Cracking and deformation of axially reinforced members subjected to pure tension

Abstract

. (2005) 'Cracking and deformation of axially reinforced members sub jected to pure tension.', Magazine of concrete research., 57 (10). pp. 611-621.Further information on publisher's website:http://dx.doi.org/10. 1680/macr.2005.57.10.611 Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. This paper describes work carried out as part of a major experimental and theoretical investigation into tension stiffening. This work was carried out at the universities of Leeds and Durham. The experimental work enabled a detailed study to be undertaken of the behaviour of concrete in tension surrounding reinforcing bars. This study showed that a more-or-less linear variation in concrete and steel stress occurred in the region affected by a crack and also that behaviour of the concrete in the region of a crack remained substantially elastic. The experimental study permitted equations to be developed to predict the deformations and crack widths in axially reinforced tension members. Tests of the formulae for crack widths are reported and the formulae are shown to be satisfactory. A more detailed model of the behaviour in the region of a crack is proposed and shown to be reasonable. NotationA c area of concrete A s area of reinforcement c cover E c modulus of elasticity of the concrete E s modulus of elasticity of the reinforcement f c compressive strength of concrete f ct tensile strength of the concrete L the length of the specimen (or the length over which measurements are taken) N axial tension force n number of cracks S o the transfer length within which there is a transfer of force by bond between the reinforcement and the concrete S rm average crack spacing s the slip at the point considered s 1 the slip at the maximum bond stress w the crack width w av the average crack width AE a coefficient AE e modular ratio ¼ E s /E c a the extension of a specimen prior to cracking˜b the extension of the reinforcement over the length 2S o centred on a crack c the shortening of the concrete over the distance 2S o on formation of a crack â a constant of integration such that the shaded area in Fig. 5(b) is given by 2S o â(å s2 Àå o ) å cm average strain in the concrete (used in MC 90) å cs strain caused by shrinkage (used in MC 90) å o the strain in an uncracked tension member å sm average strain in the reinforcement ¼ the average strain in a tension member å s2 the strain in the reinforcement at a crack (concrete carries no tension) r A s /A c ó ct stress in the concrete ô the bond stress. ô...

Modelling short-term tension stiffening in tension members

“…The present paper reviews the validity of the MC90 1 bond-slip relationship in light of Beeby and Scott's [2][3][4] experimental data from tension specimens with internally strain gauged bars. Beeby and Scott [2][3][4] questioned the validity of bond-slip relationships owing to the 'necessity for the concrete to be able to slip past the ribs on the bar'.…”

“…5 Beeby and Scott proposed an elastic model for the concrete bar interaction, incorporating springs of varying stiffness chosen to develop a uniform distribution of bond stress along the reinforcement. While theoretically valid, the current authors believe that Beeby and Scott's [2][3][4] fundamental objection to bond-slip models is irrelevant in the context of numerical models for bond-slip which relate bond stress to the relative displacements between the concrete, which surrounds the internal cracking zone, and steel.…”

“…Beeby and Scott [2][3][4] questioned the validity of bond-slip relationships owing to the 'necessity for the concrete to be able to slip past the ribs on the bar'. They went on to suggest that the incompatibility between the strains in the concrete and reinforcement is accommodated by internal cracking in the concrete around the bar of the type first observed by Goto.…”

“…More significantly, Beeby and Scott [2][3][4] questioned the use of bond-slip models since they found that bond stresses were almost constant between cracks, initially increasing with load, before reaching a constant value. The conclusion that bond stress is uniform between cracks, and increases with load, would seem to invalidate the use of the MC90 bond-slip relationship, which assumes that bond stress increases with slip.…”

Reinforced Concrete Panels Subjected to Uniaxial and Biaxial Tension

“…(1983). (Leonhardt 1977;Beeby 1972;and Rizkalla et al 1983). To enable an accurate crack spacing measurements to be obtained, the tested panels were carefully inspected at each load step.…”