ACI STRUCTURAL JOURNAL TECHNICAL PAPER
Title no. 105-S65
Shear Strength of Reinforced Concrete Beams under
Uniformly Distributed Loads
by Prodromos D. Zararis and Ioannis P. Zararis
An analytical theory for shear resistance of reinforced concrete shear reinforcement must satisfy to restrain the growth of
beams subjected to uniformly distributed loads is presented. Slender diagonal cracking and prevent brittle failure.
beams with a span length-to-depth ratio (l/d) greater than 10, as In this study, the previously referred theories are adapted
well as deep beams in which l/d 2.5) without shear reinforcement under two-
load has been defined as a = /4, where is the span length of point loading (or one-point loading at midspan), the critical
beam. This is probably why this particular type of loading is crack, leading to collapse, typically involves two branches
not mentioned in the current provisions for shear in international (Fig. l(a)). The first branch is a slightly inclined shear crack,
codes, such as the ACI 3188 or Eurocode 2.9 As a result, the height of which is approximately that of the flexural
the shear strength of beams is calculated using the known cracks. The second branch initiates from the tip of the first
empirical formulas that apply to any type of loading. Such a branch and propagates toward the load point crossing the
consideration, however, is not correct. Tests show that compression zone, with its line meeting the support point.
the shear strength of beams under a uniform load is Failure occurs by the formation of this second branch. The
considerably higher than the strength under a one- or second branch of the critical diagonal crack is caused by a
two-point loading arrangement. type of splitting of concrete in the compressive zone. The
Theories have been proposed in previous works10-12 that stress distribution along the line of splitting, however, is not
use the internal forces at diagonal shear cracks13-14 to similar to that occurring in the common split cylinder test
describe the diagonal shear failure in slender beams as well (Fig. 2).
as the shear compression failure in deep beams under The theory10 results in a simple expression Vcr = (c/d)fct bwd,
concentrated loads. These theories determine:1) the ultimate where bw is the width of the beam. The nominal shear stress
shear capacity of slender beams with or without stirrups
under concentrated loads; 2) the ultimate shear capacity of ACI Structural Journal, V. 105, No. 6, Nov.-Dec. 2008.
deep beams with or without stirrups under concentrated MS No. S-2007-142 received April 20, 2007, and reviewed under Institute publication
policies. Copyright © 2008, American Concrete Institute. All rights reserved, including the
loads; 3) the impact of size effect and how it relates to diagonal making of copies unless permission is obtained from the copyright proprietors. Pertinent
discussion including author’s closure, if any, will be published in the September-October
shear failure; and 4) a criterion that the minimum amount of 2009 ACI Structural Journal if the discussion is received by May 1, 2009.
ACI Structural Journal/November-December 2008 711
The shear force Vcr in Eq. (1) represents the ultimate shear
ACI member Prodromos D. Zararis is a Professor of civil engineering at the Aristotle
University of Thessaloniki, Thessaloniki, Greece. He received his MSc and DIC in force of a slender beam without shear reinforcement
concrete structures and technology from the Imperial College of Science and Technology, subjected to one- or two-point loads acting at a distance a
London, UK, and his PhD from Aristotle University. His research interests (shear span) from the support.
include the study of behavior of reinforced concrete structural elements under
various loading conditions. The depth c of the compression zone in Eq. (1) is given by
the positive root of the following equation11
Ioannis P. Zararis is a Chartered Civil Engineer. He is a PhD candidate at the Aristotle
University of Thessaloniki. His research interests include the study of behavior of
reinforced concrete structural elements under various loading conditions.