Concluding Remarks

The ACI design code is dangerously unconservative when applied to the shear design of large concrete beams and one-way slabs constructed without stirrups. The ACI method is capable of accurately predicting Vc of members without stirrups only if their height is similar to the original experimental set used to calibrate the equation. To provide an adequate level of safety, the current ACI equation for Vc must be replaced with an expression that can account for the size effect in shear.

The primary mechanism of shear transfer in slender beams constructed without stirrups is aggregate interlock. It is incorrect to assume that the entire shear force is transferred in the compression zone. Clearly, then, any shear design provision that claims to be theoretically sound must be based on a theory that recognizes the critical importance of aggregate interlock in shear transfer. In this regard, the SMCFT represents a clear improvement over the ACI method.

The risks of basing design code provisions on empirical relationships rather than sound theory have been demonstrated in this paper. Developers of structural design codes owe it to the profession to base provisions wherever possible on rational theory rather than risky empiricism.

Figure 8: Calculation of Shear Carried in Uncracked Compression Zone, Specimen SB-10-N-2 References

ACI Committee 318 (2005) Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary, American Concrete Institute, Farmington Hills, MI, USA

ACI-ASCE Committee 326 (1962) “Shear and Diagonal Tension,”ACI J., Proc., 59: 1-30, 277-344, 352-396

Bazant, Z., Yu, Q. (2005) “Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams Without Stirrups,”

ASCE J. Struct. Engrg, 131(12) “I: Formulation” 1877-1885, “II: Verification and Calibration” 1886-1897

Bentz, E. C., F. J. Vecchio and Collins, M. P. (2005) “The Simplified MCFT for Calculating the Shear Strength of Reinforced Concrete Elements, ACI Struct. J., submitted April 2005, 45pp.

CSA Committee A23.3. 2004. Design of Concrete Structures (CSA-A23.3-04), Canadian Standards Association, Rexdale, ON Fenwick, R. C. and Pauley, T. (1968) “Mechanisms of Shear Resistance of Concrete Beams,” ASCE Struct. J., 94(ST10): 2235­2250

Lubell, A., Sherwood, T., Bentz, E. and Collins, M. P. (2004) “Safe Shear Design of Large, Wide Beams,” Concrete International, January, 26: 66-78

Morsch, E. 1909. Concrete-Steel Construction. McGraw Hill Inc., New York, NY, USA

Sherwood, E. G., Bentz, E. and Collins, M. P. (2005a) “The Behaviour of Large, Lightly Reinforced Concrete Beams and One­Way Slabs,” CSCE Annual Conference, Toronto, Ontario, June 2-4, 2005, Paper GC-167

Sherwood, E. G., Lubell, A., Bentz, E. and Collins, M. P. (2005b) “One-Way Shear Strength of Thick Slabs,” ACI Struct. J., 40pp., submitted July 2005

Sherwood, E. G. (2006) Behaviour and Design of Large, Lightly-Reinforced Concrete Flexural Elements Subjected to Shear, Ph. D. Thesis, University of Toronto, in progress

Tureyn, A. K. and Frosch, R. J. (2003) “Concrete Shear Strength – Another Perspective,” ACI Struct. J., 100(5): 609-615 Vecchio, F and Collins, M. P. (1985) “The Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to

Shear,” ACI Journal, 83(2): 219-231