the heat transfer and stress analyses are not signifi-

then the soil stiffness should be removed after

cantly affected by exceeding the maximum.

30 days to allow the piles to carry the entire load. If

the structure is rock founded, then the structural engi-

neer may choose between modeling the foundation

with continuum elements, developing vertical and

(1) Gravity loads. Gravity loads (self weight of

lateral stiffness spring coefficients to model the rock

the structure) will be included in all NISA analyses.

properties, or using super elements to model a major

It is unnecessary to include formwork as a part of the

portion of the foundation. The use of super elements

stress analysis due to the method in which the gravity

(or substructuring) is a technique of modeling where

load of the concrete is applied at early times. In

a super element represents the stiffness of a large

newly placed lifts, the concrete has not aged suffi-

number of regular elements.

ciently to use element body forces to model gravity

loads without causing excessive displacement and

(3) Time increments. The maximum time incre-

cracking. At these times in an analysis, gravity load-

ments to be used in a stress analysis should be the

ing of the newly placed lift shall be applied as an

same as the heat transfer analysis and the increments

equivalent uniform load acting on the top surface of

are given in Table A-2. The small increments at the

the supporting lift. In locations where the newly

early times are necessary to capture the effects of

placed lift spans a void in the supporting lift, the

creep, shrinkage, and the aging modulus of elasticity,

equivalent uniform load shall be applied to the sur-

since it is at the early times that these properties

face at the bottom of the void. Application of the

change the most.

gravity load over a void in this manner is consistent

with normal construction practice where formwork

(4) Smeared crack model. NISA is based on an

supports the new lift by transferring vertical loads to

interactive stress-strain cracking criterion as described

the floor of the void. Equivalent uniform loads

in Annex 2 of Appendix A. The basis for the crite-

should be removed and replaced with element body

rion is data from the slow load test. The aging

forces after the modulus of elasticity in the newly

modulus of elasticity makes the cracking criterion

placed lift has aged to 1,000,000 psi. The time at

age-dependent. The ANACAP-U software checks

which the modulus of elasticity reaches this limit may

calculated stresses and strains against the cracking

be determined from the modulus versus time curve

criterion at each timestep. If the criterion is exceeded

obtained from material testing. The change in gravity

at any integration point (elements used in a NISA

loading can then be made during the nearest subse-

typically have four integration points for each rectan-

quent timestep shown in Table A-2.

gular element), a crack will be introduced perpendicu-

lar to the direction of maximum principal strain. If a

(2) Foundation model. For soil or pile founda-

crack is introduced, the constitutive matrix for the

tions, the foundation material should be included in

element is reformulated and a new stress state is

the model using spring constants. For soil-founded

developed based on zero stress perpendicular to the

structures, the soil can be replaced by springs which

crack. The new constitutive matrix and stresses are

model the stiffness of the soil. For pile-founded

then used for subsequent calculations until the crack

structures, the springs should account for the stiffness

closes. The cracks will close when placed in a com-

of the soil and the piles, including any lateral stiff-

pressive state, and the material will again be able to

ness that the piles provide. Failure to include the

carry compressive loads. With this approach, the

stiffness associated with the soil at nodes between the

entire element matrix is affected if a crack is deter-

nodes where the pile stiffness is modeled will allow

mined at any integration point. This is referred to as

the concrete to develop excessive deformations

a smeared crack model, and it will provide informa-

between the piles at early times. If the results of an

tion which indicates the depth and extent of cracking.

analysis are to be used in evaluating a pile design,

Days after lift placed

0-2

2-5

5-15

15-35

35-100

100+

Maximum time increment (days)

0.25

0.5

1.0

2.0

5.0

10.0

A-20

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