## Steel Stress Block

Area for combined anchorage

End section: four anchorages

Area for combined anchorage

(b) Reinforcement

From figure 11.19b. the tensile force in the tie of the equivalent truss is given by

Area of tensile steel required (assuming stress in the steel is limited to 300 N/mm2)

This can be provided by three 10mm closed links (471 mm2) at, say. 50. 125 and 200 mm from the end face: that is. distributed over a length equal to the largest dimension of the anchorage block (200 mm). Note that in each direction there are two legs of each link acting to resist the tensile force.

(c) Check compressive stress in the struts

Allowable compressive stress 0.4(1 - fa/250)fa

Force in strut

Cross-sectional area

The effect of the combined anchorage can be considered by considering the total prestress force of 1000 kN acting on an effective end block of 400 x 400 mm. The tensile force in the lie of the equivalent truss is given by

Area of tensile steel required

This can be provided by six 12 mm closed links (1358 mm2) distributed over a length ^equal lo the largest dimension of the anchorage block, that is. 400 mm.

11.5 Analysis and design at the ultimate limit state

After a prestressed member has been designed lo satisfy serviceability requirements, a check must be carried out to ensure that the ultimate moment of resistance and shear resistance are adequate to satisfy the requirements of the ultimate limit state. The partial factors of safety on loads and materials for this analysis are the normal values for the ultimate limit stale which are given in chapter 2. However, in consideration of the effect of the prestress force this force should be multiplied by a partial factor of safety, 7p, of 0.9 (UK National Annex) when the prestress force is considered to be, as is usual, a 'favourable effect'.

### 11.5.1 Analysis of the section

As the loads on a prestressed member increase above the working values, cracking occurs and the prestressing steel begins to behave as conventional reinforcement. The behaviour of the member at the ultimate limit state is exactly as that of an ordinary reinforced concrete member except that the initial strain in the steel must be taken into account in the calculations. The section may easily be analysed by the use of the equivalent rectangular stress block described in chapter 4.

Although illustrated by a simple example this method may be applied to a cross-section of any shape which may have an arrangement of prestressing wires or tendons. Use is made of the stress-strain curve for the prestressing steel shown in figure 11.21 to calculate tension forces in each layer of steel. The total steel strain is that due to bending added to the initial strain in the steel resulting from prestress. For a scries of assumed neutral axis positions, the total tension capacity is compared with the compressive force developed by a uniform stress of 0.567/,*, and when reasonable agreement is obtained, the moment of resistance can be evaluated.

Figure 11.21

Stress-strain curve for prestressing steel

205kN/mm2

205kN/mm2

Strain

( EXAMPLE 11.10 1

### Calculation of ultimate moment of resistance

The section of a pretensioned beam shown in figure 11.22 is stressed by ten 5 mm wires of 0.1% proof stress /po.ik l600N/mm2. If these wires are initially stressed to 1120N/mm" and 30 per cent losses are anticipated, estimate the ultimate moment of resistance of the section if class C35/45 concrete is used. The stress-strain curve for prestressing wire is shown in figure 11.23.

Stress in steel after losses = 7p x 1120 x 0.7 = 0.9 x 1120 x 0.7 = 705 N/mm2 therefore

/wy{ »uj x 1u which is less than fv, the yield strain.

Bending Strains

Stress Block

Section

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