Shear performance of ultra-high performance concrete deep beams

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0. introduction

Ultra High Performance Concrete (UHPC) has ultra-high compressive strength, certain tensile strength, and good durability, and has great application prospects in civil engineering structures. A large amount of research on the stress performance of UHPC structures has been carried out^[1-4]In terms of the shear performance of beams, previous research has mainly focused on UHPC short beams and shallow beams^{[5, 6-12]}Some UHPC structural design specifications or guidelines, such as France (AFGC 2013), Switzerland (SIA 2052), Japan (JSCE 2006), etc., have provided relevant design calculation methods^[13-14].

Deep beams have a wide range of applications in engineering, such as shear wall bottom conversion beams, basement wall foundation beams, and transverse diaphragm beams in bridge structures. Extensive research has been conducted on the shear performance of ordinary concrete and high-performance concrete deep beams^[15-22]With the continuous deepening of research and application of UHPC structures^[23]Recently, people have begun to pay attention to the application of UHPC in deep beams, and corresponding research has also begun on its shear performance. Aziz et al^[24]Shear performance tests were conducted on 9 UHPC deep beams, 3 C40 concrete deep beams, and 3 C60 concrete deep beams. The results showed that the concrete strength and shear span ratio had a significant impact on the shear bearing capacity of the beams. When the concrete strength changed from C40 to C60 and C140, the shear bearing capacity of the beams increased by 40% and 150%, respectively. The shear span ratio had a more significant impact on the shear diagonal cracks of the beams than on the bending cracks; Fahmi et al^[25]By changing the shear span ratio and silica fume content, shear performance tests were conducted on 7 UHPC beams. The results showed that the shear span ratio not only affects the shear bearing capacity of the beams, but also the failure mode of the beams. When the shear span ratio exceeds 1.75, the beams will undergo bending failure. The increase in silica fume content is beneficial for the accumulation of UHPC matrix particles and improves the microstructure of the matrix, thereby increasing the shear bearing capacity of the beams; Muhaison et al^[26]Shear performance tests were conducted on six UHPC deep beams with different steel fiber contents and hole sizes using monotonic and repetitive loading methods. The results showed that under monotonic and repetitive loading, there was little difference in the ultimate load of different types of deep beams, and the influence of steel fibers on the shear strength of beams was significant. Under repetitive loading, the ultimate load of 1% steel fiber perforated deep beams was 2.27 times smaller than that of un perforated deep beams.

1. 试验概况

1.1 试件

Figure  1.  Details of deep beam specimen (unit: mm)

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1.2 Test piece material

Cement is made of P O 42.5 cement; SiO in silica fume₂The content is greater than 90%, and the specific surface area is 1.89 × 10⁴m²·kg^-1Fine sand particle size not exceeding 0.63 mm, with an average density of 2600 kg · m^-3The water reduction rate of CX-8 polycarboxylate superplasticizer is over 25%; Adopting straight drawn SSF ultra strong steel fibers, with a nominal diameter of about 0.2 mm, a nominal length of about 13.0 mm, a length to diameter ratio of about 65.0, an elastic modulus of 200 GPa, and a tensile strength of 2200~2350 MPa.

Table  1.  Mix proportion of UHPC

材料	水泥	硅灰	石英砂			石英粉400目	减水剂	水	钢纤维/%
			40~70目	20~40目	10~20目
配合比	1.00	0.30	0.14	0.41	0.53	0.09	0.03	0.21	0.5~3

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Table  2.  Mechanical properties of UHPC

试件编号	v/%	fc/MPa	fu/MPa	ft/MPa	E/GPa	fs/MPa
L1-1	0.5	113.4	132.3	6.18	44.9	14.1
L1-2	1.0	125.6	145.5	7.19	45.6	15.1
L1-3	2.0	151.4	175.2	9.54	46.2	19.5
L1-4	3.0	173.6	198.6	13.56	47.9	26.6
L2-1	0.0	46.9	53.3	3.24	38.5	7.4
L2-2	0.0	86.5	98.3	4.23	41.7	9.8

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1.3 试验装置、加载制度与数据采集

The deep beam is loaded using a 10 MN electro-hydraulic servo long column pressure testing machine. The jack is lifted upwards from the bottom of the specimen, and a 100 mm × 150 mm × 90 mm steel pad is used to load the component through a steel reaction frame. The loading device is as follows:Figure 1As shown. Pre loading was carried out before formal loading to eliminate inelastic strain and to inspect the loading equipment. The preloading shall not exceed 5% of the calculated bearing capacity of the test beam.

During the formal test, graded loading is used, with each level of load holding for 3-5 minutes. Load 20 kN per level before the specimen cracks. After the occurrence of abdominal shear cracks, load 50 kN per level. When the load reaches 80% of the ultimate load, load with displacement control.

In the experiment, the DH3816 static strain testing system was used to automatically collect the vertical displacement, concrete strain, and steel bar strain in the middle of the mid span and shear span sections. The strain of concrete includes the strain distributed along the inclined section of the shear compression zone and the height direction of the section, while the strain of steel bars includes the strain of longitudinal bars, horizontal web bars, and stirrups.

Figure  2.  Layout of measuring points

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2. 试验结果分析

2.1 Testing process

Figure  3.  Load to mid-span deflection curves of specimens

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Figure  4.  Cracks in specimens at failure

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For UHPC deep beams, when the load is 13% to 22% of the ultimate load, bending shear cracks first occur, and when the load reaches 18% to 34% of the ultimate load, belly shear diagonal cracks occur. For L1-1 and L1-2 beams with low steel fiber content, after the occurrence of diagonal cracks in the belly shear, the stiffness is weakened to a certain extent and the curve shows nonlinearity. However, for L1-3 and L1-4 beams with high steel fiber content, The tensile strength of UHPC is relatively high, and the bridging effect of steel fibers is obvious. Cracking has little effect on the stiffness of the beam, and the load deflection curve at mid span still develops approximately in a straight line. Subsequently, as the load increases, the bending shear crack extends upward from the bottom of the beam, and the web shear diagonal crack extends from the middle of the line connecting the loading point and the support to both ends. When the Type 2 crack extends to a depth of 100 mm below the loading point, the load reaches about 80% of the ultimate load, and the structural stiffness further decreases. When the ultimate load is reached, the widest diagonal crack develops into the main diagonal crack, the longitudinal reinforcement yields, the concrete in the shear compression zone reaches compressive strength, and the deep beam undergoes shear compression failure.

For C40 and C80 concrete deep beams, when the load reaches 15% to 16% of the ultimate load, the first bending shear crack appears, but the development of the bending shear crack is not obvious. When the load reaches 43% to 49% of the ultimate load, diagonal shear cracks will occur. After the occurrence of diagonal cracks in the belly shear, the stiffness of the beam weakened significantly, and the curve showed a noticeable turning point. Subsequently, as the load increased, the diagonal cracks in the belly shear developed rapidly towards the loading point and the support. Finally, without yielding the longitudinal bars, the concrete in the compression zone was crushed and the specimen suffered from oblique compression failure. Due to the small diameter of the rollers on the supports, concrete cracking and peeling occurred at the supports of C40 and C80 concrete deep beams during the testFigure 4The main reason for the uneven deflection of the load span of L2-1 and L2-2 beams.

2.2 Mechanism of stress on beams and arches

By substituting equation (2) into equation (1) and organizing it, we can obtain

Figure  5.  Shear transfer for each type of stress mechanism in beam

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For shallow beams, the force mechanism of the beam dominates, and the influence of the arch force mechanism can generally be ignored. For deep beams, the arch force mechanism dominates, so its influence cannot be ignored. Research has shown that shallow beams^[27]Short beams^[33]Generally, the assumption of a flat section is satisfied, while deep beams do not meet the assumption of a flat section, mainly due to the influence of the arch's stress mechanism.

Figure  6.  Load-hoop strain curves of specimen L1-3

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Figure  7.  Forces of free body of deep beam

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InsulatorBCEDSimilar to applying a pair of prestress, the deep beamABCWhen the load is large, the concrete at a distance from the pressure line will experience tensile stress. When the tensile stress is greater than the ultimate tensile strength of the concrete, a reverse arch phenomenon will occurFigure 4 (e)、(f)The cracks shown in. For four UHPC deep beams (L1-1~L1-4), Due to its high tensile strength, there were no tensile cracks present here.

3. Shear bearing performance of UHPC deep beams

The ultimate load of all specimens and the incremental shear bearing capacity based on the L2-1 specimen are as follows:Table 3As shown.

Table  3.  Results of shear bearing capacity tests on deep beams

试验梁	fu/kN	受剪承载力Ve/kN	增量/%	破坏形态
L2-1	53.3	466.07		斜压破坏
L2-2	98.3	609.42	30.76	斜压破坏
L1-1	132.3	873.31	87.38	剪压破坏
L1-2	145.5	1 089.40	133.74	剪压破坏
L1-3	175.2	1 356.96	191.15	剪压破坏
L1-4	198.6	1 407.18	201.92	剪压破坏

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Figure  8.  Relationship curves between shear bearing capacity and concrete strength in deep beam

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According to the analysis in section 2.2, UHPC deep beams, like C40 and C80 concrete deep beams, have arch and beam effects when subjected to shear, so a tension compression bar model can be used for calculation. The calculation of shear bearing capacity of concrete deep beams in the "Code for Design of Concrete Structures" (GB 50010-2010) is based on the truss arch model and the span to height ratiol₀/h(l₀Calculate the span length for the beam,hTaking the beam height as a variable, the tension compression rod model of the deep beam is regarded as an extension of the shallow beam truss arch model, and the calculation method for the shear bearing capacity of shallow beams and deeply bent members is unified.

The calculation of the shear bearing capacity of ordinary concrete deep beams in the "Code for Design of Concrete Structures" (GB 50010-2010) is based on the shear compression failure of specimens. The test results of UHPC deep beams in this paper are also shear compression failure. Therefore, it is feasible to refer to the calculation formula of the shear bearing capacity of ordinary concrete deep beams for the calculation of UHPC deep beams. The specific calculation formula is

$\begin{array}{l}V{}_{\text{e}}\le \frac{1.75f{}_{\text{t}}bh{}_0}{\lambda +1}+\frac{l{}_0/h-2}{3}f{}_{\text{v}}\frac{A{}_{\text{v}}h{}_0}{s{}_{\text{h}}}+\\ \frac{5-l{}_0/h}{6}f{}_{\text{h}}\frac{A{}_{\text{h}}h{}_0}{s{}_{\text{v}}}(4)\end{array}$

In the formula:λCalculate the shear span ratio for the beam, whenl₀/h< At 2 o'clock, takel₀/h=2, λTaking 0.25, in order to prevent instability of the beam, the specifications have set it separatelyλThe upper and lower limits are 0.92l₀/h-1.58 and 0.42l₀/h-0.58, which means the span to height ratio range of deep beams is 1.38 ≤l₀/h≤1.72;bThe width of the beam section;f_vandf_hThe design values of tensile strength for hoop reinforcement and web reinforcement respectively;A_vandA_hThe cross-sectional areas of the hoop reinforcement and web reinforcement are respectively;s_vands_hThey are the spacing between the hoop reinforcement and the horizontal web reinforcement.

Substituting the parameters of 6 deep beam specimens into equation (4), the average ratio of the calculated shear bearing capacity of UHPC deep beams to the experimental value is 0.89, with a mean square error of 0.15. Equation (4) is the design formula, wheref_tThe measured uniaxial tensile strength of concrete is used in the calculation of experimental beams. FromFigure 8It can be seen that the calculation results in the "Code for Design of Concrete Structures" (GB 50010-2010) also show an exponential growth relationship with concrete strength, similar to the experimental law, and most of the calculation results are smaller than the experimental values. Therefore, until a more accurate calculation method is available, it can be temporarily used for the shear bearing capacity calculation of UHPC deep beams.

4. conclusion

(2) During the entire stress process of UHPC deep beams, both beam and arch stress mechanisms coexist. When the load is less than 50%~70% of the ultimate load, the beam stress mechanism plays a dominant role, and then the arch stress mechanism plays a dominant role, and some stirrups in the shear span section change from tension to compression. Compared with C40 and C80 concrete deep beams, The cracks in UHPC deep beams are numerous and dense.

(3) The shear bearing capacity of the test beam calculated using the method in the "Code for Design of Concrete Structures" (GB 50010-2010) is similar to the experimental value, and most of the calculated results are smaller than the experimental value. Therefore, until a more accurate calculation method is available, it can be temporarily used for the shear bearing capacity calculation of UHPC deep beams.

(4) Due to the limited number of specimens in this article, The precise algorithm for the shear bearing capacity of UHPC deep beams still needs further development. At the same time, for the L1-4 beam with the highest concrete strength (198.6 MPa), the calculated value in the "Code for Design of Concrete Structures" (GB 50010-2010) is significantly higher than the experimental value, and the reasons for this need further research. Therefore, a thorough analysis of the shear stress mechanism of UHPC shallow beams, short beams, and deep beams, and the construction of compatible and continuous calculation formulas by considering various factors, are also the next steps that need to be studied.