Analysis of Fiber Reinforced Concrete Deep Beams with Large Opening Strengthened by CFRP Laminates

In this study, the behavior of reinforced concrete deep beams with large opening, used for efficient creation of doors, windows, and passage openings, which were strengthened by carbon fiber-reinforced polymer (CFRP) sheets, is examined. This analysis was carried out using finite element method and ANSYS computer program. The fiber reinforced concrete deep beams were subjected to a point monotonic loading. The results of the suggested analysis procedure were verified with experimentally tested deep beams given in reference [1]. The parametric study examined the CFRP sheets configuration and their thickness used as external reinforcement, and the results of strengthened beams are compared with reference unstrengthen deep beams to insure the effectiveness of external reinforcing method. The strengthened beams indicate an increase in load carrying capacity up to 25, 53 and 59% for vertical orientation CFRP sheets with 0.7, 1.4 and 2.8 mm thickness respectively. On the other hand, horizontal strengthening raises beams strength by 54, 78 and 90% for 0.7, 1.4 and 2.8 mm thickness respectively. Meanwhile deep beams with ring type configuration sheets augmented the strength by 85, 92 and 97% for the three types of the used sheet thicknesses. Load-deflection relationships indicate that the combined reinforced concrete and CFRP laminate system possess some nonlinear deformability. The use of CFRP laminates on the deep beams was found to have an influence on the stress concentration and the mode of failure. Anchoring the CFRP laminates around the opening regions helped in using a larger portion of the strength of the laminates. The deep beams strengthened by CFRP sheets exhibited diagonal shear cracks that were developed at a much slower rate and were ultimately accompanied by the peeling off of the CFRP laminates.


1.INTRODUCTION
According to ACI 318-14 the simply supported beam is classified as deep beam when the clear span is equal to or less than four times the overall depth or the application of concentrated load is within a distance equal to or less than two times the depth from the support face [2]. In most code specifications empirical formulas are used to design these members without considering the existence of the openings. One of the effective methods used by the researchers in the analysis and design methods is strut-tie models (STM) based on a series of concrete compressive struts and steel tensile ties connected at frictionless joints [1, 3 and 4]. However, the existence of any large opening between the applied loading force point and the support will disrupt the flow of force and may reduce the concrete strut in the truss analysis as the stress field exceeds the yield criteria causing significant reduction in load carrying capacity. The direct load paths between the applied load point and support points would interfere with the size and location of the selected opening [4,5].

2.FINITE ELEMENT IDEALIZATION
Modeling of the specimens in ANSYS, finite element program is performed using four different element idealizations for concrete; rebar reinforcement; steel plates; and CFRP sheets.

Reinforced Concrete Idealization
SOLID65 element is used for the 3-D modeling of fiber reinforced concrete. The solid is capable of plastic deformation, cracking in tension and crushing in compression. In addition the rebar has capability of modeling reinforcement behavior. The element is defined by eight nodes having three degrees of freedom at each node, translation in x, y, and z directions. The geometry and node locations of this element are shown in Figure.(1). Smeared cracking approach has been considered in modeling the concrete cracks in this study [12].

Steel Reinforcement Rebar Idealization
LINK8 element is used for modeling the 3-D reinforcement rebar with three degrees of freedom at each node: translation in the nodal x, y, and z directions. Bending of the element is not considered, while plasticity, stress stiffening, and large deflection capabilities are included. The geometry, node locations, and the coordinate system for this element are shown in Figure.(2) [12].  Figure.(2): Reinforcement bar element LINK8 geometry [12]

Steel Plate's Idealization
SOLID45 element is used for the steel plates at supports and under the load application points. The element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions.
The element has plasticity, stress stiffening, large deflection, and large strain capabilities. The geometry, node locations, and the coordinate system for this element are shown in Figure.(3).
This element is added at these locations to distribute the stresses, avoid stress concentration problems and to prevent local crushing of concrete elements near the support points and load application locations.

CFRP Sheets Idealization
SHELL41 element is used to simulate the CFRP sheets in the strengthened beam.
SHELL41 is a 3-D element having membrane (in-plane) stiffness but no bending (out-ofplane) stiffness. It is intended for structural parts where bending of the elements is of secondary importance compared with membrane force through sheets. The element has three degrees of freedom at each node: translations in the nodal x, y, and z directions.
The geometry, node locations, and the coordinate system for this element are shown in Figure.(4).The element has variable thickness, stress stiffening, and large deflection characteristics.

3.REAL CONSTANTS
In the finite element simulation, the second step after choosing the elements types is to prescribe the real constants of the elements. For Solid65 all data in this article are equal to zero and that physically means no smeared reinforcement was used in this simulation, where the analysis was directed toward discrete reinforcement approach, and the cross sectional area for the existed longitudinal steel reinforcement was (79 mm 2 ) as stipulated in the real constant of link8 elements. The loading plate and support plates were simulated using SOLID45 element which does not require any real constant as it's a three dimensional element and its dimensions can be specified by the space occupied by the elements. The CFRP element SHELL41 has three different types of real constants according to its thickness 0.7, 1.4 and 2.8 mm.

4.MATERIAL PROPERTIES
In this research, material nonlinearity is considered for both steel reinforcement and concrete, while steel plates for loading and support are considered elastic with isotropic properties. Five point stressstrain curve was selected for concrete with compressive strength of (34.5) MPa. The equations that were first presented by Desayi, P. and Krishnan [13] are used to describe the stress-strain relation of concrete. The equations are given below, and applications of these equations are shown in Figure.  Similarly for the beam strengthened in the vertical direction, the Young's modulus is taken to be 240x10 3 MPa in the y-axis while E for the other axes is 6.89 MPa.

5.BEAM MODELING
In order to verify the application of the suggested method to the analysis of deep beams with large opening by finite element method, the tested beam by Dipti et. al. [1] was  Figure 7 and Figure 8 respectively.

Meshing
In order to obtain accurate simulation of this beam with exact location of the opening, concrete covers and location of steel rebars, small element length of 32 and 38 mm were chosen and that leads to significant numbers of nodes and elements. On the other hand, these large element numbers allow the model to capture the real behavior of the beam. A total of (2944) nodes, (1656) concrete, (54) steel rebar, and (36) steel base plate elements in addition to a variable CFRP elements existed along the tested beam.

Supports
The supports were modeled in such a way that pin reaction was created in one end by

6.RESULTS AND DISCUSSION
A comparison between the experimental test results [1] and F.E. modeling response is presented in Figure 9, where a good agreement has been achieved between the two curves, although the experimental beam showed a more ductile behavior than FE modeling because a numerical solution cannot achieve the descending part of the load-deflection curve.  [1] and simulated by ANSYS The suggested method of analysis was used to investigate the behavior of deep beams with a unique large opening strengthened with CFRP sheets around the opening. In these processes three arrangements of CFRP sheets were used with three different thicknesses for each arrangement in the process of strengthening around the opening. In the first case, horizontal sheets were used, while in the second case vertical sheets were used. In the last case, ring strengthening was applied around the opening.
In Table.(1) the designation and properties of analysis of strengthened deep beams are shown according to direction of CFRP sheets and their thickness.  Figure.(10) represents load-deflection curve for strengthened deep beams with CFRP sheets of 0.7 mm thickness. The results show increase in load carrying capacity by 25, 54 and 85% for vertical, horizontal and ring type orientation of sheets respectively, compared with non-strengthened deep beam. Figure.(11) and (12) show the same curves for CFRP sheets of 1.4 mm and 2.8 mm thickness respectively. These curves illustrate increase in beam capacity by 53, 78 and 92% for sheets of 1.4 mm thickness while rise in strength for 2.8 mm thickness sheets which is not greater than 59, 90 and 97% compared with non-strengthened beam.
Further investigation of the above mention curves Figure. Figure.(16) confirms the stress distribution contour shown in Figure.(17).

7.CONCLUSIONS
From the analysis of results of deep beams with large opening strengthened by CFRP sheets, the following conclusions can be drawn concerning the efficiency of strengthening types and the ANSYS program to perform further types of analysis: -The load-deflection relation for deep beams with large opening shows a good agreement between the experimentally tested beams and that simulated by ANSYS program. -The Load-deflection curves for deep beams strengthened with horizontal CFRP sheets show approximately the same flexural rigidity and deflection at ultimate load when the sheet thickness is increased, but in vertical orientation of these sheets this property is reduced by 33% and 93% when the thickness is changed from 0.7 mm to 1.4 mm and to 2.8 mm respectively. Whereas the ring type strengthening revealed an inverse behavior as the deflection at ultimate load is increased by 8% and 12% respectively when the thickness is increased at the same degree.
-The crack generation around the large opening in strengthened by CFRP sheets displays diagonal shear cracks which were developed at a much slower rate.
-The cracks generation pattern and the stress distribution couture indicate the weakest point around the large opening is at the most top point above the support which needs further studies to enhance the region strengthening.