Khanloo et al 2021b - Revision history

Rimni: /* 4. Validity */

2021-12-14T15:32:48Z

‎4. Validity

Rimni at 15:32, 14 December 2021

2021-12-14T15:32:18Z

Rimni at 14:36, 14 December 2021

2021-12-14T14:36:26Z

Rimni at 14:35, 14 December 2021

2021-12-14T14:35:47Z

Rimni at 14:35, 14 December 2021

2021-12-14T14:35:34Z

Rimni: /* 3.1. Theory relationship */

2021-12-14T13:42:35Z

‎3.1. Theory relationship

Rimni at 13:12, 14 December 2021

2021-12-14T13:12:17Z

Rimni at 12:15, 20 August 2021

2021-08-20T12:15:06Z

Rimni at 12:12, 20 August 2021

2021-08-20T12:12:56Z

Rimni: /* References */

2021-08-20T12:10:48Z

‎References

@@ Line 161: / Line 161: @@
 {| style="text-align: center; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math display="inline">p=0.5\ast \frac{5430}{1.1}\ast 13.5\ast 0.1=3331.05</math>
+| style="text-align: center;" | <math display="inline">p=0.5\ast \displaystyle\frac{5430}{1.1}\ast 13.5\ast 0.1=3331.05</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" |(5)

@@ Line 151: / Line 151: @@
 {| style="text-align: center; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" |<math>g_2 =\min\left| \begin{matrix}\frac{1}{8}\ast \left( 0.361+{g}_{2}\right) \ast (2\ast 600{)}^{2}<0.33\ast 2400\ast 429\\\frac{5}{384}\ast \left( \frac{0.361+{g}_{2}}{2\ast {10}^{6}\ast 5790}\right) \ast (2\ast 600{)}^{4}\leq \frac{1}{800}\ast \left( 2\ast 600\right) \quad \quad \quad \end{matrix}\right.\rightarrow {g}_{2}= 0.282</math>
+| style="text-align: center;" |<math>g_2 =\min\left| \begin{matrix}\displaystyle\frac{1}{8}\ast \left( 0.361+{g}_{2}\right) \ast (2\ast 600{)}^{2}<0.33\ast 2400\ast 429\\\displaystyle\frac{5}{384}\ast \left( \frac{0.361+{g}_{2}}{2\ast {10}^{6}\ast 5790}\right) \ast (2\ast 600{)}^{4}\leq \displaystyle\frac{1}{800}\ast \left( 2\ast 600\right) \quad \quad \quad \end{matrix}\right.\rightarrow {g}_{2}= 0.282</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" |(4)

@@ Line 308: / Line 308: @@
 |}
-===5.2. Numerical results of reinforced steel beam with one to three layers of bi-directional CFRP composite===
+===5.2 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 [[#tab-5|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. As illustrated in [[#img-5|Figure 5]], the use of bidirectional fiber in reducing bending stress values is effective than the corresponding bending fibers. As shown in [[#img-6|Figures 6]], changing the angle of the composite fibers improve the flexural stress values only in unidirectional fiber mode.

@@ Line 101: / Line 101: @@
 In this research, the results of bending stresses are investigated using the relation between theory and software modeling.
-===3.1. Theory relationship===
+===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:
@@ Line 136: / Line 136: @@
 It is noteworthy that in the aforementioned relationships, <math>A_f</math> is steel beam compression wing area, <math>A_{cfrp}</math> is cross-sectional area of composite sheet, <math>F_{fk}</math> is tensile stress value due to composite fibers, and   <math display="inline">{\gamma}_{f}</math> is the relationship coefficient value as shown in Eq.(2).
-===3.2. Software modeling===
+===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.

@@ Line 47: / Line 47: @@
 ==2. Materials properties==
-===2.1. Steel beam===
+===2.1 Steel beam===
 In this research, steel beams with geometrical and technical properties as shown in [[#img-2|Figure 2]] and in [[#tab-1|Table 1]] are used as follows.
@@ Line 80: / Line 80: @@
 |}
-===2.2. Composite fibers===
+===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 [[#tab-2|Table 2]] are used as follows.

@@ Line 129: / Line 129: @@
 {| style="text-align: center;vertical-align: top;margin:auto;width: 100%;"
 |-
-| <math>{g}_{2}=min\left| \begin{matrix}\frac{1}{8}\ast \left( {g}_{1}+{g}_{2}\right) \ast (2L{)}^{2}\leq 0.33\ast Fy\ast Sx\\\frac{5}{384}\ast \left( \frac{{g}_{1}+{g}_{2}}{E\ast I}\right) \ast (2L{)}^{4}\leq \frac{1}{800}\ast (2L)\end{matrix}\right.</math>
+| <math>{g}_{2}=min\left| \begin{matrix}\displaystyle\frac{1}{8}\ast \left( {g}_{1}+{g}_{2}\right) \ast (2L{)}^{2}\leq 0.33\ast Fy\ast Sx\\ \displaystyle\frac{5}{384}\ast \left( \displaystyle\frac{{g}_{1}+{g}_{2}}{E\ast I}\right) \ast (2L{)}^{4}\leq \displaystyle\frac{1}{800}\ast (2L)\end{matrix}\right.</math>
 |}
 |  style="text-align: right;vertical-align: center;width: 5px;text-align: right;white-space: nowrap;"|(3)

@@ Line 21: / Line 21: @@
 One of the most common methods of strengthening concrete structures is the use of composite fibers such as FRP. These fibers have found a special place in structural retrofitting methods due to a number of specific ability including lightness and ease of performance. Reinforced concrete structures have long been considered by design engineers for the possibility of retrofitting high strength composite steel structures. In this study, twenty-two steel beam models were modeled by ANSYS software. Variable parameters studied in the modeled steel beams can be referred to the number, orientation and thickness of composite layers.
-'''Keywords:''' Steel beams, CFRP, unidirectional and bi-directional, bending stress.
+'''Keywords:''' Steel beams, CFRP, unidirectional and bi-directional, bending stress
 ==1. Introduction==

@@ Line 89: / Line 89: @@
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''E'''
+! '''E''' !! '''ƃ''' !! '''Ɣ''' !! '''µ'''
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''ƃ'''
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''Ɣ'''
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''µ'''
 |-
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|1.4e6
+|  style="text-align: center;vertical-align: top;"|1.4e6
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|5430
+|  style="text-align: center;vertical-align: top;"|5430
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|1.9e-3
+|  style="text-align: center;vertical-align: top;"|1.9e-3
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|0.2
+|  style="text-align: center;vertical-align: top;"|0.2
 |}

@@ Line 65: / Line 65: @@
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
-|  style="text-align: center;"|l
+!  l !! h !! b !! t !! E !! F<sub>y</sub> !! F<sub>u</sub> !!ɣ !! S<sub>X</sub> !! I<sub>X</sub> !! g
-|  style="text-align: center;"|h
-|  style="text-align: center;"|b
-|  style="text-align: center;"|t
-|  style="text-align: center;"|E
-|  style="text-align: center;"|F<sub>y</sub>
-|  style="text-align: center;"|F<sub>u</sub>
-|  style="text-align: center;"|ɣ
-|  style="text-align: center;"|S<sub>X</sub>
-|  style="text-align: center;"|I<sub>X</sub>
-|  style="text-align: center;"|g
 |-
 |  style="text-align: center;"|600
@@ Line 89: / Line 79: @@
 |  style="text-align: center;"|0.361
 |}
 ===2.2. Composite fibers===

@@ Line 443: / Line 443: @@
 ==References==
 [1]  Selvaraj S.,  Madhavan M.,  Dongre S.U. Experimental studies on strength and stiffness enhancement in CFRP-strengthened structural steel chanel sections under flexure. J. Compos. Constr., 04016042:1-12, 2016.
@@ Line 469: / Line 470: @@
 [13]  Bennati S., Colonna D.,  Valvo P.S. Evaluation of the increased load bearing capacity of steel beams strengthened with pre-stressed FRP laminates. Frattura ed Integrita Strutturale, 38:377-391, 2016.