Torsional behavior of triangular web profile (TRIWP) steel section by experimental study

Abstract

A triangular web profile (TriWP) is a modified section where the flanges are connected to a web plate of triangular profile. This study examined the torsional behavior of TriWP steel sections and compared to that of the flat web (FW) steel sections. Three types of specimen sizes were used: 180 mm × 75 mm × 5 mm × 2 mm, 200 mm × 100 mm × 8 mm × 6 mm, and 200 mm × 100 mm × 6 mm × 5 mm. All the specimens were loaded vertically until the maximum load was achieved and then the load was released. For both types of specimens, it was observed that the torsional rotation for bigger size [200 mm × 100 mm × 8 mm × 6 mm] were smaller than that of smaller size [180 mm × 75 mm × 5 mm × 2 mm] of the specimens. At the maximum torsional loading, the experimental result was compared to the theoretical calculation. The comparison showed that the percentage difference ranged from 1.10% to 16.80%. From the graph of torsional load versus rotational angle, the torsional rotation for all TriWP steel sections were smaller than that of the FW steel section under the same torsional loading i.e., 0.2 kNm and 1 kNm. The range between FW and TriWP were 3.74 to 71.83 at 0.2 kNm while 14.5 to 75.1 at 1.0 kNm. The findings were shown that the TriWP steel sections had better resistance against torsion in comparison to FW steel section.

Keywords

corrugated web / i-beam / non uniform steel section / torsion resistance / torsion angle / triangular web profile steel section

Introduction

Steel is widely used as a building material in steel construction. This is because of a number of factors, including its mechanical properties, available in a variety of useful and practical shapes, economy, design simplicity, and ease and speed of construction. Steel can be produced with a variety of properties to suit the different requirements. The principal requirements are strength, ductility, weldability, and corrosion resistance. With those advantages, though, come some challenges that are best solved by better understanding of how the metals actually performed in a structure [ 1]. Resistance to uniform torsion and resistance to uniform warping resulted from torsion in the thin-walled open section member. Resistance to uniform torsion was developed by shear stresses which vary linearly across the thickness of the section wall while resistance to uniform warping developed with equal and opposite flange bending and shear action [ 2].

Recently considerable research on the problem of non-uniform torsion bars of variable cross section with pioneer of work has been done by Sapountzakis and Mokos [ 3] adopting the boundary element method (BEM). They investigated approximate method in the analysis of a symmetric core structures in tall buildings subjected to torsion. By assuming that the core twist about a fixed vertical axis of rotation, a closed form of the solution was achieved [ 4]. Several researchers had dealt with the steel members for the shear strain distribution, and combined bending and torsion [ 2, 5, 6]. The beam undergoes large rotation before failure. To predict the same behavior of beam without slender elements, the beam was modeled using finite element analysis as beam elements or shell element. In the case of beams with slender elements, local buckling influences the behavior [ 2]. Investigations into behavior, analysis and design of member subjected to combined torsion and bending was done [ 2]. In the first study, the torsion loads were considered to be resisted by uniform torsion alone, and the plastic collapse load factor was determined by using the sand heap analogy. In the second study, only warping torsion was considered, and the plastic collapse mechanisms of the flange were analyzed as in the plastic analysis of beam bending.

Corrugated webs were used to increase the resistance against torsion of the steel webs of beams and to increase the stiffness of the beam. Eldib [ 7] presents shear buckling strength and design of curve corrugated steel webs of bridges. The curve corrugated webs provides high shear buckling strength and produces light weight steel webs related to trapezoidal corrugated web. Moreover, previous researches have been carried out to study the performance of corrugated steel web subjected to shear behavior, pure torsion, bending behavior, and lateral torsional buckling under pure bending [ 8– 11].

An investigation on the trapezoidal corrugated web by experimental study and finite element study proved that the torsional rotation of the trapezoidal corrugated web was less than the normal flat web beam by 30 percent [ 12]. In addition, research on the trapezoidal corrugated web has been done on shear strength and design, interactive shear buckling behavior and lateral torsional buckling behavior [ 13– 15]. Corrugated steel webs used in the composite bridges have excellent properties, such as short construction period, optimum force distribution, good seismic performance, lightness of girders, efficiency of introducing prestress forces and aesthetics appearance which have greatly improved the application of such bridges [ 16, 17].

Normally flexural members as shown in Fig. 1 are subjected to a combined action of bending and torsion. When horizontally thin-walled member is subjected to vertical loads only, these loads are resisted internally by a combined action of bending and torsion. Although linear theories for elastic bending and torsion of straight members are well established, the failure prediction of beams subjected to both vertical and torsional loading has not been adequately developed.

Triangular web profile (TriWP) steel section

Triangular web profile (TriWP) steel section as shown in Fig. 2 is a built-up steel section made up of two flanges connected to a web plate of triangular profile. This TriWP section is a modified section from trapezoidal web profile steel section where the eccentric stiffeners of trapezoidal section were eliminated and changed to slanting stiffeners [ 18]. Table 1 illustrates some earlier studies done on TriWP.

Experimental study of torsional behavior of TriWP steel section was presented in this paper. The first objective of this research is to conduct an experimental study on torsional behavior of TriWP steel section and the second objective is to compare the torsional resistance of TriWP steel section with that of the flat web (FW) steel section.

The analysis of structures of variable cross section subjected to twisting moments is one of the problems often encountered in the practice of engineering. Beam structures of variable height, long span box shaped bridges and I-shaped steel beam are the most common examples. To overcome this problem, corrugated steel webs have recently been used to replace the stiffened steel webs of plate or box shapes bridges. This research study will prove that the TriWP steel section have better resistance to torsion compared to the flat web steel section through an experimental study.

Numerical study on TriWP subjected to torsion behavior already conducted from previous research by using LUSAS software [ 22].The result of torsional rotation then compared with FW steel section at difference of web and flange thickness. The results of the decreasing value of rotation angle for increasing value of thickness was shown in the Table 2. This was because the thickness of flange and web were inversely proportional with the rotation angle in theory of torsion. Thickness of flange and web have been applied in calculating the value of torsion constant,(J). Figure 3 shows the deformation of TriWP steel section after fail. This type of beam section gave the smaller results on this analysis for differences thickness compared to that of normal flat web section. One of the recommendation from the researchers which is a test using the actual structure can also be done to verify the design manually and compared using finite element analysis. To respond that recommendation, the experimental study will be proposed in this research.

Theory

Torsion

When the torsional moment is subjected at any point along the length of a member, the cross section will rotate through an angle q as shown in Fig. 4. The shear center, s of a cross section located on the longitudinal axis about which the section would twist if torsion acts on the section. No twisting will occur if the resultant force acts through the shear center and resulting zero torsional stresses. The shear center and the centroid, c are not necessarily coincident. However, in rolled I or H section, which is symmetric about both principal axes, the shear center, coincides with the centroid, as shown in Fig. 5.

Non-uniform torsion and warping phenomenon on steel beam

The total resistance of a member to torsional loading is composed of the sum of two components known as ‘uniform torsion’ (known as St Venant torsion) and ‘warping torsion’. When warping is included in the torsional resistance, the member is in a state of ‘non-uniform torsion’. Warping is a phenomenon in a member of thin open section. The torsional response of a thin open section is very different from that of a solid circular shaft, where all cross sections normal to the beam axis remain plane under torsional loading. If the cross section is not circular, plane cross section does not remain plane under torsion: they warp. Warping introduces longitudinal strains as the section twists and significantly affects the torsional stiffness [ 19].

For non-uniform torsion, the rate of change of the angle of twist varies along the length of the member. In this case, the warping deflexions vary along the member and, to resist the applied torque, an additional shear stresses act in conjunction with those due to uniform torsion. The stiffness of the member associated with these additional shear stresses is proportional to the warping rigidity EH, where E is the modulus of elasticity and H is the warping constant. The non-diameter torsion parameter of the member is:

(1) K=\sqrt{（{\displaystyle \frac{n^{Z}EH}{GJL{n}^Z}}）}.

When the torsional rigidity, GJ, of the section is very large compared with the warping rigidity, EH, K becomes small; the member will effectively be in a state of uniform torsion. For example is closed sections, angles and tee sections .Conversely, if the torsional rigidity of the section is very small compared with the warping rigidity, K becomes very large and the member will effectively be in a state of warping torsion. This condition is closely approximated for thin walled open section such as cold formed sections. Between these two extremes, the members will be in a state of uniform torsion and the loading will therefore be resisted by a combination of uniform and warping torsion. This is the condition which occurs in hot rolled I, H and channel sections [ 20].

As explained before, the torsional rigidity, GJ of a closed section is very large compared with its warping rigidity, EH, and hence a closed section may reasonably be regarded as subject to pure torsion only.

The total angle of twist q is given by:

(2) \theta ={\displaystyle \frac{T_{q}L}{GJ}},

where T_q = applied torque, L = length of the member subject to T_q, G = shear modulus of steel, J = torsion constant for the section, q= angle of rotation per unit length

If a torque is applied at the ends of the member in such a way that the ends are free to warp, then the member will only develop pure torsion. The resulting shear stresses vary linearly across the thickness of each element. Equation (2) provides convenient method for determining the modulus of rigidity of given material. In this study the value modulus of rigidity used is 79 000 kN/m². The corresponding value of the angle of twist, q at length L of the specimen can be indicated by increasing the magnitude of torque, T. Plotting q against T will give a straight line. The slope of this line represents the quantity of JG/L, from which the torsion constant J may be calculated. The value of J for a beam with normal flat web is J = S(1/3)bt³. Thus by considering the relation qvs.T, torsion constant J for beam with trapezoid corrugated web can be calculated.

Non-uniform torsion is illustrated in Fig. 3 where an I-section fixed at one end is subjected to torsion at the other end. Here the member is restrained from warping freely as one end fixed. Torsional warping is defined as the differential axial displacement of the points in a section perpendicular to the axis due to the torque. The warping restraint causes bending deformation of the flanges (known as Bi moment) in their plane in addition to twisting. The bending deformation is accompanied by a shear force in each flange.

Warping stresses are also generated in members of open section when the applied torque varies along the length; even if the ends are free to warp. For an I section member, the action of warping resistance can be visualized as follows. The torque T_q is resisted by a couple comprising forces equal to the shear forces in each flange, and acting at lever arm equal to the depth between the centroids of the flanges. If each flange is now treated as a beam, the bending moments produced by the above forces lead to direct stress, s_w in the flanges as shown in Fig. 6.

Methodology

To determine the torsion behavior of TriWP steel section, the torsion collar for free end support and the I-beam steel section on the free end support was fabricated earlier before the experiment was set up. The torsion collar as shown in Fig. 7(a) was used to clamp the specimen on the free end support. It was able to rotate in y-direction when the load was applied. The I-beam steel section as shown in Fig. 7(b) was welded together to the torsion collar as functions as load transfer to the section. Load cell as shown in Fig. 8 was vertically attached to the I-beam when the load ready to transferred.

Test specimens

Torsion test was conducted on three sets of beams sizes. Each consists of two TriWP and two FW. FW beam act as a control specimen to observe the differences in terms of torsional rotation. The difference between each sizes such as flange and web thickness and span length. Table 3 shows the dimensions and configurations of each type of beam.

Test procedure

The photograph in Fig. 9 shows the view of the test set up. Two types of support were used, i.e., fixed end support and free end support. The distance between these two supports depends on the span length i.e., 2000 mm and 2500 mm. The torsion collar was used to clamp the specimens at the free end support. The specimen was installed at 788 mm height. The hydraulic cylinder was attached at the fabricated I-beam (at the free end support) so that the load can be applied to cause twisting of the specimens. Linear Variable Differential Transformer (LVDT) were placed at three different locations as shown in Fig. 10 to measure the vertical and horizontal deflection of the beams. Two Inclinometers were placed on both supports to measure the torsional rotation. While the load was applied, the data logger records the value of loading and displacement value while manual record of the Inclinometer’s value was taken simultaneously based on the value of the loading. The test was stopped as soon as the specimen failed as indicated on the graph of the load versus vertical displacement. In the test, all beams were found to have maintained their elastic state even after the test. The relationship between load (P) and displacement (d) increase linearly. Then, the increases become nonlinear, followed by the stage where the beams were failed.

Result and discussion

Torsional rotations of the specimen

Specimen size 180 mm × 75 mm ×5 mm × 2 mm

For the specimen size 180 mm × 75 mm× 5 mm× 2 mm, the angle of ϴ₂ was increased after the increasing of the torsional loading. From the represented graph in Fig. 11, the value of torsion at 0.2 kNm was chosen to indicate the value of the angle ϴ₂. For FW 2d, TriWP 2c and TriWP 2d, the values of ϴ₂ were 34.2°, 32.8° and 18.9° respectively at 0.2 kNm. The values of the angle ϴ₂ at 0.2 kNm were equal or less than on that flat web.

Specimen size 200 mm ×100 mm ×8 mm × 6 mm

From the represented graph in Fig. 12, the value of torsion at 0.2 kNm and 1 kNm were chosen to find the value of the angle ϴ₂. At 0.2 kNm, for FW 3a, TriWP 3a, FW 3b and TriWP 3b, the values of ϴ₂ were 3.6°, 0.1°, 3.5° and 1.0° respectively. While at 1.0 kNm, for FW 3a, TriWP 3a, FW 3b and TriWP 3b the values of ϴ₂ were 22.1°, 5.0°, 22.0°, and 6.0° respectively. The values of the angle ϴ₂ for TriWP at 0.2 kNm and 1.0 kNm are less than to that FW.

Specimen size 200 mm × 100 mm × 6 mm×5 mm

From the represented graph in Fig. 13, the value of torsion at 0.2 and 1 kNm were chosen to find the value of the angle ϴ₂. At 0.2 kNm, for FW 3c, TriWP 3c, FW 3d and TriWP 3d, the values of ϴ₂ were 2.6°, 2.2°, 2.8° and 3.0° respectively. While, at 1.0 kNm, for FW 3c, TriWP 3c, FW 3d and TriWP 3d, the values of ϴ₂ were 16.9°, 13.0°, 17.0° and 16° respectively. The values of the angle ϴ₂ for TriWP at 0.2 kNm and 1.0 kNm are less than to that FW.

Summary of the result

From the plotted graph, 0.2 and 1.0 kNm of torsional loading were chosen to indicate the value of torsional rotation, ϴ₂. It was indicated that the different of torsional rotation for different size of specimens shown at the same torsional loading. The reason of choosing 0.2 and 1.0 kNm were because of its shows the best slope of straight line from curved graph. The data were listed as shown in Table 4. At the torque of 0.2 and 1 kNm, the flat web specimen with small sectional size i.e., FW 2d had higher torsional rotation compared to those with a bigger size of flat web. The TriWP with a small sectional size i.e., TriWP 2d had higher torsional rotation compared to those with a bigger size of TriWP. The average torsional rotation for FW at 0.2 kNm was in the range of 2.7% to 34.2%, while 16.95% to 22.05% at 1.0 kNm. For TriWP, the average torsional rotation at 0.2 kNm ranged from 2.6% to 25.85%, while 5.5% to 14.5% at 1.0 kNm

In addition, the average percentage difference for FW and TriWP at 0.2 kNm ranged from 3.74% to 71.83%. Meanwhile, at 1.0 kNm ranged from 14.5% to 77.3%. The formulae to calculate the average percentage difference was shown in the Eq. (3). For specimen size 180 mm × 75 mm × 5 mm × 2 mm, at 1.0 kNm of torque, it did not have any values because the specimens had failed before 1.0 kNm (refer Fig. 11).

(3) averagepercentagedifference=\left|{\displaystyle \frac{average\%differenceforTriWP-average\%differenceforFW}{average\%differenceforFW}}\right|.

The theoretical value of torsional rotation, ϴ was compared with that of experimental value in order to study the percentage difference. For theoretical calculation, the deflection, d of the specimen was used to calculate the torsional rotation. For the deflection value, FW steel section shows higher value of deflection compared to that of the TriWP steel sections after the torsional loading was applied.

The deflections, d of both models were indicated in the Table 5. Trigonometric function was used to calculate the torsional rotation. From the experimental set up, the LVDT was set up about 15 mm from the center of the web of specimen as shown in Fig. 14. The torsional rotation was calculated based on the trigonometric equation where tanϴ was equal to the adjacent side (15 mm) divided by opposite side (d) as shown in Eq. (4).

The range between experimental results and theoretical calculation was about 1% to 17%. That percentage difference was acceptable since the maximum value for laboratory testing was 20%. The torsional rotation, ϴ for FW was higher in comparison with that of TriWP steel section under torsional loading. It proved that the TriWP steel sections had better resistance against torsion compared to the FW section. The use of TriWP steel section had led to a stiffer beam which was advantageous from the structural behavior viewpoint. Nevertheless, it were considered as a big differences between the experimental and theoretical results due to some of reasons. This was probably due to the bolt connection at the end support which causing the movement that affecting the whole beam. Inconsistency of the loading condition and the inclinometer due to improper calibration may also cause the difference between experimental and theoretical values. Both specimens which have undergone torsion failure after maximum torsional loading were presented in the Fig. 15 and Fig. 16 for TriWP and FW respectively. In this research, the models were face non-uniform torsion were the section fixed at one end and subjected to torsion at the other end. It could be observed that the section deflected at the end of load applied and the torsion collar at the end support restrained the longitudinal deformation of the specimen. According to the Saint Venant theory, warping could be restrained at the support with presence of thick plate attached to the specimen.

Conclusion

Based on the result presented earlier on the torsional behavior of triangular web profile (TriWP) steel section, the following conclusions can be made:

1) There were four variables that could influence the torsional behavior of triangular web profile (TriWP) steel section, i.e., the thickness of flange and web, beam length, and incremental loading.

2) Rotational angle values of triangular web profile (TriWP) steel section were smaller than the flat web steel section. Hence, it was proved that triangular web profile (TriWP) steel section had better resistance against torsion compared to the flat web steel section.

3) The triangular shape at the web act as a stiffener resulting the smaller of torsional rotation and the section is harder to rotate.

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