Fig. 4: Schematic of the repair completed in Structure B, with 4.75 in. flanges (Note: 1 in. =
25 mm; 1 ft = 0.3 m)
immediately on Structure B after the failure in that structure
(Fig. 4). On February 9, 2016, the owner of Structures A and B
filed suit against the contractor, precast manufacturer, and others.
As required by the construction contract, the owner’s
demands for restitution of damages resulting from the
failures went to arbitration. The proceedings regarding
Structure A concluded in April 2018. We will not report on
the agreed terms related to Structure A or the lawsuits for
Structures B and C, as they are not relevant to our central
We do not know if the DTs on Structure C have been
repaired. However, Structure C remains closed, and the
owner is pursuing litigation against the contractor.
Dimensions and properties
In a guide specification provided to designers by a
consortium comprising many precast concrete producers and
the grid producer, the grid is termed an “epoxy-coated
interlaid carbon-fiber mesh.”5 According to information
published by the grid supplier, each strand in the carbon-fiber
portion of the grid contains about 50,000 carbon-fiber filaments,
and the strand is termed C50 strand. Per Reference 2, the
filaments total about 0.00286 in.2 (1.85 mm2) in crosssectional
area. We have observed that the epoxy coating
results in a very smooth surface on a somewhat irregularly
shaped band that is about 1/16 in. (1.6 mm) thick by 1/8 in.
(3.2 mm) wide.
In Structures A and B, the C50 strands were spaced at 2.7 in.
on center, giving a unit area of carbon filament of 0.0127 in.2/ft
(26.8 mm2/m). The design documents show that the grid
product was to be placed in the flange with a nominal cover
of 0.75 in. (19 mm) from the top surface of the concrete.
The grid arrangement consisted of continuously looped
C50 strand bonded to orthogonal polymer-coated glass-fiber
strands on approximately 1.5 in. (38 mm) centers (Fig. 2).
The polymer coating bonded the intersections of the C50
and glass-fiber strands and thus set the spacing of the
strands in each direction. Because the grid sheets are not as
wide as the DT flanges, the producers installed at least three
sheets across a DT flange. The sheets overlapped, and
loops in the C50 strands would be expected to provide
34 SEPTEMBER 2019 | Ci | www.concreteinternational.com
The Resistance Side of the
The following discussion is focused
on Structure A. As previously noted, the
DT flanges in Structure A were 3.5 in.
thick. The cantilever length on a typical
DT flange was 37-3/8 in. (949 mm) (the
length is from Reference 2—the
dimension may vary slightly in the
structures). The contract documents
indicate that the 1/16 in. thick grid was
to be placed with a nominal 0.75 in.
cover, giving a design effective depth d
of 2.7 in. Normalweight concrete was specified. A concrete
strength fc′ of 6000 lb/in.2 (41 MPa) is assumed in the
Strand force and resistance factor
The moment capacity is computed as strand force times
lever arm. Calculations provided in Reference 2 use a mean
strength of a C50 strand (1218 lb 5.42 kN) as the strand
While the mean strength may be useful when trying to
understand test results, we do not believe it is suitable for
design. Based on product documents published
contemporaneously with the DT fabrication for Structure A,
the grid producer reported a tensile strength of 830 lb (3.69 kN)
per strand, reportedly based on mean test strength μ minus 2
times the standadard deviation σ. In contrast, ACI 440.1R-06,
Section 3.2.1,1 recommends that “Manufacturers should report
a guaranteed tensile strength” of μ − 3σ. Application of the
recommendations in References 1 and 6 to the design of the
structure would have resulted in a tensile strength of 683 lb
(3.04 kN) per strand. Further, as noted in Reference 2 and
quoted in the textbox at the beginning of this article, the DT
producer made the decision to use a strength reduction factor
ϕ of 0.75 for flexure, rather than ϕ of 0.55 as recommended by
ACI Committee 4401 and supported by reliability analyses
provided in Reference 7.
Lever arm and capacity
The simplest approach for finding the lever arm is to adopt
the usual equation for nominal moment Mn
Mn = Af ff (d − a/2) (1)
where Af is the fiber area in the strand; ff is the stress in the
fiber; and a is given by a = Af ff /(b(0.85fc′)). This introduces a
strain compatibility problem: when the carbon-fiber strand
fractures, the extreme fiber strain in the concrete will be well
below the usually assumed compression strain of 0.003. Even
so, we believe it gives a reasonably good estimate of the lever
arm and moment capacity.
An alternative approach is to calculate the moment based
on an elastic cracked section, which can be stated as: