Strut-and-tie modeling - Computational Analysis and Design of Bridge Structures - page 407

According to AASHTO LRFD Bridge Design Specifications 3rd Edition
(sects. 5.6.3.5 and 5.5.4.2), stress limit for nodes is
f cu = 0.85 f c ′ when nodes are bounded by struts and/or bearing areas
f cu = 0.75 f c ′ when nodes anchor only one tie
f cu = 0.65 f c ′ when nodes anchor more than one tie
and resistance factors are
f = 0.7 for struts and nodes
f = 0.9 for ties
13.2 Hand-calculation exaMPle of StM
Two hand-calculation cases are covered in this section; the first case is a
Hammerhead Pier originally reported by Fu et al. (2005), and the second
case is a pier-supported footing covered in the final report of NCHRP
Project 20-07 Task 217 (Martin and Sanders 2007).
13.2.1 Hammerhead Pier no. 49 of thomas
Jefferson Bridge, Maryland
A simple model is designed by hand to demonstrate the procedures for STM
(Fu et al. 2005). The same structure will be seen in Section 13.64 under
Case Study 4—Pier Cap 2. Also a finite element method analysis will be
done for the same pier cap where loading was increased to see the forma-
tion of cracks.
13.2.1.1 Data
Material strength: f c ′ = 24.13 MPa (3.5 ksi); f y = 275.8 MPa (40 ksi)
Load from each girder: P = 1289.92 kN (290 kip)
Strength reduction factor for struts, ties, and nodes: f = 0.75 (ACI 9.3.2.6)
Through nodes 2 and 3 reactions are transferred to the pier. At each point
2 P = 580 kip (2579.84 kN) load is transferred. The 3D of the pier and the
cap is 1524 mm (60″) thick (Figure 13.9).
Putting b = 1.524 m (60″) and b s = 1.0 (ACI A.3.2.1)
The length of bearing area required L bearing = 2 P /f(0.85b s f c ′) b = 110 mm
(4.332″)
13.2.1.2 Determination of member forces
P 1 = P /sin(59.93°) = 335.100 kip (1490.525 kN)