بسم الله الرحمن الرحيم صدق الله العظيم

PERFORMANCE OF STEEL FIBERS REINFORCED CONCRETE DEEP BEAMS BENHA UNIVERSITY FACULTY OF ENGINEERING AT SHOUBRA جامعـــــه بنــــهــــــا كلـــــيـــــه الـهـــنـــدســـه بشـــــبــــرا Ph.D. Research on PERFORMANCE OF STEEL FIBERS REINFORCED CONCRETE DEEP BEAMS Presented by Eng. Ahmed Abd El-Aziz Abd El-Hay El-Barbary ( M.Sc., Structural Engineering, Cairo University, 2006) Supervision Committee Prof. AHMED A. MAHMOUD Dr. FOUAD B. A. BESHARA Professor of R.C. structures Associate professor Civil Engineering Department Civil Engineering Department Faculty of Engineering, Shoubra Faculty of Engineering, Shoubra

Contents 1. Research Background. 2. Objectives of Current Research. 3. Description of Experimental Program. 4. Experimental Results of the Tested Beams. 5. Finite Element Predilections of the Tested Beams. 6. Strut-and-Tie Modeling of HSSFRC Deep Beams. 7. Conclusions.

Deep Beam receive a single load 1- Research Background 1.1. Function of Deep Beams: Deep beams are structural elements having a depth comparable to the span length, and are used as load distribution elements such as transfer girders in high rise buildings, bent caps in bridge, pile caps in foundations. Deep Beam receive a single load Bridge Bent Cap

1.2. Code Definitions for Deep Beams: Egyptian Code (ECCS) defines the deep beam as: Le/d < 1.25 for Single Span American Code (ACI) defines the deep beam as: Le/h < 4 for Single Span CIRIA Guide of the U.K defines the deep beam as: Le/h < 2 for Single Span

1.3. Earlier Researches on Non-Fibrous Deep Beams: Researcher Year Concrete Type Variables Mansur, M. A. 1991 Normal fc ',a/d, ρv Warwick, W. B., 1993 High Strength fc ',a/d, ρv, ρh Tan K. H., 1995 a/d, le 1997 ρv, ρh Foster, S.J., 1998 Oh, J.K., 2001 a/d, ρv, ρh, ρs Aguilar, G., 2002 fc ', ρv, ρh Rigotti, M., a/d, ρv, ρh Tan, K. H., 2003 Opening Location Russo, G., 2005 Mahmoud, A. A., 2007 a/d, ρs and Opening Location Abolfazl A., 2011 fc ',a/d, ρs Hawraz K., 2013 Opening Size and Location Alsaeq, H. M.,

1.3. Earlier Researches on Non-Fibrous Deep Beams (Cont.): Test results showed that: 1. The a/d ratio has a significant influence on the ultimate strength. The concrete compressive strength fc’ had a significant effect on the ultimate shear strength. For deep beams with (a/d 1.13), the horizontal web steel is more efficient than the vertical web steel of the same steel ratio.

1.4. Earlier Researches on Fibrous Deep Beams: Swamy, R. N. 1981 Normal fc ',a/d, ρs, Vf Narayanan, R. 1988 High Strength fc ',a/d, ρv, ρh, Vf Mansur, M. A. 1991 fc ',a/d, ρv, Vf Yousef , A. M. 2003 Kumar, S. K. 2007 Jansson, A. 2011 Campione, G. 2012 fc ',a/d, Vf, lf /ff Patel,V. R. Minelli, F. 2013 Test results showed that: The inclusion of fibers increase strength, ductility, and toughness. 2. The aspect ratio lf /ff has a significant influence on the ultimate strength. The inclusion of fibers can be replaced by the web reinforcement in beams. 4. Steel fibers reduce the deflection and increase the ductility of deep beams.

1.5. Previous Analytical Studies for Deep Beams: Strut-and-Tie Models Researcher Year Analytical Model Schlaich, J., 1986 Strut and Tie Model Mau, S. T., 1987 Truss Models Rogowsky, D. M., Hsu, T. C., 1988 Softened Truss Model Warwick, W. B., 1993 Belarbi, A., 1995 MacGregor, J. M., 2011 Finite Element Studies Researcher Year Computer Software Rigotti, M., 2002 ADINA Foster, S. J., 2003 ANSYS Salamy, M. R., DIANA 2006 Ammar, Y. A., 2009 Enem, J. I., 2012 Patil, S. S., 2013 Mohamed, A. R., 2014

2- Objectives of Current Research Very few experimental and analytical studies were performed on HSSFRC deep beams. An experimental and theoretical research program was conducted on HSSFRC deep beams in order to: To study of the response characteristics under monotonic static loading such as loading carrying capacity, stiffness, deflection, ductility, cracking patterns, and failure modes. 2. To study the effect of the main following parameters: – Fiber contents (Vf) – Shear Span-to-Depth Ratio (a/d) – Fiber aspect ratios (lf/ff) – VL & HL Shear RFT Ratios (ρv ) & (ρh ) To modified failure criteria and constitutive relations are needed to be implemented in standard program such as ANSYS for nonlinear analysis steel fibers deep beams. To develop a strut-and-tie model as analysis and design tool for HSSFRC deep beams with comprehensive verifications and parametric studies.

3. Description of Experimental Work Specimen of type (A) (a/d = 0.4) Specimen of type (B) (a/d = 0.8) Specimen of type (C) (a/d = 1.0)

Specimen (H3) Specimen (V3)

3. Description of Experimental Work (cont.) Beam No. Width (b) mm Height (h) Shear Span (a) Span (Le) mm a/d Vf % lf ff   Sv rv (%) Sh rh A0 120 500 200 700 0.44 0.00 75 1.12 A1 0.50 80 A2 1.00 60 A3 B0 365 900 0.81 B1 B2 B3 C0 450 1000 C1 C2 H1 50 1.68 H2 100 0.84 H3 V1 V2 V3

3. Description of Experimental Work (Cont 3. Description of Experimental Work (Cont.) Typical Test Setup and Instrumentation for all Tested Beams

4. Experimental Results for Deep Beam 4 4. Experimental Results for Deep Beam 4.1 Behavior of Non-Fibrous and Fibrous Deep Beam Beam (C0) Without Fibers Beam (C0) With Fibers

4.2 Modes of Failure and Cracking Patterns Shear Compression Failure Beam (A2) Beam (A3) Spalling of Concrete cover 350-450 kN 300 kN

4.2 Modes of Failure and Cracking Patterns (cont.) Crushing of Strut Failure Beam (C2) Beam (V3) Spalling of parts Between inclined cracks 320-450 kN 320-450 kN

4.2 Modes of Failure and Cracking Patterns (cont.) Daigonal Splitting Failure Beam (C1) Beam (V2) 250-450 kN 190-400 kN

** Comparison between Diagonal Cracking Load and Ultimate Load 4.3 Load-Deflection Response 4.3.1 Effect of Fiber Volume Content (Vf) a/d = 0.44 lf /ff = 80 f f f f f ** Comparison between Diagonal Cracking Load and Ultimate Load a/d = 0.44 lf /ff = 80 a/d = 0.81 lf /ff = 80    

** Comparison between Diagonal Cracking Load and Ultimate Load 4.3.2 Effect of Fiber Aspect Ratio (lf / ff) a/d = 0.44 Vf = 1.0 a/d = 0.81 Vf = 1.0 ** Comparison between Diagonal Cracking Load and Ultimate Load   a/d = 0.81 Vf = 1.0 a/d = 0.44 Vf = 1.0  

** Comparison between Diagonal Cracking Load and Ultimate Load 4.3.3 Effect of Shear Span-to-Depth Ratio (a/ d) Vf = 1.0 lf/ff = 80 Vf = 0.5 lf/ff = 80 ** Comparison between Diagonal Cracking Load and Ultimate Load   Vf = 0.5 lf/ff = 80 Vf = 1.0 lf/ff = 80  

** Comparison between Diagonal Cracking Load and Ultimate Load 4.3.4 Effect of Web Reinforcement Ratios (rv & rh) ** Comparison between Diagonal Cracking Load and Ultimate Load    

4.4 Load-Longitudinal Steel Strain Response 4.4.1 Effect of Fiber Volume Content (Vf) f f f f f f 4.4.2 Effect of Fiber Aspect Ratio (lf / ff)

4.4.3 Effect of Shear Span-to-Depth Ratio (a/ d) Vf = 0.5 lf/ff = 80 Vf = 1.0 lf/ff = 80

5. Finite Element Analysis using (ANSYS) Program Typical Idealization of the Beams for Concrete Element (Solid65) Typical Idealization of the Beams for Steel Element (Link8) The effect of steel fiber on failure surface Offering high confinement which increases the strength of concrete.

5.1 Stress-Strain Model for Fibrous Concrete in Compression and Tension Simplified compressive uniaxial stress- strain curve for concrete Tension Stiffening Model tf = ftf / Eci   ftf = ft (1+ 0.016 Nf 1/3 + 0.05p ff lf Nf )   Nf = ho (4 Vf / p ff 2 )     am = pc / ftf   etu = 6.tf

5.2 Finite Element Predictions for Tested Beams by (ANSYS) At 25% of Pu At 50 % of Pu At 85 % of Pu Beam (A2) Shear Compression Failure Beam (B2) Crushing of Strut Failure Beam (C2) Diagonal-Splitting failure

5.3 Finite Element Predictions Vs Experimental Results: Load-Deflection Response Beam (B2) Beam (A1) Beam (C1) Beam (H3)

5.3 Finite Element Predictions Vs Experimental Results (cont.): Load-Longitudinal Steel Strain Response Beam (A2) Beam (B3) Beam (C2) Beam (V2)

6. Modified Strut-and-Tie Modeling of HSSFRC Deep Beams 6 6. Modified Strut-and-Tie Modeling of HSSFRC Deep Beams 6.1 Geometrical Properties MSTM MSTM consists of: Horizontal Prismatic Strut BC with compression force (Fu,BC) Diagonal Tapered Struts AB and DC with compression forces (Fu,AB),(Fu,CD) Composite Tie AD with tension force (Fu,AD)

6.1 Geometrical Properties MSTM (cont.) 6.2 Derivation of Internal Forces   & 25o < q < 85o Astr2t = b. wst = b. (ws cosθ + lb sinθ)   Astr1= b. ws Act= b. wct   Astr2b = b. wsb = b. (wct cosθ + lb sinθ)

6.3 Main Assumptions and Modifications Top strut is always prismatic, and the diagonal struts are tapered shape. Improvement in compression strength of concrete due to fiber inclusion fcuf = fcu(1+0.1066 F) 3) Tensile resistance in composite tie is due to tension of main steel reinforcement and post-cracking strength of steel fiber. Tct = fy . As + pc . (Aseff – As) 4) The strut efficiency factor (sf ) and nodal zone stress condition factor (nf ) of fibrous concrete are instead of strut efficiency factor (s) and nodal zone stress condition factor (n) of normal concrete. sf = s + 0.28 F nf = n + 0.28 F

Increase (ws) and (wct) Check on dimension (wct) of Nodal zone [A] Start Increase (ws) and (wct) Assume Vu Internal Forces Calculations       Checks of Stresses in Diagonal Struts And Nodal zones No Check Stress in the Diagonal Strut (AB) Fu,AB < FallDS Yes No Check on dimension (wct) of Nodal zone [A] wct req < wct Yes

Check on dimension (ws) of Nodal zone [B] Yes No Check on dimension (ws) of Nodal zone [B] ws req < ws Yes Calculations of shear carrying capacity (Vu)   Accuracy Check No Check on accuracy to be less than 0.01 (assumed Vu - capacity Vu) / capacity Vu < 0.01 Yes End

Average value of (Pu Exp /Pu MSTM)=1.20 7.5 Ultimate Strength Predictions by the Modified STM No. of Specimens = 79 No. of Sources = 6 Average value of (Pu Exp /Pu MSTM)=1.20 STDEV = 0.08

7.6 Ultimate Strength Predictions by the STM of ECCS and ACI Design Codes No. of Specimens = 79 Average value of (Pu Exp /Pu STM (ACI) )=1.36 STDEV = 0.09 No. of Specimens = 79 Average value of (Pu Exp /Pu STM (ECCS) )=1.43 STDEV = 0.09

Conclusions

a) Conclusive points from the experimental results 1. The inclusion of steel fibers affect on the mode of failure to be changes form sudden brittle failure mode such as (Shear-Compression failure , Crushing of Strut) to less brittle (ductile) mode, such as Diagonal- Splitting failure mode. 2. The increase in fiber volume content (Vf) or fiber aspect ratio (lf /f) leads to an increase in ultimate load Pu(EXP), shear cracking load (Pcrs) and displacement ductility (fu) while it reduces the ultimate deflection (∆u ). Such as For fiber content (Vf) = 1%, the average increase in (Pu(EXP)), (Pcrs), (fu) was 21%, 50%, 35% respectively. The mean reduction in (∆u) was 25%. 3. The increase in shear span to depth (a/d) ratio leads to an increase in Pu(EXP), (Pcrs) while it reduces the (fu) and (∆u ). For Example, The change of (a/d) ratio from 1.00 to 0.44 increases (Pu(EXP)) by 70%, rises (Pcrs) by 25%,while reduces (fu) by 56% and decreases (∆u) by 61%. 4. The increase of web reinforcement improves (Pu(EXP)), and (fu), while decrease in ultimate deflection (∆u). 5. The horizontal web reinforcement is more efficient in shear capacity than the vertical web reinforcement.

b) Conclusive points from (FE) and Modified Strut-and-Tie (MSTM) Models 1. The predicted values for loading and deflection at ultimate and first cracking levels result from the nonlinear Finite Element (FE) analysis using ANSYS program show a good agreement with the experimental results due to the modifications in material properties in both compression and tension. 2. The ratio between ultimate load capacity for the experimental tests and the (FE) analysis (Pu(EXP) / Pu(FE)) is 1.10. Also, the ratio (Pcrs / Pu) for the experimental tests and the (FE) analysis is 1.12. 3. Comparison of the predictions of the modified (MSTM) with 79 test results indicates that the model generally performs well in predicting the ultimate load carrying capacities for HSSFRC deep beams. The ratio between the experimental strength to the predicted strength using MSTM (Pu(EXP) / Pu(MSTM))) is 1.21, with a standard deviation of 0.08. 4. The predictions of STM of the Egyptian Code (ECCS) code and the American code (ACI) are more conservative than the (MSTM). The overall average value of (Pu(EXP) / Pu(ACI)) and (Pu(EXP) / Pu (ECCS)) are (1.36 and 1.43%), respectively, with overall standard deviation as (0.09).

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