Góc học tập
17/04/2019 10:11:42 AM

Prestressed Concrete Flat Slabs - Design Methods

Prestressed Concrete Flat Slabs - Design Methods

 

 1. Preliminary Manual Design

The method recommended depends on the load-balancing method made popular by Lin.

 Prestressing is treated analytically by removing the prestressing tendon and replacing it by the equivalent forces that it

applies to concrete. (Diag. 2.1).

By taking reverse curvature of the tendon into account, the complete prestress loading diagram on the slab is derived

(Diag. 2.2).

The system may be described as follows:

1. Decide on column centres, concrete grade (usually 30 or

more) and preliminary slab thickness, as well as drops,

capitals, etc. Choose a preliminary thickness from

paragraph 3.2.2, and from shear considerations. The shear

will often govern, unless capitals or drops are used, and

should be checked first.

2. Decide on the amount of load to be balanced. (This is an

economic decision)

3. Using the maximum drape possible, decide on the

preliminary geometry of the tendon. From (2) and (3)

calculate the prestress force required.

For a parabolic tendon of drape h, length L, Prestress P,

the equivalent upward load is given by W = PL2 /8h and if

L and W and h are known, P may be calculated (see also

4.2).

4. Analyse the slab for Dead Load, Live Load (for pattern

loading see 4.1) and prestress load (use a preliminary

estimate for losses)

5. Calculate the working stresses at various points and

check for allowable tensile stress and deflections. It should

be noted that the limitation of tensile stress is not a good

way to limit cracking, but is acceptable for preliminary

design. Final design should be based on limiting

crackwidth.

6. Calculate the reinforcement required and check the

maximum compressive stress in the concrete for the

ultimate limit state.

7. Check the shear stress, and calculate the reinforcement required, if any.

8. Depending on the results of (5) and (6) it may be necessary to adjust the thickness and prestress, and perhaps to supply

additional non-prestressed reinforcement to control cracking or shear. Non-prestressed reinforcement is always required

over columns, and in external spans.

9. Check the prestress losses due to shrinkage, creep, friction etc. and adjust the prestress loading.

It should be noted that although the sample calculations take account of the variation in prestress along the length of the

structure, and of the effect of curvature of cables over the supports, it is sufficient for preliminary design to assume a

uniform prestress along the length of the structure (except where the prestress is varied by changing the number of tendons,

and to assume that the cables hang from the supports i.e. there is only upward distributed load from the tendons, and

downward point loads at the supports. (See

Diag 3.4) In deciding whether to vary the

number of tendons, it may be taken as a rule

of thumb that 7m of tendon is equal to the

cost of two anchorages.

Some designers make the above assumptions even for final design. Howeverit should be realised that one is designing the non-prestressed reinforcement for the

difference between the downward loads dueto permanent load and live load, and theupward load due to prestress. The differencebetween these quantities may be sensitive tosmall variations in either one.