Keywords: short beams, shear strength, reinforced concrete, structural design, span to depth ratio.

Reinforced concrete short beams and deep beams are often used in tall building construction, offshore structures, and complex foundation systems. In spite of their widespread use, both the BS8110 [1] and the EC2 [2] do not provide any special design provisions for short beams. In practice the beams that have ratios less than 2.5 and higher than 1 are called short beams. The beams that have ratios less than 1 are specifically called deep beams.

Currently, the main design documents for deep beams are the ACI 318-95 [3], the Canadian Code CAN-A23.3-M84 [4] and the CIRIA Guide of the UK [5]. Among the three design requirements, the CIRIA Guide is the most extensive guide on the subject. The guide gives good fit to the normal strength short beams that have shear span to depth ratios less than 0.9. The Canadian Code is based on the strut and tie modelling approach and incorporates the softening of the concrete stresses due to increasing principal tensile strain. The Canadian Code then stipulates some maximum allowable stresses for the nodal regions.

A previous study [6] shows that none of these codes gives reliable estimates of the shear strengths of short beams. The mean values are usually very low and the standard variations are too high. Thus a more conservative estimate of the shear strength of short beams is required.

In order to achieve this, several short beam tests without shear reinforcement is brought together. The database consists of beams that have ratios higher than 1 and less than 2.5. Several parametric studies are carried out on this experimental database. It is apparent from these parametric studies that the shear strength of short beams without shear reinforcement increases when the concrete cylinder strength and the beam longitudinal reinforcement ratio increase. When the shear span to depth ratio () increases, the shear strength of short beams without shear reinforcement decreases.

Based on these parametric studies, a design equation is proposed for predicting the shear strength of short beams without shear reinforcement as shown in Equation (121.1).

where:
is the area of the longitudinal reinforcement,
is the concrete cylinder strength in MPa,
is the shear span,
is the depth of the beam,
is the width of the beam.

The proposed design equation is applied on the experimental database. It is apparent that the proposed equation gives very accurate predictions of the shear strength of short beams without shear reinforcement with minimal standard deviation.

1

BS8110: Structural Use of Concrete-Part 1, General Rules and Regulations for Buildings, English Edition, British Standards Institution, London, 1985.

2

EC2: Eurocode 2, `Design of Concrete Structures, Part1, General Rules and Regulations for Buildings', English Edition, British Standards Institution, London, 1992.

3

ACI Committee 318, `Building Code Requirements for Structural Concrete (318-95) and Commentary (318R-95)', American Concrete Institute, Farmington Hills, 1995.

4

Canadian Standards Association, `Design of concrete structures for buildings (CAN3-A23.3-M84)', CSA, Rexdale, Ontario, 281 p.,1984.

5

CIRIA, `CIRIA Guide 2: The Design of Deep Beams in Reinforced Concrete', Ove Arup and Partners, Construction Industry Research and Information Association, London, 1977.

6

Tan K.H., Fung K.K., Weng L.W., `High-strength reinforced concrete deep and short beams: Shear Design Equations in North American and UK practice', ACI Structural Journal, 95, 318-329, 1998.

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