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A Summary on Critical Assessment of ACI 318 Eq. (18-3), by Devalapura and Tadros.

Due to the fact that Eq. (18-3) of the ACI code 318 is a semi-empirical formula used to compute

the prestressing steel stress at nominal flexural strength, it less accurate. However, it can be used in lieu of

more accurate methods based on strain compatibility to get more accurate results if fps is less than 0.5fpu.

The new approach based the strain compatibility accounts for the presence of nonprestressed steel but it

makes the computation more complex.

Some of the limitation of Eq. (18-3) include: it was developed for rectangular cross-sections but

doesnt recommend anything about other types of shapes which may have a paramount effect especially if

the compression zone is non-rectangular; it was developed for only specific type of steel; it assumes

nonprestressed steel to be mild steel reinforcement.it cant be sued when top reinforcement is used to

control concrete stresses at release of prestress; it is invalid if fse gets lower than 0.5fpu; and also it is not

clear when it comes to approach composite topping using a compressive block theory.

In spite of the limitations, it has got some advantages, which are: the equations at the different

version have given acceptable results when used within their scope of application, it is easy to calculate

and verify, and it doesnt require iteration.

Some researchers such as Harajli and Naaman, Mattock, loov have made efforts to reduce some

of the limitations of the equation but none of their formulas accounted for composite constructions, nor

can they handle sections with nonprestressed tendons or tendons with low initial prestress.

However, an alternative method based on defining the stress-strain curve of prestressing steel by

the so-called power formula, can provide an extremely accurate representation of the entire stress-strain

relationship for all types of steel. This was developed after conducting extensive surveys on the actualstress-strain curves provided by tendon manufacturers and suppliers. Laboratory testing was also

conducted and test results compared with the results provided by strand manufacturers and showed

consistency.

Finally, the following recommendations were presented: to put the equation in the Commentary

and indicate that an equation exist in the commentary for non-iterative semi-empirical calculation of fps

and that the equation gives acceptable accuracy in most applications for which it is valid; to indicate the

validity of the equivalent rectangular stress block, plane section remain plane after bending , and

compatibility of strain in steel and the surrounding concrete in bonded prestressed concrete construction;

to indicate that for prestressing steel, any mathematical model accurately representing the material and

meeting ASTM minimum requirements may be used to represent its stress-strain relationship; and to give

the power formula as an example of the state-of-the-art of steel-strain relationship, and give constants for

commonly used steel types.

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A Summary on Prestress Losses in partially Prestressed High Strength Concrete Beams, by

Naaman and Hamza.

The prestressing force initially applied to a concrete member decrease with time due several

sources of losses. These sources of losses differ based on the type of prestressing, type of concrete, etc. Inhigh strength partially prestressed concrete members, the two main parameters affecting the loss are the

partially prestressing ratio, PPR, and the concrete compressive strength. The PPR describes the relative

contribution of the prestressing steel and the reinforcing steel to the resistant of the section.

In general, the estimation of the prestress losses may be carried out at several different levels,

namely: lump sum estimates of total prestress losses, TPL; lump sum estimates of the separate prestress

losses due to a particular effect, such as shrinkage, creep, or relaxation; and accurate determination of

cumulative losses by time-step (T-S) method.

The time-step method is the most accurate technique to determine time-dependent losses due to

steel relaxation, creep and shrinkage of concrete. It requires accurate determination on the time dependentmaterial properties. The main equations used in the study for the calculation of prestress losses include

elastic shortening, relaxation of the tendons, shrinkage of concrete and creep of concrete, by the time-step

method.

An extensive parametric evaluation of prestress losses in high strength, prestressed and partially

prestressed concrete members was conducted using three computer programs. The first program was used

to calculate the live load moment for simple span bridges according to the AASHTO specification. The

second program was used to calculate the required areas of prestressing steel, A ps, and reinforcing steel,

As, the PPR approach, using the ultimate strength design method according to the ACI Building Code.

The third program was developed to compute prestress losses by the time-step method. Parameters and

variable included the type of beam cross section, the PPR, the concrete compressive strength, the type ofprestressing steel, environmental conditions, the strength and grade of the reinforcing steel.

After conducting the parametric study, it was confirmed that either a number of observations

made in previous studies, or a number of logical inferences on the effects of shrinkage, creep and

relaxation on time dependent prestress losses in partially prestressed concrete members.

Some of the relevant conclusions made from the study include: the prestress loss due to creep

decrease with a decrease in the PPR while the loss due to relaxation of the prestress steel increases with a

decrease in PPR; the time dependent stress loss in the prestressing steel generally decrease with a

decrease in the partially prestressing ratio keeping all other parameters constant; the time-dependent stress

loss in the prestressing steel generally decrease with an increase in the compressive strength; timedependent losses are influenced by the type of cross section; the loss due to elastic shortening decreases

with a decrease in the level of prestress; the current estimate from the lump sum approach should not be

used ; and in partially prestressed concrete members, the loss of compression force in the concrete due to

time dependent effects I not equal to the loss of tension force in the prestressing steel.