A similar FE modelling scheme to that used in the previous section was then employed to study the effects of a number of the varied geometrical and mechanical parameters on the efficiency of the proposed FRP retrofit. These varied parameters included: direction of the applied cyclic loading
(diagonal loading rather than vertical loading), the geometrical properties of the FRP angles, the elastic moduli of both the FRP angle and the adhesive material, and the location where the FRP attachments were employed (i.e. attachments bonded to the stiffener and web or to the web and flange instead of angles attached to the stiffener and flange). The FE model used for structural stress analysis of the FRP- retrofitted specimen in the previous section was considered as a benchmark (FE-B). Loading P was applied so that a structural stress equal to 100 MPa could be calculated for the FE-B specimen. The same load P was then applied to all subsequent analyses. The effect of each parameter was studied separately by using an FE model as described in the following paragraphs.
A diagonal load was applied in model FE-L. In the experimental study, a vertical cyclic load was
applied through the up and down movement of a jack, as dictated by laboratory constraints. However, in actual steel bridges, out-of-plane web displacements are caused by cross frame members, which are often diagonal rather than vertical with respect to the web. In the FE-L model, a diagonal loading with the same magnitude of P in both the vertical and horizontal directions was applied.
The FE-M1 and 2 models were used to investigate the effect of the elastic modulus (E) for the FRP and adhesive material on the efficiency of the proposed retrofit method. In FE-M1 model, lengthwise (LW) flexural modulus of 12.4 GPa was used for the GFRP material (a 125% increase). For FE-M2, a high modulus adhesive (SikaFast®-3131) with E = 3.6 GPa was modeled (a 3500% increase).
27
The FE-G1 to 4 models were used to study the effects of geometrical properties of the FRP angle, as described in Table 2.7.
Table 2.7: Models FE-G1 to 4
FE model Varied dimension New value (in.) % increase FE-G1 a (short leg) 5.2 24 FE-G2 b (long leg) 8.5 13 FE-G3 l (length) 6 20 FE-G4 t (thickness) 0.5 33
Distortion-induced fatigue damage usually happens in locations that are not easily accessible for
implementing retrofits. The proposed method may then not be applicable to some structural details. Still, FRP attachments can be used at other locations with the goal of reducing the stress demand in the web gap region. Two cases were studied herein. In the FE-WS model, FRP angles were attached to the stiffener and web to provide more connectivity between the stiffener and the web. In the FE-WF1 and 2 models, FRP angles were used to create a load path between the flange and web on the stiffener and opposite sides (see Figure 2.11).
Figure 2.11: FE model geometries
Results for the FE-based parametric study are presented in Figure 2.12. In addition to the 11 FE models described earlier, FE results for an unretrofitted (as-welded) specimen are added for comparison (FE- AW). As can be seen, FE-M1 and FE-WS were the most and least efficient methods studied herein, respectively.
28
Figure 2.12: FE-based study results
Results are summarized in Table 2.8. For the FE-M and G models, the proportional benefit is defined as the percent variation in the structural stress value per one percent variation in the varied mechanical or geometrical parameter. For instance, according to the table, a 1% increase in FRP’s elastic modulus resulted in a 0.25% decrease in the structural stress value in FE-M1.
Table 2.8: Fatigue tests results
FE model % increase in the varied parameter (%) HSS (MPa) HSS reduction % Proportional benefit (%)
FE-AW N.A. 195 N.A. N.A.
FE-B N.A. 100 N.A. N.A.
FE-L N.A. 106 -6 N.A.
FE-M1 125 69 +31 0.25 FE-M2 3500 100 0 0 FE-G1 24 97 +3 0.12 FE-G2 13 99 +1 0.08 FE-G3 20 96 +4 0.20 FE-G4 33 89 +11 0.33
FE-WS N.A. 191 -91 N.A.
FE-WF1 N.A. 167 -67 N.A.
FE-WF2 N.A. 171 -71 N.A.
29
The HSS increased slightly when a diagonal (45º) load was applied rather than a vertical load in FE-B. Although the structural stress did not change significantly, adding a force component parallel to the web was seen to induce additional stresses in both the FRP angle and adhesive.
Using a higher modulus FRP material resulted in a significant increase in the efficiency of the proposed retrofit method.
Using a higher modulus adhesive did not change the HSS value. When applied to in-service bridges, using a high modulus adhesive will generate higher stresses in the adhesive layer which, consequently, will make the retrofit vulnerable to a sudden failure of the adhesive.
Among the geometrical properties of the FRP angle, the highest benefit was achieved by increasing the thickness, followed by increasing the length. Although increasing two other dimensions (a and b) did not affect the HSS value significantly, an angle with bigger legs may be needed to provide more bonding area between the FRP angle and steel.
Attaching the FRP angles to the stiffener and web, resulted in an almost no reduction in HSS comparing to the unretrofitted case (FE-AW). This can be explained by the fact that no extra stiffness was provided to the weak web gap region as a result of this retrofit.
Attaching the FRP angles to the web and flange was not as efficient as attaching the angles to the stiffener and flange. However, some improvement (up to 15% reduction in HSS) was achieved compared to the unretrofitted case. When attaching the FRP angles to the stiffener and flange is not possible due to geometrical constraints, this method can be used. It is expected that higher HSS reductions will be achieved when longer and thicker FRP
attachments are used. Moreover, the modeled FE-WF2 retrofit can be used in combination with the retrofit discussed in FE-B.