STEEL FIBER REINFORCED CONCRETE BEAMS SUBJECTED TO COMBINED BENDING AND TORSION - SKEW BENDING APPROACH

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1 STEEL FIBER REINFORCED CONCRETE BEAMS SUBJECTED TO COMBINED BENDING AND TORSION - SKEW BENDING APPROACH D. Tensing*, Karunya Institute of Technology, India L. S. Jayagopal, PSG College of Technology, India 28th Conference on OUR WORLD IN CONCRETE & STRUCTURES: August 23, Singapore Article Online Id: The online version of this article can be found at: This article is brought to you with the support of Singapore Concrete Institute All Rights reserved for CI Premier PTE LTD You are not Allowed to re distribute or re sale the article in any format without written approval of CI Premier PTE LTD Visit Our Website for more information

2 28 th Conference on OUR WORLD IN CONCRETE & STRUCTURES: August 23, Singapore STEEL FIBER REINFORCED CONCRETE BEAMS SUBJECTED TO COMBINED BENDING AND TORSION - SKEW BENDING APPROACH D. Tensing*, Karunya Institute of Technology, India L. S. Jayagopal, PSG College of Technology, India ABSTRACT Steel fiber reinforced concrete technology has grown over the last three decades into a matured industry in all over the world. Its improvements are continually being made by industry to optimize its application. A current need is to consolidate the available knowledge of a SFRC and incorporate it into design code. A method of analysis applicable to SFRC members subjected to combined loading is presented. Wellaccepted theories used for designing reinforced concrete members are extended to incorporate the effect of fibers. The derived equations are validated by subsequent test results For this experimental investigation, a total number of 48 beams were cast and tested for different conditions required for obtaining the above modes of failures. The size of the beam cast was.15m x.23m x 2.3m. The percentage volume of fiber content was varied as %,.5% & 1%. Mix design was done as per IS method for M2grade of concrete using 53 grade of cement. Steel fibers of aspect ratio 6 were adopted in this investigation. Based on the skew bending theory for the beams subjected to combined bending and torsion, three modes of failure are possible. In this investigation two modes of failure are investigated and the effect of fiber inclusion in concrete was studied. For each failure mode, final interaction equations are presented based on the investig2tion. The relationships between torsion and bending due to the incorporation of fibers have been plotted in the graph and the curves obtained are two-degree polynomial curves. The equilibrium equations obtained does not show much deviation. KEY WORDS: Steel Fibers, reinforced concrete, torsion, bending, cracks, twist, failure 1. INTRODUCTION A large number of investigations were carried out on the behavior of R.C.beams in combined bending and torsion under ultimate load conditions. Here, bending, torsion an"d shear are inseparable effects in R.C. beams probably there is no structure subjected only to pure torsion or to pure bending. In members subjected to combined bending and torsion, the individual effects of either of the causes cannot be easily separated and the combined effect mayor may not have a close relationship with either of these 553

3 effects. The final result mostly depends upon the interaction between bending and torsion although other factors such as quality of the material, quantity of reinforcement etc, may also affect the behavior to some extent. Failure under combined bending and torsion is sudden not giving any warning before failure without the margin of safely. In modern structural configurations, it is necessary to study the combined bending and torsional behavior and is an important practical problem. An approach to the improvement of concrete flexural and torsional strength by incorporating randomly dispersed steel fibers into the concrete was successively tried in this investigation. When steel fibers are added to plain concrete, flexural, torsional and energy absorbing capacity increases. Studies have shown that the primary factors affecting the characteristics of fiber reinforced concrete were the fiber type, volume fraction, aspect ratio of the fibers and the nature of defgrmation and orientation of fibers. ~n this investigation, corrugated round steel fibers of aspect ratio 6 was used for casting specimens and the test results on incorporation of steel fibers in various percentage in reinforced concrete beams subjected to combined bending and torsion are presented and discussed. 2. EXPERIMENTAL INVESTIGATION Test specimens were cast using three fiber volume fractions, namely %,.5% and 1 % with aspect ratio 6. Companion specimens in plain concrete were also cast. Ordinary Portland cement conforming to IS , river sand and coarse aggregate with 2mm maximum size was used. The design mix was arrived at based on IS 1262:1982. The mix was designed for a 28-day cube compressive strength of 2 Nlmm 2 The details specimens cast are shown in table 2. For this investigation, beams were designated as A, B, & C which represent beams of unequal top and bottom reinforcement and, E & F which represent beams with equal top and bottom reinforcement. 1,2,3 and 4 represents application of torsion in measures of %, 3%, 6% and1 % of ultimate torque respectively. Table - 2 Specimens cast for the investigation: SL.NO % OF STEEL DESIGNATION OF NO. OF NO. OF COMPANION SPECIMENS FIBERS SPECIMEN BEAM CUBES CYLINDERS BEAMS A1,D A2,D % A3,D A4,D B1, E % B2,E B3,E B4,E C1, F % C2,F C3, F C4,F COMBINED BENDING AND TORSION TEST ON BEAMS The support conditions were fabricated in such away that combined bending and torsion could be applied on the concrete beams. The Torsion brackets with a loading truss held the ends of the beams. For applying torsion uniformly, a pair hydraulic jacks were used. For applying flexural load, two point loading arrangement was made on the beam and the load was applied by means of a hydraulic Jack fitted to the loading frame. A proving ring of capacity SOT measured the load. 554

4 The torque was found by multiplying the load on the truss by the distance between the point of application of the load and center of the beam. Weight of the truss with bracket was also considered in the calculation of torque. For measuring the angle of rotation, glass plates were fixed on the top of the beam at both ends and the deflections were measured with the help of 4 deflectometers for different loadings. The twist at each point was calculated by using the mathematical relation Arc Length = Angle of Twist x Radius. Arc length was taken as equal to the deflection. The average twist was calculated and Torque - Twist curves were drawn and the behavior of beams under combined bending and torsion with and without steel fibers were analyzed and discussed. The deflections were measured by means of dial gauges set at the center of the span of the beam and at the one third and two third span points. Fig. 1. Test setup - Combined Bending and Torsion Fig. 2. Tested Beam specimens 3.1 METHOD OF TESTING: In this investigation the testing was done for pure torsion, pure bending and combined bending and torsion. Combined bending and torsion tests were conducted by applying pure torsion to a predetermined value and increasing the bending values upto failure. One set of beams was provided with less top steel than bottom steel and another set with equal top and bottom steel. Torsion was applied in terms of %, 3%, 6% and 1% of the value of ultimate torque value and then the flexural load was applied till failure. The first set of beams were made to carry substantial flexural moment and small torsion and the failure was found to be Mode 1 failure as per the skew bending theory. In the second set of beams, the failure was observed in the form of crushing of sides and the failure was classified as Mode 2 failure. 3.2 TEST RESULTS The Experimental results are shown in Table 3 SI. Aspect % of No. Ratio Fiber Beams with less steel at top Beams with Equal amount of than bottom steel steel both at top and bottom Bending Bending Torque KNM Torque KNM moment KNM moment KNM (Mt) (Mt) (Mbl (M b )

5 4. ANALYSIS OF TEST RESULTS: 4.1 Interaction Curves: The relationship between bending and torsion is termed as "the interaction curve between bending and torsion". Lampert and Collins suggested that the determination of strength of a member in combined bending and torsion requires the knowledge of pure flexural and pure torsional strengths. and also their interaction behaviour. Skew bending theory is effective when the flexure predominates torsion. A polynomial curve could be obtained when the experimental values are plotted on a graph For beams with less top steel than bottom steel (Mode 1 failure) Figure 3 shows the curves between torsion and flexure for the beams with two numbers of 12mm rods on the top and three numbers of 12mm rods at the bottom. Torsion Vs Bending Moment - SFRC 7 O%fibre 6 E.5%fibre z 5 ~.5 4 1% fibre c: 3 ~ {! 2 y=o Bending Moment in KNm Fig.3 Interaction Curves for Mode 1 failure y= =.4 The relations obtained between torsion and bending for various fiber content and for y =.4 are shown below: % Steel Fiber :.5% Steel Fiber 1 % Steel Fiber : Tu = -.27(Mu) (Mu) Tu = -O.28(Mu) (Mu) Tu = -O.27(Mu)2 - O.33(Mu) Unit Interaction Curve: In non-dimensional form this curve was drawn. Relation between and were obtained by plotting various points in the graph (Fig. 4). The relation obtained in the graph is termed as unit interaction curve. This curve is of help in designing for torsional moments. 556

6 Torsion-flexure Interaction Diagram y=oa :::J t:.6 :::J I-.4 o Mu/Muo Fig. 4 Unit Interaction Curve for Mode 1 Failure The relation obtained from the Unit Interaction Curve is Tu Tuo S MU }.17 Mu L s L MUO LMUOJ For beams with equal top and bottom steel (Mode 2 failure) Figure 5 shows the curves between torsion and flexure for the beams with two numbers of 12mm rods on the top and two numbers of 12mm rods at the bottom. The experimental values are plotted in the following graph and relation between torsion and moment are presented based on drawing a fit curve. 6 Torque Vs Flexure % Fibre E 5 ~ % Fibre 'S 1::.3 <II I- 1 y= Flexure (Mu) KNm Fig. 5 Interaction Curves for Mode 2 failure y= =.6 557

7 The relations obtained between torsion and bending for various fiber content are shown below: % Steel Fiber :.5% Steel Fiber: 1 % Steel Fiber : T u = -.59(Mu) (Mu) Tu = -.62(Mu)2 -.29(Mu) Tu = -.62(Mu) (Mu) Unit Interaction Curve: Fig.6 shows the unit interaction curve for the beam with equal top and bottom reinforcement. Torque-Flexure Interaction Diagram t:: =.6 ~ =.4.2 y= Mu/Muo Fig.6 Unit Interaction Curve for Mode 2 Failure The relation obtained from the Unit Interaction Curve is Tu Tuo {MU }:.158 {~ Muo _ MUf S Behavior of the Companion Specimens: TABLE - 3 TEST RESULTS ON THE COMPANION SPECIMENS SI. % of Fiber Cube Split Tensile Flexural Cylinder No. Compressive Strength in Strength in compressive Strength in N/mm2 N/mm2 Strength in N/mm2 N/mm

8 4.4. Torque-Twist Relations: From the curves obtained for Torque Vs Twist, it was found that the twist for beams without steel fibers were more than the beams with steel fibers. The beams with 1 % by volume of steel fibers have shown in Figure 6 that the twist under torque was lower when compared to all the other beams. Torque Vs Twist (aspect ratio - 6) 7 6 ~5 ~.5 4 ~3 C' 52 I- 1. 5% fibre 1% fibre ~~ % fibre Twist in radians (1E 6) 5. CONCLUSIONS: Fig. 6 Torque Vs Twist Curves 1. Compressive Strength, Flexural Strength and Split Tensile strength of the companion specimens increase upto 1 % fiber by volume and the increase was found to be 1%, 24% and 11 % respectively. 2. For beams with high moment torque ratio primary bending failure takes place with the formation of compression hinge at the top. 3. Presence of torsion decreases the deflection of the beam comparative to when it is subjected to pure flexure and the presence of fibers further reduces the deflection of the beam compared to the beam without fibers. 4. By Torque-Twist curves, it was found that the addition of steel fiber reduces the angle of twist. 5. The cross section deformation was very little only 6. The presence of small amount of torsion decreases the bending moment only slightly. Here the decrease is only 6% for 3% of ultimate torque. The decrease in bending moment was 4% when the torque applied was 6% of ultimate torque. 7. The presence of steel fibers in beams upto 1% increases the ultimate torque value to 28% and 22.5% for the beams with unequal and equal top and bottom reinforcement respectively. 8. The interaction curves proposed by the authors for the mode 1 and mode 2 failure as per skew bending theory may be used in the design of steel fiber reinforced concrete beams subjected to combined bending and torsion. The interaction curves were fitting to two-degree polynomial curves and the corresponding equations were presented. 9. There is no much deviation in the constants of the interaction equations for the variation in addition of different percentage of fibers. 559

9 6. REFERENCES: 1) Mansur, M.A., and Paramasivam, P. - 'Steel fiber Reinforced Concrete Beams in Pure Torsion', International Journal of Cement composites, Vol.4, No.1, 1982, pp ) Pandit and Warwaruk - 'R.C. Beams in Combined Bending and Torsion', Torsion of Structural Concrete - special publication no. 18, ACI, Detroit, 1969, pp ) Sundararaja Iyengar & Vijayarengan - "Strength and stiffness of R.C. Beams under Combined bending and torsion': ACI, Detroit, pp ) Goode and Helmy - Ultimate strength of reinforced concrete beams in combined bending and torsion. Torsion of Structural Concrete special publication No. 18, ACI pp ) M. JackSynder and David R. Lankard, 'Factors affecting the Flexural Strength of steel fibrous concrete' - ACI Journal, February, 1972 pp ) Adams Csikos and Istvan Hegedus, Torsion of Reinforced concrete beams' - Z'd International PhD symposium in Civil Engineering 1998 Budapest. 7) Elfren L. et al., (1974), Torsion- Bending. Shear Interaction for Concrete Beams. J. StructDiv. Am. Soc. Civ. Engrs,1,ST 8, ) KAMALODEEN F., (1993), Strength and Behavior of Fiber reinforced concrete beams under combined bending, shear and torsion. PhD thesis, University of the West Indies, 1993,489. 9) Lampert, P. and M.P. Collins, Torsion, Bending and confusion - an attempt to establish the facts', Journal of the ACI, Vo1.69, No.8, August, 1972, pp