After the validation of FE models, various scenarios such as corrosion damage and web opening cutout were considered, to study the behavior of steel beams and the efficacy of CFRP sheets in restoring the load capacities of the altered beams. To strengthen the beams subjected to corrosion damage, CFRP sheets were applied to their bottom flanges, whereas six CFRP strengthening configurations were studied in detail to determine the efficient strengthening configuration to strengthen steel beams with web openings (SBWOs). The subsequent section presents the parametric study carried out on the validated FE model of the control beam, ‘CV00’, which is the undamaged steel beam. Other beams, ‘CD-20’ and ‘RB-20-2L’, were validated to enhance the accuracy of developed FE models.
5.1. Effect of Corrosion and CFRP Strengthening
The effect of corrosion in steel beams was incorporated in the FE model by reducing the thickness of the bottom flange. The study was conducted in five distinct levels of corrosion damage, i.e., 2.5%, 5%, 10%, 15%, and 20% thinning of the bottom flange, corresponding to 0.26 mm, 0.52 mm, 1.04 mm, 1.56 mm, and 2.08 mm thinning, respectively. The thinning was introduced to 80% of the beam effective span (refer to
Figure 8) to emulate non-localized corrosion cases and maximize the effects due to thinning.
The FE beam models are named to indicate the damage level and number of layers of CFRP sheets used for rehabilitation. The model ID is divided into two parts, using a dashed line if the model is a strengthened beam. The first and second parts specify the type of damage and number of layers of CFRP sheets, respectively. In the first part, the letter ‘D’ indicates that the beam is damaged. The number following the letter ‘D’ indicates the level of corrosion damage. In the second part, the first letter ‘R’ indicates that the beam has been rehabilitated and the remaining letters ‘nL’ refers to the number of layers of CFRP sheets used for strengthening. The beams without rehabilitation do not have the second part in their IDs.
The effect of thickness loss of the bottom flange on the yield and ultimate load of the beam is tabulated in
Table 3. The load versus mid-span displacement diagram is shown in
Figure 9. As the level of bottom flange damage (thickness loss) increased, the reduction in the yield and the ultimate load also increased. Both the reduction in yield and ultimate loads followed a linear trend, as shown in
Figure 10.
To strengthen the damaged beams, successive layers of CFRP sheets were attached to the bottom face of the bottom flange, covering the damaged (thinned out) area, as shown in
Figure 11. The unidirectional CFRP sheets were oriented along the longitudinal axis of the beam.
Seventeen FE models were developed for different levels of corrosion damage. The initial number of layers of CFRP sheets for each level of corrosion damage was based on the number of layers required by the previous level of corrosion damage and the layers were added successively until both the target yield and ultimate capacities were reached. The observed yield and the failure loads for each FE model are shown in
Table 4. The failure load was reached when the CFRP sheets began to rupture. Debonding was prevented in the experiment using cross-wraps [
8]. Therefore, the debonding of the CFRP sheets was not allowed in the FE models.
The study focused on the optimum number of layers of CFRP sheets needed to restore the yield and the ultimate load capacities of the damaged beam to the original undamaged state (to that of CV-00). By doing so, an improvement in the serviceability requirements in terms of reduction in the mid-span deflection due to the application of CFRP was also observed.
For the beam with damage level of 2.5% (D2.5 beam), one layer of CFRP strengthening would be sufficient to restore the yield load capacity; whereas, three layers were required to restore the ultimate load capacity to that of the undamaged control beam ‘CV00’ (
Table 4). Similarly, for the ‘D5’ beam, two layers of CFRP sheets were sufficient to restore the yield load capacity; however, three layers were needed to restore the ultimate load capacity. For the ‘D10’ beam, three layers of CFRP sheets were just sufficient to reach the yield and ultimate load capacities and four layers were needed to exceed those capacities. For the ‘D15’ beam, four layers were sufficient to restore the ultimate load capacity, whereas six layers were needed to exceed the target yield load capacity. For the ‘D20’ beam, five layers were needed to exceed the target ultimate load. However, eight layers were needed to exceed the target yield load.
It is also observed that the failure load of the ‘D2.5-R1L’, ‘D2.5-R2L’, ‘D5-R1L’, and ‘D5-R2L’ strengthened beam models (
Table 4), which correspond to CFRP rupture, is less than the ultimate load of the damaged beams ‘D2.5’ and ‘D5’ (
Table 3). It may give the impression that the strengthening worked to the opposite effect. However, the load versus mid-span deflection curves of these beams shows a considerable improvement in the stiffness of the inelastic regime and the reduction in the mid-span deflection, due to strengthening. Consequently, the lower number of CFRP sheet layers in these beams was subjected to higher levels of stresses, due to which they ruptured at lower load levels.
Figure 12 shows the load versus mid-span deflection curves for all FE beam models. It is observed that a higher number of CFRP layers resulted in a reduced mid-span deflection and improved stiffness and the adequate number of layers of CFRP sheets that depends upon the level of damage, as presented in
Table 4, could fully restore the yield and ultimate load capacities of corroded beams to the level of the undamaged beam.
5.2. Effect of Web Openings
Past studies [
12,
13,
16] have shown that the performance of steel beams with circular web openings is superior to that of other opening shapes. For the same opening area, steel beams with circular web openings had a higher ultimate load capacity and lower stress concentrations around their edges. Therefore, circular openings were considered in the present study. Since the bending stresses are at a maximum at the extremities and the shear stress is the highest at the neutral axis of the cross-section, the flanges and the web should be able to resist high bending stresses and high shear, respectively Therefore, it is prudent to provide openings in the web (where shear stress is at a maximum) in the regions of low shear forces. One study [
14] concluded that the openings are to be provided in the bending predominant region instead of in the shear predominant region, and the optimal location of web openings is the middle two-thirds of the beam’s span, which is a bending predominant region.
Under the four-point bending load, the middle-third span of the beam is subjected to pure bending and there is no shear force. Therefore, openings were introduced at this location of the beam, as shown in
Figure 13. Design guidelines across the globe have provisions and limits on the dimension and location of openings, spacing between openings, etc. Therefore, an offset from point load ‘C’ and clear spacing between openings ‘S’, in this study, were chosen based on the SCI P355 [
23], which suggests generalized design methods for discrete or closely spaced web openings.
In total, four FE beam models with different sets of web openings were studied, with the number of openings ranging from one to four, as shown in
Figure 13. The total area of openings in all the beams was kept nearly constant. The details and dimensions of the beam models are described in
Table 5.
The nomenclature of the beams is such that the first character ‘D’ indicates the damage induced by the web opening and the remaining characters, ‘nH’, indicate ‘n’ number of circular web openings or holes in the beam. The load versus mid-span deflection curves for the FE models are shown in
Figure 14. The maximum load attained is the ultimate failure load, after which, the load started to drop upon further increase in applied displacement.
To obtain the reduction in the load capacities, as tabulated in
Table 6, the beam models with openings (D1H, D2H, D3H, and D4H) were compared to that of the undamaged beam (CV-00).
For SBWOs with an opening ratio <0.5 (D3H and D4H), the maximum reduction in ultimate load capacity was 5% and there was no effect on the yield load capacity. However, for model D1H with an opening ratio >0.5, the reduction in the ultimate and yield load capacities was the highest. In general, it was observed that beams with a higher number of circular web openings and smaller sizes had higher load capacities, as compared to those with a smaller number of bigger openings, if the total area of the openings was kept constant.
Based on previous studies [
15,
21], commonly observed global failure modes in SBWOs are flexural, Vierendeel mechanism, and web-post buckling. The flexural failure mode, also known as the flexural mechanism, is predominant in the region with high bending moments, as it could lead to yielding of T-regions below and above the web openings and the consequent formation of plastic hinges. The Vierendeel mechanism is a failure due to the formation of plastic hinges at the corners of the T-regions above and below the openings, causing them to deform. It is observed in the region with high shear forces. Web-post buckling generally occurs when the openings are closely spaced without sufficient clear spacing between the adjacent openings. Since the openings were introduced in the middle-third of the beam span, where it was subjected to high bending moments and low shear, the flexural failure mode was anticipated in all four beam models, D1H, D2H, D3H, and D4H. The stress diagrams of the beam models at the ultimate load are shown in
Figure 15. The stress contour shows that both the top and bottom Ts at the opening locations had yielded as the average stress in those T-regions were higher than the yield stress. Therefore, it was confirmed that the governing mode of failure was the flexural failure mode.
The maximum ultimate load reduction of 10.9% (refer to
Table 6) occurred in model D1H, which had an opening ratio of 0.71 (refer to
Table 5). The area of the web opening was equal to 4.8% of the total area of the web, along the span of 1500 mm.
Most available design guidelines, including SCI P355 [
23], allow for a maximum opening ratio of 0.8. Therefore, another model—D1H*, with maximum permissible opening ratio of 0.8—was developed.
Figure 16 shows the dimensions and location of the opening. The load versus mid-span deflection curve for D1H* is shown in
Figure 17, which is compared against the steel beam without an opening (CV00).
Compared to the control undamaged beam (CV00), reductions of 9.6% and 14.5% in the yield and ultimate load capacities were observed for D1H*. The stress distribution diagram of D1H* at the ultimate stage is shown in
Figure 18. The stress on the top and bottom Ts exceeded yield stress and were close to ultimate strength of steel. Therefore, the governing failure mode for D1H* was the flexural mechanism.
5.3. CFRP Strengthening of Steel Beams with Openings
The use of FRP is generally more efficient in strengthening weak beams compared to strong beams. Therefore, the beam model D1H*, with the highest loss of load capacity due to opening, was selected for CFRP strengthening. Six different CFRP strengthening configurations (schemes) were examined. The mode of application of CFRP sheets for each scheme is shown in
Figure 19, where the shaded blocks represent CFRP sheets. The first strengthening layout was selected based on the failure of the D1H* beam, which failed in the flexural mechanism, with high stresses observed at the bottom and top flanges. Consequently, each strengthening arrangement was selected based on the predicted failure or limitation of the previous configuration. The aim of adopting various strengthening arrangements is to determine the most efficient strengthening configuration to strengthen steel beams with web openings. The specifics of each strengthening scenario are discussed in detail in the subsequent paragraphs. It is noted that all CFRP sheets were oriented along the longitudinal axis of the beam, including the ones applied to the beam’s web.
The first strengthening strategy, ‘Scheme-I’ was based on the application of CFRP sheets on the bottom of the beam’s bottom flange, as shown in
Figure 19a. The total length of the CFRP sheet was taken as four times the size of the opening. Therefore, the CFRP sheets were extended beyond the edge of the opening, by 1.5 times the opening size, from both sides, as shown in
Figure 19. The selection of this length was based on a previous study [
24] on the optimal length of CFRP to strengthen steel beams with openings. The analysis was carried out starting with one CFRP sheet layer at the bottom flange and more layers were added successively to study their effects on the structural performance of the beam. Beams strengthened with a lower number of layers of CFRP sheets failed due to the CFRP rupture at lower load levels. As the number of layers of CFRP sheets increased, the mode of failure changed from CFRP rupture to plastic hinge formation at the top T-region, as shown in
Figure 20. CFRP application at the bottom flange strengthened the bottom T-region and improved its stiffness. However, the un-strengthened top T-region, being subjected to higher flexural compressive stresses, failed in the observed manner.
It was also observed that a plateau was reached and any additional layer beyond four layers had a negligible increase in the ultimate load of the beam. Therefore, Scheme-I was ineffective in strengthening SBWOs, since a plastic hinge was formed in the top T-region before the target load was reached for any additional layers of CFRP sheets.
The second strategy ‘Scheme-II’ was studied with the intent to address the limitation of the first scheme. Therefore, CFRP sheets were applied only to the bottom of the top flange, as shown in
Figure 19b. The application of FRPs to the beam’s top flange offers several advantages, such as increasing the beam’s load capacity and stiffness, enhancing the top flange’s resistance to local buckling and providing tensile strength during reversed loading situations, like those encountered by beams in bridges [
21]. The CFRP sheet layers were successively increased and the model was analyzed. Scheme-II was also found to be ineffective. The reason was that the bottom T-region around the opening yielded and the plastic hinge was formed, as shown in
Figure 21. Moreover, the application of additional layers of CFRP sheets also did not play a role in achieving the target load, due to the prior bottom T-region failure.
In the third strengthening configuration, ‘Scheme-III’, CFRP sheets were applied to both the top and bottom flanges, as shown in
Figure 19c. This strengthening scenario was adopted after the first two schemes proved ineffective in restoring the strength of the undamaged beam. The beam performed better than the previous cases, in terms of improving both the strength and stiffness, resulting in lower stress levels at both the top and bottom flanges at failure. However, localized stress concentrations were observed at the top and bottom T-regions (
Figure 22) adjacent to the openings, prior to reaching the desired load level. This indicated that the strengthening of the flanges alone was not sufficient and needed to be extended to the web as well. Therefore, the fourth strengthening configuration, ‘Scheme-IV’, was considered next.
In ‘Scheme-IV’, CFRP sheets were applied to the bottom of both flanges, as well as on both sides of the web, as shown in
Figure 19d. An equal number of layers of CFRP sheets were added successively. With six layers of CFRP sheets below the top and bottom flanges and on both sides of the web, this scheme was able to strengthen D1H* successfully, which sustained a load of 338 kN prior to failure (CFRP rupture). The stress distribution on the steel beam at failure for ‘Scheme-IV’ is shown in
Figure 23. It can be seen from the figure that the excessive stress was shifted away from the critical region near the opening toward the end of the CFRP sheet. This resulted in a higher load capacity and a more even stress distribution at the mid-span.
As an alternative to ‘Scheme-IV’, another strengthening configuration, ‘Scheme-V’, was also studied. CFRP sheets were applied to the bottom of the top flange, to the top of the bottom flange, and on both sides of the web, as shown in
Figure 19e. Like ‘Scheme-IV’, this strategy was also able to strengthen D1H* successfully with six CFRP sheet layers, which sustained a load of 332 kN prior to failure. The stress distribution on the steel beam at failure for ‘Scheme-V’ is shown in
Figure 24.
For the application of strengthening scheme-IV, it can be noted that the CFRP sheet must be cut into various pieces. To avoid such cuts, in the scheme-V strengthening configuration, continuous CFRP sheets were used on each side of the web and were extended to the total width of the flange as one piece. The difference in the failure load observed was negligible between the two schemes (338 kN and 332 kN). Additionally, the stress distribution in the CFRP sheets alone, as used in the ‘Scheme-V’ strengthening configuration, is shown in
Figure 25, which indicates a lower stress level in the CFRP sheets towards the middle portion of the web. The reason behind such an observation was because the opening was in the bending-dominant low-shear region and the middle portion of the web in such a region would be subjected to a lower stress level. Thus, to economize ‘Scheme-V’, a final strengthening configuration of ‘Scheme-VI’ was proposed.
In ‘Scheme-VI’, CFRP sheets were applied on the bottom of the top flange, the top of the bottom flange, and on both sides of the web, covering only the top and bottom T-regions of the beam, as shown in
Figure 19f. An equal number of layers of CFRP sheets was added successively. As anticipated, this scheme was also able to strengthen D1H* successfully with six CFRP sheet layers, which sustained a load of 331 kN prior to failure. The stress distribution of the strengthened beam at the ultimate stage for ‘Scheme-VI’ is shown in
Figure 26, which closely resembles that of ‘Scheme-V’ (depicted in
Figure 24), showing minimal differences.
In conclusion, three strengthening configurations, Scheme-IV, V, and VI, were able to strengthen D1H* to the desired level of strength. In all these strategies, a minimum of six CFRP sheet layers were needed. The load versus mid-span deflection diagram for D1H*, with these strengthening configurations, using six CFRP layers is shown in
Figure 27. When compared with the control (CV-00) and damaged D1H* beam models, the strengthened beams had considerable enhancement in the stiffness in the inelastic regime after the yield point is reached. On the other hand, all strengthened models had an almost similar behavior with a slightly higher inelastic stiffness improvement, as the beam strengthened with scheme-IV. Based on the above observations, scheme-VI was found to be more efficient due to the lower material usage and greater cost-effectiveness.