Strut-and-tie modeling - Computational Analysis and Design of Bridge Structures - page 414

13.2.2.4 Check the detailing for the anchorage of the ties
The no. 8 bars are required to develop a force of 190 kip (845.16 kN) at the
inner face of the piles. The original plans called for no hooks or any other
anchorage device. The stress in the no. 8 bars at the inner faces of the piles is

190
6 0 79

f s = = 40 ksi( 275 80 . MPa)

× .

In accordance with AASHTO LRFD paragraph 5.11.2.1.1, the basic tension
development length of a no. 8 bar, l d , is 868.68 mm (34.2″). The develop-
ment length can be reduced as a function of the amount of stress in the bar;
hence (40/60) × 34.2 = 584.2 mm (23″). Because a development length of
609.6 mm (24″) is provided, the original anchorage details are acceptable.
In this section a very simple structure was analyzed to demonstrate the
STM method. But when the structure is more complicated with larger num-
bers of members or when the structure is indeterminate, STM goes beyond
the limits of hand calculation. Since the procedure is based on trial and error
to get the optimum STM model, a computer program will be necessary.
CAST ( c omputer- a ided s trut-and- t ie), a state-of-the-art program developed
by Kuchma (2005) sponsored by the National Science Foundation, is a very
useful tool with a user-friendly graphics interface.
The following case studies will demonstrate the usage of STMs in the
transportation-related field. All cases can be simulated by using planar STM
models. The first four cases were solved earlier by hand calculations (Fu et al.
2005) and later by CAST for verification. The fifth case is for an integral pier
bent, which was covered in the final report of NCHRP Project 20-07 Task
217 (Martin and Sanders 2007) and then solved by CAST for this chapter.

13.3 2d illuStrated exaMPle 1—aButMent on Pile

An abutment on piles is widely used in bridges, and one under construction
can be seen in Figure 13.11a and b (Fu et al. 2005). For the case study, the
abutment considered is 10.06 m (33′) long, 0.91 m (3′) wide, and 0.91 m (3′)
deep. Eleven prestressed concrete deck beams bearing on elastomeric pads
are supported at an interval of 0.91 m (3′) along the length of the abutment.
The concrete slabs span 15.24 m (50′) and transfer 107.61 kip (478.67 kN)
factored load on each elastomeric pad. The abutment is supported on six
piles spaced at 1.83 m (6′) on center. With this geometry, where depth is
half the distance between the supports, this abutment is a special deep
beam where Bernoulli's region does not exist and there is a disturbed region
throughout. AASHTO states that Bernoulli's region does not exist when
the depth-to-span ratio exceeds two-fifth. This beam exceeds that limit.
According to one of the criteria of St. Venant's principle, D-regions are