Structural Concrete - Hassoun

CHAPTER8
DESIGN OF DEEP
BEAMS BY THE
STRUT-AND-TIE
METHOD
Deep-beam flexural-shear failure.
8.1 INTRODUCTION
A strut-and-tie model of a structure is a valuable tool for the analysis and design of concrete members
especially for regions where the plane sections assumption of beam theory does not apply. A
strut-and-tie model visualizes a truss-like system in a structure and transmits forces from loading
points to the supports. This method can be applied effectively in regions of discontinuity in the
structural member, such as support areas, zones of load application, or areas with sudden change in
the geometrical dimensions such as brackets and portal frames. In these regions, the plane sections
do not remain plane after bending.
The ACI Code, Chapter 23 [1], and AASHTO [2] Section 5.6.3 introduce similar methods
and will be discussed later in this chapter.
8.2 B- AND D-REGIONS
St. Venant’s principle indicates that stresses due to axial load and bending approach a linear distribution
at a certain distance from the discontinuity. This distance is generally taken as the larger
dimension of the member cross section, that is, depth h or width b.
The region where stresses cannot be computed from the flexure formula are called D-regions
(Fig. 8.1). The other regions of beam where bending theory and linear strain relationship applyes
are called B-regions (Fig. 8.1).
If two D-regions overlap or meet, they can be considered as a single D-region. ACI defines a
D-region as the portion of the member within a distance equal to the member heights, h or depth d
from a force discontinuity or a geometric discontinuity. For D-regions, maximum length-to-depth
ratio would be equal to 2.
8.3 STRUT-AND-TIE MODEL
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The strut-and-tie model can be represented by an idealized truss model with force acting at the
different nodes. Compression members are defined as struts, tension members are defined as ties,
and joints are defined as nodal zone. These three elements are illustrated in Fig. 8.2.