In past decades, numerous experimental and numerical investigations on I-shape steel beams with stiffeners have been carried out to improve their behavior to lateral-torsional buckling. Hotchkiss [1] studied the behavior of I-shaped steel beams with longitudinal stiffeners at the ends only as shown in Fig. 1a. This type of stiffeners and the use of welded plates perpendicular to the flange and web at the beam ends were evaluated by Vacharajittiphan and Trahair [2,3]. Plum and Svensson [4] nalytically studied the resistance of lateral-torsional buckling of I-shaped steel beams with box-type stiffeners welded to web and flanges of sections as shown in Fig. 1b.

Figure 1 Source: The authors.

Szewczak et al. [5] evaluated numerically the effectiveness of longitudinal, box-type, transversal, and cross stiffeners as shown in Fig. 1a-1d. This study showed that the box-type stiffener was the most efficient, whereas the transversal stiffener was the least efficient in terms of lateral-torsional buckling. Smith [6] studied the same aforementioned four types of stiffeners, including the effect of using cross stiffeners on both sides of the web, on only one side and alternated. Ojalvo [7,8] assessed the use of channels as stiffeners with the web of the channel parallel to the web of the beam, resembling a box-type stiffener. This type of stiffener was evaluated by Heins and Potocko [9], who presented two analytical methods that included one with rigorous assumptions and the other with approximations.

Ojalvo and Chambers [10] studied the effect of box-type stiffeners located only at the ends of the beam. In addition, these authors evaluated the behavior of diagonal stiffeners as shown in Fig. 1e. The lateral buckling of the I-shaped steel beams with longitudinal and transverse stiffeners arranged arbitrarily were demonstrated theoretical and experimentally by Takabatake [11] and Takabatake et al. [12], respectively.

The aforementioned studies concluded that the box-type, longitudinal, diagonal, and cross stiffeners have improved the behavior to the lateral-torsional buckling of I-shaped steel beams. However, the literature review showed that the assessment of the flexural capacity of I-shaped steel beams have not been carried out with different laterally unbraced lengths (L _b ). Recently, other authors studied the effect of stiffeners in other types of structural elements.

Erdal [13] evaluated the use of stiffeners to optimize the behavior in perforated steel beams. Zarsav et al. [14] assessed the contributions of supplemental stiffeners on the hysteretic behavior of the link-to-column connection. Stavridou et al. [15] analyzed the structural response of steel wind towers with internal stiffeners. Shaterzadeh and Foroutan [16] evaluated the post-buckling response of cylindrical shells with spiral stiffeners and Rahmzadeh et al. [17] studied the effect of the rigidity and arrangement of stiffeners on the buckling behavior of plates.

Therefore, this work focuses on the experimental evaluation of the flexural capacity improvement of I-shaped steel beams with longitudinal stiffeners and different laterally unbraced lengths (L _b ). This type of stiffener is chosen for economy and constructive ease, especially in countries where to do this type of work, is better option (economic manpower) than to use an I-shaped steel beam bigger.

The expected improvement is evaluated in terms of the measured flexural capacity, the lateral displacement of the compression flange, and the failure twist angle of the specimens. These aspects are beneficial for the design of steel beams of large span lateral unbraced, e.g. industrial building roofs.

The experimental program of this research was carried out in a loading frame at the Universidad Pontificia Bolivariana in Bucaramanga, Colombia. Thirty-three (33) IPE-140 steel beams were tested to bending. Dimensions such as depth (d), flange width (b _f ), flange thickness (t _f ), and web thickness (t _w ), are shown in Fig. 2. Cross-sectional properties of the IPE-140 specimens (Table 1) such as the gross area (A _g ), moment of inertia (I), elastic section modulus (S), radius of gyration (r), plastic modulus (Z), torsion constant (J), and torsional warping constant (C _w ) were calculated according to the equations available in the literature [18,19].

Table 1

Source: The authors.

Figure 2 Source: The authors.

Average values of the mechanical properties of steel beams such as yield stress (f _y ), modulus of elasticity (E), and yield strain (ε _y ) are listed in Table 2.

Table 2

Source: The authors.

These values were measured from tension tests from four samples cut from the IPE-140 beam as shown in Fig. 3a.

Figure 3 Source: The authors.

The longitudinal strain of the specimens was measured using YHFLA-5-3L type large strain gauges that were located in half of the reduced section of the samples, whereas the stress was recorded by means of the 500 kN universal machine. Fig. 3b shows the stress-strain relationship of the samples tested. The tension tests were performed according to the requirements outlined in ASTM E8/E8M [20].

In accordance with the limit of width-to-thickness ratio of the flanges and the web and using the values of the mechanical properties shown in Table 2, the section is classified as compact since the width-to-thickness ratios of the elements are lower than the limit of maximum slenderness ratio for compact elements. The limits of width-to-thickness ratios were calculated using the requirements outline in ANSI/AISC 360 [21]. These values are summarized in Table 3.

Table 3

Source: The authors.

The I-shaped steel beams satisfied the permissible tolerances in the cross-section and longitudinal straightness (camber and sweep) in accordance with ASTM A6/A6M [22]. The laterally unbraced length between the plastic and inelastic buckling zones (L _p = 0.69 m) and between the inelastic and elastic buckling zones (L _r = 2.40 m) were calculated according to the requirements outlined in ANSI/AISC 360 [21] using eq. (1)-(3).

Where,

h ₀ = distance between flange centroids.

c= coefficient equal to 1.0 for doubly symmetric I-shaped beams, and

Based on the values above, the bending tests were performed using laterally unbraced lengths (L _b ) of 0.69, 1.55, 2.40, 3.60, 4.80, and 6.00 m. For each test length, six specimens were considered. The six specimens included three with longitudinal stiffeners and three without stiffeners, except for the length of 0.69 m, which had no lateral displacement problems (plastic buckling zone). For this length, only three specimens with no longitudinal stiffeners were tested. Longitudinal stiffeners consisted of steel plates with widths b _s = 62 mm, corresponding to 85% of the flange width (b _f ) and a thickness equal to the thickness of the web of the section (t _w ) as shown in Fig. 4a.

Figure 4 Source: The authors.

Longitudinal stiffeners were welded to the top and bottom edge of the flanges as shown in Fig. 4b. Stiffeners were spaced following an ratio, e/d defined in this research as the center-to-center spacing of the stiffeners divided by the depth of the section. Taking into account the economic factor and a quick constructive process, the authors considered testing an e/d ratio of 3, which represented a spacing between the longitudinal stiffeners equal to e= 0.42 m.

The typical test setup is shown in Fig. 5a. The specimens were tested in a 1000 kN capacity load frame, which is fixed to the laboratory’s reaction floor. All specimens were tested by applying upward point loads located at one third of the specimen length from each end.

Figure 5 Source: The authors.

The vertical load was applied with 200 and 500 kN capacity hydraulic actuators located at a height of 3.4 m from the ground and fixed to the load frame. Each actuator was used depending on the expected load of failure of the specimen. The actuator was connected to a load cell with equal load capacity, and then connected to a transition steel beam (IPE 330) letting the load to be transferred as point loads at the central third of the beam, by means of high-strength threaded rods as shown in Fig. 5b.

The specimens were supported at their ends on a set of steel plates and a ball joint system as shown in Fig. 6. This arrangement of plates provided both vertical and lateral restraint similar to a pinned support. Therefore, the span between the support was equal to the laterally unbraced length (L _b ). It is worth noting that the set of steel plates were fixed to the loading frame by means of 4 high-strength steel threaded rods that were 25 mm in diameter and six bolts that were 12 mm in diameter. This setup allowed for the application of an upward load. The threaded rods and bolts satisfied the requirements outlined in ASTM-F3125/F3125M [23].

Figure 6 Source: The authors.

A ball joint system similar to the aforementioned system allowed for lateral-torsional buckling of the specimens at points where the point load was applied as shown in Fig. 7. This ball joint system was connected to the high-strength threaded rods by means of plates with a hole and bolt system, allowing rotation to occur due to the deflection of tested specimens. The reason to apply an upward load was to simplify the manufacturing of all steel pieces with the final purpose of allowing for lateral-torsional buckling of the specimens to occur.

Figure 7 Source: The authors.

The specimens were instrumented by means of 12 displacement transducers. Displacement transducers were placed at halves and quarters of the specimens’ length to record the lateral and vertical displacements of the top and bottom flanges as shown in Fig. 8a.

Figure 8 Source: The authors.

Due to the deflection of the specimens, it was necessary to connect a U-shaped aluminum element to the stem of the displacement transducers to ensure there was permanent contact with the specimens as shown in Fig. 8b.

Additionally, strain gauges were installed in the half of the specimens’ length with and without stiffeners as shown in Fig. 9a, 9b, respectively.

Figure 9 Source: The authors.

The vertical load during the tests was displacement-controlled at a rate of 0,5 mm/min, until the lateral-torsional buckling was reached. Data acquisition was carried out by means of a computer-controlled data logger and recorded ever 3 seconds.

Fig. 10 shows the lateral-torsional buckling developed by the specimen without stiffeners with a laterally unbraced length of 6.00 m after performing the test.

Figure 10 Source: The authors.

Table 4 shows the values of the theoretical and measured maximum moments obtained from all tested specimens. The values of theoretical moment were calculated according to the requirements outlined in ANSI/AISC 360 [21] through the use of eq. (4)-(7).

Where,

C _b = coefficient equal to 1.0 for the case of uniform moment, and

The specimens were designated with a nomenclature where the first three digits represent the laterally unbraced length in millimeters. The fourth digit corresponds to the letter N (without stiffeners) or Y (with stiffeners), and last digit represents the specimen number tested for each length with and without stiffeners as listed in the third column of Table 4.

Table 4

Source: The authors.

The performed tests in this study showed that the use of longitudinal stiffeners on I-shaped steel beam increased the moment capacity in the elastic buckling zone in an interval from 34 up to 82%, for specimens with a L _b /L _r ratio of 1.0 and 2.5, respectively. Nonetheless, for the inelastic buckling zone (L _b = 1.55 m), although the results indicated an increase in the moment capacity of 7%, this value does not represent a significant increase.

In addition, the use of longitudinal stiffeners provided an acceptable lateral stability on I-shaped steel beams subjected to bending stresses. The use of these elements decreased the lateral displacement of the compression flange in an interval from 40 up to 72% for specimens with a L _b /L _r ratio of 1.0 and 2.5, respectively, corresponding to the elastic buckling zone. Whereas for the specimens in the inelastic buckling zone with a L _b /L _r ratio of 0.65, showed that there was a low decrease of the lateral displacement of the compression flange of 27%.

Another advantage of using longitudinal stiffeners on I-shaped steel beam was the decrease in the failure twist angle both in the elastic and inelastic buckling zones. This decrease reached a maximum value of 79 and 90% for specimens with a L _b /L _r ratio of 2.0 and 2.5, respectively.

According to the experimental results of this research, the use of longitudinal stiffeners could be a good solution to improve the bending moment capacity and to provide better lateral stability of I-shaped steel beams, especially in countries where manpower is low-cost, allowing the manufacturing of stiffening plates which represent an option for reducing costs, rather than using I-shaped beams with higher moments of inertia (heavier elements). Nevertheless, it is advisable to carry out these tests on I-shaped steel beams at greater depths.