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 MC /Z term is positive or negative depending on whether it is Zt or Zb , and;
• the Pe /Z term is negative for Zt since Zt is positive and e is negative and the term is positive for Zb since now both Zb 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: