CHAPTER 1 INTRODUCTION

Transcription

1 1 CHAPTER 1 INTRODUCTION 1.1 GENERAL Till the 1960s the design engineers generally ignored torsion. It was assumed that torsion effects were minor and could be taken care of by the large safety factor used in flexural design. Torsion design began to arouse serious interest by the late 1950s because of three major stimuli. Firstly, ultimate strength design method was accepted as a replacement for the working stress design method. In the new ultimate strength design method, flexural analysis of reinforced concrete members was refined and safety factors were more accurately defined so that negligence of torsion effects was no longer acceptable. Secondly, the rapid advances in electronic computer application in structural analysis allowed engineers to consider many more design factors. Thirdly, in the post-world war II development, modern architectural concepts such as buildings, considered as three-dimensional structures rather than flatplane objects, out of plane loading, curved beams, skew structures and irregular shapes were introduced. The new design often required structural members to resist large torsion moments. Post-Second world war design engineers neglected the effects of torsion but only considered bending, shear and axial forces. We may raise a question about the emphasis on analyzing torsion. The reasons for this are

2 2 many. Few of them are as follows: Firstly, even small torsion moments can raise considerable stress and can change the response of the whole structure. Secondly torsion can be easily calculated using modern computational method. Thirdly, torsion is a major factor to be considered in the design of many kinds of reinforced concrete structures including space frames, beams that support cantilever slabs, balconies, spiral staircases, horizontally curved beams, spandrel beams, beams next to floor openings, wall foundation beams, skew staircases, skew bridges and circular beams (e.g. the ring beam under a circular water tank supported on columns). These reasons clearly demonstrate why torsion analysis in structural design is of such great importance. 1.2 TYPES OF TORSION Many types of loading produce torsion in reinforced concrete members. The resultant torsion may be classified into two types. 1. Primary or equilibrium torsion 2. Secondary or compatibility torsion The first type is that which is required to maintain basic static equilibrium, and the second to maintain only compatibility condition between members. In general, one may say that torsion in statically determinate structures is of the equilibrium type and in statically indeterminate structures either of the equilibrium or the compatibility type. In statically indeterminate structures, there are more than one load path along which loads can be distributed and equilibrium maintained, so that the structure can be made safe without taking minor torsional effects into account. Such neglect, at most, may

3 3 produce some cracking, but not failure. However, in structures in which a large part of the load is applied unsymmetrically, torsion will have to be considered carefully. Torsion is a major factor if it is of the equilibrium type as also in situations where the torsional stiffness of the members has been taken into account in the structural analysis. In other cases of secondary torsion, provision for nominal shear reinforcements according to codes of practice may be given to take care of the incidental effects. Thus the small amount of unintentional torsion in most of the conventional beams and slabs can be ignored in design and can be taken care of by proper detailing of reinforcements. 1.3 PRINCIPLES OF DESIGN OF SECTIONS FOR TORSION BY DIFFERENT CODES The design procedure to be adopted when torsion is present in reinforced concrete members depends on the code to be used. The Indian Standard (IS), British Standard (BS) and American Concrete Institute (ACI) propose different methods for torsion design, even though the resultant design is considered equally safe. When torsion is present along with bending shear, IS recommends the use of an equivalent shear for which the shear steels are calculated. According to IS when torsion is present when combined with bending, an equivalent bending moment is calculated and reinforcement for this equivalent bending moment is provided as longitudinal steel.

4 4 As per BS practice, the section is separately analyzed for maximum torsional stress and, depending on the magnitude of the resultant stress, the torsional reinforcements are calculated. Steel is also calculated separately for shear and bending moments. The values of reinforcements thus calculated individually are combined and provided as stirrups and longitudinal steel. The ACI procedure for torsion design is to accommodate torsional shear in the same way as in flexural shear, i.e. part of the torsional moment may be considered as carried by concrete without web steel and the remainder by the stirrups Design for torsion by BS 8110 It has already been pointed out that, according to BS 8110, torsion is treated and provided for separately. This method gives an insight into the fundamentals of design of reinforced concrete beams for torsion Area of stirrups A simple expression for the area of the stirrups to withstand torsion can be obtained by assuming the cracking pattern in torsion (which is in the form of a helix) to be inclined at 45 to the horizontal. T u = 0.8A sv (0.87f S v y )x 1 y 1 (1.1)

5 5 T u is design torsional moment f y is yield stress of stirrups A sv is area of the both legs of stirrups x 1, y 1 is centre-to-centre distance of links S v is spacing of stirrups Area of additional longitudinal steel At least four numbers of steel bars should be placed symmetrically inside the four corners of the links for the links to be effective. It is usually specified that the clear distances between these bars should not exceed 300mm. These bars are meant to take care of the component of the tensile force in the longitudinal direction. According to this concept, the volume of the longitudinal steel required will be the same as the volume of the transverse hoops. Taking a distance equal to the spacing of the stirrups and equating the forces, we get the area of additional longitudinal steel as A f sv y A s1 = (x1 y1) (1.2) S f v y 1 A s1 is total area of the additional steel A sv is area of the both legs of stirrups f y1 is yield stress of the longitudinal steel f y is yield stress of stirrups x 1, y 1 is centre-to-centre distance of links

6 Principles of design for combined bending, shear and torsion by IS 456 In the design procedure for torsion according to IS 456, it is not necessary to calculate the shear stress produced by torsion separately as in BS The former gives the analysis for combined effects of torsion shear and bending shear. Bending shear and torsion are combined to an equivalent shear V e. Similarly, the bending moment and torsional moment are combined to an equivalent bending moment M e. The reinforced concrete section is then designed for V e and M e Calculation of equivalent shear and design for stirrups An empirical relation for equivalent shear due to the combined effects of torsion and shear has been suggested in IS 456, as V e 1.6Tu Vu (1.3) b V e is equivalent shear V u is shear force T u is design torsional moment b is breadth of beam The formula for design of shear steel has been suggested in IS 456, as A S sv v (0.87f y ) T u u (1.4) b d 1 1 V 2.5d 1

7 7 A sv is area of the both legs of stirrups S v is spacing of stirrups f y is yield stress of stirrups T u is design torsional moment b 1, d 1 is center-to-center distance of links V u is shear force Calculation of equivalent bending moment and design for longitudinal steel In IS 456 the effect of bending moment and torsion is converted into an equivalent total bending M e as given in IS 456. M e = M u (bending) M t (equivalent torsion) (1.5) The equivalent bending moment M t due to torsion T u is given by M t D Tu 1 b (1.6) 1.7 The equivalent total bending moment is given by M e D Tu 1 b M u (1.7) 1.7

8 8 T u is design torsional moment M u is design-bending moment D is overall depth of the beam b is breadth of the beam M e is equivalent total bending moment M t is equivalent bending moment due to torsion The above equation for bending moment is derived from the interaction curve between bending moment and torsion and the three possible modes of failure. Thus in combined bending and torsion the longitudinal steel should be designed for this equivalent total moment given by M e1 D Tu 1 b M u (1.8) Design for compression steel If M t > M e, then there can be reversal of moment, and longitudinal steel has to be provided on the flexural compression face also, so that the beam can withstand the equivalent moment M e2 = M t - M u (1.9) of the beam. Additional steel is provided for this moment on the compression side

9 Detailing of torsion steel by IS 456 IS 456 gives the rules regarding detailing of torsion steel. These rules can be summarized as follows: y 1. The spacing of stirrups should not exceed x 1, or x or 300mm 2. There should be at least one longitudinal bar placed at each corner of the stirrups. When the cross-sectional spacing exceeds 450mm, additional longitudinal bars should be provided to satisfy the minimum reinforcement and spacing rules regarding side face reinforcement. That is, there should be a minimum of 0.1 percent longitudinal steel, spaced at not more than 300mm or thickness of the web Design for torsion by ACI The ACI procedure for design for torsion is to accommodate torsional shear in the same way as in flexural shear, i.e. part of the torsional moment may be considered as carried by concrete without web steel and the remainder by the stirrups Design of beams without web steel under shear and torsion It has been found that for beams without web reinforcement the equation is as follows:

10 10 T T u uo 2 V V u uo 2 1 (1.10) V uo is shear strength of beam without torsion T uo is torsional strength without shear T u, V u is the design torsion and shear respectively This equation has been adopted by ACI in its design Design of beams with web steel under shear and torsion For beams with web reinforcement the equation is T T u uo V V us uso 1 (1.11) T u is design torsional moment V us is shear force carried by the web steel out of the total shear force in the section V uso is shear strength of reinforcement assuming no torsion is present T uo is torsional strength of reinforcement assuming no shear is present The above equation has been assumed by ACI in its design of transverse reinforcement for combined torsion and shear.

11 FIBRE REINFORCED CONCRETE AS A STRUCTURAL MATERIAL Definition Fibre reinforced concrete is concrete made of hydraulic cements containing fine and coarse aggregates and discontinuous discrete fibres. Fibres have been produced from steel, plastic, glass and natural materials in various shapes and sizes Historical background and its suitability Historically fibres have been used to reinforce brittle materials since ancient times. Straw was used to reinforce sun-baked bricks, horsehair to reinforce plaster and, more recently, asbestos fibres are being used to reinforce Portland cement. The low tensile strength and brittle character of concrete have been overcome by the use of reinforcing steel in the tensile zone of the concrete since the middle of the 19 th century. The research by Romualdi and Batson, Romualdi and Mandel on closely spaced wires and random fibres in the late 1950s and early 1960s was the basis for a patent based on fibre spacing. Another patent based on bond and aspect ratio of the fibres was granted in In the early 1960s, experiments using plastic fibres in concrete with and without steel reinforcing rods or wire meshes were conducted. Experiments using glass fibres have been conducted in the United States since the early 1950s as well as in the UK and Russia.

12 12 Application of fibre-reinforced concrete has been made since the mid 1960s for road and floor slabs, refractory materials and concrete products. Considerable research has been done on fibre reinforced concrete employing varieties of fibres like nylon, polypropylene, fibre glass, vinyl coated fibre glass, asbestos and chopped steel wires. Of these discontinuous steel fibres have been exclusively used by the researchers for structural use, mainly because of suitability, availability and ease of application. Steel fibres have been widely used in order to increase the strength of the concrete structure. The use of steel fibre depends on the following parameters, which are strength characteristics of fibres, bond and fibre interface, ductility of fibres, volume of fibre and aspect ratio. From the above observations it is clear that steel fibre has vast potential as a viable structural material for structural application. 1.5 CONCLUDING REMARKS From the above observations, we clearly understand that more emphasis is needed in the area of structural members under torsion and also considerable research is required to improve the torsion capacity, in this pursuit of which sufficient literature survey has been done and presented in the next chapter.