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\title{Failure Modes for I-Section GFRP Beams}
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\begin{document}

             \author[1]{Mamadou  Konate}

             \author[2]{Mamadou  Konate}

             \author[3]{Zia  Razzaq}

             \affil[1]{  Old Dominion University}

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\date{\small \em Received: 10 June 2015 Accepted: 30 June 2015 Published: 15 July 2015}

\maketitle


\begin{abstract}
        


This paper presents calculations for the failure modes for I-section Glass Fiber Reinforced Polymer (GFRP) beams with single mid-span web brace. Theoretical predictions are made using ASCE-LFRD Pre-Standard for FRP structures. For the member length considered, it is found that for small and medium I-sections the failure mode is governed by lateral-torsional buckling and for bigger I-sections the failure mode is governed by material rupture. The outcome of the predicted lateral-torsional buckling mode is compared with that observed experimentally.

\end{abstract}


\keywords{failure modes, I-section GFRP ASCE-LFRD standard for FRP structures.}

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\let\tabcellsep& 	 	 		 
\section[{I. Introduction}]{I. Introduction}\par
azzaq, Z, Prabhakaran, R., and Sirjani, M. B \hyperref[b0]{[1]} have conducted an experimental and theoretical study of the flexural-torsional behavior of reinforced beams using LFRD approach. The same authors have also provided a load and resistance factor design (LFRD) approach for fiber-reinforced plastic (FRP) \hyperref[b1]{[2]}. The paper presents the outcome of a study on failure modes for I-section GFRP beams. 
\section[{II. Experimental Study}]{II. Experimental Study}\par
A 93 inches long GFRP beam with a 8 x 4 x 0.5 in. is tested as shown in Figure  {\ref 1}. 
\section[{Fig. 1 : Schematic of I-Section GFRP beam}]{Fig. 1 : Schematic of I-Section GFRP beam}\par
The test procedure involved applying the load, P, in small increments and recording the resulting deflections. Figure  {\ref 2} shows the experimental test setup. In this figure, the ends have shear-type connections and a hydraulic jack of 50-kip capacity with load cell and a loading device are also shown.  ?? ð??"ð??" = Distance from the neutral axis to the extreme fiber of the flange, in. ?? ?? = Distance from the neutral axis to the extreme fiber of the web, in. The resistance factor ? = 0.65 is used.?? ???? = 4?? ???? ?? (6) ?? ð??"ð??"???? = 4??ð??"ð??" ???? ?? (7) ?? ?????? = 4???? ???? ?? (8) ?? ð??"ð??"ð??"ð??" = 4?? ð??"ð??"ð??"ð??" ?? (9)\par
In Equations 6 through 9, ?? ???? , ?? ð??"ð??"???? , ?? ?????? , and ?? ð??"ð??"ð??"ð??" are the load-carrying capacities due to lateraltorsional buckling, local instability in the flanges, local instability in the webs, and material rupture, respectively.\par
If ?? ???? = ?? ð??"ð??"???? = ?? ?????? = ?? ð??"ð??"ð??"ð??" = ?? ð??"ð??" is the loadcarrying capacity of the member, a LFRD approach is proposed as follows:?? ð??"ð??" ??? ??\textbf{(10)}\par
where ?? ?? is the minimum of the values obtained in Equations 6-9. The resistance factor ? = 0.7, 0.8, and 0.65 depending whether the failure is due to lateral torsional buckling, local instability in the flanges or webs, and rupture of the materials, respectively. The beam design load is expressed as:?? ?? = 1.2?? ?? + 1.6?? ??\textbf{(11)}\par
?? ?? ? ?? ð??"ð??" (12) For 8 x 4 x 0.5 in., the experimental lateraltorsional buckling load is found to be 4.70\% higher than the predicted result. However, the experimental cracking Lastly, applying the formula of maximum moment for a simply supported beam with a point load as shown in Figure  {\ref 1}, the respective loads are obtained: in which ?? ?? and ?? ?? are the dead and live loads for the beam. The proposed LFRD approach criterion for the member can finally be written as:\par
where ?? ?? and ?? ð??"ð??" are defined in Equations 10 and 11, respectively. Table \hyperref[tab_1]{1} shows the maximum loads for the following I-beams: 3x1x0.25 in., 6x3x0.375 in., 8x4x0.5 in., 10x5x0.375 in., and 12x6x0.5 in. load is 27.60\% lower than the predicted result. As seen in Table \hyperref[tab_1]{1}, for the first three I-sections namely 3x1x0.25, 6x3x0.375, 8x4x0.50, the failure mode is governed by lateral-torsional buckling. However, for the last two Isections namely 10x5x0.375 and 12x6x0.5, the failure mode is governed by material rupture. 
\section[{IV.}]{IV.}\par
A study on failure modes for I-section GFRP beams is presented. The predicted buckling load for the GFRP beam is in agreement with the experimental value. Based on the analysis for the member length considered, the failure mode is governed by lateraltorsional buckling for smaller and medium cross sections. However, the material rupture governs the failure mode for the bigger sections.\begin{figure}[htbp]
\noindent\textbf{22233}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 2 :) 2 2 + 3 ?? ?? ?? ?? 3 ,}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Failure}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.2622340425531915\textwidth}P{0.13111702127659575\textwidth}P{0.14468085106382977\textwidth}P{0.17180851063829786\textwidth}P{0.14015957446808508\textwidth}}
I -Section\tabcellsep ?P LB\tabcellsep ?P fLB\tabcellsep ?P wLB\tabcellsep ?P cr\\
in.\tabcellsep lbs\tabcellsep lbs\tabcellsep lbs\tabcellsep lbs\\
3x1.5x0.25\tabcellsep 170\tabcellsep 2526\tabcellsep 35389\tabcellsep 8867\\
6x3x0.375\tabcellsep 2041\tabcellsep 8506\tabcellsep 162479\tabcellsep 4980\\
8x4x0.50\tabcellsep 8026\tabcellsep 20162\tabcellsep 385136\tabcellsep 11804\\
10x5x0.375\tabcellsep 13581\tabcellsep 15522\tabcellsep 279162\tabcellsep 13890\\
12x6x0.5\tabcellsep 37399\tabcellsep 20220\tabcellsep 592231\tabcellsep 26635\end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Razzaq et al. (30 January-1 February)]{b0}\label{b0} 	 		‘Flexural-Torsional Behavior of FRP Channel Section Beams’.  		 			Z Razzaq 		,  		 			R Prabhakaran 		,  		 			M B Sirjani 		.  	 	 		\textit{Proceding 50 th Annual Conference, Composites Institute, The Society of the Plastic Industry},  				 (eding 50 th Annual Conference, Composites Institute, The Society of the Plastic IndustryInc., Cincinnati, Ohio)  		30 January-1 February.  	 
\bibitem[Razzaq et al. ()]{b1}\label{b1} 	 		‘Load and Resistance Factor Design (LRFD) Approach for Reinforced-Plastic Channel Beam Buckling Composites’.  		 			Z Razzaq 		,  		 			R Prabhakaran 		,  		 			M B Sirjani 		.  	 	 		\textit{Engineering International Journal}  		1996. p. .  	 
\bibitem[Pre-Standard for Load and Resistance Factor Design (LFRD) of Pultruded Fiber Reinforced Polymer (FRP) Structures, Submitted to: American Composites Manufacturers Association (ACMA) (2010)]{b2}\label{b2} 	 		\textit{Pre-Standard for Load and Resistance Factor Design (LFRD) of Pultruded Fiber Reinforced Polymer (FRP) Structures, Submitted to: American Composites Manufacturers Association (ACMA)},  		September 10, 2010. ASCE.  	 
\end{bibitemlist}
 			 		 	 
\end{document}