Structural Concrete - Hassoun

8.6 Deep Members 303
This equation is the same as the ACI equation only F Y is used instead of ( Δf p ).
{
0.9 for reinforced concrete
φ =
1.0 for prestressed concrete
3. Nodal Zone. For the nodal zone the AASHTO recommends φ = 0.7 for all cases, and the
effective width strength coefficient, β n , is taken as 0.85 for CCC nodes, 0.75 and for CCT
nodes, 0.65 for CTT and TTT nodes.
Minimum Reinforcement: AASHTO suggest that the D-region should contain orthogonal
grid reinforcement near each face with maximum spacing less than or equal to 12 in. Orthogonal
grid reinforcement requirement is not applicable for slabs and footing. The minimum
steel ratio in each orthogonal direction should not be less than 0.003.
8.6 DEEP MEMBERS
Flexural members should be designed as deep beams if the ratio of the clear span, l n (measured
from face to face of the supports; Fig. 8.10), to the overall depth, h, is less than 4 (ACI Code,
Section 9.9.1.1). The members should be loaded on one face and supported on the opposite face
so that compression struts can develop between the loads and supports (Fig. 8.10). If the loads are
applied through the bottom or sides of the deep beam, shear design equations for ordinary beams
given earlier should be used. Examples of deep beams are short-span beams supporting heavy loads,
vertical walls under gravity loads, shear walls, and floor slabs subjected to horizontal loads.
The definition of deep flexural members is also given in ACI Code, Section 9.9.1. The code
defines flexural members as members where when the ratio of the clear span, l n , to the overall depth,
h (Fig. 8.10), is less than 4, regions loaded with concentrated loads within twice the member depth
from the face of the support are considered deep flexural members. Such beams should be designed
using nonlinear analysis or a strut-and-tie model (Fig. 8.11a).
8.6.1 Analysis and Behavior of Deep Beams
Elastic analysis of a deep beam is meaningful in the uncracked state only before cracking.
Deep-beam cracking occurs generally at one-third or one-half of the strength load. After cracks
develop, a redistribution of stresses is necessary. Elastic analysis shows the distribution of stresses
w, K/ft
h
Main steel
d
l n
Figure 8.10
Single-span deep beam (l n
/d < u).