31 Dec 93
7-1. Two-dimensional monoliths.
three-dimensional monoliths may be done by
performing several two-dimensional analyses which
capture and envelop the three-dimensional behavior.
a. Lock monoliths that meet the following
requirements can be considered two dimensional for
b. Typically, a three-dimensional analysis will
be performed using finite elements. A three-
(1) The cross section of the monolith, transverse
dimensional finite element analysis of any structure is
to the lock centerline, is constant or nearly constant.
a complicated technique. Caution is required when
performing a three-dimensional analysis, and it should
(2) Loads acting on the monolith do not cause
be performed only by an engineer who is familiar
significant overturning of the monolith in the direc-
with finite elements and with the behavior of the
tion parallel to the lock centerline.
structure being analyzed. In most cases a three-
dimensional finite element analysis is not required
(3) Loads acting on the monolith do not cause
since reasonable results can be obtained through
torsion of the monolith. Torsion is considered to be
several two-dimensional approximations. However,
rotation about a vertical axis through the center of
these approximations also require structural design
gravity of the monolith.
experience, judgment, and insight.
Monoliths which meet these requirements can be
c. If a frame analysis is used for analysis of a
analyzed using a typical strip. Generally, chamber
three-dimensional monolith, strips are modeled using
monoliths, and for some cases culvert valve mono-
a plane frame with in-plane loads and shear loads
liths and intake/discharge, can be considered to act
transferred from adjacent monoliths/strips. Strips in a
two dimensionally. In certain cases the loading and
miter gate monolith exhibit three-dimensional behav-
geometry may be such that some of the above
ior due to increasing bearing pressure towards the
requirements are not completely satisfied but a two-
downstream end of the monolith. The increase is due
dimensional analysis may still be used to accurately
to vertical shears transferred between strips (see
model portions of the monolith.
paragraph 7-3b). Accounting for the shear transferred
between the strips in the two-dimensional model is
b. Much of the analysis of U-frame locks can
essential to obtain stresses which can be compared
be performed using frame analysis methods as
with three-dimensional results. If the shear transfer is
described below. For two-dimensional frame analysis
not properly accounted for within the two-
no additional loads from adjacent monoliths/strips
dimensional model, then it is likely that the loads will
should be applied. Should investigation of a mono-
be unbalanced, particularly if the foundation pressures
lith indicate that a frame analysis is not adequate for
or pile loads applied were obtained from a three-
analysis of the structure (e.g., a monolith which has
walls with a low member length-to-depth ratio), a
finite element analysis should be performed. Typi-
7-3. Frame analysis.
cally, for a finite element analysis of a two-
dimensional structure, a plane strain analysis should
a. General. Frame analysis is the most widely
be performed. Another application of finite element
used engineering tool for analyzing U-frame locks
analysis for two-dimensional analysis is to calibrate
due to its ease and speed of use. Most lock mono-
and verify the results from frame analyses.
liths have complicated geometry, but can be modeled
as a linear elastic plane frame with the use of simpli-
7-2. Three-dimensional monoliths.
fying assumptions. The frames are analyzed using
CWFRAME (Jordan and Dawkins 1990), CFRAME
a. Lock monoliths which do not meet the
(Hartman and Jobst 1983), or other programs. Typi-
requirements for two-dimensional monoliths must be
cally a representative strip is determined for analysis.
analyzed as three-dimensional monoliths. Gate mon-
oliths are usually considered to act three dimension-
ally and in some cases intake/discharge monoliths are
(1) For pile-founded U-frame locks, strip selec-
also considered to act three dimensionally. Since
tion should consider pile spacing, layout pattern,
actual three-dimensional modeling is not a common
stiffness, and batter. For soil-founded locks, a
practice for most designers, analysis of