three-dimensional monoliths may be done by

performing several two-dimensional analyses which

capture and envelop the three-dimensional behavior.

requirements can be considered two dimensional for

analysis purposes:

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

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 7-3*b*). Accounting for the shear transferred

between the strips in the two-dimensional model is

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

dimensional analysis.

walls with a low member length-to-depth ratio), a

finite element analysis should be performed. Typi-

cally, for a finite element analysis of a two-

dimensional structure, a plane strain analysis should

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-

fying assumptions. The frames are analyzed using

CWFRAME (Jordan and Dawkins 1990), CFRAME

(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

A-15

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