 # G.15.5 Prestress and Poststress Member Load

Members in a structure may be subjected to prestress load for which the load distribution in the structure may be investigated. The prestressing load in a member may be applied axially or eccentrically. The eccentricities can be provided at the start joint, at the middle, and at the end joint. These eccentricities are only in the local y-axis. A positive eccentricity will be in the positive local y-direction. Since eccentricities are only provided in the local y-axis, care should be taken when providing prismatic properties or in specifying the correct BETA angle when rotating the member coordinates, if necessary. Two types of prestress load specification are available; PRESTRESS, where the effects of the load are transmitted to the rest of the structure, and POSTSTRESS, where the effects of the load are experienced exclusively by the members on which it is applied.
1. The cable is assumed to have a generalized parabolic profile. The equation of the parabola is assumed to be

 y = ax2 + bx + c

where
 a = 1/L2 (2es - 4em + 2ee) b = 1/L (4em - ee - 3es) c = es es = eccentricity of the cable at the start of the member (in local y-axis) em = eccentricity of the cable at the middle of the member (in local y-axis) ee = eccentricity of the cable at the end of the member (in local y-axis) L = Length of the member
2. The angle of inclination of the cable with respect to the local x-axis (a straight line joining the start and end joints of the member) at the start and end points is small which gives rise to the assumption that

sinθ = θ = dy/dx

Hence, if the axial force in the cable is P, the vertical component of the force at the ends is P(dy/dx) and the horizontal component of the cable force is,

P[1 - (dy/dx)2]1/2

Users are advised to ensure that their cable profile meets this requirement. An angle under 5 degrees is recommended.

3. The member is analyzed for the prestressing / poststressing effects using the equivalent load method. This method is well documented in most reputed books on Analysis and Design of Prestressed concrete. The magnitude of the uniformly distributed load is calculated as

 udl = 8⋅Pe/L2

where
 P = Axial force in the cable e = (es + ee)/2 - em L = Length of the member
4. The force in the cable is assumed to be same throughout the member length. No reduction is made in the cable forces to account for friction or other losses.

5. The term MEMBER PRESTRESS as used in STAAD.Pro signifies the following condition. The structure is constructed first. Then, the prestressing force is applied on the relevant members. As a result, the members deform and depending on their end conditions, forces are transmitted to other members in the structure. In other words, "PRE" refers to the time of placement of the member in the structure relative to the time of stressing.

6. The term MEMBER POSTSTRESS as used in STAAD.Pro signifies the following condition. The members on which such load is applied are first cast in the factory. Following this, the prestressing force is applied on them. Meanwhile, the rest of the structure is constructed at the construction site. Then, the prestressed members are brought and placed in position on the partially built structure. Due to this sequence, the effects of prestressing are "experienced" by only the prestressed members and not transmitted to the rest of the structure. In other words, "POST" refers to the time of placement of the member in the structure relative to the time of stressing.

7. As may be evident from Item (6) above, it is not possible to compute the displacements of the ends of the POSTSTRESSED members for the effects of poststressing, and hence are assumed to be zero. As a result, displacements of intermediate sections (See SECTION DISPLACEMENT command) are measured relative to the straight line joining the start and end joints of the members as defined by their initial JOINT COORDINATES.