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Frontiers of Structural and Civil Engineering

Front Struc Civil Eng    2013, Vol. 7 Issue (3) : 316-324     https://doi.org/10.1007/s11709-013-0211-0
RESEARCH ARTICLE
Calculation methods of the crack width and deformation for concrete beams with high-strength steel bars
Jianmin ZHOU(), Shuo CHEN, Yang CHEN
College of Civil Engineering, Tongji University, Shanghai 200092, China
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Abstract

Three groups of concrete beams reinforced with high-strength steel bars were tested, and the crack width and deformation of the specimens were observed and studied. To facilitate the predictions, two simplified formulations according to a theory developed by the first author were proposed. The advantages of the formulations were verified by the test data and compared with several formulas in different codes.

Keywords concrete beam      high-strength steel bar      crack width      deformation     
Corresponding Author(s): ZHOU Jianmin,Email:tjzhou2008@163.com   
Issue Date: 05 September 2013
 Cite this article:   
Jianmin ZHOU,Shuo CHEN,Yang CHEN. Calculation methods of the crack width and deformation for concrete beams with high-strength steel bars[J]. Front Struc Civil Eng, 2013, 7(3): 316-324.
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http://journal.hep.com.cn/fsce/EN/10.1007/s11709-013-0211-0
http://journal.hep.com.cn/fsce/EN/Y2013/V7/I3/316
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Jianmin ZHOU
Shuo CHEN
Yang CHEN
Group 1fcu/MPab×h×L(mm×mm×mm)c/mmsteel bar ①Group 2fcu/MPab×h×L(bf×hf)(mm×mm×mm)c/mmsteel bar ①
B5F134.01251 × 403 × 4000253Ф16JL128.7250 × 400 × 4500303Ф20
B5F234.01250 × 402 × 4000252Ф25JL228.7250 × 450 × 4500303Ф20
B5F356.16253 × 403 × 4000253Ф16JL328.7250 × 450 × 4500302Ф25
B5F456.16249 × 401 × 4000252Ф25JL428.7250 × 450 × 4500403Ф25
CB5-134.01251 × 402 × 4000602Ф25JL528.7250 × 500 × 4500405Ф20
CB5-234.01303 × 454 × 4000602Ф32JL644.0250 × 400 × 4500502Ф25
CB5-356.16255 × 406 × 4000603Ф25JL744.0250 × 450 × 4500303Ф20
CB5-456.16254 × 403 × 4000602Ф32JL844.0250 × 450 × 4500403Ф25
SB5F134.01250 × 400 × 4000602Ф25JL944.0300 × 500 × 4500402Ф321Ф20
SB5F234.01300 × 450 × 4000602Ф32JL1044.0250 × 500 × 4500503Ф25
SB5F356.16250 × 400 × 4000602Ф25TL1128.7250 × 400 × 4500500 × 80303Ф25
SB5F456.16300 × 450 × 4000602Ф32TL1228.7250 × 450 × 4500550 × 80405Ф20
SB5F556.16300 × 450 × 4000602Ф32TL1344.0250 × 450 × 4500550 × 80402Ф32
SB5F634.01250 × 400 × 4000602Ф25TL1444.0300 × 500 × 4500550 × 80503Ф25
Tab.1  Properties of Groups 1 and 2
Group 3b×h×L(mm×mm×mm)fcu/MPapresressed strandsteel bar
ap(mm)σcon(MPa)σpe(MPa)c/mm
PC-1251 × 453 × 451039.83?s15.29111498222Ф183Ф202Ф1432
PC-2252 × 452 × 450939.83?s15.215111497782Ф183Ф202Ф1433
PC-3252 × 453 × 451239.83?s15.28911497482Ф182Ф252Ф1431
PC-4251 × 452 × 451339.83?s15.215211497542Ф182Ф252Ф1433
PC-5253 × 452 × 451839.84?s15.29211497522Ф183Ф202Ф1432
PC-6252 × 452 × 451538.44?s15.215311497702Ф182Ф252Ф1433
PC-7253 × 451 × 451138.44?s15.2887643892Ф183Ф202Ф1432
PC-8252 × 452 × 451838.44?s15.21477644402Ф182Ф252Ф1431
PC-9308 × 608 × 601850.34?s15.211611508352Ф183Ф204Ф1442
PC-10304 × 604 × 601550.34?s15.217511508622Ф183Ф204Ф1443
PC-11303 × 603 × 601750.34?s15.211811508622Ф183Ф254Ф1441
PC-12306 × 602 × 601950.34?s15.217611508882Ф183Ф254Ф1439
RC-1252 × 452 × 451839.80002Ф183Ф202Ф1432
RC-2252 × 453 × 451839.80002Ф182Ф252Ф1432
Tab.2  Properties- of Group 3
Fig.1  Positive loading setup
Fig.2  Cross section of specimens.dwg
Fig.3  Cross-section stress distribution.dwg
itemGB50010-2010 [3]JTGD62-2004 [4]ACI318-08 [5]EN 1992-1-1:2004 [6]Zhou, 2000 [2]suggested
RCbeamlcrμ1.069???0.942?
δ0.192???0.182?
ωmc/ωmtμ1.1181.2390.8861.3001.1331.019
δ0.3010.3150.2780.2850.2810.245
PRCbeamlcrμ1.134???1.137?
δ0.122???0.120?
ωmc/ωmtμ1.0330.9730.7951.2341.2020.979
δ0.1300.1630.1670.2190.1500.136
Tab.3  Comparison of calculation results
Fig.4  Fitting result with Eq. (13)
Fig.5  M-f relationship before concrete failure
itemGB50010-2010 [3]JTGD62-2004 [4]ACI318-08 [5]EN 1992-1-1:2004 [6]Zhou, 2000 [2]suggested
RCbeamμ1.0600.9411.0790.9431.0601.065
δ0.1650.2240.2820.2250.2010.258
PRCbeamμ0.9640.8501.0820.8531.0380.961
δ0.2380.2780.1520.2780.2650.224
Tab.4  Comparison of calculation results ()
Fig.6  Influence of n on calculation for Beam B4-1
Fig.7  Crack width calculated from the suggested equation compared with tested values for RC beam
Fig.8  Crack width calculated from the suggested equation compared with tested values for PRC beam
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