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: