The University of Hong Kong conducted a comprehensive laboratory test program involving 65 web failure tests of square and rectangular hollow sections of high-strength steel. The slenderness of the sample webs ranged from 8. The reliability analysis was carried out to evaluate the reliability of the prepared web crippling design clauses. So far, many researchers have conducted numerous experiments on the compressive strength or ultimate bearing capacity of the webs of cold-formed steel and high-strength steel.
Now, high-strength cold-formed steel was widely used in practical projects, and it has different mechanical properties and failure modes due to high strength, thin thickness, poor ductility, and other properties. Generally, HSCF thin-walled steel suffers local crippling before global buckling; thus, it is necessary to study its local crippling behavior.
For instance, Li and Young [ 33 ] conducted the web crippling tests of HSCF steel rectangular hollow sections under load conditions at the end and interior, and they also verified the effectiveness of the proposed finite element model FEM by comparing the experimental results with the numerical values.
Meanwhile, the web crippling of HSCF steel tubes under other loading conditions has been studied [ 34 , 35 ], and it is found that the existing codes are not very practical since there is an obvious difference between measured strength and the nominal strength stipulated via codes.
Thus, based on the experimental and numerical results, they evaluated and improved the existing codes about web crippling. And through the method of the comparison, it showed that, t , the current codes of practice are mostly conservative for the design of HSCF tubes subjected to uniform bending moment, but no suitable formula for calculating ultimate bearing capacity was proposed.
Some web crippling tests of HSCF channels were implemented by Young and Hancock [ 37 ], and the results indicated that the web crippling strength was more than half of the predicted value under IOF or ETF loading conditions. Zhou and Young [ 38 ] studied the web crippling of HSCF stainless steel at high temperatures via FEM, and the numerical results showed that the numerical analyses could predict the behavior of web crippling.
In this paper, the web crippling performance of HSCF rectangular steel tubes under concentrated load was studied. The stress and strain distribution at the web area and the total displacement of the loading end were measured. The deformation and failure of HSCF rectangular steel tubes under concentrated load were observed and analyzed, and their ultimate bearing capacity was recorded. Numerical simulations were performed, and their effectiveness was verified via experiments.
Finally, the calculation equations for the ultimate bearing capacity of HSCF rectangular steel tubes were proposed, which could provide a good guidance for future work.
In order to research the web crippling properties of HSCF steel tubes, thirty-six such tubes with different boundary and loading conditions were tested in this paper. The main function of the bearing plate is to ensure that concentrated load is applied locally to the specimen. As mentioned above, specimens are tested under four loading conditions, i. To eliminate the influence of boundary conditions, the distance from the edge of the bearing plate to the end of the specimen was set to the value that is more than 1.
Figure 2 is a schematic of web crippling tests under four boundary and loading conditions, and photos of webs under four boundary and loading conditions are shown in Figure 3.
In Table 1 , the specimens were labeled to easily identify the boundary and loading condition, the nominal dimension of the specimen, the width of the bearing plate, and web crippling ultimate capacity of HSCF rectangular steel tubes Pcr. The material properties of steel used in this paper were determined by standard tensile tests.
Three standard specimens used for tensile testing were sampled from the surface of each HSCF rectangular steel tube. After processing, we use the grinding wheel to Polish the nonsmooth parts of the standard sample. The values of the tensile yield stress, ultimate tensile stress, elongation after fracture, and elastic modulus measured via the tests are presented in Table 2.
When the strain entered plasticity or displacement gauges increased rapidly i. In practice, the upper limit of hierarchical loading is adjusted according to displacement feedback. Three strain gauge rosettes S1—S3 were distributed with the same interval on the web of high-strength cold-formed rectangular steel tube, as shown in Figure 4.
A right angle strain flower is arranged in the upper, middle, and lower part of the web corresponding to the center line of the supporting plate. The failure modes of the HSCF rectangular steel specimen tubular section damaged by the web were out-of-plane buckling of the webs. Obvious plastic hinge area appeared in the middle of the webs. Under IOF boundary and loading conditions, one loading flange was concaved.
The variation parameters of Figures 6 and 7 are the widths of the bearing plate and width-to-height ratio, respectively.
It can be seen from Figures 6 and 7 that the load-displacement curves of all specimens have basically the same trend. During the whole loading process, the deformation of the specimen can be divided into three stages: elasticity, buckling, and failure. The yield of steel is a gradual process, and there is no obvious yield point in the load-displacement curve.
At the failure stage, the bearing capacity does not drop vertically, indicating that the ductility of the component is good. According to Figure 6 , we can find that the ultimate bearing capacity increases with the increase of the width of the bearing plate under the condition of the same length-width ratio of section and loading conditions. In addition, it can be seen that the specimens subjected to interior bearing load have higher ultimate strength and deformation capacity.
Based on Figure 7 , we can find that the ultimate bearing capacity increases with the increase of length-width ratio of section under the condition of the same bearing plate width and loading conditions. Meanwhile, it can be seen that specimens subjected to interior bearing load have higher ultimate strength and deformation capacity.
The strain gauge used in this paper is resistance strain gauge. Data were collected through the collection box of DH static strain test system, and the actual collected strain data of the collection box requires calibration. It is found that the actual strain value should be divided by The section length-width ratios of specimen are 2, 1.
The distribution of strain measuring points is shown in Figure 4. The results show that the strain measuring point S2 in the middle of the compression web under four boundary and loading conditions all enter into plasticity.
Except for the test point S1 on the upper side of the web under the loading condition of the inner flange, the other test points on the upper and lower parts did not enter the plasticity.
Based on results in Figures 8 and 9 , when the steel tubes are in the elastic stage, the strain of the specimens increases linearly with the increase of load. When the steel tubes enter the elastic-plastic stage and the plastic stage, the strain value suddenly increases, and the specimens begin to buckle.
The change of strain reflects that the change of specimens is consistent with the test phenomena. The ultimate bearing capacity and the deformation capacity of the specimen increase with larger width of the bearing plate, as depicted in Figure 8.
Moreover, we can see from Figure 9 that the ultimate bearing capacity of specimens with the length-width ratio of 2 is the highest, followed by specimens with the length-width ratio of 1.
This indicates that the ratio of width to height is proportional to the ultimate bearing capacity. After entering the plastic stage, the specimens with smaller width-to-height ratio have lower ductility. Since the bearing capacity of the specimen with a small bearing plate width is low, the strain of the specimen with a small bearing plate width is large under the same load.
Currently, many kinds of finite element software have been developed and put into use, and ABAQUS is a powerful and widely used engineering simulation software, ranging from solving linear analysis problems to analyzing complex nonlinear problems. As a widely used simulation tool, it can not only solve a large number of structural stress-displacement problems but also address other engineering fields.
By comparing the stress curves and buckling modes of the rectangular with triangular stiffeners, it is found that the shear capacity of the cold-curved thin-walled section steel with the rectangular stiffeners is the most obvious. Ren et al. Cevik [ 42 ] used the programming method to establish the web buckling strength calculation formulas of various cold-formed components under various working conditions and compared with the test results and the current strength calculation standard formula to verify its accuracy.
Young and Ellobody [ 43 ] carried out experimental research on three cold-curved thin-wall equilateral rolled triangular section columns with different lengths and different thicknesses fixed at both ends.
By comparing the test results with the results simulated by ABAQUS finite element software, they found that the finite element software could accurately simulate the forces on the components.
During the simulation, the surface load was applied to the bearing plate. The yield strength, ultimate tensile strength, and elastic modulus of the material were obtained via measured values in the tests. In addition, the eight-node solid element with reduced integration C3D8R was used to simulate high strength cold-formed rectangular tube and the bearing plates. The residual stress of cold-formed thin-walled steel members is closely related to the production process.
Rolling and bending are the two most common cold bending methods. The residual stress mainly consists of bending stress and membrane stress. The film stress is the most common in the rolled member, which is generally distributed in the corner of the member, so the residual stress at the corner is large.
Moen et al. The bending stress is mainly determined by the processing technology of cold-formed thin-walled steel members, which is not considered here. Then, to verify the accuracy of the proposed numerical model of HSCF rectangular tubes under web crippling, we analyzed thirty-six high strength cold-formed rectangular steel tubes with web failure and compared the finite element results to experimental values.
The simulation results of failure modes and ultimate bearing capacity of HSCF rectangular steel tubes subjected to web crippling were also compared with the test results. The experimental results of failure modes as shown in Figure 5 of HSCF rectangular tubes under web crippling were compared with the numerical prediction results, as illustrated in Figure It can be seen that the failure mode predicted by the numerical method is in good agreement with the experimental results.
Moreover, the comparison of the ultimate bearing capacity between the tests and numerical analyses is presented in Table 3.
The test results conform to the numerical analyses with the maximum error of 3. Overall, the results demonstrate that the test results are in good agreement with the numerical simulation in the web crippling strength and failure mode. Figures 11 and 12 show the load-displacement curves obtained by experiment and finite element simulation, respectively. It is found that the load—displacement curves obtained by experiment and the finite element method are in good agreement.
Based on material strength failure of HSCF rectangular steel tubes under local compression, the calculated value of the Chinese steel structures design code is much higher than the test value. On the other hand, the influence of the bearing plate width on web crippling strength is ignored in the European steel structures design code, which tends to be conservative. Regarding that the calculation of ultimate bearing capacity in European steel structures design code is complicated and conservative, we developed new calculation equations 1 — 4 of web ultimate bearing capacity for HSCF rectangular steel tubes in this paper by considering the influence of the bearing plate width.
The calculation results conform to the experimental values well. The average values of the ratios of calculated values and test values for the four formulas of boundary and loading modes are 0. The coefficients of variation are 0. The comparison results are given in Table 3. In this paper, the experimental and numerical investigations are conducted on high strength cold-formed HSCF rectangular steel tubes under concentrated loading at web positions along the transverse direction.
Some conclusions can be drawn as follows: 1 The ultimate capacity of HSCF rectangular steel tubes under web crippling increases with larger bearing plate width and width-to-height ratio 2 The HSCF rectangular steel tube subjected to interior bearing load has higher ultimate strength and deformation capacity than the counterpart that is subjected to end bearing load 3 Under the same width of bearing plates, the ultimate bearing capacity and deformation capacity of HSCF rectangular steel tubes do not change significantly under four loading conditions 4 Finite element model is established, and the comparison between it and experimental results demonstrates that the proposed numerical model can accurately predict the behavior of HSCF rectangular steel tubes under web crippling 5 The calculation equations of web ultimate bearing capacity for HSCF rectangular steel tubes are developed in this paper, and they can predict the experimental values well.
Recent literature has reported the efficiency of the piezoelectric transducers enabled the structural health monitoring method [ 45 , 46 ] and the percussion-based method [ 47 ] in detecting structural damages; we will apply these approaches to identify the damages in the high strength cold-formed rectangular steel tubes in the future.
The data are real and reliable in this paper, including original experimental data and software analysis data. The data used to support the findings of this study are available from the corresponding author upon request. The authors expressed their gratitude to Xinfeng Steel Processing Plant for the processing of test specimens. The support provided by the laboratory staff is gratefully acknowledged. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Journal overview. Special Issues. Academic Editor: Jiang Jin. Received 01 Jul Revised 13 Sep Accepted 16 Oct Published 29 Oct Abstract To research the web crippling performance i.
Introduction The past decades have seen the rapid advances in structural engineering, and many new structural materials and configurations, such as cold-formed steel [ 1 ], high-strength steel HHS [ 2 — 4 ], concrete-filled steel tubes CFSTs [ 5 — 7 ], and fiber-reinforced polymer FRP structures [ 8 — 10 ], have been developed and applied to engineer practice. Experimental Investigation 2. Test Specimens In order to research the web crippling properties of HSCF steel tubes, thirty-six such tubes with different boundary and loading conditions were tested in this paper.
Figure 1. Figure 2. Schematic of web crippling tests in four boundary and loading conditions. Figure 3. Photos of web crippling tests under four boundary and loading conditions. Table 1. Parameter sand ultimate capacity of rectangular steel tubular sections under web crippling.
Table 2. Figure 4. Figure 5. Photos of failure modes under four boundary and loading conditions. This limit state is to be checked at each location where a concentrated force is applied transverse to the axis of a member. SCM specification J The basic limit state follows the standard form. The statement of the limit states and the associated reduction factor and factor of safety are given here:. The two equations are needed to account for the difference in available web material between the web at the end of the beam and the web away from the end of the beam.
The same principle was discussed in the section on web yielding. It is a buckling equation and has numerous terms. Equations J apply at the ends of the member. The two equations are slightly different and depend on the ratio of bearing length to overall depth of the beam.
The given spreadsheet example computes the reaction capacity, R n , as controlled by web crippling for a typical W section. The input values are in the grey shaded cells and the results in the yellow highlighted cells.
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