. Nel quarto capitolo è descritta la procedura di modellazione per due diverse tipologie di pareti a pannelli, riferite ai casi di muro non armato dominata da taglio e armato dominato da flessione. Nel quinto capitolo i risultati ottenuti sono analizzati e confrontati con i dati sperimentali, focalizzando l’ attenzione sul comportamento in campo plastico del sistema strutturale. Le conclusioni relative al presente lavoro di tesi e le raccomandazioni per ulteriori ricerche sono elencate nel capitolo sesto. …

10

1 Introduction

1.3 The autoclaved aerated concrete The autoclaved aerated concrete (AAC), a form of cellular concrete, is a lowdensity cementitious product of calcium silicate hydrates in which the low density is obtained by the formation of macroscopic air bubbles, mainly by chemical reactions within the mass during the liquid or plastic phase. The air bubbles are uniformly distributed and are retained in the matrix on setting, hardening, and subsequent curing with high-pressure steam in an autoclave to produce an homogeneous structure of macroscopic voids, or cells. AAC typically has one-sixth to one-third the density of conventional concrete, and about the same ratio of compressive strength, making it suitable for cladding and infill panels and for bearing-wall components of low- to medium-rise structures. The thermal conductivity of AAC is 6 to 7.5% that of conventional concrete, making it energy-efficient. Its fire rating is slightly longer than that of conventional concrete of the same thickness, making it useful in applications where fire resistance is important. AAC has excellent acoustical properties. Because of its characteristic high internal porosity, AAC has very high sound absorption. AAC can be used to make unreinforced, masonry-type units, and also factoryreinforced floor panels, roof panels, wall panels, lintels, beams, and other special shapes. These elements can be used in a variety of applications, including residential, commercial, and industrial construction. Focusing on the Ytong buildings using the AAC material, the construction system is an economical and modern solution for earthquake and fire resistant housing. It allows to built one house in only few weeks and the final result possesses many advantages such as thermal insulation, less energy costs, lightweight property and flexibility. The Ytong Construction elements can be easily mounted on all known loadbearing structures such as wood, steel, reinforced concrete etc. The load-bearing vertical wall panels are manufactured in various thicknesses from 20 cm to 30 cm 11

1 Introduction

and the lengths up to 300 cm. Roof and floor slabs are special interlocking profiled elements with a thickness from 10 cm to 30 cm and a length up to 600 cm; after their positioning, the construction is completed with the necessary rebar connections and the filler grout into the joints. Reinforced Ytong lintels are used to span window and door opening in load-bearing and non-load bearing walls and they are laid quickly and easily in a thin mortar bed and can immediately be subjected to load. In Figure 1.3-1 the wall section for a multiple stories building is represented to show the configuration of the system.

Figure 1.3-1 Exterior wall section for multiple stories with vertical reinforcement [4]

12

1 Introduction

Loads are transferred from the diaphragm to the shear walls through the shear resistance (adhesion) at the interface, and also through reinforcement in the grouted keys, anchored into the ring beam. In Figure 1.3-2 the ring beam between the shear walls of different floors is represented along with the details of the AAC floor panels joints, while Figure 1.3-3 reports an actual application of the Ytong construction system.

Figure 1.3-2 Ring beam and joint detail [4]

Figure 1.3-3 Ytong building realization in progress

13

1 Introduction

…

Il materiale “autoclaved aerated concrete” (AAC) è una forma di cemento cellulare caratterizzato da un cemento di idrati silicati di calcio in cui la bassa densità è ottenuta attraverso l’inclusione di microscopiche bolle d’aria. Quest’ultime sono distribuite uniformemente e sono trattenute nella matrice grazie ad una procedura per passi successivi di maturazione, indurimento ed essiccamento tramite vapore ad alta pressione all’interno delle autoclavi, in modo da produrre una struttura omogenea di microscopici vuoti. AAC ha tipicamente tra un sesto ed un terzo della densità di un cemento convenzionale e circa lo stesso rapporto di resistenza alla compressione, rendendolo adatto a rivestimenti, tamponature esterne e componenti per muri portanti di strutture di bassa e media elevazione. La conducibilità termica dell’AAC è circa il 6-7,5% di quella del calcestruzzo tradizionale, il che rende il materiale vantaggioso dal punto di vista dell’efficienza energetica. La sua capacità di conservare ruolo statico, tenuta ed isolamento durante un evento termico è leggermente migliore di quella del calcestruzzo convenzionale dello stesso spessore, conferendogli idoneità nelle applicazioni dove la resistenza al fuoco è importante. L’AAC ha eccellenti proprietà acustiche infatti grazie alle sua caratteristica elevata porosità interna, ha un alto coefficiente di assorbimento acustico. Il presente materiale può essere usato per creare pannelli per pavimentazioni, per coperture e per muri verticali, architravi, travi, ed altre figure speciali. Può essere impiegato in elementi non rinforzati, in componenti prefabbricati-armati ed in unità per strutture in muratura. Questi elementi possono essere utilizzati in un’ampia varietà di applicazioni che comprende le costruzioni residenziali, commerciali e industriali. Concentrandosi sugli edifici Ytong in AAC, il sistema di costruzione è una soluzione economica e moderna per permettere una buona risposta in caso di eventi sismici o termici. Esso permette di costruire una casa in poche settimane ed il risultato finale possiede molti vantaggi, quali l'isolamento termico, i minori costi energetici, la leggerezza e la flessibilità. Gli elementi strutturali Ytong possono essere facilmente montati anche su strutture portanti in altri materiali come il legno, acciaio, cemento armato ecc. I pannelli portanti per pareti verticali sono realizzati in diversi spessori da 20 cm a 30 cm e le lunghezze fino a 600 cm . I componenti per coperture e solai sono speciali elementi ad incastro profilati con uno spessore da 10 cm a 30 cm e una lunghezza fino a 600 cm; dopo il loro posizio-

14

1 Introduction

namento, la costruzione si completa con le armature necessarie e la malta di riempimento nei giunti. Le architravi rinforzate Ytong sono utilizzati per aperture di finestre e porte nei muri portanti e non; esse sono semplicemente adagiate in un letto di malta sottile e possono essere sottoposte immediatamente a carico. Nella Figura 1.3-1 la sezione delle pareti di un edificio multipiano mostra la configurazione del sistema. I carichi sono trasferiti dal diaframma alle pareti di taglio attraverso l’adesione delle interfacce tra elementi e anche attraverso le armature di ancoraggio della trave di connessione tra pareti in senso verticale. Nella Figura 1.3-2 l’anello che congiunge le pareti di taglio dei diversi piani è rappresentato con tutti i dettagli delle connessioni tra i pannelli del solaio, mentre la Figura 1.3-3 riporta una reale applicazione del sistema di costruzione Ytong in via di realizzazione. …

15

2 Evaluation and Synthesis of Available Data

2 Evaluation and synthesis of available data In this chapter the main sources of available data, tests information and proposed values from the guidelines of the involved materials and structural elements are evaluated and summarized.

2.1 Sources of available data The main sources from where the experimental data were collected are the following: •

The public domain references are Fouad et al. (2002), Tanner (2003) and Varela (2003), Argudo (2003),Cancino (2003).

•

Twelve AAC masonry shear-wall specimens were tested by Hebel in Germany and tests were essential to address the case of shear walls with un-mortared head joints.

•

The University of Alabama at Birmingham (UAB) tested AAC masonry units and reinforced panels from three different manufacturers (Hebel, Ytong and Contec) and grades (PAAC-2, PAAC-3 and PAAC-4), under the sponsorship of the Autoclaved Aerated Concrete Products Association (AACPA). For reinforced AAC panels, tests were conducted on floor panels, lintels, and vertical wall panels.

•

In 1999, tests were performed by Construction Technology Laboratories to evaluate the performance of reinforced floor and wall panels manufactured by AACOA. Tests on compressive strength on cubes and prisms, and flexural bond strength of two blocks bonded with thick bed mortar were also performed.

•

The Construction Research Center of The University of Texas at Arlington evaluated the performance of Ytong AAC block assemblages with respect to modulus of rupture and diagonal tensile strength.

•

Under the AAC research carried out at Ferguson Structural Engineering Laboratory at UT Austin, seventeen shear walls and one two-story assemblage were tested to develop design provisions for AAC masonry shear walls.

16


2.2 Available Data on Mechanical Properties of Materials In this paragraph mechanical properties of the involved materials are evaluated and analyzed to achieve an idealized model, which is able to summarize the main features of the involved elements. This thesis focuses on the Ytong material and therefore tests performed on Ytong samples are primarily considered; unfortunately the available data are not sufficient and the missing information are deduced from tests on AAC material from other suppliers.

2.2.1 Mechanical Properties of AAC In the next sections compressive strength, stress-strain curve and tensile strength of AAC concrete are discussed in order to select a list of representative values for its behavior. 2.2.1.1 Compressive strength of AAC Results for the compressive strength and density for UT Austin and UAB data are presented in Table 2.2-1. ASTM C1386 gives requirements for average and minimum compressive strengths for 102 mm cubes tested in the dry conditions. Table 2.2-1 Summary of results for compressive strength and density [3]

17


Focusing on the AAC-Ytong material, results for the compressive strength and density for UT Austin and UAB data are extracted in Table 2.2-2. Table 2.2-2 Summary of Ytong results for compressive strength and density

Data Source

Material

Calculated Density

Measured Compressive Strength fAAC

pcf

kg/m3

psi

MPa

UAB

YtongYG1

29.7

475.8

330

2.3

UAB

YtongYG2

38.5

616.7

630

4.3

UAB

YtongYG3

45.1

722.4

400

2.8

UT

Ytong-2

37.7

603.9

650

4.5

Weighted Av. fAAC (MPa)

3.5

A weighted average value for the compressive strength is 3.5 MPa. To compare the experimental strength with the proposal design strength, typical material characteristics of AAC in different strength classes are listed in Table 2.2-3. Table 2.2-3 Typical characteristics of AAC in different strength classes [4]

Other strength classes within these ranges and densities may be produced depending on specific design requirements. In the present thesis a compressive strength of 3.5 MPa is assumed, with an average density of 600 Kg/m3.

18


2.2.1.2 Stress-strain behavior and modulus of elasticity of AAC At UT Austin [5], the stress-strain behavior was measured using 2:1 cores for 6 shipments from 4 manufacturers. Data are very consistent and there are also information available on Ytong samples. Table 2.2-4 Modulus of elasticity for test from UAB and UT Austin [4]

It is proposed to determine the modulus of elasticity EAAC as a nonlinear function of the compressive strength fAAC, as shown in the following equation: 0 .6 E AAC = 6500 f AAC

2.2.1-1

where fAAC and EAAC are in psi [4]. For the compressive strength a value of 3.5 MPa (507.6 psi) was adopted, thus a value of 1882.6 MPa (273040.0 psi) for the modulus of elasticity is worked out from equation 2.2.1-1. This value will be assumed for the stress-strain curve. Stress-strain curves for each test performed at UAB and UT Austin are available in the Tanner dissertation, but the focus is on the Ytong samples results, which are shown in Figure 2.2-1. Other stress-strain curves are worked out by Cancino [6] and the range of maximum strains was less than the values reported by Tanner [5]. The value of the maximum strain is directly dependent on compressive strength, and indirectly related to vital behavioral characteristics such as nominal flexural capacity, and the available ductility and drift capacities. In the current thesis the 19


properties are specifically related to Ytong results and the stress-strain stress curve is extracted directly from the test test. The stress-strain strain behavior chosen is shown in Figure 2.2-1.

Figure 2.2-1 Compressive stress versus strain for Ytong shipment 2.0 2.

The he curves show an elastic range up to a stress of 3.5 MPa (which is also the assumed compressive st strength fAAC) and a strain of 0.0019; an hardening part up to a stress of 4.5 MPa and a strain of 0.0032; a softening part down to a stress of 3.5 MPa and a ultimate strain of 0.005. 2.2.1.3 Tensile strength of AAC Tensile strength testing of AAC includes both splitting tting tensile test and one or two bending points test. Data for splitting tensile strength of material in each AAC shipment were obtained at UT Austin using tests performed in accordance with ASTM C1006 and are reported in Tanner [5]. Equations relating the splitting tensile strength and the square root of the comco pressive strength are re proposed but, as explained in Argundo [3],, the th 2.2.1-2 is the most suitable relationship between ft and fAAC:

f t = 2.4 f AAC where ft and fAAC are in psi [4].

20

2.2.1-2


Table 2.2-5 Results of splitting tensile strength tests performed (UT Austin)0

Table 2.2-6 Results of splitting tensile strength tests performed (UAB)[6]

For the AAC-Ytong the average values of ft are 0.38 MPa and 0.43 MPa, for shipment Ytong1 and Ytong2 respectively. From the proposed formula a value of 0.42 MPa is calculated and it is assumed for the tensile strength, which is also consistent with the tests data. Data on modulus of rupture are reported in Table 2.2-7 and Table 2.2-8. Those tables refer to a “Method 1” and a “Method 2” shown in Figure 2.2-2 and Figure 2.2-3. “Method 1” involves midpoint loading with an a/d ratio (shear span to depth) of 1.25. “Method 2” is a modified ASTM C78 method with two third-point loads and an a/d of 1.75.

21


Table 2.2-7 Modulus of rupture for “Method 1” [4]

Table 2.2-8 Modulus of rupture: “Method 2” [4]

Figure 2.2-2 Set up for m modulus of rupture test for “Method 1” [4]

22


Figure 2.2-3 Set up for modulus of rupture test for “Method od 2” 2 [4]

A relationship between the splitting tensile strength and modul modulus us of rupture was determined and it was necessary to consider the effects of moisture content on tensile strength. The reported moisture contents for the modulus of rupture tests ranged from 8 to 12%. Table 2.2-9 shows values of m modulus of rupture reported for different classes and corresponding oven-dry dry densities of AAC. The average ratio between the reported modulus of rupture and the calculated splitting tensile strength is 2.26, with a coefficient of variation (COV) of 19.1%. F For or design purposes, a ratio of 2.0 is proposed to provide the simple yet con conservative equation 2.2.1-3 :

fr = 2 ft

2.2.1-3

where fr is the modulus of rupture and ft is the splitting tensile ensile strength [4]. Table 2.2-9 Modulus odulus of rupture to splitting tensile strength ratios [4]

For Ytong material the fr values are extracted in Table 2.2-10 and an average value of 0.815 MPa is determined, whereas a value of 0.84 MPa was calculated from the proposed posed equation 2.2.1-3.

Table 2.2 2.2-10 Modulus of rupture for the Ytong samples

23


Material

Modulus of rupture (MPa) Method 1

Method 2

Ytong-YG1

0.66

0.41

Ytong-YG1

1.22

0.73

Ytong-YG1

0.73

0.66

UT-Ytong2

1.08

1.03

2.2.2 Mechanical properties of the grout material In the following sections compressive strength, stress-strain curve and tensile strength of grout material are discussed in order to select a list of representative values for its behavior, as already made for the AAC material. 2.2.2.1 Compressive strength of grout material Results of tests for compressive strength and density of ASTM C476 coarse grout cores are presented in Table 2.2-12. Table 2.2-11 Summary of results for compressive strength of grout cores

According to the Guide for Design and Construction with Autoclaved Aerated Concrete Panels [4] the specified compressive strength for grout f´g ranges between 13.8 MPa and 34.5 MPa. The Ytong grout was not tested, therefore an average value is calculated from the available data, excluding the tests ended early due to load cell at maximum reading. The average compressive strength for the grout material gives a value of 21.2 MPa (3077 psi) which fall into the specified range and therefore is assumed for the present thesis. 24


Results from the tests carried out from YTONG & RD Center at Schrobenhausen (Germany)[7] are given in Table 2.2-13 for the material Ytong-mortar M10-type A. The compressive strength for a standard storing is an average value of 21.2 MPa. This value perfectly matches both the testing series on compressive strength for the grout, therefore it is assumed for next stages. Table 2.2-12 Results for the material Ytong-mortar M10-type A

2.2.2.2 Stress-strain behavior for grout material The stress-strain curves for the ASTM C476 coarse grout cores are presented in Figure 2.2-4. The maximum strains range from 0.001 to 0.0038.

25


Figure 2.2-4 Compressive stress versus strain for grout cores (Babb Babb AAC) AAC [3]

Results for the modulus of elasticity of ASTM C476 coarse grout cores, range from 24.0 GPa to 33.0 GPa, Pa, with an average of 28.6 GPa,, which is assumed for the present thesis. 2.2.2.3 Tensile strength of g grout material Data for bending ing tensile strength of grout cores were obtained from the tests carried out from YTONG & RD Center at Schrobenhausen ((Germany Germany [7]) and an average value for standard storing of 3.9 MPa was found. The tensile strength of concrete is usually considered about one-tenth one of the compressive strength; thus, if a compressive value of 21 MPa is assumed, it is reasonable to assume a tensile strength of 3.9 MPa

2.2.3 Bonds properties The design esign of the assemblage of AAC elements required verification of the direct shear capacity between elements. For that purpose modified and standard stand direct shear tests from UAB and UT Austin were conducted on AAC modular m units to determine the direct-shear shear capacity of different types of joints joints. The tests were developed to determine the direct direct-shear shear capacity between ASTM C476 coarse grout and AAC, and between thin thin-bed bed mortar and AAC, or between a 26


thin-bed mortar (Figure 2.2-5, Figure 2.2-6 and Figure combination of groutt and thin 2.2-7). Additional specimens were developed to determine the coefficient of friction between AAC and AAC.

Figure 2.2 2.2-5 Views of direct-shear specimens (grout) [3]

Figure 2.2-6 View iews of direct-shear specimens (thin-bed mortar) mortar [3]

Figure 2.2-7 Views of direct direct-shear specimens (thin-bed bed mortar and grout) [3] Table 2.2 2.2-13 Dimensions of direct-shear specimens [3]

27


2.2.3.1 Properties of the thin-bed mortar joint The thin-bed mortar used to bond the AAC panels is more like a structural adhesive than a conventional masonry mortar. It is typically laid only in joints that are approximately 1/32 in. to 1/8 in. (1 mm to 3 mm) thick. It is made from a mix of portland cement, fine silica sand, polymers such as latex or vinylester, and admixtures such as water-retention admixtures. The compressive strength of the thin-bed mortar is greater than that of the AAC itself. In general the measured tensile bond strength between AAC and thin-bed mortar is equal to the modulus of rupture of AAC for material with a compressive strength of the AAC less than 450 psi (3.1 MPa), and is limited to about 94 psi (0.65 MPa) for material with compressive strength above 450 psi (3.1 MPa) [5]. Three AAC units were joined by mortar and tested in flexure using a modified ASTM C78 method. The specimen height was 33 in. (838 mm), and the joint length was 15 in. (381 mm). The thin-bed mortar specimens were constructed on their sides. This allowed the weight of the block to apply pressure on the thin-bed mortar joint, and represents field conditions for either panels or blocks. The failure modes for these specimens ranged from a bond failure at the joint to a combined joint and material failure 0. Force-displacement graphs for the direct-shear specimens (thin-bed mortar only) are presented in Figure 2.2-8. The load reduced abruptly when a crack formed in one joint. In three cases, the load increased beyond the initial peak.

28


Figure 2.2-8 Force vs. dis displacement for direct-shear tests (thin-bed bed mortar) mortar [3] Table 2.2-14 Summary of results from direct direct-shear tests (thin-bed bed mortar ) [3]

Due to the large variation in the test results for the direct shear strength, it was suspected that the thin-bed bed mortar may be sensitive to the mixing process, but with additional tests no sensitiveness tto o the construction was recorded (Table ( 2.2-15).

29


Table 2.2-15 Results for additional direct-shear tests (thin-bed mortar) [4]

The final average of all the specimens is 0.44 MPa (63.9 psi) with a corresponding COV of 44%. The proposed design value for the shear strength of a joint is 0.12 MPa (18 psi) corresponding to a 5% lower fractile of the test results [4]. 2.2.3.2 Properties of the grout-AAC joint Direct shear tests were designed and performed at UT Austin to determine the shear capacity between grout and AAC. The specimen height was 686 mm, and the joint length was 559 mm (Table 2.2-16). Table 2.2-16 Summary of results from direct-shear tests (grout) [5]

Results for Force-displacement curves are shown in Figure 2.2-9 and the mean shear strength is 0.4 MPa (58 psi), with a COV of 22%. The proposed design shear strength of this joint is 0.25 MPa (36 psi) which corresponds to the 5% lower fractile, of this test data. For all failure surfaces, at least 30% of the surface area was covered by AAC, indicating that failure was governed by the strength of the AAC material itself, rather than by shear bond or the strength of the grout.

30


Figure 2.2-9 Force vs. displacement for direct direct-shear tests (grout) (grout [3]

2.2.3.3 Properties of the bond between thin-bed mortar and grout Direct-shear shear specimens with ASTM C476 coars coarse grout and thin--bed mortar were designed to analyze the shear bond failure modes. IIn n the performed tests at UT Austin, tin, some failures occurred around the perimeter of the grouted cell rather than straight through the joint..0 Results are reported in Table 2.2-17 and the he mean shear strength is 0.3 MPa (44 psi) with a COV of 11%. The 5% lower fractile for this test data is 0.24 MPa (36 psi). Table 2.2-17 Summary of results from direct direct-shear (grout and thin-bed bed mortar) mortar [3]

Force-displacement displacement graphs for direct direct-shear shear specimens (combined grout and thinth bed mortar) are presented in Figure 2.2-10.. In these tests, the load dropped at the formation of a crack in the grout or at crushing of a ccorner orner of the lower AAC unit [3].

31


Figure 2.2-10 Force vs. displ. for direct-shear tests (grout/thin-bed bed mortar) mortar 0

2.2.3.4 Properties operties of the bond between AAC elements Direct shear tests were cconducted onducted on plain AAC specimens as well and the equation 2.2.3-1 can be used to estimate the nominal direct shear capacity of AAC:

fυ = 0.1 f AAC

2.2.3-1

where fAAC and fv are in psi [4]. A value of 0.35 MPa is worked out from the equation for the direct shear strength of AAC [4]. 2.2.3.5 Properties of the bond between bedding mortar and AAC The bedding mortar material constitutes a leveling bed joint between the AAC panelss and the boundary elements. T The he tensile bond strength across this joint and the modulus of rupture of the AAC govern the flexural cracking at the base of the walls. From the walls specimens tests, the proposed design value for bedding mortar and AAC bond strength should not exceed 0.35 MPa.

32


2.2.3.6 Coefficients of friction The coefficient of friction between AAC and ASTM C270 Type S leveling mortar was determined based on sliding observed at UT Austin [4]. The coefficient of friction was calculated by dividing the lateral load by the corresponding applied axial load at each time sliding occurred. The average of those four values is 1.0, with a COV of 4% 0 [4] [8]. Because the coefficient of friction between AAC and AAC may differ from that between AAC and leveling mortar, additional direct-shear tests were performed using unmortared AAC units clamped together with threaded rods running through the centerline of a 3 in. (76 mm) core in each AAC modular block. A 10% lower fractile is 0.76, and the proposed design value for coefficient of friction between AAC and AAC is 0.75 [4].

2.2.4 Stress-strain behavior of reinforcement Stress-strain tests were performed at UT Austin on both shear wall and two-story assemblage reinforcement. From the Guide for Design and Construction with Autoclaved Aerated Concrete Panels the specified yield strength f s y shall not exceed 413.7 MPa. And the actual strength should not exceed 1.3 times the specified one [4] [8]. 2.2.4.1 Stress-strain behavior of shear walls reinforcement Three of the #5 (16 mm diameter, REBAR1) reinforcing bars used in the shear wall specimens were tested at UT Austin. The average yield strength was 530 GPa, and an yield strain of 0.006 were obtained for all three specimens. The ultimate strength of the reinforcement is 758 GPa (Figure 2.2-11).

33


Figure 2.2-11 Reinforcement einforcement behavior (#5, REBAR1) in shear walls [4]

2.2.4.2 Stress-strain strain behavior of two two-story story assemblage reinforcement Stress-strain strain tests were also performed on four of the #4 (13 mm diameter, REBAR2)) reinforcing bars used in the two two-story assemblage specimen pecimen. The yield strength is 520 GPa in two bars and 450 GPa in another two bars.(Figure bars 2.2-12).A weighted average of 485 GPa for the yield strength. and a value of 0.0025 for the yield strain were obtained.

Figure 2.2-12 Reinforcement behavi behavior (#4, REBAR2) in the two-story story assemblage 0

34


2.2.5 Summary of available data on mechanical properties of materials A summary of the available data on mechanical properties of materials and bond types characteristics is presented in Table 2.2-18. Afterwards most of the listed parameters

35

are

used

and

calibrated,

for

the

shear

walls

modeling.

16

13

Reinforcement

REBAR1

REBAR2

36

Yield Tensile Strength (MPa)

Assemblage

Shear Walls

Specimen

4.85E+05

5.30E+05

2.50E-03

6.00E-03

Yield Tensile Strain

1.94E+08

8.83E+07

Modulus of Elasticity (MPa)

0.3

0.3

Poisson´s Ratio

0.76

AAC and AAC

0.24

Shear bond failure around the perimeter of grouted cell

7.85E-06

7.85E-06

Mass Density (kg/mm3)

< 413.7

< 413.7

Guideline Specified Yield Strength(MPa)

0.75

1