Strength and behaviour of deep beams - Reinforced Concrete Deep Beams - page 36

2.4 Compressive force path concept

An attempt to summarise the experimental information discussed in the
preceding sections and present it in a unified and rational form has led to the
concept of the 'compressive force path' (Kotsovos, 1988a). On the basis of this
concept, the load-carrying capacity of an RC structural member is associated
with the strength of concrete in the region of the paths along which compressive
forces are transmitted to the supports. The path of a compressive force may be
visualised as a flow of compressive stresses with varying sections perpendicular
to the path direction and with the compressive force, representing the stress
resultant at each section (Figure 2.13). Failure is considered to be related to the
development of tensile stresses in the region of the path that may develop due to
a number of causes, the main ones being as follows.

Figure 2.13 Compressive force path.

i) Changes in the path direction. A tensile stress resultant ( T in Figure

2.13) develops for equilibrium purposes at locations where the path
changes direction.

ii) Varying intensity of compressive stress field along path. The

compressive stress will reach a critical level at the smallest cross-
section of the path where stress intensity is the highest before that level
is reached in adjacent cross-sections. As indicated in Section 2.3, this
level marks the start of an abrupt, large material dilation which will
induce tensile stresses ( t 1 in Figure 2.13) in the surrounding concrete.

iii) Tip of inclined cracks. It is well known from fracture mechanics that

large tensile stresses ( t 2 in Figure 2.13) develop perpendicular to the
direction of the maximum principal compressive stress in the region
of the crack tip (Kotsovos, 1979; Kotsovos and Newman, 1981a).

iv) Bond failure (Kotsovos, 1986). Bond failure at the level of the tension

reinforcement between two consecutive flexural cracks changes the
stress conditions in the compressive zone of the beam element between
these cracks, as indicated in Figure 2.14. From the Figure, it can be
seen that the loss of the bond force results in an extension of the right-
hand side flexural crack sufficient to cause an increase dz of the lever
arm z, such that Cdz=Va . Extension of the flexural crack reduces the
depth of the neutral axis and thus increases locally the intensity of the
compressive stress block. This change in the stress intensity should
give rise to tensile stresses as described in ii).