Structural Concrete - Hassoun

8.4 ACI Design Procedure to Build a Strut-and-Tie Model 299
a. Strength of Struts. The nominal compressive strengths of a strut without longitudinal reinforcement,
F ns , shall be the smaller value of F ns at the two ends of the strut such that:
F ns = f ce A cs (8.3)
where
A c = cross-sectional area at one end of strut
f ce = smaller effective compressive strength of concrete in strut and nodal zone.
That is the smaller of Eqs. 8.4 and Eqs. 8.5.
Effective compressive strength of the concrete in a strut:
f ce = 0.85β s f ′ c (8.4)
where β s equals 1.0 for a prismatic strut; 0.75 for struts with the width of the midsection
is larger than the width at the nodes (bottle-shaped struts) with adequate reinforcement to
resist transverse tensile stresses; 0.60 λ for struts with the width of the midsection is larger
than the width at the nodes (bottle-shaped struts) without adequate reinforcement to resist
transverse tensile stresses (λ = 1.0 for normal weight concrete, 0.85 for sand–lightweight
concrete, and 0.75 for all lightweight concrete); 0.40 for struts in tension members or
tension flanges of member; and 0.60λ for all other cases.
Effective compressive strength of the concrete of a nodal zone:
f ce = 0.85β n f ′ c (8.5)
where β n equals 1.0 in nodal zones bounded by struts or bearing areas, or both, C–C–C
node; 0.80 in nodal zones anchoring one tie, C–C–T node; and 0.60 in nodal zones anchoring
two or more ties, C–T–T or T–T–T node.
b. Reinforcement Crossing Struts. The value β s = 0.75 is for bottle-shaped struts where reinforcement
required is related to the tension force in the concrete due to the spreading of
the strut. The axis of the strut shall be crossed by reinforcement, which is resisting the
transverse tensile force resulting from the compression force spreading in the strut. The
compressive force in the strut may be assumed to spread at a 2:1 slope (Fig. 8.8).
For f ′ c ≤ 6 ksi, the value of transverse reinforcement can be calculated from
∑ ( A si
bs i
)
(sin γ i ) ≥ 0.003 (8.6)
where
A si = total area of reinforcement in ith layer crossing strut
s i = spacing of reinforcement in ith layer adjacent to surface of member
b = width of member
γ i = angle between axis of strut and bars in ith layer of bars crossing strut
The transverse reinforcement as mentioned above shall be placed in either two orthogonal
directions at angles α 1 and α 2 to the axis of the strut or in one direction at an angle
α to the axis of the strut. If the reinforcement is only in one direction, α shall not be less
than 40 ∘ .
c. Compression Reinforcement in Struts. Compression reinforcement can be used to increase
the strength of a strut. The nominal strength of a longitudinal reinforced strut is
F ns = f ce A c + A ′ sf ′
s (8.7)