resists lateral loads applied to the pile bent but in order to model it the soil properties
have to be known and several springs need to be used in the analysis. For simplicity the
soil effect was ignored. Ignoring the soil effect is a conservative approach. Load case 1
has a single lateral load at the cap beam level, which results in maximum moments in the
piles just under the cap beam and at the fixed base. If the cap beam stiffness is assumed
large relative to the piles, then the moments at the ends of the piles are all equal, which
results in the simultaneous formation of plastic hinges at each of those locations. At each
plastic hinge location rotational springs were used to control the stiffness of the joints
(see Figs 7-3 and 7-4) after moments became sufficiently high to cause nonlinear
behavior. Once all plastic hinge rotations reached failure rotations the pile bent system
formed a collapse mechanism and it was considered to have failed.
Determining plastic hinge length is a complicated matter and no universal equation
exists. Many empirical equations that estimate the plastic hinge length (lp) have been
proposed. For the purpose of this study an empirical equation proposed by Caltrans
(2004) was used because it relates to bridge drilled-shaft reinforced concrete piles that are
closer to this case compared to equations derived based on reinforced concrete beam and
column tests. The empirical equation used to estimate the plastic hinge length (lp) was the
following:
lp = D + 0.08 H (7-1)
where D is pile/column diameter or section depth and H is the distance from the location
of maximum moment to the point of contraflexure. The plastic hinge lengths for the
various types of piles investigated can be seen in Table 7-1.
Table 7-1. Plastic hinge length of various types of piles
Pile type Shape D (in) H (ft) d (in)