Experimental study of the bearing capacity of compressed steel struts of an I-beam profile in conditions of constrained torsion

. Wide application in the construction of thin-walled steel rods of an open profile requires taking into account the peculiarities of the work of load-bearing structural elements under the action of the entire complex of loads. For a number of rod systems consisting of I-beam profiles, it is impossible to exclude torsion under the action of compressive forces, which leads to the appearance of additional normal stresses in the profile. In this regard, it is necessary to study the actual operation of compressed I-beams under the action of torsional loads. The bearing capacity of a compressed I-beam profile strut with constrained torsion is considered. The method of conducting an experimental study of a centrally and off-center compressed I-beam profile strut under the action of longitudinal force and bimoment is presented. The analysis of the effect of the bimoment on the bearing capacity of a centrally and off-center compressed thin-walled rod of an open profile with constrained torsion is performed. The bearing capacity of the centrally and off-center compressed I-beam profile strut from the action of longitudinal force and bimoment was experimentally determined, which was compared with the results of numerical calculations in finite element formulation, taking into account geometric and physical nonlinearity in conditions of constrained torsion. According to the results of the experiment, the possibility of using numerical modeling to assess the stability of centrally and off-center compressed thin-walled rods was established. open profile with constrained torsion under various schemes of external force.


Introduction
Steel structures made of thin-walled open-profile rods are widely used in backyards and structures for various purposes.Basically, rod structures are designed so that the individual elements forming the structure work for compression or stretching with bending in one or two planes.However, for a number of rod systems, it is impossible to completely prevent torsion.The operation of thin-walled steel rods in conditions of pure torsion has been studied in detail, the calculation and design of such systems is carried out taking into account the requirements and recommendations of existing regulatory documents.It is worth noting that pure torsion, assuming the freedom of deplanation of cross sections, practically does not occur in real operating conditions of structures made of thin-walled steel rods.This is due to the peculiarities of the operation of the support nodes and the coupling of the rods.In the nodes, as a rule, free deplanation is impossible, and due to the constraint of the deplanation of the cross sections in the rod, additional normal and tangential stresses develop from constrained torsion.A significant number of works of domestic and foreign scientists have been devoted to experimental studies of the operation of thin-walled steel open rods in conditions of constrained torsion.Initially, with constrained torsion, the operation of thin-walled steel structures made of open-profile rods with elastic steel work was experimentally studied.It was found that when the deformation is constrained, the torsion of such rods is accompanied by the occurrence of additional normal stresses in the rod.During bending or compression, normal stresses due to constrained torsion lead to an earlier onset of plastic deformations in steel and exhaustion of the bearing capacity of the thin-walled rod being tested [1][2][3][4][5][6][7][8][9].The critical condition of a bent or compressed rod when calculating stability is characterized not by qualitative, but by quantitative changes in constrained torsion, due to the action of the bimoment as a torsional load.At the same time, it is worth noting that there are no other forms of equilibrium with loss of stability.Further studies [10][11][12] allowed us to establish that an earlier loss of stability of a thinwalled steel element, and, as a consequence, the loss of its bearing capacity occurs when additional sectorial stresses occur under conditions of constrained torsion and significant rotation angles of sections of thin-walled rods, which in many cases are simply unacceptable [13][14][15].In this regard, it is worth making an important practical conclusion: the basis for studying the limiting states of a thin-walled rod in conditions of constrained torsion is not so much strength as some desired amount of twisting deformations [16][17][18][19][20].To date, the solution to this issue has not been reflected in the existing design standards, which does not allow us to assess and determine the impact on the stability and bearing capacity of thin-walled open rods with their constrained torsion.To assess the effect on the bearing capacity with central and off-center compression of constrained torsion, it is necessary to conduct experimental studies.This article presents a methodology for experimental studies of a centrally and off-center compressed steel I-beam rod under the action of a bimoment.Experimental studies were carried out using equipment and with the participation of specialists from the Head Regional Center for the Collective Use of Scientific Equipment and Installations of the NRU MGSU (grant No. 075-15-2021-686) [21].

Materials and Methods
The purpose of the experimental study is to study the operation of steel rods of an open Ibeam profile with constrained torsion under conditions of combined action of longitudinal force and bimoment.The main objectives of the conducted experimental research are as follows: study of the stress-strain state and the process of loss of stability during operation of centrally and off-center compressed steel rods of I-beam profile in conditions of constrained torsion; determination of parameters affecting the bearing capacity of the rods under study; The parameters of the test rods were selected based on the results of numerical studies previously carried out in a nonlinear formulation (in the Femap with NX Nastran software package) and the characteristics of the equipment used for the experiment.Experimental samples are made of I-beam 10B1 according to GOST R 57837-2017.In the lower section, the I-beam is welded to a 30 mm thick plate, which is used for mounting to the press bed.The large thickness of the support plate makes it possible to exclude bending deformations of the I-beams in their supporting part.In the upper section of the I-beam, a 3 mm thick rib is welded, ensuring the immutability of the contour of the section.The load is applied to the sample in the upper section in the form of one or two concentrated forces (Fig. 1).The accepted loading schemes ensured the transfer of centrally or off-center applied force to the upper end and the bimoment.At the height of the I-beam h and the width of the shelf bf, the value of the bimoment was determined by the following formulas.in the first variant, the bimoment is equal to:  = ℎ  /2,, in the second variant:  = ℎ  /4.In the second loading variant, in addition to these loads, two bending moments act on the rod: The loading schemes adopted during the tests made it possible to use a testing machine for complex loading, including torsion, applying only longitudinal force to the sample.At the same time, the bimoment and bending moments changed in proportion to the magnitude of the longitudinal force.Annular stops made of high-strength M10 nuts were welded onto the head of the rod to accurately transfer the concentrated load through the steel balls of the testing machine.In the load application zone, vertical plates made of steel sheet with a thickness of 8 mm are welded to the shelves on both sides, eliminating local loss of shelf stability during loading.
In order to determine the deformations of the fibers of the shelves and the walls of the rods under study and, as a result, the normal stresses that arise, strain gauges of the Russian production type TKFO were fixed to the test racks in ten places-5-120( 5) [22].The sensors were installed in two sections at the base plate and in the upper part of the I-beam.There were 5 sensors in each section.One sensor was attached to the middle of the wall, the other four on the edges of the shelves.To determine the twisting angles, as well as the vertical movements of the shelves of the test rods, 4 electronic digital indicators "IC 0-50 0.01 MICRONS" were installed with a set range of 50 mm and the accuracy of measurements up to 0.01 mm. Figure 2 shows a general view of the tested samples.Figure 3 shows the layout of strain gauges and digital deflection meters

Results
To test the measuring instruments, a trial loading of samples was carried out to stresses not exceeding the yield strength of steel (310 MPa).After the trial loading, the main test of the sample was carried out.The loading of the experimental racks was carried out in stages with a step of increasing the load of 0.3 kN/sec.Each stage consisted of 10 loading steps and was accompanied by a 30-second "shutter speed" to evaluate intermediate results and record all data from measuring sensors.As the applied load increased and the stress-strain state of the test rod approached the limit, there was a significant increase in the difference between the two adjacent readings taken, not only according to the numerical data of the deflection meters, but also visually.As soon as the deformations of the studied strut continued to increase without further increasing the load, the bearing capacity of the rod was taken as exhausted, and the value of the force (bimoment) as the limit.It is worth noting that in the process of conducting experimental studies, there was no local loss of shelf stability.Figure 6 shows a 620 mm long rack after the test.

Fig. 6. Sample after the test
The exhaustion of the bearing capacity of the 620 mm long rack occurred at 58 kN. Figure 7 shows the results of testing a 620 mm long rack with central compression.The figures show the dependence of the stresses at the characteristic cross-section points on the applied load.When the load reaches 58 kN at the points of section 1 and 8 of the stress, I reach the yield point and the growth of deformations overtakes the growth of the load.After reaching the yield point in the shelves, the rack is able to perceive an increasing load.Despite the further increase in the load, it is the load at which the yield point is reached that can be considered the limit.At the same time, significant vertical movements of the points of application of the load, twisting of the upper section, deplaning of the section and bending of the shelves in the plane of the shelves were observed.A further increase in the load is accompanied by a less rapid increase in normal stresses, which indicates the development of plastic deformations in the shelves.At a load of 100 kN, the complete exhaustion of the bearing capacity of the rack is recorded.After unloading, due to the intensive development of plastic deformations, the rack does not return to its original state.Under the action of the maximum load, the compressive normal stresses at points 1 and 8 reached 420 MPa and approached the temporary resistance.At points 2 and 7, tensile normal stresses were applied, reaching values of 240-280 MPa, which is 77-90% of the yield strength.At the lower end, the maximum compressive normal stresses are noticeably less (1.63 times) than at the upper end.This is due to the nonlinear nature of the bimoment distribution, which reaches maximum values at the place of application of the load.Numerical calculation of the experimental sample is performed.The finite element model is shown in Fig. 4. The results of numerical calculation are presented in Fig. 6 in the form of dotted graphs.Comparison of experimental and numerical data showed their good qualitative coincidence.The experimental shape of the deformed sample is close to its shape according to the results of numerical calculation.The value of the load at which normal stresses reach the yield point at points 1 and 8 is from 57 to 65 kN, or on average 61 kN, which is 5.2% more than the experimental value.

Conclusions
Based on the conducted experimental and numerical studies, the following conclusions can be drawn:  Tests of the samples confirmed the possibility of using the developed finite element model for nonlinear analysis of the bearing capacity of centrally compressed I-beam rods under the action of a bimoment. A good qualitative and quantitative correspondence of the test results and numerical calculation has been established.The error in determining the maximum load for a centrally compressed rod under the action of a bimoment was 5.2%. The necessity of placing transverse ribs at the place of application of the load to ensure the non-deformability of the cross-sectional contour in both elastic and elastic-plastic stages of operation has been experimentally confirmed. The distribution of relative deformations over the cross section is fixed in accordance with the law of sectorial areas. After reaching the yield point in the most loaded fibers, a redistribution of stresses from the more loaded sections of the shelves to the less loaded ones was observed. The limiting state of the rods was characterized by a noticeable increase in deformations in the area of external load, an increase in the angle of twisting, deflanation and deflection of the shelves in the plane of the shelves.
This work was financially supported by the Ministry of Science and Higher Education of Russian Federation (grant # 075-15-2021-686).Tests were carried out using research equipment of The Head Regional Shared Research Facilities of the Moscow State University of Civil Engineering

E3S
Web of Conferences 410, 02044 (2023) https://doi.org/10.1051/e3sconf/202341002044FORM-2023 evaluation of the possibility of further operation of I-beam rods taking into account the combined action of longitudinal force, bending moments and bimoment.

Fig. 1 .
Fig. 1.Design scheme of the studied thin-walled I-beam rod: a -central compression; b -off-center compression

Fig. 7 .
Fig. 7. Stress-force graph in the upper section of the rod under central compression: solid linesexperimental data; dotted lines -data obtained by numerical analysis