Uncertainty of concrete strength in shear and flexural behavior of beams using lattice modeling

doi:10.1007/s11709-022-0890-5

Front. Struct. Civ. Eng.

2023, Vol. 17

Issue (2) : 306-325 https://doi.org/10.1007/s11709-022-0890-5

RESEARCH ARTICLE

Uncertainty of concrete strength in shear and flexural behavior of beams using lattice modeling

Sahand KHALILZADEHTABRIZI, Hamed SADAGHIAN, Masood FARZAM(

)

Department of Civil Engineering, University of Tabriz, Tabriz 5166616471, Iran

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Abstract

This paper numerically studied the effect of uncertainty and random distribution of concrete strength in beams failing in shear and flexure using lattice modeling, which is suitable for statistical analysis. The independent variables of this study included the level of strength reduction and the number of members with reduced strength. Three levels of material deficiency (i.e., 10%, 20%, 30%) were randomly introduced to 5%, 10%, 15%, and 20% of members. To provide a database and reliable results, 1000 analyses were carried out (a total of 24000 analyses) using the MATLAB software for each combination. Comparative studies were conducted for both shear- and flexure-deficit beams under four-point loading and results were compared using finite element software where relevant. Capability of lattice modeling was highlighted as an efficient tool to account for uncertainty in statistical studies. Results showed that the number of deficient members had a more significant effect on beam capacity compared to the level of strength deficiency. The scatter of random load-capacities was higher in flexure (range: 0.680–0.990) than that of shear (range: 0.795–0.996). Finally, nonlinear regression relationships were established with coefficient of correlation values (R²) above 0.90, which captured the overall load–deflection response and level of load reduction.

Keywords lattice modeling shear failure flexural failure uncertainty deficiency numerical simulation

Corresponding Author(s): Masood FARZAM

Just Accepted Date: 07 December 2022 Online First Date: 17 February 2023 Issue Date: 03 April 2023

Cite this article:

Sahand KHALILZADEHTABRIZI,Hamed SADAGHIAN,Masood FARZAM. Uncertainty of concrete strength in shear and flexural behavior of beams using lattice modeling[J]. Front. Struct. Civ. Eng., 2023, 17(2): 306-325.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0890-5
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I2/306

Fig.1 Geometric details of beam specimens. (a) 3D layout; (b) 2D layout [47].

Fig.2 “Nonlinear Cementitious2” material model in ATENA under (a) uniaxial stress; (b) biaxial stress; and (c) triaxial stress [56].

Tab.1 Plastic parameters of concrete in ABAQUS

Fig.3 Concrete damage plasticity in ABAQUS under (a) uniaxial tension and (b) uniaxial compression [58].

Fig.4 Definition of parameters in a sample lattice block.

Fig.5 Stress?strain curves of materials. (a) Concrete; (b) steel.

Fig.6 Flowchart of the lattice modeling.

Fig.7 Mesh sensitivity analyses for lattice beams. (a) Flexure-dominant; (b) shear-dominant.

Tab.2 Computational efficiency of different models

Tab.3 Comparison of experimental and numerical load capacities

Fig.8 Crack pattern for the flexure-dominant beam. (a) ABAQUS; (b) ATENA; (c) lattice; (d) experiment (specimen FD2-50%) [47]. (Reprinted from ACI Structural Journal, 117(3), Banjara N K, Ramanjaneyulu K, Effect of deficiencies on fatigue life of reinforced concrete beams, 31–44, Copyright 2020, with permission from ACI.)

Fig.9 Load?deflection curves for the flexure-dominant beam.

Fig.10 Crack patterns for the shear-dominant beam. (a) ABAQUS; (b) ATENA; (c) lattice; (d) experiment (specimen SD3-60%) [47]. (Reprinted from ACI Structural Journal, 117(3), Banjara N K, Ramanjaneyulu K, Effect of deficiencies on fatigue life of reinforced concrete beams, 31–44, Copyright 2020, with permission from ACI.)

Fig.11 Load?deflection curves for the shear-dominant beam.

Tab.4 Correlation results for relative average value of beams failing in flexure

Fig.12 Scatter plots of analyses for the lattice simulation of deficiencies in flexure-dominant beams. (a) F-M5S10; (b) F-M5S20; (c) F-M5S30; (d) F-M10S10; (e) F-M10S20; (f) F-M10S30; (g) F-M15S10; (h) F-M15S20; (i) F-M15S30; (j) F-M20S10; (k) F-M20S20; (l) F-M20S30.

Fig.13 (a) Load?deflection curves of flexure-dominant beams with different levels of deficiency; (b) colormap of correlation between strength deficiency, number of deficient members and average load.

Tab.5 Statistical parameters for beams with different levels of deficiency failing in flexure

Tab.6 Best fit distributions for beams with different levels of deficiency failing in flexure

Fig.14 Statistical distributions of flexure-dominant beams with different levels of deficiency. (a) F-M5S10; (b) F-M5S20; (c) F-M5S30; (d) F-M10S10; (e) F-M10S20; (f) F-M10S30; (g) F-M15S10; (h) F-M15S20; (i) F-M15S30; (j) F-M20S10; (k) F-M20S20; (l) F-M20S30.

Fig.15 Typical crack patterns of flexure-dominant beams.

Fig.16 Linear correlation of energy absorption with deflection for the flexure-dominant beams with (a) deficiency and (b) with 30% strength deficiency in 20% of members.

Tab.7 Fitting parameters for load?deflection curves of flexure-dominant beams

Fig.17 Nonlinear fitting curve for the flexure-dominant beam with (a) no deficiency and (b) 30% strength deficiency in 20% of members.

Fig.18 Nonlinear 3D fitting surface accounting for deficiency parameters in flexure-dominant beams.

Fig.19 Scatter plots of analyses for the lattice simulation of deficiencies in the shear-dominant beams. (a) S-M5S10; (b) S-M5S20; (c) S-M5S30; (d) S-M10S10; (e) S-M10S20; (f) S-M10S30; (g) S-M15S10; (h) S-M15S20; (i) S-M15S30; (j) S-M20S10; (k) S-M20S20; (l) S-M20S30.

Fig.20 Load?deflection curve of shear-dominant beams with different levels of deficiency.

Tab.8 Correlation results for relative average value of beams failing in shear

Tab.9 Statistical parameters for beams with different levels of deficiency failing in shear (0.05)

Tab.10 Best fit distributions for beams with different levels of deficiency failing in flexure

Fig.21 Statistical distributions of shear-dominant beams with different levels of deficiency. (a) S-M5S10; (b) S-M5S20; (c) S-M5S30; (d) S-M10S10; (e) S-M10S20; (f) S-M10S30; (g) S-M15S10; (h) S-M15S20; (i) S-M15S30; (j) S-M20S10; (k) S-M20S20; (l) S-M20S30.

Fig.22 Typical crack patterns of shear-dominant beams.

Fig.23 Linear correlation of energy absorption with deflection for the shear-dominant beam with no deficiencies. (a) S-M0S0; (b) S-M15S20.

Tab.11 Fitting parameters for load?deflection curves of shear-dominant RC beams.

Fig.24 Nonlinear fitting curve for the shear-dominant beam with (a) no deficiencies and (b) 30% strength deficiency in 20% of members.

Fig.25 Nonlinear 3D fitting surface accounting for deficiency parameters in shear-dominant beams.

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