{"id":1709,"date":"2026-05-31T06:24:21","date_gmt":"2026-05-31T06:24:21","guid":{"rendered":"https:\/\/r-maher.com\/?p=1709"},"modified":"2026-05-31T09:33:06","modified_gmt":"2026-05-31T09:33:06","slug":"flexural-analysis-of-damaged-rc-beams-retrofitted-with-cfrp-laminates","status":"publish","type":"post","link":"https:\/\/r-maher.com\/?p=1709","title":{"rendered":"Flexural Analysis of Reinforced Concrete Beams with Pre-Existing Damage and Composite Strengthening"},"content":{"rendered":"<p>This study investigates the flexural performance of reinforced concrete (RC) beams under four-point bending conditions. The focus is on evaluating how <strong>pre-existing internal damages<\/strong> and the application of <strong>external composite strengthening (CFRP laminates)<\/strong> affect structural behavior.<\/p>\n<p>The tested beams fall into three major categories:<\/p>\n<ul>\n<li>Control beam (CB) without damage<\/li>\n<li>Beams with internal pre-cracks or rebar damage<\/li>\n<li>Damaged beams strengthened with externally bonded FRP laminates<\/li>\n<\/ul>\n<p>Each beam had a cross section of 25\u00d725 cm and a clear span of 180 cm. Loading was applied through a four-point bending configuration.<\/p>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3><span style=\"font-size: 16px;\"><img decoding=\"async\" class=\"alignleft wp-image-914\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/Picture4-1.png\" alt=\"\" width=\"50\" height=\"53\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/Picture4-1.png 191w, https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/Picture4-1-184x194.png 184w\" sizes=\"(max-width: 50px) 100vw, 50px\" \/><br \/>\n<strong>Damage Scenarios and Beam Identification<\/strong><br \/>\n<\/span><\/h3>\n<p>Based on the classification in the original study (as defined in experimental setup and material datasheets):<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-1714\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/02.png\" alt=\"\" width=\"899\" height=\"720\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/02.png 899w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/02-300x240.png 300w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/02-768x615.png 768w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/02-184x147.png 184w\" sizes=\"(max-width: 899px) 100vw, 899px\" \/><\/p>\n<p>Each crack was pre-defined by inserting voids or initiating cracks to simulate field-like degradation.<\/p>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3><img decoding=\"async\" class=\"alignleft wp-image-912\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/document_search_magnifying_glass_icon_187087.png\" alt=\"\" width=\"50\" height=\"50\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/document_search_magnifying_glass_icon_187087.png 256w, https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/document_search_magnifying_glass_icon_187087-150x150.png 150w, https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/document_search_magnifying_glass_icon_187087-184x184.png 184w\" sizes=\"(max-width: 50px) 100vw, 50px\" \/><br \/>\nProject Highlights<\/h3>\n<ul>\n<li>Concrete grade: C25 (f\u2019c = 25 MPa) (as defined in experimental setup and material datasheets)<\/li>\n<li>Longitudinal reinforcement: \u03d510 (4 bars) and \u03d514 (2 bars)<\/li>\n<li>Shear reinforcement: \u03d510 stirrups at 16 cm spacing<\/li>\n<li>Effective beam span: 180 cm<\/li>\n<li>Failure in unstrengthened beams generally occurred at or near pre-damaged zones<\/li>\n<\/ul>\n<p>After experimental damage characterization, several beams were retrofitted with externally bonded CFRP laminates.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1715\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/03.png\" alt=\"\" width=\"1280\" height=\"382\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/03.png 1280w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/03-300x90.png 300w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/03-1024x306.png 1024w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/03-768x229.png 768w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/03-184x55.png 184w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/03-1200x358.png 1200w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/p>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-911\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/Picture2-5.png\" alt=\"\" width=\"50\" height=\"54\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/Picture2-5.png 216w, https:\/\/r-maher.com\/wp-content\/uploads\/2024\/11\/Picture2-5-184x198.png 184w\" sizes=\"(max-width: 50px) 100vw, 50px\" \/><\/p>\n<h3>FE Analysis Tips and Tricks<\/h3>\n<ul data-spread=\"false\">\n<li>Damage zones modeled explicitly using cut or weakened regions<\/li>\n<li>Shell elements and solid modeling hybrid used to simulate cracks<\/li>\n<li>Interface contact behavior (for FRP debonding) should be carefully tuned<\/li>\n<li>Experimental deflection results were used to calibrate numerical models<\/li>\n<\/ul>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>Material Selection<\/h3>\n<h4>\u2022 Concrete (C25):<\/h4>\n<ul data-spread=\"false\">\n<li>f\u2019c = 25 MPa, E = 27.4 GPa, \u03bd = 0.2, Density = 2400 kg\/m\u00b3<\/li>\n<\/ul>\n<h4>\u2022 Reinforcing Steel:<\/h4>\n<ul data-spread=\"false\">\n<li>f\u1d67 = 422 MPa (longitudinal), 430 MPa (stirrups)<\/li>\n<li>E = 200 GPa, \u03bd = 0.3, Density = 7850 kg\/m\u00b3<\/li>\n<\/ul>\n<h4>\u2022 CFRP \u2013 Epoxy Carbon UD Prepreg:<\/h4>\n<ul data-spread=\"false\">\n<li>E\u2081 = 200 GPa, E\u2082 = 8.6 GPa, \u03bd\u2081\u2082 = 0.27, G\u2081\u2082 = 4.7 GPa<\/li>\n<li>Tensile strength: 4.95 GPa (fiber), 29 MPa (transverse)<\/li>\n<li>Shear strength: 60 MPa (XY\/XZ), 32 MPa (YZ)<\/li>\n<li>Interface weakening factor: 0.8<\/li>\n<\/ul>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>Geometry Editing<\/h3>\n<ul data-spread=\"false\">\n<li>Beam size: 25 cm \u00d7 25 cm cross-section, 210 cm span<\/li>\n<li>Strengthening with 1 or more CFRP layers on tension face only<\/li>\n<li>CFRP layer width = 8 cm, spacing = 7 cm<\/li>\n<li>Applied on beams with damage in mid-span, third-span, or combined<\/li>\n<\/ul>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>Mesh Generation<\/h3>\n<ul data-spread=\"false\">\n<li>Element size: Refined near damage zones<\/li>\n<li>Explicit Dynamic solver used to capture post-peak and failure behavior<\/li>\n<li>Reinforcement bars modeled using Line Body elements and embedded in concrete<\/li>\n<li>Numerical results validated using peak load and crack pattern comparison<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1717\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/04.png\" alt=\"\" width=\"1280\" height=\"426\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/04.png 1280w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/04-300x100.png 300w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/04-1024x341.png 1024w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/04-768x256.png 768w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/04-184x61.png 184w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/04-1200x399.png 1200w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/p>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>Analysis Settings<\/h3>\n<ul data-spread=\"false\">\n<li><span class=\"selection-highlight cursor-text group is-comment transition-colors bg-yellow-100 dark:bg-yellow-400 dark:bg-yellow-400\/30 group-[.is-comment]:bg-opacity-40\" data-comment-id=\"tdc-2-a70ccae4-3939-41ae-8eae-b38d4b07c4fd\">Explicit dynamic simulation to capture post-cracking behavior<\/span><\/li>\n<li>Load applied gradually through two concentrated points<\/li>\n<li>Supports modeled as pinned and roller<\/li>\n<\/ul>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>Connection Types<\/h3>\n<ul data-spread=\"false\">\n<li>Rebars fully embedded (no slip)<\/li>\n<li>CFRP\u2013concrete interface modeled using bonded contact (no slip allowed)<\/li>\n<\/ul>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>Boundary Conditions<\/h3>\n<ul data-spread=\"false\">\n<li>Simply supported setup<\/li>\n<li>Supports: pinned and roller<\/li>\n<li>CFRP applied only to tension face<\/li>\n<\/ul>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>Load Conditions<\/h3>\n<ul data-spread=\"false\">\n<li>Four-point bending<\/li>\n<li>Load introduced symmetrically across central region<\/li>\n<\/ul>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>\ud83d\udd04 Results Interpretation<\/h3>\n<h4>Experimental vs. FEM Results \u2013 With and Without Composite (CFRP)<\/h4>\n<table>\n<tbody>\n<tr>\n<th><strong>Specimen<\/strong><\/th>\n<th><strong>Experimental (No CFRP)<\/strong><\/th>\n<th><strong>FEM (No CFRP)<\/strong><\/th>\n<th><strong>Error %<\/strong><\/th>\n<th><strong>Experimental (CFRP)<\/strong><\/th>\n<th><strong>FEM (CFRP)<\/strong><\/th>\n<th><strong>Error %<\/strong><\/th>\n<\/tr>\n<tr>\n<td><strong>CB<\/strong> (Control)<\/td>\n<td>61.5<\/td>\n<td>57.6<\/td>\n<td>6.3%<\/td>\n<td>75.0<\/td>\n<td>64.6<\/td>\n<td>13.8%<\/td>\n<\/tr>\n<tr>\n<td><strong>BDRS<\/strong><\/td>\n<td>22.5<\/td>\n<td>25.7<\/td>\n<td>14.2%<\/td>\n<td>80.0<\/td>\n<td>81.9<\/td>\n<td>2.3%<\/td>\n<\/tr>\n<tr>\n<td><strong>BDRA<\/strong><\/td>\n<td>16.5<\/td>\n<td>19.0<\/td>\n<td>15.2%<\/td>\n<td>70.0<\/td>\n<td>62.0<\/td>\n<td>11.4%<\/td>\n<\/tr>\n<tr>\n<td><strong>BDCM15-2.5<\/strong><\/td>\n<td>41.5<\/td>\n<td>39.9<\/td>\n<td>3.9%<\/td>\n<td>71.0<\/td>\n<td>66.0<\/td>\n<td>7.1%<\/td>\n<\/tr>\n<tr>\n<td><strong>BDCM10-2.5<\/strong><\/td>\n<td>27.5<\/td>\n<td>30.2<\/td>\n<td>9.8%<\/td>\n<td>80.0<\/td>\n<td>71.5<\/td>\n<td>10.6%<\/td>\n<\/tr>\n<tr>\n<td><strong>BDCO15-2.5<\/strong><\/td>\n<td>54.0<\/td>\n<td>52.3<\/td>\n<td>3.2%<\/td>\n<td>82.0<\/td>\n<td>73.7<\/td>\n<td>10.2%<\/td>\n<\/tr>\n<tr>\n<td><strong>BDCM15-1.5<\/strong><\/td>\n<td>33.5<\/td>\n<td>33.5<\/td>\n<td>0.1%<\/td>\n<td>75.0<\/td>\n<td>71.6<\/td>\n<td>4.5%<\/td>\n<\/tr>\n<tr>\n<td><strong>BDCM15-1.5+O10-1<\/strong><\/td>\n<td>42.5<\/td>\n<td>41.1<\/td>\n<td>3.4%<\/td>\n<td>61.0<\/td>\n<td>68.8<\/td>\n<td>12.7%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>\ud83d\udd0d Interpretation Highlights<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1720 alignright\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/06.png\" alt=\"\" width=\"1108\" height=\"591\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/06.png 1108w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/06-300x160.png 300w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/06-1024x546.png 1024w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/06-768x410.png 768w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/06-184x98.png 184w\" sizes=\"(max-width: 1108px) 100vw, 1108px\" \/><\/h4>\n<ul data-spread=\"false\">\n<li><strong>Best FEM Accuracy (No CFRP):<\/strong> BDCM15-1.5 (0.1% error)<\/li>\n<li><strong>Best FEM Accuracy (With CFRP):<\/strong> BDRS (2.3% error)<\/li>\n<li><strong>Worst FEM Prediction (With CFRP):<\/strong> BDCM15-1.5+O10-1 (12.7% error)<\/li>\n<li><strong>Trend:<\/strong> CFRP strengthening generally improves agreement in beams with symmetrical or controlled damage. In complex or combined damage, deviation may increase due to nonlinear effects or modeling assumptions.<\/li>\n<\/ul>\n<p>The results compared experimental peak load vs. FEA for each beam:<\/p>\n<ul>\n<li><strong>Error without CFRP<\/strong> was highest for severely damaged beams (up to ~15%)<\/li>\n<li><strong>Strengthening with CFRP<\/strong> reduced the relative error significantly (most below 7%)<\/li>\n<li>Beams with dual damage zones benefitted most from FRP wrapping<\/li>\n<\/ul>\n<p>The analysis demonstrated that using CFRP can effectively compensate for internal damage and restore or exceed original flexural capacity.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1718\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/05.png\" alt=\"\" width=\"1063\" height=\"323\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/05.png 1063w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/05-300x91.png 300w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/05-1024x311.png 1024w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/05-768x233.png 768w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/05-184x56.png 184w\" sizes=\"(max-width: 1063px) 100vw, 1063px\" \/><\/p>\n<div contenteditable=\"false\">\n<hr \/>\n<\/div>\n<h3>\ud83d\udcca Summary<\/h3>\n<p>This project confirms that:<\/p>\n<ul>\n<li>Accurate modeling of internal damage is critical for flexural FEA<\/li>\n<li>External CFRP retrofit significantly improves accuracy and performance<\/li>\n<li>Layer width, spacing, and fiber properties must be aligned with manufacturer guidelines<\/li>\n<\/ul>\n<p>By combining experimental setups with calibrated FE models, engineers can reliably simulate and optimize real-world RC beam retrofitting scenarios.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1719\" src=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/07.png\" alt=\"\" width=\"1130\" height=\"256\" srcset=\"https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/07.png 1130w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/07-300x68.png 300w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/07-1024x232.png 1024w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/07-768x174.png 768w, https:\/\/r-maher.com\/wp-content\/uploads\/2026\/05\/07-184x42.png 184w\" sizes=\"(max-width: 1130px) 100vw, 1130px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This study investigates the flexural performance of reinforced concrete (RC) beams under four-point bending conditions. The focus is on evaluating&#8230;<\/p>\n","protected":false},"author":2,"featured_media":1711,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[165,169,164,168,166,73,170,167,171],"class_list":["post-1709","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-analysis","tag-cfrp","tag-civilengineering","tag-concretestructures","tag-damagesimulation","tag-explicitdynamics","tag-finiteelementanalysis","tag-numericalvalidation","tag-rcbeams","tag-simulation-based-design"],"acf":[],"_links":{"self":[{"href":"https:\/\/r-maher.com\/index.php?rest_route=\/wp\/v2\/posts\/1709","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/r-maher.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/r-maher.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/r-maher.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/r-maher.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1709"}],"version-history":[{"count":5,"href":"https:\/\/r-maher.com\/index.php?rest_route=\/wp\/v2\/posts\/1709\/revisions"}],"predecessor-version":[{"id":1721,"href":"https:\/\/r-maher.com\/index.php?rest_route=\/wp\/v2\/posts\/1709\/revisions\/1721"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/r-maher.com\/index.php?rest_route=\/wp\/v2\/media\/1711"}],"wp:attachment":[{"href":"https:\/\/r-maher.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1709"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/r-maher.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1709"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/r-maher.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}