Structural Concrete - Hassoun

300 Chapter 8 Design of Deep Beams by the Strut-and-Tie Method
Strut
boundary
Axis of
strut
A s1
Strut
γ 1
S 2
γ 2
A s1
S 1
Figure 8.8 Reinforcing bars crossing a strut. Courtesy of ACI 318-14.
where
F ns = strength of longitudinal reinforced strut
A ′ s = area of compression reinforcement in strut
f s ′ = steel stress for A′ s (f s ′ = f y for grades 40–60)
Compression reinforcement should be properly anchored and parallel to the axis
of the strut. This reinforcement should be located in the strut and enclosed in ties or
spirals.
3. Design of Ties. The tie includes the reinforcement and the prism of concrete around the tie.
Tie design involves selecting the area of steel; and reinforcement is properly anchored and
ensures that the reinforcement fits within the tie width.
Strength of Ties. The nominal strength of a tie F nt is
where
F nt = A st f y + A ps (f se + Δf p ) (8.8)
A st = area of non-prestressed reinforcement in tie
A ps = area of prestressing reinforcement
f se = effective stress after losses in prestressed reinforcement
Δf p = increase in prestressing stress due to factored loads
A ps = for nonprestressed members
f se + Δf p ≤ f py
It is permitted to take Δf p = 60 ksi for bonded prestressed reinforcement or 10 ksi for
unbonded prestressed reinforcement.
The axis of reinforcement in a tie shall coincide with the axis of the tie in the strut-and-tie
model. The effective tie width (w t ) depends upon distribution of the tie reinforcement.
If the bars in the tie are in one layer, then
w t = diameter of bar in tie + 2(cover to surface of bars) (8.9)