Numerical Verification of Interaction between Masonry with Precast Reinforced Lintel Made of AAC and Reinforced Concrete Confining Elements
Abstract
:Featured Application
Abstract
1. Introduction
2. Laboratory Tests
3. Material and Numerical Models
3.1. General Comments and Strategy Employed for Masonry Modelling
- (a)
- (b)
- The mezzo-model—a variant of the macro-model that is similar to the periodic micro-structure, which includes non-linear relations between mean stresses and mean deformations of the element, composed of masonry units and mortar layers equivalent to a given medium (of the same dimensions). Its basic element (representative volume element [35]) contains the required geometrical and physical information about any type of component for the masonry elements [36,37];
- (c)
- The micro-model, which identifies the masonry structure as a heterogeneous material. Classification into finite elements is made for each material (mortar, masonry unit). Different non-linear behaviour is assumed for bricks and mortar, including potential interaction forces between them. This type of model is usually used to analyse small constructions or to perform in-depth analysis. Its description requires information about the characteristics of components and the contact between them [22,32,33,34,35,36,38,39,40].
3.2. Material Models
- Non-linear behaviour under compression, including hardening and softening
- Material cracking resulting from tension, based on non-linear mechanics of cracking
- Defined failure criterion for the material exposed to biaxial compression
- Softening of the material due to tension
- Reduced stiffness of the wall after cracking
- Possible modelling of cracks with set or changeable direction
3.2.1. Model of Concrete in Confining Elements—Elastic-Based Degradation Model
- The model of fictitious cracks resulting from the cracking mechanics and the accepted rule for crack width,
- The model of local deformations of a material point.
3.2.2. Model of the Wall and Lintels—Elastic–Plastic-Based Degradation Model
3.2.3. Model of Contact (Interface) Elements
3.2.4. Model of Reinforcement
3.2.5. Numerical Models of Whole Walls and Their Parts
4. Results of Numerical Analysis
4.1. Parts of Walls
4.2. Full-Scale Walls
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Element Name | Model Drawing | Model during Tests | Number of Models |
---|---|---|---|
1 | 2 | 3 | 4 |
N1 | | | 4 |
N2 | | | 4 |
N3 | | | 6 |
Element Name | Model Drawing | Model during Tests | Number of Models |
---|---|---|---|
1 | 2 | 3 | 4 |
MNSO | | | 2 |
MSO | | | 2 |
M2SO | | | 2 |
Parameter | Test Formula or Results | Concrete in Confining Elements and Tie Beams |
---|---|---|
Uniaxial compressive strength , N/mm2 | Obtained from tests on cylindrical specimens ø150 × 300 mm | 25.5 |
Deformations corresponding to uniaxial compressive strength of concrete εc | 1.682 × 10−3 | |
Uniaxial tensile strength , N/mm2 | Obtained from “Brasilian Test” for cylindrical specimens ø 150 × 300 mm | 2.32 |
Initial modulus of elasticity , N/mm2 | Obtained from tests on cylindrical specimens ø 150 × 300 mm | 3032 |
Poisson’s ratio | 0.2 | |
Fracture energy Gf, MN/m | Calculated from the relationship | 5.793 × 10−5 |
Weakening function at tension | Assumed softening described by the exponential function | exponential |
Displacement wc under tension, m | Displacements were calculated from the equation | −5.0 × 10−4 |
Model of cracks | developing in uniform directions | fixed |
Weakening under compression | Assumed default value of displacement | 0.05 mm |
Reduced compressive strength in the direction parallel to cracks | Assumed default value of coefficient c | 0.8 |
Parameter | Test Formula or Results | Masonry | Lintel |
---|---|---|---|
Uniaxial compressive strength fb, N/mm2 | Assumed from the tests | 4.04 | 3.71 |
Plastic strain under compression εcp | Assumed from the tests | 3.33 × 10−4 | 3.771 |
Uniaxial tensile strength fbt, N/mm2 | Assumed from the tests | 0.61 | 0.61 |
Initial modulus of elasticity Ec, N/mm2 | Assumed from the tests | 2204 | 2198 |
Poisson’s ratio ν | Assumed from the tests | 0.200 | 0.179 |
Fracture energy Gf, MN/m | Assumed from the tests | 1.07 × 10−5 | 1.602 × 10−5 |
Weakening function at tension | Assumed softening described by the exponential function | -- | -- |
Displacement wc under tension [m] | Displacements were calculated from the equation | 4.36 × 10−4 | -- |
Crack spacing smax [m] | Assumed constant value | 0.5 | 0.5 |
Coefficient of tensile strength reduction at the softening phase cts | Assumed constant value for unreinforced material | 0 | 0 |
Model of cracks | developing in uniform directions | -- | -- |
Critical displacement under compression, m | −5.0 × 10−4 | −5.0 × 10−4 | |
Reduction of compressive strength caused by cracking fc-lim | 0.8 | 0.8 | |
Compressive stiffness of cracks sF | 20.0 | 20.0 | |
Size of aggregate particles [m] | Determined on the basis of macroscopic observations of the masonry units | 0.02 | 0.02 |
Eccentricity of elliptical function e | Determined from the tests | 0.5 | 0.5 |
Direction of plastic flow | Assumed as for incompressible material | β = 0 | β = 0 |
Parameter | Test Formula or Results | Bed Joint | Head Joint |
---|---|---|---|
1 | 2 | 3 | 4 |
Normal stiffness Knn, MN/m | Calculated from the equation: E—the greater of the elasticity moduli of adjacent materials; a—dimension of finite element | 1.02 × 106 | 1.02 × 106 |
Shear stiffness Ktt, MN/m | Calculated from the equation: E—the greater of the shear moduli of adjacent materials; a—dimension of finite element | 4.51 × 105 | 4.51 × 105 |
Tensile strength fbt, N/mm2 | Determined from tests | 0.29 | 0 |
Cohesion fv0 | Determined from tests | 0.31 | -- |
Friction coefficient tgα | Determined from tests | 0.626 | 0.92 |
Normal stiffness Knn,min, MN/m | Calculated as 0.01 Knn | 1.02 × 104 | 1.02 × 104 |
Shear stiffness Ktt,min, MN/m | Calculated as 0.01 Ktt | 4.51 × 103 | 4.51 × 103 |
Fracture energy under shearing , MN/m | Determined from tests | 2.37 × 104 | -- |
Displacement u1c, mm | Calculated from the equation: | −6.13 × 104 | -- |
Equivalent displacement , mm | Calculated from the equation: | 4.09 × 104 | -- |
Weakening function at tension | -- | Assumed default relationship acc. to Figure 3b | |
Softening function at tension | Assumed as for incompressible material | Assumed two-section relationship acc. to Figure 3a | Assumed default relationship acc. to Figure 3b |
Parameter | Test Formula or Results | Bed Joint | Head Joint |
---|---|---|---|
1 | 2 | 3 | 4 |
Normal stiffness Knn, MN/m | Calculated from the equation: | 3.92 × 106 | 1.02 × 106 |
Shear stiffness Ktt, MN/m | Calculated from the equation: | 1.67 × 105 | 4.51 × 105 |
Tensile strength fbt, N/mm2 | Assumed value as for the wall | 1.5 | 1.5 |
Cohesion fv0 | ∞ | ∞ | |
Friction coefficient tgα | ∞ | ∞ | |
Normal stiffness Knn,min, MN/m | Calculated as 0.01 Knn | 3.92 × 104 | 1.02 × 104 |
Shear stiffness Ktt,min, MN/m | Calculated as 0.01 Ktt | 1.67 × 103 | 4.51 × 103 |
Type of Reinforcement and Dimensions of Rebar Cross-Section, mm | Parameter | |||||
---|---|---|---|---|---|---|
Es N/mm2 | ν | Rp0,2 N/mm2 | ET N/mm2 | Rt N/mm2 | εlim % | |
Longitudinal reinforcement in lintels (round rebars with a diameter of 8 mm) | 198,000 | 0.3 | 520 | 245 | 544 | 9.9 |
Transverse reinforcement in lintels (round rebars with a diameter of 4.5 mm) | 201,000 | 479 | 233 | 501 | 9.6 | |
Longitudinal reinforcement in confining elements and tie beams (round rebars with a diameter of 12 mm) | 179,330 | 616 | 242 | 644 | 11.9 | |
Transverse reinforcement in lintels (round rebars with a diameter of 10 mm) | 178,500 | 685 | 261 | 716 | 12.3 |
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Drobiec, Ł.; Jasiński, R.; Mazur, W.; Rybraczyk, T. Numerical Verification of Interaction between Masonry with Precast Reinforced Lintel Made of AAC and Reinforced Concrete Confining Elements. Appl. Sci. 2020, 10, 5446. https://doi.org/10.3390/app10165446
Drobiec Ł, Jasiński R, Mazur W, Rybraczyk T. Numerical Verification of Interaction between Masonry with Precast Reinforced Lintel Made of AAC and Reinforced Concrete Confining Elements. Applied Sciences. 2020; 10(16):5446. https://doi.org/10.3390/app10165446
Chicago/Turabian StyleDrobiec, Łukasz, Radosław Jasiński, Wojciech Mazur, and Tomasz Rybraczyk. 2020. "Numerical Verification of Interaction between Masonry with Precast Reinforced Lintel Made of AAC and Reinforced Concrete Confining Elements" Applied Sciences 10, no. 16: 5446. https://doi.org/10.3390/app10165446
APA StyleDrobiec, Ł., Jasiński, R., Mazur, W., & Rybraczyk, T. (2020). Numerical Verification of Interaction between Masonry with Precast Reinforced Lintel Made of AAC and Reinforced Concrete Confining Elements. Applied Sciences, 10(16), 5446. https://doi.org/10.3390/app10165446