DESIGN METHOD FOR NORMAL SECTION OF HYBRID REINFORCED (STEEL AND FRP BARS) BEAMS UNDER BENDING
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摘要: 钢和纤维复合筋混杂增强混凝土(hybrid reinforced concrete,Hybrid-RC)梁具有较好的承载力、耐久性和延性。然而,基于文献调研发现,现有设计方法对Hybrid-RC梁正截面受弯的破坏形态还未能做出准确的预测。因此,该文修正了现有的设计方法,并通过数据库对比,验证了其有效性。在此基础上,对Hybrid-RC梁提出了一种新的设计思路,以减少使用成本,并得到更高的使用荷载。
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关键词:
- 混杂配筋(Hybrid-RC)梁 /
- 破坏形态 /
- 抗弯承载力 /
- 设计程序 /
- 数值模拟
Abstract: The hybrid reinforced concrete (Hybrid-RC) beam consisting steel bars and fiber-reinforced polymer bars can provide better bearing capacity, durability and ductility. However, literature review showed that the design methods for the normal section of Hybrid-RC beams under bending failed to predict the failure mode of these structures accurately. Therefore, it revises the existing design method, and verifies its effectiveness through database comparison. On this basis, a new design idea of Hybrid-RC beam is proposed to reduce the service cost and achieve higher service load. -
表 1 文献中混杂配筋梁的截面参数
Table 1. Cross section parameters of hybrid-RC beams in the literature
文献 梁号 b/mm d/mm $f_{\rm{c}}' /{\rm{MPa}}$ Af/mm2 As/mm2 fy/MPa ffu/MPa Ef/GPa 破坏形态 Qu等[20] B3 180 206 26.48 253.23 226.08 363.0 782 45.0 A B4 180 204 26.48 396.91 200.96 336.0 755 41.0 A B5 180 206 27.52 141.69 401.92 336.0 778 37.7 A B6 180 204 27.52 253.23 401.92 336.0 782 45.0 A B7 180 208 32.52 141.69 113.04 363.0 778 37.7 A B8 180 197 32.52 396.91 1205.76 336.0 755 41.0 A Aiello和Ombres[12] A1 150 175 45.70 88.31 100.48 465.0 1674 49.0 A A2 150 175 45.70 157.00 100.48 465.0 1366 50.1 A A3 150 175 45.70 235.50 226.08 465.0 1366 50.1 A C1 150 175 45.70 88.31 100.48 465.0 1674 49.0 A LauDenvid[22] G10T07 280 348 39.80 981.70 628.30 597.0 582 38.0 A G06T1 280 351 44.60 567.10 981.70 550.0 588 39.5 A Safan[26] B10/6S 100 136 30.00 56.60 157.00 530.0 780 41.0 A B10/8S 100 136 30.00 100.60 157.00 530.0 755 39.0 A B12/6S 100 135 30.00 56.60 226.00 470.0 780 41.0 A B12/8S 100 135 30.00 100.60 226.00 470.0 755 39.0 A Leung 和 Balendran[17] L2 150 145 28.50 142.60 157.00 460.0 760 40.8 A L5 150 145 28.50 213.90 157.00 460.0 760 40.8 A H2 150 145 48.80 142.60 157.00 460.0 760 40.8 A H5 150 145 48.80 213.90 157.00 460.0 760 40.8 A Al-Mahmoud[27] SC-12 150 254 35.10 113.00 226.00 600.0 1875 146.0 A LauDenvid[22] G03MD1 280 351 41.30 283.50 981.70 336.0 588 39.5 B Almusallam等[28] RW1F 150 170 36.60 78.50 157.00 408.0 743 40.0 B Rahimi 和 Hutchinson[29] RHB3 200 135 52.30 66.00 157.00 575.0 1532 127.0 B Tan[16] B2 200 375 28.24 25.12 150.70 324.4 1776 52.0 B Nguyen等[30] B2 120 140 35.68 96.00 628.30 466.0 3140 181.0 C Xiong等[31] CF1 120 130 15.68 8.11 226.20 569.0 3652 252.0 C Xiong[32] CF3 80 110 15.68 5.11 226.20 346.7 3652 252.0 C 注:A表示钢筋屈服后混凝土压溃;B表示钢筋屈服后FRP断裂;C表示的破坏形态为混凝土压溃,钢筋未屈服(但实际出现剥离破坏)。 表 2 文献中混杂配筋梁试验值和理论值的对比
Table 2. Comparison between experimental and theoretical values of the tested hybrid-RC beams
梁号 Qu[20] Lau[22] 提出的等刚度配筋 提出的等强度配筋 Mexp/
(kN·m)Ms,th/
(kN·m)Mf,th/
(kN·m)Mexp/Mth $\rho_{\rm{eff}}^1 $/
(%)$\rho_{\rm{eff,b}}^1 $/
(%)PFM $\rho_{\rm{eff}}^2 $/
(%)$\rho_{\rm{eff,b}}^2 $/
(%)PFM $\rho_{\rm{s}}^{\rm{e}} $/
(%)($\rho_{{\rm{s,b}}{\text{-}}{\text{Ⅰ}} }^{\rm{e}} $, $\rho_{{\rm{s,b}}{\text{-}}{\text{Ⅱ}} }^{\rm{e}} $)/
(%)PFM $\rho_{\rm{f}}^{\rm{e}} $/
(%)($\rho_{{\rm{f,b}}{\text{-}}{\text{Ⅰ}} }^{\rm{e}} $, $\rho_{{\rm{f,b}}{\text{-}}{\text{Ⅱ}} }^{\rm{e}} $)/
(%)PFM B3 0.76 3.57 A 0.97 0.44 A 0.76 (0.35,3.57) A 0.97 (0.44,4.51) A 38.38 35.59 35.59 1.08 B4 0.77 3.95 A 1.32 0.43 A 0.77 (0.25,3.95) A 1.32 (0.43,6.80) A 39.66 37.59 37.59 1.06 B5 1.16 4.10 A 0.85 0.40 A 1.16 (0.54,4.10) A 0.85 (0.40,3.02) A 36.36 35.25 35.25 1.03 B6 1.25 4.10 A 1.16 0.46 A 1.25 (0.49,4.10) A 1.16 (0.46,3.82) A 42.57 40.56 40.56 1.05 B7 0.37 4.21 A 0.52 0.45 A 0.37 (0.32,4.21) A 0.52 (0.45,5.86) A 23.55 27.48 27.48 0.86 B8 3.63 4.66 A 2.63 0.51 A 3.63 (0.71,4.66) A 2.63 (0.51,3.38) A 63.30 68.60 68.60 0.92 A1 0.47 3.75 A 0.44 0.17 A 0.47 (0.18,3.75) A 0.44 (0.17,3.57) A 25.14 20.74 20.74 1.21 A2 0.53 3.75 A 0.73 0.25 A 0.53 (0.18,3.75) A 0.73 (0.25,5.13) A 28.41 25.38 25.38 1.12 A3 1.09 3.75 A 1.19 0.25 A 1.09 (0.23,3.75) A 1.19 (0.25,4.11) A 35.55 33.59 33.59 1.06 C1 0.47 3.75 A 0.44 0.17 A 0.47 (0.18,3.75) A 0.44 (0.17,3.57) A 25.14 20.74 20.74 1.21 G10T07 0.85 2.38 A 1.67 0.88 A 0.85 (0.45,2.38) A 1.67 (0.88,4.68) A 261 224.86 224.86 1.16 G06T1 1.11 2.90 A 1.51 0.96 A 1.11 (0.71,2.90) A 1.51 (0.96,3.93) A 229 239.56 239.56 0.96 B10/6S 1.24 2.37 A 1.20 0.45 A 1.24 (0.47,2.37) A 1.20 (0.45,2.29) A 14.09 11.64 11.64 1.21 B10/8S 1.3 2.37 A 1.55 0.46 A 1.30 (0.39,2.37) A 1.55 (0.46,2.83) A 14.41 12.42 12.42 1.16 B12/6S 1.76 2.80 A 1.43 0.45 A 1.76 (0.56,2.80) A 1.43 (0.45,2.27) A 14.89 13.27 13.27 1.12 B12/8S 1.82 2.80 A 1.79 0.46 A 1.82 (0.47,2.80) A 1.79 (0.46,2.75) A 16.33 13.85 13.85 1.18 L2 0.86 2.78 A 1.09 0.46 A 0.86 (0.36,2.78) A 1.09 (0.46,3.55) A 22.23 16.25 16.25 1.37 L5 0.92 2.78 A 1.42 0.46 A 0.92 (0.30,2.78) A 1.42 (0.46,4.28) A 23.07 17.89 17.89 1.29 H2 0.86 3.94 A 1.09 0.65 A 0.86 (0.51,3.94) A 1.09 (0.65,5.03) A 21.11 19.45 19.45 1.09 H5 0.92 3.94 A 1.42 0.65 A 0.92 (0.42,3.94) A 1.42 (0.65,6.07) A 27.06 21.82 21.82 1.24 SC-12 0.80 2.27 A 0.49 0.29 A 0.80 (0.48,2.27) A 0.49 (0.29,1.38) A 65.4 61.96 61.96 1.06 G03MD1 1.06 5.30 Fail 0.86 0.92 B 1.06 (1.13,5.30) B 0.86 (0.92,4.29) B 147.7 164.66 164.66 0.90 RW1F 0.68 3.91 A 0.65 0.56 A 0.68 (0.59,3.91) A 0.65 (0.56,3.73) A 21.84 18.32 18.32 1.19 RHB3 0.73 3.04 Fail 0.46 0.47 B 0.73 (0.74,3.04) B 0.46 (0.47,1.93) B 20.7 23.92 23.92 0.87 B2 0.21 4.40 Fail 0.07 0.11 B 0.21 (0.34,4.40) B 0.07 (0.11,1.47) B 35.25 40.61 40.61 0.87 B2 4.26 3.21 C 1.13 0.14 Fail 4.26 (0.52,3.21) C 1.13 (0.14,0.85) C 28.6 30.33 30.33 0.94 CF1 1.52 1.14 C 0.28 0.06 Fail 1.52 (0.35,1. 14) C 0.28 (0.06,0.21) C 15.42 11.68 11.68 1.32 CF3 2.64 2.24 C 0.3 0.06 Fail 2.64 (0.56,2.24) C 0.3 (0.06,0.26) C 6.09 5.79 5.79 1.05 注:PFM表示预测的破坏形态;A表示钢筋屈服后混凝土压溃;B表示钢筋屈服后FRP断裂;C表示为混凝土压溃,钢筋未屈服;Fail表示未出现预测的破坏形态。 表 3 设计混杂梁的截面参数
Table 3. Cross section parameters of the designed hybrid-RC beams
梁号 b/mm d/mm $ f_{\rm{c}}' $/MPa Af/mm2 As/mm2 fy/MPa ffu/MPa Ef/GPa Mth/(kN·m) Af /As B4 180 204 26.48 396.91 200.96 336 755 41.0 37.59 1.98 B4-1 180 204 26.48 221.01 452.39 336 755 41.0 39.66 0.49 B4-2 180 204 26.48 163.52 508.94 336 755 41.0 39.66 0.32 B4-3 180 204 26.48 42.19 628.32 336 755 41.0 39.66 0.07 G03MD1 280 351 41.30 283.50 981.70 336 588 39.5 − − G03MD1-1 280 351 20.00 74.10 1407.40 336 588 39.5 147.70 0.05 G03MD1-2 280 280 41.30 133.60 1608.50 336 588 39.5 147.70 0.08 G03MD1-3 280 351 41.30 31.20 1256.60 336 1675 49.0 147.70 0.02 B2 120 140 35.68 96.00 628.30 466 3140 181.0 − − B2-1 120 140 60.00 30.66 452.39 466 3140 181.0 28.60 0.07 B2-2 120 180 35.68 21.55 339.29 466 3140 181.0 28.60 0.06 B2-3 120 140 35.68 85.10 804.25 300 3140 181.0 28.60 0.11 表 4 模拟混杂梁的截面参数
Table 4. Cross section parameters of the Abaqus simulated hybrid-RC beams
梁号 b/mm d/mm $f_{\rm{c}}' $/MPa Af/mm2 As/mm2 fy/MPa ffu/MPa Ef/GPa Af /As Δu/Δy B3 180 206 26.48 253.23 226.08 363 782 45.0 1.12 5.18 B3-1 180 206 26.48 73.20 508.68 363 782 45.0 0.14 3.11 B6 180 204 27.52 253.23 401.92 336 782 45.0 0.63 4.38 B6-1 180 204 27.52 93.25 628.32 336 782 45.0 0.15 3.07 B7 180 208 32.52 141.69 113.04 363 778 37.7 1.25 6.51 B7-1 180 208 32.52 54.62 200.96 363 778 37.7 0.27 4.93 C1 150 175 45.70 88.31 100.48 465 1674 49.0 0.88 6.35 C1-1 150 175 45.70 49.50 226.19 465 1674 49.0 0.22 4.69 -
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