When calculating stresses for a given section, each location on the polygon is checked. This guarantees that the controlling stresses are found and accounts for all asymmetries in the section, the prestressing, and any lateral loading that may exist. If the section is composite the stresses are split into the stresses on the non-composite section and the stresses on the composite section. These stresses are calculated individually, and the total stress is the sum of the two values. Non composite stresses include forces from self-weight, non-composite dead load, topping weight, and the prestressing force. Composite stresses come from all other load types.
Symmetric Sections
For symmetric sections, the stress at a given location is as follows:
In the above equation,
Mx is the moment about the horizontal axis,
My is the moment about the lateral axis,
Pi is the axial force,
Ixx is the moment of inertia about the x axis,
Iyy is the moment of inertia about the y axis,
and Ag is the area of the concrete.
Prestress Force
The prestressing force generates both axial force and internal moments on the member. The prestressing moments generated can be about either the horizontal axis or the vertical axis depending on strand eccentricities. Lateral strand eccentricity, which generates moments about the vertical axis, can be ignored. Lateral moments generated are typically small in members such as L-Beams or asymmetric Double Ts, but in spandrels cast on their side these can generate non-insignificant stresses.
Principal Stresses
Stresses due to asymmetric sections are accounted for by modifying the stress equation above. The general form of the stress equation above is as follows:
Where Ixy is the product of inertia. Note that in the above equation, if the product of inertia is zero the equation simplifies to the same equation used for symmetric sections.