stem has on its flange. The stiffened width of the

half as many elements by taking advantage of

thinner slab depends on the specific geometry of the

symmetry. Boundary conditions can be used so that

base slab and the designer's assumptions.

only a portion of the structure, such as a single wall

or a portion of a wall, needs to be modeled as

opposed to the entire structure, once again reducing

the input and output required (see Figure A-8). This

Joint flexural design moments at the face of support-

aspect becomes very important when performing two-

ing concrete or toe of a fillet should be used. This is

dimensional analyses on portions of a three-

also where reinforcement development length starts.

dimensional monolith. The designer should use care

Moments at these points can be found easily by

in the selection of the applied boundary conditions so

modeling a joint at the desired location. Maximum

that behavior of the model represents similar behavior

midspan moments are available from computer runs

of the real structure.

or can be found using free-body diagrams. Shear

should be checked, initially, at the face of the sup-

porting concrete. Alternative locations for checking

shear, in compliance with American Concrete Insti-

dation can typically be accomplished through the use

tute (ACI) 318, can be used if required.

of elastic springs which may be computed from the

pile stiffness coefficients. Some finite element pro-

grams contain pile elements which may be used or it

may be possible to employ a soil-structure interaction

(SSI) model. Close coordination with the geotechni-

cal engineer is required when selecting the spring

cal method which can be used to determine the

constants for the foundation, whether it be a pile-

stresses, strains, and displacements. Finite element

founded or a soil-founded structure. A pile-founded

analysis can be performed in two or three dimensions.

structure should be analyzed so that the piles carry

While the finite element method is a powerful and

the entire load. If an SSI analysis is being per-

useful tool, it must be used with care. Results from

formed, then provisions must be made so that the

finite element analysis often appear accurate even

piles carry the load. Finite element modeling of the

when the input is incorrect. The apparent accuracy of

foundation is an option. In many cases it is not used

finite element results stems from the fact that results

because the increased accuracy of the results is not

are often given to the fourth or fifth decimal place.

improved enough to justify the increased cost of the

To ensure results that are accurate, it is imperative

analysis. If the foundation is modeled, guidelines for

that finite element input data be thoroughly reviewed

developing the foundation mesh can be found in

prior to proceeding with a design. Numerous texts

Jones and Foster (in preparation).

are available on the subject and guidance for model-

ing with finite elements is provided in ETL 1110-2-

332. ETL 1110-2-332 should be reviewed by any

designer who will be performing finite element analy-

thickness slabs occur only in gate monoliths, and the

sis. In addition, for the designer not familiar with

shapes that result in these monoliths can be very

finite elements, review of Will et al. (1987) is an

diverse as seen by the cross sections shown in

excellent example of how a novice should approach

Figure A-9. Because of the shape of the base and

finite element modeling. Finally, ETL 1110-2-254

because the loading on a miter gate monolith is three

should be referenced for the purpose of documenting

dimensional, a three-dimensional finite element analy-

finite element results.

sis will likely provide the best available solution for a

variable thickness slab. Due to the fact that a three-

dimensional analysis is a difficult procedure, even for

experienced finite element users, simplified two-

for two-dimensional monoliths can be found in

dimensional finite element analyses may be used to

paragraph 7-3*b *on strip selection for frames.

design a base slab. Two-dimensional models which

may be used to model a base slab using shell ele-

ments are the sloped plate model, the stepped plate

become very important when using finite elements.

model, or the offset beams model. These models are

In the case of symmetrical structures, boundary con-

described in the paragraphs below. Any of these

ditions can be used to reduce the amount of input and

models may be used by the designer. Selection of

output produced by an analysis. This is shown in

the best method may depend on the specific geometry

Figure A-7 where the structure can be modeled with

A-22

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