Effect of Improved Ductility on the Behaviour of ReinforcedConcrete Beams under Combined Bending and TensionJ Shanmugasundaram, Member

Dr N Lakshmanan, Non-member

Tanks, silos, bunkers and culvert pipes are subjected to combined bending and tension. The design of suchstructures is based on the charts given in design aids to IS : 456-1978. There are not many analytical modelswhich address the problem of large deformation under combined bending and tension as may be realisedunder blast and seismic loading. An experimental investigation on reinforced concrete beams under combinedbending and tension has been carried out for evaluating strength and developing interaction diagram underlimit state of collapse. From the experiment it is clearly seen that load-carrying capacities of the beams areincreased due to the increased failure deformations, when the beams are subjected to combined bending andtension. Further, an analytical model for evaluating the ductility of concrete beam-type elements reinforcedsymmetrically on the tension and compression faces subjected to combined tension and flexure has beendeveloped. The values of the failure loads and deformations obtained are compared with the experimentalresults and an excellent agreement is seen. The paper also brings out clearly the enhanced load carryingcapacity of a typical RC beam element with improved detailing for obtaining ductile failures.

Keywords : Reinforced concrete; Ultimate load; Bending; Tension; Ductility .

NOTATION

A : area of bar, mm2

b : breadth of the beam, mm

F„ : failure tension capacity under combined bendingand tension

Fuj, : failure capacity under pure tension

: yield strength of confining steel, Nimm2

i : impulse represented by the area of the load timecurve due to blast

: length of member

: gauge length of reinforcing bar, mm

lP: length of the plastic hinge, mm

: failure moment capacity under combined bend-ing and tension

: additional bending moment

: failure capacity under pure flexure

R : resistance of the member

wu : uniformly distributed load per unit length

z : distance to point of contraflexure from plastichinge location, nun

: failure transverse deflection

Out : failure deflection under pure flexure

es avg average strain in steel at location of the plastic

hinge

ace failure strain in concrete

J Shanmugasundaram and Dr N Lakshrnanan are with Structural En-gineering Research Centre, Madras 600 013This paper (revised) was received on September 13, 1996. Written discussionon the paper will be entertained till June 30, 1997.

asl : percentage elongation over gauge length

: average strain outside the gauge length

A, : support rotation

: ratio of failure deformation to yield deformation

p3 ratio of volume of confining steel includingcompression steel to the core volume

: natural frequency of the element, rad/s

INTRODUCTION

Reinforced concrete is by far the most widely used construc-tion material. The behaviour of reinforced concrete elementsunder axial force, flexure, shear, torsion, and combined load-ing has been investigated by various researchers. Majority ofthe investigations have been directed towards evaluation ofstrength under monotonic loading. Considerable researchwork has also been directed towards the behaviour of struc-tural elements under cyclic and fatigue loading. A number ofinvestigations have also been made on studies relating tocracking, crack width, crack spacing and on evaluation ofdeformations which have led to codal provisions on service-ability criteria. However, it cannot be said that optimal useof the potential of reinforced concrete has been made. Rein-forced concrete can be used effectively in earthquake resis-tant construction and blast resistant design of structures. Bothof these address the same problem, namely, improving duc-tility and energy absorption capacity of reinforced concretestructural elements under various types of forces by adoptingsuitable detailing techniques. Confining of concrete undercompression leads to enormous increase in failure strains ofconcrete. It has been conclusively proved that beams rein-forced with equal amounts of reinforcement on the tensionand compression faces of a beam element have enormousductility. Provision of closed stirrups at close spacing andadopting special types of reinforcing details such as lacedreinforcement provide large failure deformations in beams

Vol 78, May 1997 49

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