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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (5) : 1180-1195
Performance of fixed beam without interacting bars
Aydin SHISHEGARAN1, Behnam KARAMI2, Timon RABCZUK3,4(), Arshia SHISHEGARAN5, Mohammad Ali NAGHSH6, Mohammreza MOHAMMAD KHANI1
1. School of Civil Engineering, Iran University of Science and Technology, Tehran 13114-16846, Iran
2. International Institute of Earthquake Engineering and Seismology, Tehran 19537-14453, Iran
3. Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
5. School of Civil engineering, Islamic Azad University, Tehran 1987745815, Iran
6. School of Civil Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran
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Increasing the bending capacity of reinforced concrete (RC) elements is one of important topics in structure engineering. The goal of this study is to develop a transferred stress system (TSS) on longitudinal reinforcement bars for increasing the bending capacity of RC frames. The study is divided into two parts, i.e., experimental tests and nonlinear FE analysis. The experiments were carried out to determine the load-deflection curves and crack patterns of the ordinary and TSS fixed frame. The FE models were developed for simulating the fixed frames. The obtained load-deflection results and the observed cracks from the FE analysis and experimental tests are compared to evaluate the validation of the FE nonlinear models. Based on the validated FE models, the stress distribution on the ordinary and TSS bars were evaluated. We found the load carrying capacity and ductility of TSS fixed beam are 29.39% and 23.69% higher compared to those of the ordinary fixed beams. The crack expansion occurs on the ordinary fixed beam, although there are several crack openings at mid-span of the TSS fixed beam. The crack distribution was changed in the TSS fixed frame. The TSS fixed beam is proposed to employ in RC frame instead of ordinary RC beam for improving the performance of RC frame.

Keywords transferred stress system      bending capacity      crack opening      crack propagation      FE nonlinear model      stress distribution     
Corresponding Author(s): Timon RABCZUK   
Just Accepted Date: 25 August 2020   Online First Date: 20 October 2020    Issue Date: 16 November 2020
 Cite this article:   
Aydin SHISHEGARAN,Behnam KARAMI,Timon RABCZUK, et al. Performance of fixed beam without interacting bars[J]. Front. Struct. Civ. Eng., 2020, 14(5): 1180-1195.
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Mohammad Ali NAGHSH
Fig.1  The considered RC frame. (a) The applied static load to the RC fixed frame; (b) the moment diagram and deformed shape of the RC fixed frame; (c) the divided section of the RC frame; (d) the moment and axial force of the divided frame (the fixed beam with two short columns).
Fig.2  The fixed Ordinary frame. (a) Detail of the ordinary fixed frame (unit: cm); (b) the sections of beam and columns.
Fig.3  Detail of the fixed TSS frame (unit: cm).
Fig.4  Justifying and proving the hypothesis of this study. (a) The stress distribution on the TSS longitudinal bar; (b) the stress distribution on ordinary longitudinal bar; (c) presenting superposition for justifying TSS method.
Fig.5  Flowchart for carrying out this study.
Fig.6  Stress-strain test of steel bar. (a) Dimensional geometry of the prepared steel bar for extend meter test; (b) extend meter test for prepared steel bar.
Fig.7  The detail of experimental samples. (a) The longitudinal reinforcement bars and molding the ordinary fixed frame; (b) the longitudinal reinforcement bars of TSS fixed frame; (c) molding the sample; (d) the schematic of test setup; (e) the actual test setup.
Fig.8  The behavior of concrete under (a) uniaxial loading in tension and (b) compression.
the status variable unit value
yield stress stress MPa 400
strain % 0.4
ultimate limit stress MPa 540
strain % 27
Tab.1  Yield parameters of steel bars
Fig.9  The considered behavior for steel bar and the obtained results of behavior of streel bar from experimental test.
dilation angle, ψ() plastic potential eccentricity, ε stress ratio, σb0/σc0 shape of the yielding surface, Kc viscosity parameter, μ
31 0.1 1.16 0.667 0.0001
Tab.2  The considered plasticity parameters in the CDP model
compressive behavior compressive damage parameter
stress (MPa) crushing inelastic strain dc crushing strain
13.7 0.00000 0.000 0.00000
16.3 0.00010 0.001 0.00010
17.4 0.00015 0.005 0.00015
18.4 0.00020 0.009 0.00020
21.9 0.00040 0.029 0.00040
23.5 0.00050 0.042 0.00050
30.0 0.00150 0.265 0.00150
27.3 0.00200 0.437 0.00200
17.7 0.00250 0.680 0.00250
14.8 0.00260 0.737 0.00260
8.1 0.00280 0.862 0.00280
Tab.3  The considered compressive behavior for concrete
tensile behavior tensile damage parameter
stress (MPa) cracking inelastic strain dt cracking strain
3.3 0.00000 0 0.00000
2.3 0.00006 0.11 0.00006
1.0 0.00024 0.38 0.00024
0.0 0.00120 0.95 0.00120
Tab.4  The considered tensile behavior for concrete
Fig.10  A schematic for FE nonlinear model.
Fig.11  Connecting beam element to solid element using the coupling constraint method for simulating no interaction parts of TSS steel bars.
Fig.12  Load- deflection results of ordinary beam and TSS beam. (a) The obtained load-deflection performance of ordinary fixed beam from tests and FE nonlinear analyses; (b) the obtained load-deflection performance of the TSS fixed beam from tests and FE nonlinear analyses.
Fig.13  The crack expansion in each sample. (a) The crack expansion on the ordinary fixed frame; (b) the cracks expansion on the md-span of the TSS fixed frame; (c) the crack openings on the mid-span of the TSS fixed frame.
Fig.14  The crack expansion in each sample. (a) The cracked ordinary fixed frame; (b) the cracked TSS fixed beam.
Fig.15  The stress of longitudinal reinforcement bars. (a) The distributed stress of the longitudinal reinforcement bars of the ordinary fixed frame; (b) the distributed stress of the longitudinal reinforcement bars of the TSS fixed frame.
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