## Design of PSC members

Design of PSC Members

**Basis**

Sign Convention

In order to derive equations that enable design, we maintain a rigid sign convention:

• Moment:: Positive sag;

• Eccentricity of prestress: Positive above centroid;

• Section Modulus: Negative for the bottom of the member;

• Stress: Positive compression.

With this sign convention, we now have:

Thus the final stresses are numerically given by:

Note that the sign convention means that:

• the P/ A terms is always positive;

• the M_{C} /Z term is positive or negative depending on whether it is Z_{t} or Z_{b} , and;

• the P_{e} /Z term is negative for Z_{t } since Z_{t} is positive and e is negative and the term is positive for Z_{b} since now both Z_{b} and e are negative.

These signs of course match the above diagrams, as they should.

**Governing Inequalities**

Given the rigid sign convention and the allowable stresses in the concrete, and noting that the losses are to be taken into account, the stresses are limited as:

**Transfer**

Top fibre – stress must be bigger than the minimum allowable tensile stress:

Bottom fibre – stress must be less than the maximum allowable compressive stress:

**Service**

Top fibre – stress must be less than the maximum allowable compressive stress: