1. Introduction Steel structures have certain advantages compared to the concrete structures due to two parameters of light weight and rapid performance. Today, parameters such as changes in gravity and lateral loading code, changes in existing application, design and performance errors, corrosion and damage due to collision of random and environmental loads has caused the structures not to have adequate bearing capacity against the new loads and thus needs to be improved. Conventional retrofitting methods can be used to strengthening steel structures using a steel jacket coating method. In this method, by increasing the flexural, shear and axial load bearing capacity of the members, we can strengthen the weak members. Although this method is effective, but due to the difficult application conditions and increase of the structural sections weight as well as the emergence of new materials such as composite fibers (FRP), design engineers have used structural strengthening method by polymeric composite fibers. These polymer fibers are now extensively growing and exploiting worldwide in a variety of industries, including the marine, aerospace, and automotive, road and building industries.

Fig. 1- The use of FRP composite fibers in industry

Important advantages of polymer fibers are their longevity and their good resistance to environmental conditions. In fact, polymer fibers can minimize the cost of maintenance of steel structures by their high resistance to corrosion and fatigue. In a comparison and field study, it is quite evident that the use of polymer fibers in reinforcing concrete structures is older than steel structures. Selvaraj et al. [1] investigated the enhanced strength and hardness of CFRP-reinforced steel channel sections. They tested 210 laboratory models with different arrangements of polymer fibers under 4-point testing, which ultimately found that unidirectional polymer fibers were more effective in increasing the strength and stiffness of steel sections than in bi-directional polymer fibers. John et al. [2] investigated the theoretical and experimental study of CFRP-reinforced notched steel beams. The results of experiments have shown that the strength and ductility of the notched beams, twice reinforced by polymer fibers, have been improved. Zhao et al. [3] examined the sections of FRP-reinforced steel tubes under impact load. In this study, they posit 13 laboratory samples covered by composite fibers under impact load. Ultimately, the results of investigating bearing capacity and deformations indicated that due to the presence of polymer composite fiber coatings, the capacity of impulsivity capacity of sections is increased by 29% with the decrease of lateral displacement values compared to the non-coating composite fibers. In an experimental study, Sedan et al. [4] investigated the bending response of steel beams reinforced with anchored composite sheets. In this study, they impacted 11 beams by 3-point loading. The important results of their research are the increase in final bearing capacity of sections due to the increase in length and thickness of the composite fibers. In a study, Zhi-Yu Wang et al. [5] investigated the tensile behavior of CFRP-reinforced anchored steel sheets. In another study, Selvaraj et al. [6] investigated the flexural reinforcement of steel angular sections using CFRP fibers. They tested 30 laboratory models under 4-point loads in two states of with- and- without composite fiber coating, the most important of which can be significant increase in hardness and strength reinforced with composite fiber. Rizkalla et al [7] examined steel sheets reinforced with CFRP micro-strands. The results showed that the use of low-diameter composite fibers preserves the adhesion properties of the substrates under pressure and tension. In another experimental study, Zhao et al. [8] investigated thin CFRP-reinforced steel sheets affected by shear load. They reinforced three thin steel sheet specimens with different arrangement of polymer plates compared to the uncoated composite fiber sample. One of the important results of this study is the increase in the final strength and the increase in the hardness of the energy absorption sequence due to the reinforcement. In a study, Harris et al. [9] investigated the enhancement of the durability of steel structural sections with FRP fibers. The results show that the presence of composite fiber strips improves the dynamic behavior and provides a stable cyclic response of the steel sections under cyclic loads. Rahgozar et al. [10] numerically examined the increase in compressive capacity of long hollow box steel columns reinforced with FRP-composite. They investigate 62 steel column samples with abutment conditions of one end is fixed and one end is pinned. The results indicated an increase in critical load of hollow box steel columns due to the coating of composite fiber layers.

2. Materials Properties 2.1. Steel Beam In this research, steel beams with geometrical and technical properties in Table 1 are used as follows.

Table 1- Technical and Geometric Properties of Steel Beam l h b t E Fy Fu ɣ SX IX g 600 27 13.5 1.02 2e6 2400 3700 7850e-6 429 5790 0.361

Fig. 2- Geometric Properties of Steel Beam

2.2. Composite Fibers In this study, based on the information available in Journal 345 of deputy of planning and strategic oversight of the President [11] and research by Reddy [12], the high-strength carbon composite properties available in table 2 are used as follows.

Table 2- CFRP Composite Technical Properties
E ƃ Ɣ µ
1.4e6 5430 1.9e-3 0.2

3. Methodology In this research, the results of bending stresses are investigated using the relation between theory and software modeling.

3.1. Theory Relationship: In one study, Benati et al. [13] compute bearing capacity enhancements of steel beams reinforced by FRP-prestressed fiber. In this study, steel beams with conventional IPE sections were reinforced with FRP polymeric composite strips, which eventually bearing capacity of mentioned sections were investigated in two plastic and elastic states. Equation (1) indicates the flexural stresses caused by gravity loads in the presence of composite fibers in the beams: σ^±=(-p)/A_f ±0.5*((g_1+g_2 )*L^2-ph)/Sx (1) p=0.5*F_fk/Ɣ_f *A_CFRP (2) In equation (1), the value of g1 (unit weight of steel beam length) has been studied while the value of g2 is a permanent load from non-structural members that can be calculated based on the minimum value of below equation: g_2=min|█(1/8*(g_1+g_2 )*(2L)^2≤0.33*Fy*Sx@5/384*((g_1+g_2)/(E*I))*(2L)^4≤1/800*(2L))┤ (3) It is noteworthy that in the aforementioned relationships, Af is steel beam compression wing area, Acfrp is cross-sectional area of composite sheet, Ffk is tensile stress value due to composite fibers, and Ɣ_f is the relationship coefficient value equal to 1.1

3.2. Software Modeling Today, with the advent of computer science, the accuracy of specialized software computing has increased dramatically. ANSYS software is one of the good soft wares that is used in engineering analysis such as structure and mechanics. This software is finite element software that aims at analyzing the modeling. In this software, the basis of solving equations is to split the model into smaller elements. These types of elements can be structural, thermal, or other, depending on the number of degrees of freedom and the type of analysis method. One of the methods of analysis in this software is static nonlinear analysis. There are various ways to analyze nonlinear equations in this method, including Newton-Raphson iterative method. The basis of using a nonlinear static method is that the software gradually increases the amount of load until the structure reaches a failure and instability boundary and it is noteworthy that the convergence of the solutions obtained by this method is activated by automatic time step algorithm.

4. Validity To evaluate the validity of the software model used in this study, the stress values obtained by software for steel beam model with unidirectional carbon fiber with 1mm thickness are compared with theoretical relationship in Section 3 that is described in equation 1 to 3 in this section and slight difference in table 3 shows the validity of the software analysis.

Table 3- Validation of Software Modeling Results Theory Bending Stress Software Bending Stress Changing Ratio 77.04 77 0.5%

g_2=min|█(1/8*(0.361+g_2 )*(2*600)^2<0.33*2400*429@5/384*((0.361+g_2)/(2*〖10〗^6*5790))*(2*600)^4≤1/800*(2*600) )→g_2=0.282┤ p=0.5*5430/1.1*13.5*0.1=3331.05 σ^∓=(-3332.05)/((13.5*1.02) )∓((0.361+0.282)*〖600〗^2-3332.05*27)/429*0.5 σ^∓=-241.98∓164.94=|█(-77.04 O.K.@+406.92 N.G)┤

4. Discuss the Results 4.1. Numerical Results of Reinforced Steel Beam by One to Three Unidirectional CFRP Composite Layers The specimens modeled in software with the results extracted from the presence of one to three unidirectional composite layers are described in Table 4, as shown in the results, the highest and the lowest increase in bending stress compared to the first model (one unidirectional composite layer with 1mm thickness) is equal to 155% and 45% respectively.

Table 4- Numerical results of reinforced steel beam by one to three unidirectional CFRP composite layers Models NO Layers NO Layer Thickness Angle Degree Bending Stress Increasing Ratio 1 1 0.1 0 77 0 2 1 0.125 0 126 63% 3 1 0.15 0 168 118% 4 1 0.2 0 196 155% 5 1 0.3 0 168 118% 6 1 0.5 0 133 73% 7 2 0.1 0,0 140 82% 8 2 0.15 0,0 182 136% 9 2 0.1 90,0 77 0% 10 3 0.15 90,0 112 45% 11 3 0.1 0,0,0 182 136%

4.2. Numerical Results of Reinforced Steel Beam with One to Three Layers of Bi-Directional CFRP Composite The characteristics of the modeled samples in software along with the results obtained from the presence of one to three bi-directional composite layers are presented in Table 5. The results showed that the highest and lowest increase in bending stress compared to the first model (one unidirectional composite layer with 1mm thickness) is equal 73% and 7% respectively.

Table 5- Numerical results of reinforced steel beam by one to three bi-directional CFRP composite layers Models NO Layers NO Layer Thickness Angle Degree Bending Stress Increasing Ratio 1 1 0.1 0 105 0 2 1 0.125 0 31.5 -70% 3 1 0.15 0 77 -27% 4 1 0.2 0 133 27% 5 1 0.3 0 175 67% 6 1 0.5 0 182 73% 7 2 0.1 0,0 91 -13% 8 2 0.15 0,0 133 27% 9 2 0.1 90,0 91 -13% 10 3 0.15 90,0 133 27% 11 3 0.1 0,0,0 112 7%

5. Conclusion 1. As shown in figures 3 and 4, increasing the thickness of composite fibers in unidirectional state decreases the flexural stress values due to the gravity loading of reinforced steel beams. However, the conversion of fibers from unidirectional to bi-directional modes has little effect on decreasing the values of bending stresses.

Fig. 3- Results of bending stress in reinforced steel beam by unidirectional composite layer due to increased layer thickness

Fig. 4- Results of bending stress in reinforced steel beam by bidirectional composite layer due to increased layer thickness

2. In the comparison of the numerical results of bending stresses of steel beams reinforced by unidirectional and bidirectional fiber, as illustrated in Fig. 5, the use of bidirectional fiber in reducing bending stress values is effective than the corresponding bending fibers.

Fig. 5- The effect of number of layers direction on bending stress values of steel beams reinforced by composite fiber

3. As shown in Figures 6, changing the angle of the composite fibers in two-layer mode from zero value in both layers to 90 ° in the first layer and zero value in the second layer improve the flexural stress values only in unidirectional fiber mode.

Fig. 6- The impact of layers deployment angle on bending stress values of steel beams reinforced by composite fibers in unidirectional & bidirectional stat

4- By increasing the number of layers from one layer to three layers, as shown in the results of tables 4 and 5, in the case of unidirectional composite layers, the use of more layers with less thickness compared to one layer of equal thickness had a better effect on the flexural stress results. While in the bi-directional composite fibers, the use of a thick layer equivalent to the number of thinner layers will have a better effect on the calculated flexural stress results.

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Published on 15/02/21

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