Reinforced concrete bridges - Computational Analysis and Design of Bridge Structures - page 125

transversely post-tensioned using four 25.4-mm diameter tie rods tensioned
to 355.9 kN and placed normal to the beams as shown in Figure 4.19b. Load
test was performed to measure the short-term live load strains on the bot-
tom and top surfaces of the bridge as a test vehicle drove over the bridge.
The strain data from the FEA model were compared to the strain data from
the field test, and then the model was refined based on the varying material
strengths until the results were sufficiently close to the field data.
Four main components composed the FEA model of the bridge: the pre-
cast prestressed solid concrete beams, the prestressing strands, the transverse
post-tensioning, and the concrete overlay. The precast-concrete beams and
the concrete overlay were modeled with solid brick elements, and the preten-
sioning strands in the precast-concrete beams and the post-tensioning tie rods
were modeled with link elements (Fu et al. 2011). In the first stage analysis,
concrete is assumed cracked between beams along the bonding so nonlinear
analysis was adopted. For simulating the effect of shear friction after crack
of the shear keys, contact elements (CONTA174 & TARGE170), in the finite
element program ANSYS, were employed at the location of interface between
beams. Contact friction is a material property that is used with the contact
elements and is specified through the coefficient of friction, which was taken
as 0.6 for the interface between slab beams. Both the solid brick and the link
elements have three degrees of freedom (translations) at each node. Because
this is for study and State of Maryland (U.S.) standard-generating purpose,
very refined models were made to line up all skewed angles, rod orientations,
and beam details. There were 46,080 solid brick elements and 3,520 link ele-
ments for a total of 49,600 elements for this skewed bridge.
The transverse strain from the FEA model, as shown in Figure 4.20,
shows a close fit to the field data with strain transducers marked 3215
(underneath) and 1641 (top side) along the longitudinal direction in
Figure 4.19c. The stress distribution at the concrete overlay-beam interface
and the top surface was then analyzed to examine the cause of the cracks
on the top surface of the concrete overlay. Generally, the greatest transverse
tensile stresses, with a potential of concrete cracking, exist near the abut-
ments and between the beams along the shear keys. With the model proved
valid, a series of parametric study of different post-tensioning forces and
configurations were conducted. The first stage is to study the level of post-
tensioning forces (Fu et al. 2010) by nonlinear analysis. Figure 4.21 indi-
cates that each beam behaves independently under wheel loads without a
transverse post-tensioning force. Therefore, only beams with applied wheel
loads show displacements, while the initial displacements of other beams
experience zero. Eight FEM bridge models with different span lengths
(6.10, 7.62, 9.14, 10.67, 12.19, 13.72, 15.24, and 16.67 m) were gener-
ated. As the transverse post-tensioning force of rods increases, displace-
ment significantly decreases and is stabilized approximately at 338 kN of
the post-tensioning force.