Experimental study on shear behavior of externally prestressed ultra-high performance concrete beams without stirrups
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摘要: 为研究超高性能混凝土(Ultra-high performance concrete，UHPC)无腹筋梁的抗剪性能，本次试验共制作9根体外预应力无腹筋UHPC梁，试验参数包括预应力的大小、剪跨比、纵向配筋率和钢纤维掺量，通过四点加载方法分析试验构件的破坏形态、开裂强度和极限强度。试验结果表明：无预应力无腹筋UHPC梁在剪跨比为1.0加载时发生弯曲破坏，设置钢绞线25%极限强度张拉值使无腹筋UHPC梁的正截面抗弯能力得到强化，弯矩增幅为157%，使试验梁从弯曲破坏转变为剪切破坏。张拉25%和40%控制应力的UHPC梁的开裂荷载分别提高了1.2倍和2.6倍，有效抑制了裂缝的形成。体外预应力张拉40%控制应力，剪跨比为1.0和1.5时UHPC梁均发生剪切破坏，但是剪跨比增大至2.0时，UHPC梁发生弯曲破坏，受压区混凝土压溃。规范中的抗剪公式均低估了体外预应力无腹筋UHPC梁的抗剪承载力，其斜截面抗剪强度的实验值与计算值之比的平均值分别为2.28和3.21。Abstract: In order to study the shear behavior of ultra-high performance concrete (UHPC) beams without stirrups, 9 externally prestressed UHPC beams without stirrups were fabricated. The experimental parameters included the level of prestress, shear span-to-depth ratio, longitudinal reinforcement ratio and volume fraction of steel fibers. Four-point loading method was used to obtain the failure patterns, cracking strength and ultimate strength. The results show that the non-prestressed UHPC beam under the shear span-to-depth ratio of 1.0 suffers from flexural failure. However, the flexural resistance of the normal section of UHPC beam is strengthened by a prestressing tension of 25% ultimate strength of the strands, resulting in an increase of the flexural moment by 157% and turning into a shear failure. Compared with non-prestressed UHPC beam, the cracking loads of UHPC beams tensioned by 25% prestress and 40% prestress increase by 1.2 times and 2.6 times, respectively, which effectively inhibit the formation of cracks. The UHPC beams with 40% prestress under shear span-to-depth ratio of 1.0 and 1.5 fail in shear. However, when the shear span-to-depth ratio increases to 2.0, the UHPC beam suffers from a flexural failure, which leads to concrete crushing in the compression zone. The formulae of the codes underestimate the shear capacity of the externally prestressed UHPC beams, since the average ratios of the experimental shear capacity to the calculated one of the inclined section are 2.28 and 3.21, respectively.
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图 3 加载装置及测点布置
Figure 3. Loading devices and measuring points
V1-V5—Vertical displacement transducers; H1—Horizontal displacement transducer; L1, L2—Force sensors; G–S1—Strain gauge on steel wire; G–G1, G–G2—Strain gauges on concrete surface
图 5 剪跨比λ对无腹筋UHPC试验梁的破坏影响的细节照片
Figure 5. Photos of effect of shear span-to-depth ratio λ on failure of UHPC beams without stirrups
表 1 无腹筋超高性能混凝土(UHPC)梁设计参数及命名
Table 1. Design parameters and nomenclature of ultra-high performance concrete (UHPC) beams without stirrups
Number Specimen Prestress
level/%Longitudinal
reinforcements ratio/%Volume fraction of
steel fibers/%Shear span-to-depth
ratioBeam1 P0-L2-2vol%-R1 0 2.0 2.0 1.0 Beam2 P1-L2-2vol%-R1 25 2.0 2.0 1.0 Beam3 P2-L2-2vol%-R1 40 2.0 2.0 1.0 Beam4 P2-L2-2vol%-R1.5 40 2.0 2.0 1.5 Beam5 P2-L2-2vol%-R2 40 2.0 2.0 2.0 Beam6 P2-L1-2vol%-R1 40 1.0 2.0 1.0 Beam7 P2-L3-2vol%-R1 40 3.0 2.0 1.0 Beam8 P2-L2-1vol%-R1 40 2.0 1.0 1.0 Beam9 P2-L2-1.5vol%-R1 40 2.0 1.5 1.0 
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表 2 UHPC力学性能
Table 2. Mechanical properties of UHPC
Volume fraction of
steel fiber/vol%1.0 1.5 2.0 ${f_{{\rm{cu}}}}$/MPa 163 179 171 ${f_{{\rm{ts}}}}$/MPa 12 14 16 ${f_{{\rm{ct, fl}}}}$/MPa 27 30 31 ${\sigma _{{\rm{f}}1}}$/MPa 4.31 5.62 8.94 ${\sigma _{{\rm{f2}}}}$/MPa 2.65 3.46 5.50 ${E_{\rm{c}}}$/MPa 39243 39928 40983 Notes: ${f_{{\rm{cu}}}}$—Cubic compressive strength; ${f_{{\rm{ts}}}}$—Splitting tensile strength; ${f_{{\rm{ct, fl}}}}$—Flexural strength; ${\sigma _{{\rm{f}}1}}$—Tested post-cracking strength; ${\sigma _{{\rm{f2}}}}$—Post-cracking strength for design; ${E_{\rm{c}}}$—Elastic modulus.
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表 3 预应力张拉封锚后无腹筋UHPC梁应变值
Table 3. Strain value of UHPC beams without stirrups after prestress anchorage
Number Steel strand Longitudinal reinforcement Bottom of UHPC beam Top of UHPC beam Strain/10−6 Stress/MPa Strain/10−6 Stress/MPa Strain/10−6 Stress/MPa Strain/10−6 Stress/MPa Beam1 0 0 0 0 0 0 0 0 Beam2 1546 301 −90 −18 −295 −12 45 2 Beam3 2577 503 −83 −17 −465 −19 129 5 Beam4 2724 531 −110 −22 −520 −21 123 5 Beam5 2476 483 −35 −7 −712 −29 99 4 Beam6 2832 552 −110 −22 −556 −23 130 5 Beam7 2476 483 −55 −11 −429 −18 85 3 Beam8 2557 499 −130 −26 −232 −9 111 4 Beam9 2582 503 −29 −6 −416 −17 126 5
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表 4 无腹筋UHPC梁的应力与应变值
Table 4. Stress and strain of UHPC beams without stirrups
Number Steel strand Longitudinal reinforcement Bottom of UHPC beam Top of UHPC beam Strain/10−6 Stress/MPa Strain/10−6 Stress/MPa Strain/10−6 Stress/MPa Strain/10−6 Stress/MPa Beam1 0 0 2397 479 3566 146 −1714 −70 Beam2 4832 942 1 915 383 2257 92 −2220 −91 Beam3 6077 1185 504 101 553 23 −2733 −112 Beam4 5820 1135 76 15 1110 45 −2347 −96 Beam5 8236 1606 145 29 755 31 −3452 −141 Beam6 6046 1179 239 48 290 12 −1735 −71 Beam7 4078 795 271 54 1243 51 −1670 −68 Beam8 5535 1079 550 110 1183 48 −2114 −86 Beam9 5717 1115 285 57 604 25 −1 845 −75
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表 5 实验结果汇总
Table 5. Summary of test results
Number Specimen name Cracking load/kN Northern load/kN Southern load/kN Failure mode Tested peak load/kN Beam1 P0-L2-2vol%-R1 50 170 180 Flexural failure 175 Beam2 P1-L2-2vol%-R1 110 424 450 Southern shear failure 450 Beam3 P2-L2-2vol%-R1 180 486 513 Northern shear failure 486 Beam4 P2-L2-2vol%-R1.5 150 330 346 Southern shear failure 346 Beam5 P2-L2-2vol%-R2 90 283 305 Flexural failure 294 Beam6 P2-L1-2vol%-R1 160 435 451 Southern shear failure 451 Beam7 P2-L3-2vol%-R1 160 485 494 Northern shear failure 485 Beam8 P2-L2-1vol%-R1 150 427 457 Northern shear failure 427 Beam9 P2-L2-1.5vol%-R1 120 456 459 Southern shear failure 459
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表 6 无腹筋UHPC梁斜截面抗剪强度的实验值与计算值
Table 6. Experimental and calculated values of shear strength on the inclined section of UHPC beams without stirrups
Number Vu,test /kN French code NF P 18-710[24] Chinese code GB 50010—2010[29] Vc/kN Vf/kN Vu1/kN Vu,test/Vu1 Vc/kN Vp/kN Vu2/kN Vu,test/Vu2 Beam1 175 37.1 182.9 219.9 0.80 140.0 0.0 140.0 1.25 Beam2 450 41.1 182.9 224.0 2.01 140.0 4.2 144.2 3.12 Beam3 486 43.5 182.9 226.4 2.15 140.0 7.0 147.0 3.31 Beam4 346 43.5 182.9 226.4 1.53 140.0 7.4 147.4 2.35 Beam5 294 43.5 182.9 226.4 1.30 116.7 6.8 123.4 2.38 Beam6 451 43.5 182.9 226.4 1.99 140.0 7.7 147.7 3.05 Beam7 485 43.5 182.9 226.4 2.14 140.0 6.8 146.8 3.30 Beam8 427 42.8 88.2 130.9 3.26 105.0 7.0 112.0 3.81 Beam9 459 44.3 115.0 159.2 2.88 122.5 7.0 129.5 3.54 For all beams Mean of Vu,test/Vu1=2.01; STDEV=0.76 Mean of Vu,test/Vu2=2.90; STDEV=0.79 For shear-failure beams Mean of Vu,test/Vu1=2.28; STDEV=0.59 Mean of Vu,test/Vu2=3.21; STDEV=0.46 Notes: Vu,test—Tested shear strength; Vu1—Calculated shear strength of French code; Vu2—Calculated shear strength of Chinese code; Vc—Calculation of UHPC contribution; Vf—Calculation of fiber contribution; Vp—Calculation of prestress contribution.
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