Structural Concrete - Hassoun

8.5 Strut-and-Tie Method According to AASHTO LRFD 301
Also, a practical upper limit of the tie width, w t , can be taken as follows (ACI Code, Section
R23.8.1):
w t(max) = F nt
f ce b s
(8.10)
where f ce is the compressive strength of the nodal zone as computed in Eq. 8.5.
The concrete is included in the tie to establish the width of the faces of the nodal zone
acted on by the ties. The concrete in a tie does not resist any load. Ties help in the transfer of
loads from strut to ties or to bearing areas by bonding to the reinforcement.
4. Design of Nodal Zone. If all the strut stresses are equal at a node, a hydrostatic nodal zone
can be used. The face of such a nodal zone is perpendicular to the axis of the strut and the
width of the faces of the nodal zone is proportional to the forces in the strut.
The thickness of the nodal zone is generally taken the same as the thickness of the member.
Calculation of the width of nodal zone is useful to calculate the width of compression strut
first.
Nodal zones are generally triangular in shape; it is often necessary to determine one side
of the triangle given others.
5. Strength of Nodal Zones. The nominal compression strength of a nodal zone, F nn ,is
F nn = f ce A n (8.11)
where A n is the smaller of:
• The area of the face of the nodal zone on which F nn acts; The area shall be taken perpendicular
to the line of action of F nn .
• The area of the section through the nodal zone is, taken perpendicular to the line of action
of the resultant force on the section.
a. Confinement in Nodal Zones. Unless confining reinforcement is provided within the nodal
zone and its effect is supported by tests and analysis, the calculated effective compressive
stress on the face of a nodal zone due to the strut-and-tie forces should not exceed the
following:
f ce = 0.85β n f c ′ (8.12)
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.
8.5 STRUT-AND-TIE METHOD ACCORDING TO AASHTO LRFD
AASHTO uses a design approach similar to ACI’s (Fig. 8.9). However, AASTHO uses different
strength and resistance factors from those used by the ACI Code.
1. Strut. Resistance of compressive strut is given by
F r = φF n (8.13)
where
φ = 0.7 for strut-and-tie model
F n = nominal compression resistance
{
fce A
F n = cs for unreinforced struts (8.14)
f ce A cs + A ss f y for reinforced strut (8.15)