Structural Concrete - Hassoun

294 Chapter 8 Design of Deep Beams by the Strut-and-Tie Method
• Ties can overlap struts or other ties.
• Minimum angle between struts and ties should be 25 ∘ .
• Tie should yield before strut crush (ductility).
• Tension in concrete is neglected.
• External forces should apply at nodes. If uniform load is present, that should resolve in concentrated
load to apply at node.
• Prestressing is an external load.
• Reinforcement should be adequately anchored and provide sufficient detailing.
8.4.2 Check for Shear Resistance
ACI Code, Section 9.9.2.1, specifies the following limitations for deep beams. This check is necessary
prior to building a strut-and-tie model:
where
V n = shear strength
b w = web width
d = effective depth of section
V n ≤ 10 √ f ′ cb w d (8.1)
If this equation is not satisfied, the cross section of the member should be increased.
8.4.3 Design Steps According to ACI Section 23.2
a. Define and isolate each region. This should be defined as shown in Fig. 8.5 and Section 8.2.
If the beam is shallow (with a large span-to-depth ratio), B-region can be much longer. In that
type of beam, shear span is defined as being > 2h. If the beam has a small span-to-depth ratio,
the D-region would cover the whole beam. And shear span is defined as < 2h.
b. Determine the resultant forces actingoneach D-region boundary. Determine loads on structure
and locate concentrated force either from reactions or from applied loads. Uniform load
can be resolved into equivalent force resultant at node points.
c. Select a truss model to transfer the resultant forces across the D-region. In determining the
geometry of a truss, the dimension of the struts, ties, and nodal zones shall be taken into
account. The axes of the struts and ties should coincide, approximately, with the compression
and tension fields. The selection of model geometry is the most important task in design.
The selection of truss geometry may be done by visualizing the stress field that develops in
a structure. For simple structures such as simple supported beams, the flow of stresses may
be easily visualized. For a more complex structural system, the selection of a suitable truss
model is more difficult.
d. Compute the forces in strut and ties. The strut-and-tie model should be in equilibrium with
the applied loads and reactions. To calculate force in strut and ties, start computing forces at
the joint. There are two equation of equilibrium, one for horizontal force and one for vertical
force. These equations must be satisfied at each node.
e. Determine the effective widths of the struts and nodal zones based on the concrete and steel
strengths and the truss model chosen. The effective width of the struts and nodal zones are
determined considering the force from step (d) and the effective compressive strength. The
strut, tie, and nodal zone all have finite widths that should be taken into account in selecting