玻璃钢筋混凝土梁的计算理论与实验研究
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摘要
钢筋腐蚀一直是传统钢筋混凝土结构的一个重要课题，解决钢筋锈蚀问题的一个有效办法是采用包括玻璃钢筋(GFRP筋)在内的新型纤维塑料筋代替钢筋。
与钢筋相比玻璃钢筋除了有很好的耐腐蚀性能外，还有抗拉强度高、容重较小、热膨胀系数与混凝土相近等优点，但其弹性模量较低，仅为钢筋的1/5左右。目前玻璃钢筋增强混凝土的很多力学性能并不明确，在应用方面的设计指导也不多，本文针对玻璃钢筋增强呋喃树脂混凝土梁做了一些力学实验及理论方面的研究。
(1) 将玻璃钢筋视为横观各向同性材料，推导了GFRP筋增强混凝土劈裂失效的细观力学模型，分析了玻璃钢筋周围混凝土开裂时的应力及其分布情况，得到了裂纹数量、开裂半径与玻璃钢筋/混凝土界面周围应力的定量关系。
(2) 通过对GFRP筋增强树脂混凝土普通梁和预应力梁进行四点弯曲实验，表明：利用玻璃钢筋作为增强筋在强度方面是可以满足要求的；对玻璃钢筋施加预应力来减小挠度，提高混凝土的开裂强度，以及缩小裂纹宽度是非常必要也是很有效的。
(3) 对钢筋增强水泥混凝土的挠度预测经验公式ACI 318-2002进行了修正，用于预测玻璃钢筋增强呋喃树脂混凝土梁在开裂前后的挠度。
(4) 利用有限元数值方法模拟玻璃钢筋树脂混凝土梁加载的过程，计算表明树脂混凝土材料模型的确定以及本构关系的选择是模拟精度的关键。
The corrosion of steel rods is always an important subject of the traditional structure of reinforced concrete, a effective method to deal with the problem of corrosiveness is to replace the steel rods by the FRP (fiber reinforce plastic) rods, including the GFRP bars.
Comparing with the steel rods, the GFRP rods have good corrosive-resistant property, high-tension strength, lightweight and the similar thermal expansive coefficient with the concrete. But its elastic modulus is only about one-fifth of the steel bars. At present time, many mechanics performances of the GFRP bars are remains uncertain and the instruction of design is rare. This paper is deal with some mechanical experiences and theory researches of GFRP rods concrete beams.
(1) Assuming that the GFRP rods is transversely isotropic material. Derive the micro-mechanical model of splitting failure in concrete reinforced with GFRP rods. Analysis the stress and its distribution of the cracked concrete around the GFRP rods, finding the relations of the number of cracks and the crack radius and the stress around the interface of concrete and GFRP rods.
(2) The properties of GFRP reinforced polymer concrete beams and prestressed polymer concrete beams are tested by four point bending experiments, the result show: GFRP rods can be satisfied the stiffness request; it's very necessary and effective to use prestressed beam to minish the defection, enhance the crazed load and reduce the width of the cracks.
(3) Modifying the experienced formula ACI 318-2002 which used to forecast the displacement of the steel rods reinforced cement concrete, receive a formula to forecast the displacement of GFRP rods reinforced polymer concrete beams after crazed.
(4) Using the numerical method of finite element to simulate the loading
progress of GFRP rods reinforced polymer concrete beam, the result show that
the material model and constitutive relation play an important role in receive a accurate solution.
与钢筋相比玻璃钢筋除了有很好的耐腐蚀性能外，还有抗拉强度高、容重较小、热膨胀系数与混凝土相近等优点，但其弹性模量较低，仅为钢筋的1/5左右。目前玻璃钢筋增强混凝土的很多力学性能并不明确，在应用方面的设计指导也不多，本文针对玻璃钢筋增强呋喃树脂混凝土梁做了一些力学实验及理论方面的研究。
(1) 将玻璃钢筋视为横观各向同性材料，推导了GFRP筋增强混凝土劈裂失效的细观力学模型，分析了玻璃钢筋周围混凝土开裂时的应力及其分布情况，得到了裂纹数量、开裂半径与玻璃钢筋/混凝土界面周围应力的定量关系。
(2) 通过对GFRP筋增强树脂混凝土普通梁和预应力梁进行四点弯曲实验，表明：利用玻璃钢筋作为增强筋在强度方面是可以满足要求的；对玻璃钢筋施加预应力来减小挠度，提高混凝土的开裂强度，以及缩小裂纹宽度是非常必要也是很有效的。
(3) 对钢筋增强水泥混凝土的挠度预测经验公式ACI 318-2002进行了修正，用于预测玻璃钢筋增强呋喃树脂混凝土梁在开裂前后的挠度。
(4) 利用有限元数值方法模拟玻璃钢筋树脂混凝土梁加载的过程，计算表明树脂混凝土材料模型的确定以及本构关系的选择是模拟精度的关键。
The corrosion of steel rods is always an important subject of the traditional structure of reinforced concrete, a effective method to deal with the problem of corrosiveness is to replace the steel rods by the FRP (fiber reinforce plastic) rods, including the GFRP bars.
Comparing with the steel rods, the GFRP rods have good corrosive-resistant property, high-tension strength, lightweight and the similar thermal expansive coefficient with the concrete. But its elastic modulus is only about one-fifth of the steel bars. At present time, many mechanics performances of the GFRP bars are remains uncertain and the instruction of design is rare. This paper is deal with some mechanical experiences and theory researches of GFRP rods concrete beams.
(1) Assuming that the GFRP rods is transversely isotropic material. Derive the micro-mechanical model of splitting failure in concrete reinforced with GFRP rods. Analysis the stress and its distribution of the cracked concrete around the GFRP rods, finding the relations of the number of cracks and the crack radius and the stress around the interface of concrete and GFRP rods.
(2) The properties of GFRP reinforced polymer concrete beams and prestressed polymer concrete beams are tested by four point bending experiments, the result show: GFRP rods can be satisfied the stiffness request; it's very necessary and effective to use prestressed beam to minish the defection, enhance the crazed load and reduce the width of the cracks.
(3) Modifying the experienced formula ACI 318-2002 which used to forecast the displacement of the steel rods reinforced cement concrete, receive a formula to forecast the displacement of GFRP rods reinforced polymer concrete beams after crazed.
(4) Using the numerical method of finite element to simulate the loading
progress of GFRP rods reinforced polymer concrete beam, the result show that
the material model and constitutive relation play an important role in receive a accurate solution.
引文
[1] 李继业，《新型混凝土技术与施工工艺》，中国建材出版社．
[2] 袁国青、费云鹏、华想发。拉挤玻璃钢增强混凝土研究。玻璃钢／复合材料，1999。
[3] 薛伟辰，新型FRP筋预应力混凝土梁试验研究与有限元分析，铁道学报，2003，25(5)：103-108
[4] 玻璃钢筋的生产工艺及其应用。玻璃钢／复合材料参考，2000，1。
[5] 薛伟辰．混凝土结构中新型配筋FRP的试验研究[R]．南京：河海大学．1997。
[6] 薛伟辰，康清梁．纤维塑料筋粘结锚固性能的试验研究[J]．工业建筑，1999，29(12)：5-7．
[7] Xue Weichen. Studies of Concrete Structures with FRP Bars [A]. International Conference on FRP Composite in Civil En2gineering, Hong Kong, December 2001: 1153～1160.
[8] 薛伟辰．现代预应力结构设计[M]．北京：中国建筑工业出版社，2003．
[9] 顾祥林。FRP预应力混凝土结构体系。工程力学(增)，1999。
[10] 杨正光、郑百林、贺鹏飞、李文晓、薛元德、仲政。结构混杂GFRP棒拉伸力学性能实验测试。玻璃钢／复合材料，2001(3)
[11] J.Q.Ye,Z,J,Wu,Mico-mechanical analysis of splitting failure in concrete reinforced with fiber reinforced plastic rods, Cement&Concrete Composite,2002,22:243～251.
[12] Clarke JL. Non-ferrous reinforcement. Mag Concr Res,1998. 50(1): 1～3.
[13] Cosenza E, Manfredi G, Realfonzo R. Behavior and modeling of bond of FRP Rebars to concrete. J Compos Construction,1997,1(2):40～51.
[14] Ei-Brdry MM, editor. Advanced Composite Materials in Bridges and Structures. Montr eal, Canada: Canadian Society of Civil Engineers, 1996.
[15] Bakis CE, Uppulufi VS, Nanni A, Boothby TE. Analysis of Bonding Mechanisms of Smooth and Lugged FRP rods Embedded in Concrete. Comp Sei and Tectmol, 1998; 1307～1319.
[16] Narmi A, Bakis CE, Boothby TE. Test Methods for FRP-Concrete Systems Subjected to Mechanical Loads: state-of-the-art review. J Reinf Plastics and Composites 1995, 14: 524～558.
[17] Benmokrane B, Tighiouart B, Chaallal O. Bond Strength and Load Distribution of Composite GFRP Reinforcing Bars in Concrete. ACI Mater J ,1996,93:246～253.
[18] Karihaloo BL. Tension Softening Diagrams and Longitudinally Reinforced Beam. In: Baker G, Karihaloo BL, editors. Fracture of Brittle, Disordered Materials ± Concrete, Rock and Ceramics. UK: E&FN Son, Chapman & Hall, 1995,35～50.
[19] Noghabai K. E. ect. Tension Softening on the Performance of Concrete Structures. Doctoral Thesis, Lule_a University of Technology,Sweden, 1998,150
[20] Wu ZJ, Ye JQ, Cabrera JG. 3D Analysis of Stress Transfer in Themicro-mechanics of Fiber Reinforced Composites by Using an Eigenfunctionexpansion Method. J Mech
Phys Solids 2000, 48(5): 1037-1063.
[21] Olofsson T, Noghabai K, Ohlsson U, Elfgren L Anchorage and Bond Properties in Concrete. In: Baker G, Karihaloo BL, editors. Fracture of Brittle, Disordered Materials Concrete,Rock and Ceramics. UK: E&FN Son, Chapman & Hall, 1995, 525～543.
[22] Tepfers R. Cracking of Concrete Cover along Anchored Deformed Reinforcing Bars. Mag Concr Res, 1979, 31, 3～12.
[23] Cornelius Van der Veen. Cryogenic Bond Stress-Shp Relationship. Doctoral Thesis, Delft University of Technology, The Netherlands,1990,111
[24] Wu ZJ. An Investigation on the Interface of Fiber Reinforced. composite ± theory and experiment. Ph.D. Dissertation of.Shanghai Jiao Tong University, Shanghai, 1991.
[25] Smith GE, Spencer AJM. Interfacial Tractions in a Fibre-Reinforced Elastic Composite Material. J Mech Phys Solids 1970,18:81～100.
[26] McCartney LN. New theoretical Model of Stress Transfer between Fibre and Matrix in a Uniaxially Fibre-Reinforced Composite. Proc Roy Soc Lond A 1989,425:215～244.
[27] Jones RM. Mechanics of Composite Materials, 2nd ed. Philadelphia, PA: Taylor & Francis, 1999.
[28] Reinhardt HW. Bond of Steel to Strain-Softening Concrete Takingac Count of Loading Rate. In: Bazant ZP, editor. FractureMechanics of Concrete Structures. London: Elsevier Applied Science, 1992:809～820.
[29] 薛伟辰。预应力纤维塑料筋混凝土梁的受力性能。工程力学(增)，1999
[30] 袁国青。GFP筋增强混凝土梁受力性能分析。玻璃钢／复合材料，2001，1，5～7。
[31] Nanni A. FRP Reinforcement for Concrete Structures [M]. Elsevier Science Publishers, 1993.
[32] Nanni A, Bids C E, O'Nell E F, Dxon T O. Performance of FRP Tendon2Anchor Systems for Prestressed Concrete Struc2tures[J]. PCI Journal, 1996,41(1): 34-43.
[32] Benmokrane B, Chaallal O, Masmoudi R. Flexural Response of Concrete Beams Reinforced with FRP Reinforcing Bars[J]. ACI Structural Journal, 1996,93(2): 46～54.
[33] H. A. Abdalla, Evaluation of Deflection in Concrete Members Reinforced with Fiber Reinforced Polymer(FRP) Bars,Composite structure, 2002(56):63～71.
[34] Almusallam TH. Analytical Prediction of Fexural Behavior of Concrete Beams reinforced by Fibre Reinforced Polymer (FRP) Bars. J Compos Mater, 1997, 31(7): 640～657.
[35] Cheung MS, Wiseman A. Development of Canadian Standard for Building Construction Using FRP Composites. In: Proceeding of the 3rd International Conference on Advanced Composite Materials in Bridges and Structures, August 2000; Ottawa, Canada, 2000: 841～848.
[36] Faza SS, GangaRao HVS. Theoretical and Experimental Correlation of Behavior of Concrete Beams Reinforced with Fibre Reinforced Plastic Rebars. In: Reinforced-
plastic reinforcement for concrete structures, SP-138. Detroit: American Concrete Institute, 1993: 599-614.
[37] GangaRao HVS, Vijay PV, Kalluri R, Taly NB. Flexural Behavior of Concrete T-beams Reinforced with Glass Fibre Reinforced Plastic (GFRP) bars. In: Proceeding of the 3rd International Conference on Advanced Composite Materials in Bridges and Structures, August 2000; Ottawa, Canada, 2000: 259-66.
[38] Masmoudi R, Theriault M, Benmokrane B. Flexural Behavior of Concrete Beams Reinforced with Deformed Fibre Reinforced Plastic Reinforcing Rods. ACI Struct J 1998, 95(6): 665-676.
[39] Abdalla H, El-Badry M, Rizkalla S. Behaviour of Concrete Slabs Reinforced by GFRP. In: Proceeding of the First Middle East Workshop on Structural Composites, June 1996; Sharm El-Shiekh, Egypt, 1996: 227～266.
[40] Abdalla HA, El-Badry MM, Rizkalla SH. Defection of Concrete Slabs Reinforced with Advanced Composite Materials. In: Proceeding of the 2nd International Conference on Advanced Composite Materials in Bridges and Structures, August 1996; Montreal, Canada, 1996: 201～208.
[41] CSA Standard CAN-A23.3-94, Design of Concrete Structures. Canadian Standards Association, Rexdale, Ontario, 1994.
[42] S.H.Alsayed,Y.A.Al-Salloum,T.h.Almusallam, Performance of Glass Fiber Reinforced Plastic Bars as a Reinforcing Material for Concrete Structures, Composites: Part B 2000(31):555～567
[43] Hall T, Ghali A. Long-term Deflection Prediction of Concrete Members Reinforced with Glass Fibre Reinforced Polymer Bars. Can J Civil Eng 2000;27(October):890～8.
[44] ACI Committee 440, Guide for the design and construction of concrete reinforced with FRP bars, Detroit: American Concrete Institute, 2001, 1023～1034.
[45] 谭建国，《使用ANSYS6.0进行有限元分析》，北京大学出版社。2002．
[46] 蒋咏秋，陆逢升，顾志建，《复合材料力学》，西安交通大学出版社，1989。
[47] 车宏亚等，《混凝土结构》，中国建筑工业出版社。
[2] 袁国青、费云鹏、华想发。拉挤玻璃钢增强混凝土研究。玻璃钢／复合材料，1999。
[3] 薛伟辰，新型FRP筋预应力混凝土梁试验研究与有限元分析，铁道学报，2003，25(5)：103-108
[4] 玻璃钢筋的生产工艺及其应用。玻璃钢／复合材料参考，2000，1。
[5] 薛伟辰．混凝土结构中新型配筋FRP的试验研究[R]．南京：河海大学．1997。
[6] 薛伟辰，康清梁．纤维塑料筋粘结锚固性能的试验研究[J]．工业建筑，1999，29(12)：5-7．
[7] Xue Weichen. Studies of Concrete Structures with FRP Bars [A]. International Conference on FRP Composite in Civil En2gineering, Hong Kong, December 2001: 1153～1160.
[8] 薛伟辰．现代预应力结构设计[M]．北京：中国建筑工业出版社，2003．
[9] 顾祥林。FRP预应力混凝土结构体系。工程力学(增)，1999。
[10] 杨正光、郑百林、贺鹏飞、李文晓、薛元德、仲政。结构混杂GFRP棒拉伸力学性能实验测试。玻璃钢／复合材料，2001(3)
[11] J.Q.Ye,Z,J,Wu,Mico-mechanical analysis of splitting failure in concrete reinforced with fiber reinforced plastic rods, Cement&Concrete Composite,2002,22:243～251.
[12] Clarke JL. Non-ferrous reinforcement. Mag Concr Res,1998. 50(1): 1～3.
[13] Cosenza E, Manfredi G, Realfonzo R. Behavior and modeling of bond of FRP Rebars to concrete. J Compos Construction,1997,1(2):40～51.
[14] Ei-Brdry MM, editor. Advanced Composite Materials in Bridges and Structures. Montr eal, Canada: Canadian Society of Civil Engineers, 1996.
[15] Bakis CE, Uppulufi VS, Nanni A, Boothby TE. Analysis of Bonding Mechanisms of Smooth and Lugged FRP rods Embedded in Concrete. Comp Sei and Tectmol, 1998; 1307～1319.
[16] Narmi A, Bakis CE, Boothby TE. Test Methods for FRP-Concrete Systems Subjected to Mechanical Loads: state-of-the-art review. J Reinf Plastics and Composites 1995, 14: 524～558.
[17] Benmokrane B, Tighiouart B, Chaallal O. Bond Strength and Load Distribution of Composite GFRP Reinforcing Bars in Concrete. ACI Mater J ,1996,93:246～253.
[18] Karihaloo BL. Tension Softening Diagrams and Longitudinally Reinforced Beam. In: Baker G, Karihaloo BL, editors. Fracture of Brittle, Disordered Materials ± Concrete, Rock and Ceramics. UK: E&FN Son, Chapman & Hall, 1995,35～50.
[19] Noghabai K. E. ect. Tension Softening on the Performance of Concrete Structures. Doctoral Thesis, Lule_a University of Technology,Sweden, 1998,150
[20] Wu ZJ, Ye JQ, Cabrera JG. 3D Analysis of Stress Transfer in Themicro-mechanics of Fiber Reinforced Composites by Using an Eigenfunctionexpansion Method. J Mech
Phys Solids 2000, 48(5): 1037-1063.
[21] Olofsson T, Noghabai K, Ohlsson U, Elfgren L Anchorage and Bond Properties in Concrete. In: Baker G, Karihaloo BL, editors. Fracture of Brittle, Disordered Materials Concrete,Rock and Ceramics. UK: E&FN Son, Chapman & Hall, 1995, 525～543.
[22] Tepfers R. Cracking of Concrete Cover along Anchored Deformed Reinforcing Bars. Mag Concr Res, 1979, 31, 3～12.
[23] Cornelius Van der Veen. Cryogenic Bond Stress-Shp Relationship. Doctoral Thesis, Delft University of Technology, The Netherlands,1990,111
[24] Wu ZJ. An Investigation on the Interface of Fiber Reinforced. composite ± theory and experiment. Ph.D. Dissertation of.Shanghai Jiao Tong University, Shanghai, 1991.
[25] Smith GE, Spencer AJM. Interfacial Tractions in a Fibre-Reinforced Elastic Composite Material. J Mech Phys Solids 1970,18:81～100.
[26] McCartney LN. New theoretical Model of Stress Transfer between Fibre and Matrix in a Uniaxially Fibre-Reinforced Composite. Proc Roy Soc Lond A 1989,425:215～244.
[27] Jones RM. Mechanics of Composite Materials, 2nd ed. Philadelphia, PA: Taylor & Francis, 1999.
[28] Reinhardt HW. Bond of Steel to Strain-Softening Concrete Takingac Count of Loading Rate. In: Bazant ZP, editor. FractureMechanics of Concrete Structures. London: Elsevier Applied Science, 1992:809～820.
[29] 薛伟辰。预应力纤维塑料筋混凝土梁的受力性能。工程力学(增)，1999
[30] 袁国青。GFP筋增强混凝土梁受力性能分析。玻璃钢／复合材料，2001，1，5～7。
[31] Nanni A. FRP Reinforcement for Concrete Structures [M]. Elsevier Science Publishers, 1993.
[32] Nanni A, Bids C E, O'Nell E F, Dxon T O. Performance of FRP Tendon2Anchor Systems for Prestressed Concrete Struc2tures[J]. PCI Journal, 1996,41(1): 34-43.
[32] Benmokrane B, Chaallal O, Masmoudi R. Flexural Response of Concrete Beams Reinforced with FRP Reinforcing Bars[J]. ACI Structural Journal, 1996,93(2): 46～54.
[33] H. A. Abdalla, Evaluation of Deflection in Concrete Members Reinforced with Fiber Reinforced Polymer(FRP) Bars,Composite structure, 2002(56):63～71.
[34] Almusallam TH. Analytical Prediction of Fexural Behavior of Concrete Beams reinforced by Fibre Reinforced Polymer (FRP) Bars. J Compos Mater, 1997, 31(7): 640～657.
[35] Cheung MS, Wiseman A. Development of Canadian Standard for Building Construction Using FRP Composites. In: Proceeding of the 3rd International Conference on Advanced Composite Materials in Bridges and Structures, August 2000; Ottawa, Canada, 2000: 841～848.
[36] Faza SS, GangaRao HVS. Theoretical and Experimental Correlation of Behavior of Concrete Beams Reinforced with Fibre Reinforced Plastic Rebars. In: Reinforced-
plastic reinforcement for concrete structures, SP-138. Detroit: American Concrete Institute, 1993: 599-614.
[37] GangaRao HVS, Vijay PV, Kalluri R, Taly NB. Flexural Behavior of Concrete T-beams Reinforced with Glass Fibre Reinforced Plastic (GFRP) bars. In: Proceeding of the 3rd International Conference on Advanced Composite Materials in Bridges and Structures, August 2000; Ottawa, Canada, 2000: 259-66.
[38] Masmoudi R, Theriault M, Benmokrane B. Flexural Behavior of Concrete Beams Reinforced with Deformed Fibre Reinforced Plastic Reinforcing Rods. ACI Struct J 1998, 95(6): 665-676.
[39] Abdalla H, El-Badry M, Rizkalla S. Behaviour of Concrete Slabs Reinforced by GFRP. In: Proceeding of the First Middle East Workshop on Structural Composites, June 1996; Sharm El-Shiekh, Egypt, 1996: 227～266.
[40] Abdalla HA, El-Badry MM, Rizkalla SH. Defection of Concrete Slabs Reinforced with Advanced Composite Materials. In: Proceeding of the 2nd International Conference on Advanced Composite Materials in Bridges and Structures, August 1996; Montreal, Canada, 1996: 201～208.
[41] CSA Standard CAN-A23.3-94, Design of Concrete Structures. Canadian Standards Association, Rexdale, Ontario, 1994.
[42] S.H.Alsayed,Y.A.Al-Salloum,T.h.Almusallam, Performance of Glass Fiber Reinforced Plastic Bars as a Reinforcing Material for Concrete Structures, Composites: Part B 2000(31):555～567
[43] Hall T, Ghali A. Long-term Deflection Prediction of Concrete Members Reinforced with Glass Fibre Reinforced Polymer Bars. Can J Civil Eng 2000;27(October):890～8.
[44] ACI Committee 440, Guide for the design and construction of concrete reinforced with FRP bars, Detroit: American Concrete Institute, 2001, 1023～1034.
[45] 谭建国，《使用ANSYS6.0进行有限元分析》，北京大学出版社。2002．
[46] 蒋咏秋，陆逢升，顾志建，《复合材料力学》，西安交通大学出版社，1989。
[47] 车宏亚等，《混凝土结构》，中国建筑工业出版社。