The ultimate load capacity of a prestressed concrete member is no better than that of a reinforced concrete member with reinforcement of similar tensile capacity. Then why prestress? Because at service loads, the two types of construction are markedly different.

The tensile capacity of concrete is notoriously low - only about one-tenth of its compressive capacity. Internal stresses due to shrinkage and temperature changes can often exceed this low tensile capacity, so that even unloaded members will crack.

A reinforced concrete member may be seen as an assembly of loose concrete blocks, prevented only by the reinforcement from falling apart. The reinforcement stretches as it takes tension. This allows the concrete blocks to rotate relative to each other. Corrosive agents can penetrate the cracks. Reinforced concrete deflects more and deteriorates faster than prestressed concrete.

If the concrete is put in compression wherever tensile stresses would otherwise cause it to crack, then the problems mentioned above are eliminated. This can be achieved by stretching the reinforcement to its limits and transferring the stretching load to the concrete.

Two methods exist, pre-tensioning and post-tensioning, where 'pre' and 'post' refer to the hardened state of the concrete. Precast planks are prestressed by pre-tensioning.

Unfortunately, losses of the prestress force cannot be avoided. Firstly, as the load is transferred to the concrete, the member will shorten, and some slippage between the tendons and the concrete will occur. Secondly, the concrete continues to shorten with time (a) by its nature to shrink and (b) by its plastic behaviour called creep. Thirdly, steel also displays some plasticity, although much less than concrete, and will relax its load.

The old saying Every problem has a solution, and every solution creates its own problems is also true of precast prestressed planks. The simple method of design we can employ with reinforced concrete is not enough for prestressed concrete.

The planks and structure have to be checked for a number of conditions, any of which could be critical:

Additionally, thought must be given to the differential shrinkage between the topping and the planks, and provision must be made for the planks to shorten lest the prestress force disappears into the supporting structure.

Clause 8.1.2.1 of AS 3600 states Calculations for strength of cross-sections in bending, or in bending combined with axial force, shall incorporate equilibrium and strain-compatibility considerations and be consistent with the following assumptions:

A typical stress-strain relationship for two grades of concrete is shown in Figure 1, reproduced from Clause C6.1.4 in AS 3600 Supplement 1.

The same prestress force located at a level so that the resultant stress in the top fibre is zero (Figure 2(c)) will lead to a stress in the bottom fibre twice the average stress calculated above. The level at which the prestress is then located is said to be the lower kern line (kern is German for core and defines an area inside which an applied compressive force would cause no tensile stresses anywhere in the cross-section).

If we locate the prestress force below the lower kern line, we get a rapid increase in compressive stress in the bottom fibre and a tensile stress in the top fibre as shown in Figure 2(d). The magnitude of these stresses is:

where e is the offset of the prestress force from the centroid of the section (+ve if below), Z is the modulus of section at the top and bottom fibre respectively and the other values are as previously defined.

An applied moment M (+ve if it causes tension in the bottom) will produce stresses in the top and bottom fibre of a homogeneous section equal to:

A precast plank which has tendons located below the centroid of the section will want to hog upwards when the prestress is transferred to it. This hogging effect means that the selfweight of the plank will immediately come into play. Whether the resultant effect will be a hog depends on the location of the tendons. If the superposition of the stresses due to prestress and due to part or all of the selfweight result in an average stress pattern as shown in Figure 2(b), then the plank will remain level, otherwise, it will hog.

The program assesses the combined effect of selfweight and prestress, taking into account the load factors given in Clause 3.3.1 ... Where applicable, the prestressing force, P, shall be included with a load factor of unity in each load combination, except for the case of dead load plus prestress at transfer, when the more severe of -

shall apply.

If only part of the selfweight acts while the plank is still in the stressing bed, then the plank will deflect when it is lifted. The program calculates the initial hogging or this deflection as follows:

d is the deflection (-ve if upward hogging)

w is the factored selfweight

L is the cut-off length of the plank

P is 1.15 times the prestress after cut-off losses

e is the offset of the prestress below the plank centroid

I is the moment of inertia of the plank.

It should be noted that the cut-off length is not necessarily the in-service span, for example, if cantilevers are specified at one or both ends, the cut-off length equals the span plus the cantilever(s). Since cut-off usually takes place before 28 days, the modulus of elasticity at transfer is arbitrarily reduced to the value shown in Design Parameters. If a different value applies, the results displayed in Custom Design may be simply ratioed.

Cut-off should not take place until the concrete has attained a compressive strength of at least twice this value.

Clause 3.4, Load Combinations for Serviceability Design, refers only to deflections. It is assumed that the same short-term load factors apply also to Clause 8.6.2 and the values displayed in Selection are based on this assumption.

The programmed procedure for arriving at the percentage by which the permissible stress covers the actual stress under service loads, displayed in Selection, is as follows:

Several questions arise when precast planks are combined with in-situ topping to form a composite section:

Frequently, the in-situ topping has a modulus of elasticity that is different from the plank. The answer can be found by examining the stress-strain relationship when a moment is applied to the composite section.

The diagram at left shows a typical stress state before the application of the moment.

The strain resulting from the moment is based on the basic principle that plane sections remain plane.

The resultant stress pattern to be added to the original stresses reflects the difference in concrete grades.

Consider the cross-section divided into horizontal elements. Each element has these properties:

b is its width (for example the sum of webs) at this level;

s is the stress in the element;

dy is the thickness of the element.

Two equilibrium conditions must be satisfied:

This requirement is satisfied by welded mesh to AS 1304 with a minimum yield strength of 450 MPa as follows:

Topping Minimum Nearest Actual

thickness area mesh area

30 166.7 F62 155.8

60 333.3 F92 317.9

90 500.0 F81 502.4

The previous statement that the resultant stress pattern is to be added to the original stresses is an over-simplification. In reality, the original stresses adjust themselves to the composite section through creep. To assess this adjustment, let us imagine:

How much of the external load remains after creep?

If we divide the total creep into n equal slices, we can assess the effect in each period, where f is the creep factor:

by analogy

By taking n to infinity, this equation reduces to-

concrete grade 20 25 32 40 50