### Q1:

The simply supported I beam shown below is used in a corrosive environment to carry a service load, comprising 3 kN/m dead load and 5 kN/m live load over the 13 m span, in addition to its own weight. Normal density concrete will be used. The beam is pre tensioned using 6 Size 13 (Grade 1860) horizontal strands jacked initially to 75% of ultimate as shown in the figure. The initial and total losses are 9% and 23% respectively, of jacking.

**(a)** Calculate the concrete flexural stresses at the mid-span and support sections at transfer and under final conditions.

**(b)** Compare stresses in (a) with relevant permissible values in A23.3-04 assuming fc ’ = 35 MPa and fci’ = 25 MPa

**(c)** Determine the maximum eccentricity of prestress that may be used so that no tensile stress is induced at the support section. (d) Use CONCISE to check your calculations and comment on any differences.

**(d)** Use CONCISE to check your calculations and comment on any differences.

### Q2:

The normal density concrete beam shown below has a rectangular section 200 mm wide by 600 mm deep and contains 750 mm² of Grade 1860 prestressing steel having the indicated profile. The stress in the prestressing steel at transfer is 77% of ultimate and after losses the prestress force is 80% of that at transfer. The concrete strength at transfer is fci’ = 35 MPa and the specified strength is fc ’ = 38 MPa.

**(a)** Determine, according to stress serviceability requirements only, the uniformly distributed superimposed load that can be carried by the beam in a non-corrosive environment. Assume that 40% of this load is sustained loading.

**(b)** Determine the minimum value of distance x and the related hold down force.

**(c)** Would using the minimum distance of x be the most practical solution?

**(d)** Would it be possible to use a single harp point at mid-span assuming an eccentricity of 140 mm at mid-span and zero at the end of the beam? Show suitable calculations to justify your answer.

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