Static Bearing Capacity Analysis of CFRP-Reinforced Short CHS Steel Tubular Columns under Axial Compression
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摘要: 为了研究轴压作用下碳纤维增强复合材料（carbon fibre-reinforced polymer，CFRP）加固圆形空心截面（circular hollow section，CHS）钢管短柱的极限承载力，对轴压作用下CFRP加固CHS钢管短柱进行了理论和数值分析. 理论分析中，利用等效截面法推导了两种不同粘贴方式（全环向粘贴以及环向和纵向交替粘贴）的CFRP加固圆钢管短柱在轴压作用下静力承载力的理论计算公式；数值分析中，将特征值屈曲与Riks法相结合建立了轴压作用下CFRP加固圆钢管短柱的非线性有限元分析模型. 对该模型中的环向和纵向CFRP进行应力分析后发现，环向CFRP处于拉伸状态，约束钢管的径向变形；纵向CFRP会承担轴压荷载中的部分压力，限制钢管的变形. 最后，将所建立的有限元分析模型结果和所推导的理论公式结果与已有文献的试验结果进行对比，发现三者之间的最大误差不超过2%，验证了建立的有限元模型和所推导的理论公式分析结果的准确性.
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关键词:
- CFRP加固圆钢管短柱 /
- 轴压作用 /
- 静力承载力 /
- 等效截面法 /
- 有限元分析
Abstract: To predict the ultimate strength of a short circular hollow section (CHS) steel tubular columns reinforced with carbon fibre-reinforced polymer (CFRP), both theoretical and numerical analyses were carried out. In the theoretical analysis, based on equivalent section method, the equations for calculating the load bearing capacities of CHS steel tubular columns under axial compression are deduced, which correspond to two different reinforcing methods, in which CFRPs are arranged in circumferential placement and in longitudinal-circumferential placement. In the numerical analysis, both eigenvalue buckling method and Riks method are combined to build a nonlinear finite element model of the tubular columns under axial compression. The finite element analysis for the stress distribution of the longitudinal and circumferential CFRPs shows that the circumferential CFRPs are under tension and restrain the radial deformation of the tubular columns, while the longitudinal CFRPs share the axial compression and restrain the deformation of the tubular columns. The comparison of the numerical results, theoretical results and reported experimental results show that the maximum deviation among them is no more than 2%, which verifies the finite element model and deduced equations. -
图 4 有限元和试验结果载荷-位移曲线对比
Figure 4. Comparison of load-displacement curves between FE and test results
表 1 CHS参数
Table 1. CHS parameters
组号 试件编号 ${D_{\rm{s}}}$/mm ${t_{\rm{s}}}$/mm ${E_{\rm{s}}}$/（N•mm−2） $\sigma _{\rm{y}}$/（N•mm−2） ${E_{\rm{p,CFRP}}}$/（N•mm−2） ${D_{\rm{s}}}/{t_{\rm{s}}}$ $L/{D_{\rm{s}}}$ FRP 层数和方向 1 C-1 87.25 2.36 209 571 455 — 37 3.2 — CF-1A 87.23 2.32 209 571 455 230 000 38 3.2 1H1L CF-1B 87.21 2.32 209 571 455 230 000 38 3.2 2H2L 2 C-2 86.31 2.00 209 571 455 — 43 3.2 — CF-2A 86.38 1.91 209 571 455 230 000 45 3.2 1L1H CF-2B 86.39 1.96 209 571 455 230 000 44 3.2 2L2H 3 C-3 85.75 1.57 209 571 455 — 55 3.2 — CF-3A 85.68 1.57 209 571 455 230 000 54 3.2 1H1L 4 C-4 85.11 1.13 209 571 455 — 75 3.2 — CF-4A 85.21 1.10 209 571 455 230 000 78 3.2 1H1L 5 ST1 165 4.2 206 000 339 — 39 2.7 — ST2 166 4.2 206 000 339 76 000 40 2.7 1H ST3 165 4.2 206 000 339 76 000 39 2.7 2H ST4 165 4.2 206 000 339 76 000 39 2.7 2H 
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表 2 CFRP材料属性
Table 2. CFRP material properties
${E_1}$/MPa ${E_2}$/MPa ${N_{\rm{u}}}$ ${G_{12}}$/MPa ${G_{13}}$/MPa ${G_{23}}$/MPa $t_{\rm{CFRP}}$/mm 230 000 1 900 0.3 3 387 3 387 3 387 0.176 注：当采用 文献[12 ]的模型建模时 $t_{\rm{CFRP}} = 0.17\;{\rm{mm}}$；E1 为纤维方向的弹性模量；E2 为垂直于纤维方向的弹性模量；
Nu 为泊松比；G12、G13、G23 为材料各平面内剪切模量.
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表 3 Hashin失效参数
Table 3. Hashin’s failure parameters
MPa 方向 参数 值 方向 参数 值 X 拉伸强度 XT 1 830 Y 拉伸强度 YT 31.3 压缩强度 XC 895 压缩强度 YC 124.5 剪切强度 SL 72 剪切强度 ST 62.3
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表 4 极限承载力对比分析
Table 4. Comparison and analysis of load carrying capacity
组 试件编号 Nexp/kN NFE/kN Nu/kN 提高率/% NFE/Nexp Nu/Nexp Nu/NFE 1 C-1 253 260 280 — 1.03 1.10 1.08 CF-1A 299 294 316 13 0.98 1.06 1.07 CF-1B 341 350 347 24 1.03 1.02 0.99 2 C-2 220 226 241 — 1.03 1.10 1.07 CF-2A 267 272 266 10.4 1.02 1.00 0.98 CF-2B 281 291 296 23 1.04 1.05 1.02 3 C-3 170 174 188 — 1.02 1.10 1.08 CF-3A 214 213 222 22.4 1.00 1.04 1.04 4 C-4 120 125 137 — 1.04 1.14 1.10 CF-4A 155 164 164 31.2 1.06 1.06 1.00 5 ST1 719 722 719 — 1.00 1.00 1.00 ST2 727 730 726 1.4 1.00 1.00 0.99 ST3 753 752 745 4.7 1.00 0.99 0.99 ST4 763 763 758 6.2 1.00 0.99 0.99
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