Microsoft Word - numero_60_art_xx_3137.docx O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 1 Interaction diagram for RC column strengthened by steel angles and strips Osman Shallan, Thrwat Sakr, Mahmoud Khater, Ahmed Ismail Department of Structural Engineering, University of Zagazig, Zagazig, Egypt Osmanshalan@yahoo.com, thsakr@gmail.com, khater_civil@yahoo.com a.es.gabr@gmail.com, https://orcid.org/0000-0002-5942-5340 ABSTRACT. This paper presents an analytical model to construct the interaction diagrams (normal force and moment) for the RC column strengthened using the steel jacket technique. The proposed model is defined using the strain distribution block by determining the location of the neutral axis in the concrete section. The proposed analytical formulation is verified by experimental results performed by previous researches and numerical models using the nonlinear program ANSYS. The factors affecting the capacity of the strengthened column are taken into consideration, such as the amount of loads resisted by the steel cage, steel strips spacing, and the effect of concrete confinement. The results of the proposed model are in good agreement with the results from the experimental and numerical work used in verification. A practical design formula has been presented for strengthened columns. KEYWORDS. Reinforced concrete; Strengthening; Steel angles; Strips; Eccentricity; Interaction diagrams. Citation: Shallan, O., Sakr, T., Khater, M., Ismail, A., Proposed Design Criteria for column strengthened using steel angles and strips , Frattura ed Integrità Strutturale, 60 (2022) 1-12. Received: 18.07.2021 Accepted: 05.01.2022 Online first: 22.01.2022 Published: 01.04.2022 Copyright: © 2022 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION C columns usually require strengthening to increase their capacities to sustain loads. For RC columns strengthened by steel angles and strips, four steel angles are fixed at the RC column corner and steel strips spaced at a suitable spacing and welded to the angles to form the steel jacket in this technique. Grouting is used to fill the small gaps between the steel cage and the concrete column. This strengthening system requires a limited area around the column section when compared with concrete jackets. Many researchers studied the behavior and efficiency of the strengthened column using the steel jacket under purely axial loads [1–5]. They studied the strengthening parameters as the size of the angles and strips, concrete strength, steel strips spacing, and direct or indirect loading on steel angles. Analytical models for determining the capacity of the strengthened column using the steel jacket under axial load were also carried out [4, 6–9]. They discussed the factors affecting the capacity of the strengthening columns as the amount of load resisted by the steel angles, the effect of steel strips spacing, the effect of direct and indirect loading on the steel cage, and the effect of concrete confinement. For studying the strengthened column using steel jacketing under the eccentric load and slender column, some researchers conducted experimental and numerical studies to determine the capacity and mode failure of these columns [10,11]. Others R https://youtu.be/jKyxXpDIFpQ Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 2 construct the interaction diagram N-M using the experimental and numerical investigation to predict the capacity of the strengthened column for different eccentricities [12–15]. In this study, a practical analytical formulation is presented to construct the interaction diagram for columns strengthened using steel jackets. The proposed formulation is practical for determining the capacity of the strengthened columns under different eccentricities. The proposed model is verified using previous experimental work results done by [10, 12, 14, 16]. Finite element models using the ANSYS program were also used to validate the proposed design formula . STUDYING THE BEHAVIOR OF STRENGTHENED COLUMNS USING STEEL JACKETING n order to study the behavior of concrete columns strengthened using steel jacketing (steel angles and strips), two main factors would be discussed. The first factor is the amount of load that the steel jacket can resist. The second factor is the improvement in concrete strength due to the confinement caused by the steel jacket. The majority of the researches conducted is carried out in their formulation of the ultimate load capacity of the strengthened column based on two basic modes of failure, failure caused by yielding of steel angles and failure caused by yielding in steel strips as follows. Failure in the strengthened column due to yield in angles. In case of failure due to yielding in angles, local buckling occurs in angles. Subsequently, the steel jacket is no longer able to confine the column. This behavior is based on the assumption that there are three points between every two strips, The two points at each strip are assumed to be hinged, while the point in the middle of the distance between strips is considered as a weak point in the angles as shown in Fig. (1). Figure 1: (a) The equilibrium model for the local buckling of the steel angles failure prediction. (b) Failure of the strengthened column due to local buckling in steel angles experimental work of Tarabia and Albakry [8]. Figure 2: Failure of the strengthened column due to failure in strips experimental work Tarabia and Albakry [8] I O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 3 Failure in the strengthened column due to yield in strips. In this case, failure caused by yielding in strips due to the compression load on the column which leads to lateral strain in the concrete column and the steel jacket and causes an elongation in the strips subsequently the steel jacket isn't able to confine the column and the failure of the strengthened column occurred as shown in Fig. (2). ANALYTICAL MODELS FOR LOAD-CARRYING CAPACITY: elow are some of the analytical expressions for determining the ultimate load for the strengthened column using steel angles and strips, which would be used to produce the proposed formula. Fig. (3) shows the dimensions of the strengthened column using steel angles and strips used in the equations. Figure 3: Main dimensions of the strengthened column using steel angles and strips. Eurocode (2008) [17]: Some researchers consider the column strengthened by steel angle and strips as a composite column. According to Eurocode, the ultimate load of composite columns can be expressed by the following equation:            0.85 / / 2.5    /EC c c s ys s L ap b d f A f b d f (1) where c, s, and a are the reduction factors for concrete, reinforcement, and structural steel strength at the ultimate limit states in practical design. However , for real comparison with the experimental work, these factors can be dispensed with. There are two main differences between the composite column behavior and the column strengthened by steel angle and strips, the first difference is the behavior of the composite action between the steel jacket and the concrete column. The second difference is the improvement of the concrete properties and strength due to the confinement of steel jacketing on the column, which would be addressed in the following researches. Calderon et al. [6] Calderon et al. [6] proposed a design formulation for determining the ultimate load carried by the strengthened column using steel angles and strips. The formula is based on the failure mode analysis observed in a numerical and experimental study presented in his research. The proposed design equation is expressed by the following equation:           0.85 2.5   ca c s ys L Lp b d f A f b d f N (2) The factors NL (axial load carried by steel angles) and fL (confinement pressure) are calculated by two possible failure modes: failure due to material yielding of strips or yielding in angles as formed in the following equation. AA steel strips S steel angles L1xL1xt14L b h L1 S 2 L1 L1 Sec A-A t2 t1 s2 x t2 B Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 4      1 1.5  2 2.  .  .  . s b L ystrip t s f f e s b (3) where: (fL) when failure due to yield in strips          2 16. 2 1  . p L c M f f b s s (4) where: (fL) when failure due to yield in angles. Badalamenti et al. [7] Badalamenti et al. [7] proposed a design equation for determining the ultimate load that is carried by the RC column strengthened with steel angles and strips based on the effect of concrete confinement and load carried by the steel angles. The formula is expressed as the following equation :           campione 1 18cc s ys a yLp b d f A f n L t f (5) where, fcc = compressive strength of confined concrete; na = Maximum axial force in angles; na and fcc are calculated by using the following formula.        0.87   1 4.74   lcc co co f f f f (6)             2 2 1 1 1 1 1   3   1 2 max yl yl a yl q s t f t f L n L t f (7) Campione [18] Campione [18] proposed an equation for calculating the capacity of the strengthened column using steel jacketing. To determine the confinement pressure, it is assumed that the confinement pressure is reduced in steel strips suddenly while it remains constant along the steel angle. The effect of concrete confinement and composite action between the concrete column and steel jacketing is taken into consideration, as the following equation :   1 1. . . . 8. . . .ult c a ys L yLp n b d f n L t f A f (8) where, n is the dimensionless load capacity of confined concrete core and na is the maximum axial force available indirectly loaded angles in the dimensionless as the following equation:                   0.87 1.5   1 1.42      s cc b cc s cd f f e f (9)                   1.5 11 1 2 2 1 1 1 0.63   0.5b t s b a s n e b Lt L s s t (10) O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 5 Tarabia A. M. and Albakry H. F. [8] Tarabia A. M. and Albakry H. F. [8] proposed an equation for determining the carried load by a column strengthened by steel angles and strips, compared to that proposed equation in Calderon et al. [6] only with different in determining confinement effect on concrete core and load carried by steel jacketing, as the following equation.              2 2 2.     1 2 c L c s N F b b s E s t E (11) The load carried by the steel jacketing when axial compression of the column happens called direct loading, in this case, the steel jacket resists load with the concrete column from the beginning the load carried by the strengthened column, as the following equation.    1 12ult yLp L t f (12) Campione et al. [14] Campione et al. [14] proposed a design formula to define a plane fiber-section model of the column cross-section and take into consideration the frictional action along the column-angle face. The proposed formula is calibrated and validated by experimental results. The simple analytical stress-block procedure to derive continuous and simplified axial force bending moment domains is illustrated as a method for the hand-verification of reinforced cross-sections. The stress-strain laws assumed for the materials, the equilibrium equations of a reinforced cross-section written in the following form.                  \ \ \ \u c cc s s a a s s a aN b x f A A A A (13)                                                     \ \ \ \ 2 4 1 4 2 c u c cc s s a a a a u x l M b x f d A d A d t l d A N (14) where xc = concrete block neutral axis from compression zone; σ's and σs = steel stress for top and bottom reinforcement; A's and As = steel bars areas respectively; σ'a and σa = steel stresses for top and bottom angles. Salman and Sherrawi [15] Salman and Sherrawi [15] performed a nonlinear numerical analysis in order to determine the carried load of the high- strength column with steel angles in the corner of the column. Their numerical model takes into consideration the confinement effect of the concrete column due to existing steel angles and local buckling of it. They proposed a numerical method to predict the load capacity of the composite column at failure and study the efficiency of the steel angles in confining the concrete core. According to the numerical models, the column carried a large load after concrete cover spalling as discussed in their research. PROPOSED ANALYTICAL MODEL numerical method will be discussed to construct the interaction diagram (M-N) for the strengthened column using steel angles and strips as shown in Fig. (4). The axial load is plotted versus the bending moment M till failure. This method is based on the stress-strain compatibility procedure [17]. The effect of confinement on the concrete core, A Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 6 the carried load by the steel jacket, the reduction in compression load in the steel jacket, and the steel jacket parameters are taken into consideration. The formulation is produced using the main four points from A to D as following . Figure 4: Main points used to plot the interaction diagrams for the strengthened column using steel angles and strips. Point A (pure compression load: Point A will be plotted as a point referring to pure compression failure. The maximum load-carrying capacity of the strengthened column takes into consideration the main parameters such as the concrete strength, the amount of steel reinforcement in the column, the steel yield stress, the effect of confinement on the concrete core, the carried load by steel jacket, the dimension of the steel angles and strips, and the composite action between the concrete column and steel jacket. The design model of Campione, [18] will be used to calculate the ultimate carried load capacity of the strengthened column with the equation’s parameters shown in the previous section as following :            u cc a s angles y angles s ysP f b h n A f A f (15) Point B (compression failure assumed) : Point B will be plotted as a point referring to compression failure with a minimum eccentricity of the strengthened column. The compression failure is assumed to occur when the depth of the neutral axis is greater than its depth at the balanced position, Fig. (5). Figure 5: Stress-strain distributions of Point B which are used to plot the interaction diagrams for the strengthened columns. O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 7 In this case, the tension steel stress in the steel angles and reinforcement is below the yield stress, and for simplicity, the neutral axis position is chosen at the tension steel location (c=d). Thus, the developed force in the tension steel is equal to zero. The ultimate load and moment will be illustrated as follows:        \ \ \ \au cc sc sc s ysP f b A f A f (16)                          \ 2 2 2 2 u c s c h a h h M C C d S x (17) Point C (balanced failure assumed) Point C refers to the balanced failure of the column section. The failure of the balanced section occurs when the concrete reaches its maximum strain simultaneous with the yield strain in steel Fig. (6). By definition, the point at the balanced section, the strain in the tension steel equals (s). Thus, the stress in the tension steel equals (fy). The ultimate load and moment will be illustrated as follows:             au c c s T s cc bP C S C S T f b (18)                         \a 2 2 2 2 2 b u c s c h h h M C C d S x (19) Figure 6: Stress-strain distributions of Point C which are used to plot the interaction diagrams for the strengthened column. Point D (Pure bending) In the case of a column subjected to pure bending or infinity eccentricity, the axial load is considered to be zero Fig. (7). The locating of the neutral axis must be performed by applying the equilibrium equation as following:     c c s T sC S C S T (20)                  \ 0.8 cc c s c s s ys st yst c d c x a f b c E E A f A f c c (21) VERIFICATION OF THE ANALYTICAL PROPOSED FORMULA n order to verify the results of the proposed model in this study, some experimental researches work and numerical models have been concerned with stresses, strains, and deflections for the strengthened column to verify the proposed I Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 8 formula. In this study, strengthened columns are modeled and studied using the commercial finite element software (ANSYS -Version 19.2). Figure 7 : Stress-strain distributions of Point C which are used to plot the interaction diagrams for the strengthened column. Verification using finite element models. In order to verify the proposed model finite element models established in this paper using ANSYS software, the experimental researches work used in Verification has been concerned with stresses, strains, and deflections for the strengthened column. The methods for implementing the test, and the quality of the materials, and the configuration of the specimens. Solid element 65 is used to define concrete in 3D, link element 180 is used for steel reinforcement, solid 185 is defined for steel angles and strips, and steel plates for load distribution are defined as solid element 45. The components of the model, elements used, and boundary conditions are shown in Fig. 8. Figure 8: The numerical model’s component used in the verification. O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 9 Verification using previous experimental work. Experimental work results of previous researches will be used to validate the proposed analytical model. The first experimental work was taken from Montuori et al.[16], their specimens were (E-R1, D-R1, A-R1, and B-R1a) the second experimental work was taken from Elsamny et al.[12] their specimens were (Cl T3, C2 T5, C3 T7, C4 T3, C5 T5 , C6 T7, C7 T3, C8 T5, and C9 T7) . The third experimental work was taken from Ezz-Eldeen . [10] their specimens were (CS22e1 ,CS22e2, CS22e3 and CS22e4) . The fourth experimental work was taken from compaine et al. [14] their specimens were (RCAEX1 ,RCAEY1 ,RCBEX1 and RCBEY1). Tab. 1 shows the specimen's details and experimental work results. The results of the finite element models will be discussed in the next section. Failure load Comparison Ref. specimen column section fc' steel bars steel angles strips fya e N N N EXP FEM design mm MPa mm mm MPa mm kN kN kN Montuori  et al.[16]  E-R1 150×150x500 26.4 4 φ 16 mm 4 L 30×2 15x3@125 mm 353 50 745 782.7 630 0.85 0.80 D-R1 150×150x500 26.4 4 φ 16 mm 4 L 30×2 15x3@125 mm 353 75 556 583.5 530 0.95 0.91 A-R1 150×150x500 26.4 8 φ 10 mm 4 L 30×2 15x3@125 mm 353 50 717 752.6 620 0.86 0.82 B-R1a 150×150x500 26.4 8 φ 10 mm 4 L 30×2 15x3@125 mm 353 75 524 550.1 520 0.99 0.95 Elsamny et al.[12] Cl T3 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@490 mm 320 10 390 409.5 325 0.83 0.79 C2 T5 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@245 mm 320 10 360 378 310 0.86 0.82 C3 T7 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@164 mm 320 10 340 357 305 0.90 0.85 C4 T3 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@490 mm 320 20 290 304.5 235 0.81 0.77 C5 T5 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@245 mm 320 20 250 262.5 225 0.90 0.86 C6 T7 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@164 mm 320 20 250 262.5 215 0.86 0.82 C7 T3 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@490 mm 320 30 255 267.8 185 0.73 0.69 C8 T5 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@245 mm 320 30 210 220.5 170 0.81 0.77 C9 T7 120×120x1000 15 4 φ 8 mm 4 L 20×2 20x2@164 mm 320 30 210 220.5 160 0.76 0.73 Ezz‐ Eldeen .  [10]  CS22e1 120×160x1000 28 4 φ 8 mm 4 L 20×2 20x2@250 mm 380 10 643 675.2 575 0.89 0.85 CS22e2 120×160x1000 28 4 φ 8mm 4 L 20×2 20x2@250 mm 380 20 552 579.6 510 0.92 0.88 CS22e3 120×160x1000 28 4 φ 8 mm 4 L 20×2 20x2@250 mm 380 30 474 497.7 455 0.96 0.91 CS22e4 120×160x1000 28 4 φ 8mm 4 L 20×2 20x2@250 mm 380 40 420 441 410 0.98 0.93 compaine  et al. [14]  RCAEX1 220x300x820 12.7 6 φ 12 mm 4 L 50×5 40x4@136 mm 275 65 1048 1100 1150 1.10 1.05 RCAEY1 220x300x820 12.7 6 φ 12 mm 4 L 50×5 40x4@136 mm 275 55 1205 1266 1175 0.97 0.93 RCBEX1 220x300x820 24 6 φ 12 mm 4 L 50×5 40x4@136 mm 275 65 1370 1439 1250 0.91 0.87 RCBEY1 220x300x820 24 6 φ 12 mm 4 L 50×5 40x4@136 mm 275 55 1476 1550 1350 0.91 0.87 Table 1: specimens details and experimental work results and numerical models results. RESULTS AND DISCUSSION he comparison between the result of the proposed interaction diagram, experimental and numerical models is shown in Tab. 1. It can be seen that the results obtained using the proposed interaction diagram give a difference from 2 % to 30 % with an average difference of 12 % as illustrated in Tab. 1. It can be seen that the value of the experimental and numerical is bigger than the value of the proposed model, which is considered as an advantage of the proposed method as a conservative design approach. It is also noticed that the results of the strengthened column with big eccentricity have a small difference with the proposed model results than the column with small eccentricity. Fig. from (9-12) shows the comparison between the proposed interaction diagram and the experimental work of the researches used in verification. T 𝑁 𝑑𝑒𝑠𝑖𝑔𝑛 𝑁 𝐹𝐸𝑀 𝑁 𝑑𝑒𝑠𝑖𝑔𝑛 𝑁 𝐸𝑥𝑝 Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 10 Figure 9: Comparison between the proposed I-D and the experimental work of Ezz-Eldeen, [10]). Figure 10: Comparison between the proposed I-D and the experimental work of Elsamny et al.[12] ) Figure 11: Comparison between the proposed I-D and the experimental work of (Montuori, and Rizzano [16]). Figure 12: Comparison between the proposed I-D and the experimental work of compaine et al. [14]. As shown in Fig. (9-12), the interaction diagram constructed from the proposed model comparison with the experimental work results are in good agreement and gives a practical design method for determining the capacity of the strengthened column under the different cases of loading. It can be noticed that the first point (A) which refers to pure axial load is almost underestimation, while the other points have a good agreement with the experimental and numerical results. Fig. 13 shows the results of the numerical work using the finite element program. O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 11 Figure 13: Deformation in strengthened column specimen (c1 t3) at failure comparison between numerical and experimental results for verification. CONCLUSIONS his paper presents an analytical design formulation to construct the interaction diagrams (N-M) for the RC column strengthened by steel angles and strips, and the following conclusions can be drawn within the scope of this study:  The proposed analytical interaction diagram is efficient in determining the capacity of columns strengthened using steel jackets in different eccentricities.  The proposed analytical formula takes into consideration the factors affecting the behavior and the capacity of the strengthened column as the amount of loads resisted by the steel angles, the effect of steel strips spaci ng, and the effect of concrete confinement.  The proposed analytical formula was verified using experimental and numerical models with a good agreem ent with the difference from 2 % to 25 % with an average difference of 12 %.  The finite element models using the ANSYS program give a variety in studying the parameters affecting the behavior of the strengthened column under different eccentricities and valuable for constructing and verific ation the proposed analytical formulation. REFERENCES [1] Belal, M. F., Mohamed, H. M. and Morad, S. A. (2015) ‘Behavior of reinforced concrete columns strengthened by steel jacket’, HBRC Journal, 11(2), pp. 201–212. DOI: 10.1016/j.hbrcj.2014.05.002. [2] Saraswathi, M., Saranya, S. and Saranya, S. (2016). Strengthening of RC square column using steel angles, International Journal of Emerging Technology in Computer Science & Electronics, 20(3), pp. 226–231. [3] Khalifa, E. S. and Al-Tersawy, S. H. (2014) ‘Experimental and analytical behavior of strengthened reinforced concrete columns with steel angles and strips’, International Journal of Advanced Structural Engineering, 6(2). DOI: 10.1007/s40091-014-0061-6. [4] Campione, G. (2012). Strength and ductility of R.C. columns strengthened with steel angles and battens, Construction and Building Materials, 35, pp. 800–807. DOI: 10.1016/j.conbuildmat.2012.04.090. [5] Giménez, E. et al. (2009). Full-Scale Testing of Axially Loaded RC Columns Strengthened by Steel Angles and Strips Ester, Advances in Structural Engineering, 12(2), pp. 169–181. DOI: 10.1260/136943309788251704. [6] Adam, J. M. et al. (2009). Axially loaded RC columns strengthened by steel caging. Finite element modelling, Construction and Building Materials, 23(6), pp. 2265–2276. DOI: 10.1016/j.conbuildmat.2008.11.014. T Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01 12 [7] Badalamenti, V., Campione, G. and Mangiavillano, M. L. (2010). Simplified Model for Compressive Behavior of Concrete Columns Strengthened by Steel Angles and Strips, Journal of Engineering Mechanics, 136, pp. 230–238. DOI: 10.1061/ASCEEM.1943-7889.0000069. [8] Tarabia, A. M. and Albakry, H. F. (2014). Strengthening of RC columns by steel angles and strips, Alexandria Engineering Journal, 53(3), pp. 615–626. DOI: 10.1016/j.aej.2014.04.005. [9] Cavaleri, L., Trapani, F. Di and Ferrotto, M. F. (2016). Steel jacketing of RC columns: Reliability of capacity laws for concrete, in Environment International Conference, pp. 93–104. [10] Ezz-Eldeen (2016). Steel Jacketing Technique used in Strengthening Reinforced Concrete Rectangular Columns under Eccentricity for Practical Design Applications, International Journal of Engineering Trends and Technology, 35(5), pp. 195–204. DOI: 10.14445/22315381/ijett-v35p243. [11] Nimnim, H. T. and Al-bahadli, H. A. (2019) ‘Structural Behavior of Slender High-Strength RC Columns Strengthened by Steel Angles’, 23(4), pp. 1–12. DOI: 10.1061/(ASCE)SC.1943-5576.0000393. [12] Elsamny, M. K. et al. (2013). Experimental study of eccentrically loaded columns strengthened using a steel jacketing technique, International Journal of Civil, Architectural, Structural and Construction Engineering, 7(12), pp. 1–8. [13] Al-Sherrawi, M. H. and Salman, H. M. (2015). Analytical Model for Construction of Interaction Diagram for RC Columns Strengthened by Steel Jacket, International Journal of Science and Research, 6(10), pp. 2319–7064. DOI: 10.21275/ART20177139. [14] Campione, G. et al. (2017). Frictional effects in structural behavior of no-end-connected steel-jacketed RC columns: Experimental results and new approaches to model numerical and analytical response, Journal of Structural Engineering (United States), 143(8), pp. 1–15. DOI: 10.1061/(ASCE)ST.1943-541X.0001796. [15] Salman, H. M. and Al-Sherrawi, M. H. (2018). Interaction diagram for a reinforced concrete column strengthened with steel jackeT, International Journal of Civil Engineering and Technology, 9(6), pp. 1369–1377. [16] Montuori, R., Piluso, V. and Rizzano, G. (2004). Ultimate Resistance of Reinforced Concrete Columns Strengthened with Angles and Battens: Theoretical Model and Experimental Validation, 3 th World Conference on Earthquake Engineering. [17] British Standards Institution and For, C. (2005). Eurocode 8, design of structures for earthquake resistance. Part 3, General rules, seismic actions and rules for buildings. London: British Standards Institution. [18] Campione, G. (2013). RC columns strengthened with steel angles and battens: Experimental results and design procedure, Practice Periodical on Structural Design and Construction, 18(1), pp. 1–11. DOI: 10.1061/(ASCE)SC.1943-5576.0000125. << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 5.0 i kasnijim verzijama.) /HUN /ITA /JPN /KOR /LTH /LVI /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR /POL /PTB /RUM /RUS /SKY /SLV /SUO /SVE /TUR /UKR /ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.) >> /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ << /AsReaderSpreads false /CropImagesToFrames true /ErrorControl /WarnAndContinue /FlattenerIgnoreSpreadOverrides false /IncludeGuidesGrids false /IncludeNonPrinting false /IncludeSlug false /Namespace [ (Adobe) (InDesign) (4.0) ] /OmitPlacedBitmaps false /OmitPlacedEPS false /OmitPlacedPDF false /SimulateOverprint /Legacy >> << /AddBleedMarks false /AddColorBars false /AddCropMarks false /AddPageInfo false /AddRegMarks false /ConvertColors /ConvertToCMYK /DestinationProfileName () /DestinationProfileSelector /DocumentCMYK /Downsample16BitImages true /FlattenerPreset << /PresetSelector /MediumResolution >> /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ] >> setdistillerparams << /HWResolution [2400 2400] /PageSize [612.000 792.000] >> setpagedevice