Analytical Study on FRC Deep Beam Designed by Strut and Tie Method

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1 Analytical Study on FRC Deep Beam Designed by Strut and Tie Method BobyTharu Assistant Professor, Muthoot Institute of Technology and Science, Varikoli P.O, Puthencruz, Ernakulam ABSTRACT A beam whose depth is comparable to span is known as deep beam. The present Indian Standard code recommendations are inadequate for the design of deep beams. Strut and tie method (STM) is identified as an effective tool for the design of deep beams. This study deals with deep beams designed by STM described in ACI using normal concrete and fiber reinforced concrete. The nonlinear static analysis is done using ATENA 3D. Keywords Deep beam, STM 1. INTRODUCTION The use of Reinforced deep beam has become more prevalent in recent years. In IS-456 (2000) clause 29, a simply supported beam is classified as deep when the ratio of its effective span, L to overall depth, D is less than 2. The behavior of deep beams is significantly different from that of beams of normal proportions, requiring special consideration in analysis, design and detailing of reinforcement. It has been recently understood that the strut and tie method (STM) is an effective tool for the design of both B (Bernoulli) and D (Disturbed) regions. Since the STM is a realistic approach, this has found place in many codes like American code, Canadian code and New Zealand code. Strut-and-tie modeling provides design engineers with a more flexible and intuitive option for designing structures, that are heavily influenced by shear. In this paper three Deep beam model were analyzed with varying percentage of fiber content. Different properties such as failure load, cracking, deflection etc. were compared. 2. MATERIAL AND ANALYSIS MODEL The cylinder compressive strength of concrete was 40 MPa. The various properties for the concrete were taken from the journal Stress-strain curves for steel fiber-reinforced concrete in compression for 1%and 2% fiber content. For concrete without fiber, default material available in the ATENA 3D was used. The reinforcement bars used were Fe 415 and the steel plate used was with Es = MPa. Three models analysed in the ATENA 3D were, FRC 0- without any steel fiber FRC 1-1% steel fiber FRC 2-2% steel fiber The characteristics of the concrete used are given in the Table 1 and Figure 1.The deep beam model used for the analysis is given in Figure 2. Table 1. Material properties Cylinder compressive strength (N/mm 2 ) Modulus of Elasticity (E c ) (N/mm 2 ) Tensile strength (N/mm 2 ) FRC FRC BobyTharu

2 50 stress (σ)(n/mm FRC 1 FRC strain (Ɛ) Fig 1:Stress strain curve Fig2: Analysis model 3. DESIGN OF DEEP BEAM USING STM The deep beam was designed using STM described in APPANDIX A of ACI The beams were designed against an external total load of 1000 kn, applied at the deep beams in two equal loads symmetrically. There can be many possible truss models for the given loading and geometry of the deep beams. However, the assumed theoretical STM for the applied loads is shown in Figure 3. The horizontal strut is assumed of uniform cross section, whereas the diagonal struts are assumed as bottle shaped, because of the greater width available for later. The strut capacities were checked against the forces in the respective members. The tensile force resisted by the longitudinal steel and the corresponding area of steel is calculated. The details of the reinforcement are given in Figure 4. Bearing plate of size 200 mm 150 mm is used. 100 BobyTharu Fig 3: Strut and tie model

3 Fig 4: Reinforcement details 4. ANALYSIS AND RESULTS The three models ie FRC 0, FRC 1, FRC 2 were analysed in ATENA 3D. Only symmetric half is analysed. During the analysis various characteristics such as first diagonal crack, maximum load, maximum deflection, maximum crack width etc. was noted and tabulated in Table 2. Maximum crack width was considered at serviceability load which is taken as 50 % of the ultimate load. The actual load at failure will be two times the obtained value since only symmetric half is analysed. As the fiber content increases the crack width decreases, which shows that crack propagation and widening is slow in deep beams with fiber content. Crack width is minimum for deep beams with 2% fiber. The load at which diagonal crack appear is obtained. Cracking load increases as the fiber content increases and maximum for deep beams with 2 % fiber. From the table it can be see that, STM gives a conservative result. Addition of fiber increases the factor of safety as it increases the failure load. Load at first diagonal crack (kn) 101 BobyTharu Maximum load (kn) Table 2. Analysis results Maximum deflection (mm) Maximum crack width (crack width at0.5 max load)(mm) STM predicted load (V utheory ) (kn) (V uactual )/ (V utheory ) FRC FRC FRC Strut efficiency values are obtained and is given it Table 3. Obtained values of strut efficiency for diagonal struts are more than that specified in ACI The strut efficiency factor (β) increases as the fiber content increases. This shows that addition of fiber increases the strut efficiency by reducing the cracking. The increment in strut efficiency from 0% fiber content to 1% fiber content is high compared to 1% fiber content to 2% fiber content. Efficiency of diagonal strut AB (β AB) Table 3. Strut efficiency Efficiency of Efficiency of diagonal strut as horizontal strut BC per ACI (β BC ) Efficiency of horizontal strut as per ACI FRC 0 S FRC 1 S FRC 2 S

4 load (kn) The total load was taken for plotting load-deflection curve given in Figure 5, which is obtained by multiplying two with the value obtained from ATENA 3D. From the load deflection graph, it can be see that deflection is less for deep beam with fiber in the serviceable loads. The failure load and the deflection increases as the fiber content increases. The slope of the load deflection curve changes at a particular load which can be identified as the load near diagonal crack appear. Up to that load all deep beams behave similarly. After that load beam stiffness reduces and undergoes faster deflection. After failure, load decreases suddenly for deep beam without any fiber. For beams with fiber, the reduction in load after failure is in a gradual way and it undergoes more deflection after failure frc0 frc1 frc deflection (mm) Fig 5: Load-deflection graph Crack pattern and crack width distribution of all deep beams at failure is presented in Figure 6 to Figure 8. From the crack patterns it can be observed that all beams fail by diagonal strut failure. It can also be observed that as the fiber content increases beam shows better performance in cracking. Fig 6: Crack pattern of the FRC 0 at failure Fig 7: Crack pattern of the FRC 1 at failure 102 BobyTharu

5 Fig 8: Crack pattern of the FRC 2 at failure Stress in the reinforcement bars at the time of failure is obtained and is given in Figure 8 to Figure 10. It can be observed that, the stress in the vertical reinforcement bars depends on its position relative to cracks. Reinforcement bars in the shear span region are stressed most. Fig 8: Stress in reinforcement bars (FRC 0 ) Fig 9: Stress in reinforcement bars (FRC 1) 103 BobyTharu

6 Fig 10: Stress in reinforcement bars (FRC 2) 5.CONCLUSION Nonlinear finite element analysis of the designed deep beam was done with varying the fiber content using ATENA 3D. Main conclusions from the analysis are The failure of deep beams is by the diagonal strut failure. Addition of fiber improves the beam performance in cracking and in deflection. The load at which cracking starts increases significantly as the fiber volume increases. In the case of deep beam with crack control reinforcement, addition of 1% fiber increases the diagonal cracking load by 29.53% compared to deep beam without any fiber and addition of 2% fiber increases the cracking load by 56.3%. An increase in the strut efficiencies were observed as the fiber volume increases. In the case of deep beam with crack control reinforcement, addition of 1% fiber increases the diagonal strut efficiency by 6.25% and addition of 2% fiber increases the diagonal strut efficiency by 8.75% compared to deep beam without fiber. Design using STM approach becomes more conservative as the volume of fiber increases. The stress in the vertical reinforcement depends on its position relative to cracks. Bars in the shear span region are stressed most. REFERENCES [1] ACI Committee 318, Building Code Requirements for Structural Concrete (ACI ) and Commentary (318R- 08), American Concrete Institute. [2] Rodrigues, P. F et al., Stress-strain curves for steel fiber-reinforced concrete in compression. Matéria (Rio J.), vol.15, no.2, Rio de Janeiro 2010 [3] Musmar, M., Tensile strength of steel fiber reinforced concrete. Contemporary Engineering Sciences, Vol. 6, 2013, no. 5, pp [4] Niranjan, B.R., and Patil, S.S., Analysis and Design of deep beam by using Strut and Tie Method. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), vol- 3, 2012, pp [5] Patel, V. R., Pandya, I. I. Evaluation of Shear Strength of SFRC Moderate Deep Beams Using Strut-and-Tie Models. International Journal of Modern Engineering Research (IJMER), Vol.1, Issue1, pp [6] Carlos G et al., Strength of Struts in Deep Concrete Members Designed Using Strut-and-Tie Method ACI structural journal, vol-103, 2006, pp [7] Sahoo, D. K et al., Strength and deformation characteristics of bottle shaped struts magazine of concrete research, IIT Rourkee. [8] ATENA program documentation part 4-2, Cervenka Consulting Ltd. 104 BobyTharu