Steel fiber reinforced high strength concrete (SFRHSC) is concrete made of hydraulic cements containing fine or fine and coarse aggregate and discontinuous discrete steel fibers. In tension, SFRHSC fails only after the steel fiber breaks or is pulled out of the cement matrix. A more general and current approach to the mechanics of fiber reinforcing assumes a crack arrest mechanism based on fracture mechanics. In this model, the energy to extend a crack and debond the fibers in the matrix relates to the properties of the composite. The designers may best view SFRHSC as a concrete with increased strain capacity, impact resistance, energy absorption, fatigue endurance and tensile strength

Gheorghe-Alexandru Bărbos

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Construcţii  Aspects of flexural behaviour  of SFRHSC elements • G.  Bărbos     53  ASPECTS OF FLEXURAL BEHAVIOR OF HIGH STRENGTH CONCRETE ELEMENTS WITH OR WITHOUT STEEL FIBERS  Gheorghe-Alexandru BĂRBOS Eng., Research Assistant, INCD URBAN – INCERC Sucursala Cluj, e-mail: barbos.gheorghe@incerc-cluj.ro  Abstract. Steel fiber reinforced high strength concrete (SFRHSC) is concrete made  of  hydraulic  cements  containing  fine  or  fine  and  coarse  aggregate and discontinuous discrete steel fibers. In tension, SFRHSC fails only after the steel fiber breaks or is pulled out of the cement matrix. A more general and current approach to the mechanics of fiber reinforcing assumes a crack arrest mechanism based on fracture mechanics. In this model, the energy to extend a crack and debond the fibers in the matrix relates to the properties of the composite. The designers may best view SFRHSC as a concrete with increased  strain  capacity,  impact  resistance,  energy  absorption,  fatigue endurance and tensile strength.  Key  words:  Steel  Fiber  Reinforced  High  Strength  Concrete,  Bending, Design.   1. Introduction Steel  fibers  reinforced  high-strength concrete  (SFRHSC)  is  realized  of hydraulic  cement,  career  crushed aggregate,  mineral  admixtures  (silica fume),  additives  (superplasticizers), dispersed  steel  fiber  and  water   (Magureanu,  2009).  Under  the  action  of various  loads  SFRHSC  fails  only  when steel fibers are broken or pulled out of the concrete  matrix  (cement  +  aggregate). Figure  1  shows  the  variation  law  and breaking  surface  of  an  item  tested  at bending (ACI Committee 363, 1984).      Fig. 1. Failure mode and fracture surface of an element made of SFRHSC  Urbanism. Arhitectură. Construcţii • Vol. 4 • Nr. 2 • 2013 •      54 Application of SFRC since the mid-1960s have  included  road  and  floor  slabs, refractory  materials  and  concrete products.  The  first  commercial  SFRC pavement in the United States was placed in  August  1971  as  a  truck  weighing station near Ashland, Ohio  (Hoff, 1986).  There are some applications where steel fibers have been used without reinforcing bars to carry loads. These have been short span,  elevated  slabs,  for  example,  a parking garage at Heathrow Airport with slabs  1.07  m  square  by  10  cm  thick, supported on four sides (Carter, 1971).  Till  now  it  were  made  various approaches to design SFRHSC elements. These are based on conventional design methods, generally supplemented by the contribution  of  fiber.  Additional information regarding the design of these elements  can  be  found  in  ACI  544.4R "Design  Considerations  for  fiber reinforced concrete" (ACI Committee 544, 1982).  In  this  case,  for  application  of conventional  design  method  (ACI Committee 544, 1982), it was monitoring the influence of high – strength concrete on  the  dimensioning  parameters  of concrete sections.  2. Design consideration Sizing simply reinforced concrete sections in  the  ultimate  limit  state  at  bending moment as required Eurocode 2 (Comité Européen  de  normalisation, 2006),  is  done by  applying  different  equations  of equilibrium in the most loaded section.  In case of steel fiber reinforced beams, the designing  was  made  using  different methods  developed  by  Technological Institute of New Jersey, and used after that by ACI Codes  (ACI Committee 544, 1982).  In  order  to  determine  the  ultimate bending  moment  capacity  for  beam  FT 5.1-1  (without  fibers),  the  provisions  of Eurocode  2  (Comité  Européen  de normalisation, 2006) were used, adopting the  following  scheme  of  efforts distribution in  the  section  (as  shown  in Fig. 2):   Fig. 2. Effort distribution in the beam section for beam FT5.1-1 in ULS  The bending capacity of the beam FT5.1-1 (without fibers) was calculated according to Equation (2):  d b M Eds2lim µ =                                          (1)  ) 5 . 0 1 ( lim lim lim ξ λ ξ λη µ − =   400508 . 0−− =f ck λ , for  f ck>C50/60        (2)  where:  µlim  -  coefficient  depending  on concrete strength, b – section width, d – useful  height  of  section,  f ck  -  design strength  of  concrete,  λ  –  reduction coefficient  of  compressed  area,  η  – reduction  coefficient  of  compressive strength.  Equation (1) represents the reduction of compressed  area  for  high-strength concrete.  Relation  (2)  represent  the reduce  of  compression  strength  in  the extreme  compression  fiber  for  high strength concretes.  Construcţii  Aspects of flexural behaviour  of SFRHSC elements • G.  Bărbos     55 Flexural  strength  of  beams  with  steel fibers    (ACI  Committee  544,  1982),  is calculated  according  to  the  tensile strength of concrete but especially to the contribution  assumed  by  fibers,  namely by  the  fibers volume  and  by  the  aspect ratio  l/d  (fiber  length/fiber  diameter). Below are the relationships account:  d l V V f f f m r cf / 425 843 . 0 + = σ                (3)  where: σ cf  - tensile effort,  f r – ultimate strength  of  compressed  concrete,  V m  – matrix  volume  =  1  -  V f ,  V f   –  fibers volume  =  1-  V m,  d l f /   –  aspect  ratio (fiber length / fiber diameter). For  the last  resistance  of  the  composite next relationship is used:  d l V V f f f m r cu / 494 97 . 0 + = σ                  (4)  where σ cu  is the ultimate effort.  The ultimate bending moment for beam FT  5.2-1  was  determined  using  a calculation  method  developed  by  ACI Committee  544    (ACI  Committee  544, 1982). In order to evaluate the ultimate bending  moment  for  beam  FT  5.2-1,  it were used the same principles specified by  Eurocode  2,  for  dimensioning  in USL,  adding  the  contribution  of  steel fibers. The stress distribution in section B is shown in Figure 3.  In this approach it was considered the strength  in  the  extreme  compressed fiber as limited to 3 mm / m,  yielding value  of  tensioned  reinforcing  bars. From  the  equilibrium  of  forces  on  the section,  it  was  obtained  the  bending moment capacity, as:    − +   − +  − =2 2 2 2 1 1a a h ah b fad f A M t y s nβ β   (5)  where:  As  –  tensioned  reinforcing  area, f y  –  yield  strength  of  steel,  d  –  useful height of section, a – position of neutral axis,  f t – tensile strength of concrete, b – section  width,  h  –  section  height,  β1  - reduction  coefficient  of  compressive strength.  The coefficient  β1 was considered equal to 0.85 for concretes with strength upper then 55 MPa.  The  position  of  the  neutral  axis  was determined according to rotation (Figure 4) (Mohammad and Mohd, 2011).   Fig. 3. Effort state in USL for beam FT 5.2-1   Urbanism. Arhitectură. Construcţii • Vol. 4 • Nr. 2 • 2013 •      56  Fig. 4.  Section rotation at yielding stress of reinforcement bars  and the ultimate rotation    in section B  Rotation value can be assessed using equation (6) [7] (Mohammad and Mohd,     2011).  dtags c ε ε ϕ ϕ + = =                                       (6)  According  to  Figure  4  the  neutral  axis position  can  be  estimated  as  (Mohammad and Mohd, 2011).  ϕε c x =                                                          (7)  For  beam  FT5.2-1  with  steel  fibers,  the bending moment  M n can be obtained from the value of the ultimate bending moment: M n= 95.15 kNm  The stiffness was estimated as function of the value of the bending moment and the section rotation in the same section and for the same loads, as:  ( ) ρMEI = exp                                                  (8)  3. Experimental program The  experimental  program  was performed on two high-strength concrete beams, one with steel fibers (FT 5.2-1) and the  second one  without  fiber  (FT  5.1-1). Beam sizes were 130x245x3000 mm.  Concrete properties are shown in Table 1. Geometrical characteristics of fibers were: diameter ¬= 0,40 mm, length l= 25 mm, aspect ratio I/d = 0,40/25 (mm) and elastic modulus Ea= 2000 MPa.   The reinforcement scheme  of experimental elements is presented in Figure 5.  Longitudinal  reinforcement  ratio  of  the beams was ρ s = 1,60%.  Static scheme was in the form of a simply supported  beam  with  two  concentrated forces applied in the middle third (Fig. 6). Load was applied in steps up to the value of 100 kN.  The test setup and instrumentation of the SFRHSC beams are presented in Figure 7. In the experimental program we had the following  values:  789 . 0 = λ ,  978 . 0 = η , 14 . 3 3= ε cu ‰,  43 . 1 = ε yd   ‰,  68 . 0 lim = ξ , 38 . 0 lim = µ ,  81 . 87 = M Eds  kNm.  Table 1. Concrete properties   Characteristic strength (MPa) Design strength (MPa)  Elastic modulus E (GPa) Beam  FT 5.1-1  fck = 54,48 γ cckcdff =  = 5 , 148 , 54  = 36,32   38,00 Concrete Beam  FT 5.2-1  fck = 66,80 γ cckcdff =  = 5 , 180 , 66 = 44,54   40,00  Construcţii  Aspects of flexural behaviour  of SFRHSC elements • G.  Bărbos     57   Fig. 5. Reinforcement scheme of the beams   P P1 .0 0 1 .0 03 .0 0 Fig. 6. Static scheme for beams testing    Fig. 7. Fitting mode of the beams  4. Results Evolution  of  specific  strains  was determined in the middle section of the beam and in the most compressed fiber. In  the  middle  zone  of  the  beams,  the section  rotation,  stiffness  evolution  and depth  variation  of  neutral  axis  were measured, with load evolution, as shown in Figure 8, Figure 9 and Figure 10.   Fig. 8. Section rotation of the beams   Fig. 9. Stiffness evolution (EI) of the beams   Fig. 10. Variation of the neutral axis  Urbanism. Arhitectură. Construcţii • Vol. 4 • Nr. 2 • 2013 •      58 5. Conclusions The results were obtained by analyzing the central area of the beams, especially in section B. Comparing the evolution of section rotation, it was observed that in case  of  fiber  beam,  the  value  was slightly  higher  then  the  value of  beam without fibers, phenomenon due to the section  ductilization  effect  realized  by fibers.  Regarding the evolution of stiffness (EI) at  load  increasing,  the  stiffness  of  the fiber beam FT 5.2-1 is higher in the first steps  of  loading,  until  the  cracking  of SFRHPC, when the fibers are pulled-out from the concrete matrix.   The position variation of neutral axis at load  increasing  for  beam  FT5.2-1  is influenced by the presence of steel fibers. The  additional  stress  necessary  for  pull out the fibers from the matrix due of the load increasing led to double the high of compressed  zone  as  opposed  to  beam without fibers.  REFERENCES American Concrete Institute – ACI Committee 544 (1982),  State  of  the  art  report  of  fiber reinforced concrete, pp 9-30. American Concrete Institute – ACI Committee 363 (1984), State of the art report on high strength concrete, ACI 363R-84, p. 48. Carter W. (1971), Wire – Reinforced Precast Concrete Decking  Panels,  Precast  –  Concrete  (UK), pp. 703 – 708. Comité Européen de normalisation Eurocode 2 – SR  EN  1992-1-1:2006:  Design  of  concrete structures  - Part 1-1: General rules and rules for buildings. Hoff  G.  C.  (1986),  Use  of  Steel  Fiber  Reinforced Concrete  in  Bridge  Decks  and  Pavements, Steel Fiber Concrete 1(1):67-108. Magureanu  C.  (2009),  High  Performance Concrete, Cluj – Napoca UT PRESS. Mohammad M., Mohd Z., (2011), Bending stiffness and  neutral  axis  depth  variation  of  high strength concrete beams in seismic hazardous areas:  Experimental  investigation, International  Journal  of  the  Physical Sciences 6(3):482-49.   Received: October 10, 2012 • Accepted in final format: October 12, 2012   

Aspects of flexural behavior of high strength concrete elements with or without steel fibers

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