Pre-stressed Concrete Structures (03)

Concentric Pre-Stressing and Eccentric Pre-stressing:

Concentric Pre-stressing:

Concentric Pre-stressing is that type of pre-stressing process where a Pre-stressed Force is applied at the center of the cross-section of a beam, where center of gravity of concrete (cgc) is with center of gravity of steel/strands (cgs).
Figure-01 indicates a cross-section of a concentric pre-stressed beam with its all respective stress diagram,

Drawing by Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Figure-01: Cross-section of a Concentric Pre-stressed Beam with its all respective stress diagram

In this Figure-01, the pre-stressing force F is applied with no eccentricity. That means F is applied to the beam at the centroid of its cross-section. Under that condition Beam will be subjected to a uniform compressive stress (-F/A) along its length (shown in Figure-a). A concentrated downward force P has also applied at the mid span of this cross section. The effect of this concentrated downward force P will be the maximum at the mid span and the stress due to P at mid span will vary symmetrically from a compressive stress at top (-My/I) to a tensile stress at bottom (+My/I) of the beam (shown in Figure-b). Now the combination of Figure-a) & Figure-b) will be the maximum compressive stress at top and minimum compressive stress at bottom (shown in Figure-c).

If the magnitude of (F/A) and (My/I) are being equal, then the combination of Figure-a) & Figure-b)  shows zero stress at bottom section and maximum compressive stress at top section (shown in Figure-c).

Eccentric Pre-Stressing:

Eccentric Pre-stressing is that type of pre-stressing process where a Pre-stressed Force is applied not at the center of the beam, it is applied with a value of eccentricity,e from the center of the cross-section of a beam, where center of gravity of concrete (cgc) is not at the center of gravity of steel/strands (cgs).

Figure-02 indicates a cross-section of a eccentric pre-stressed beam with its all respective stress diagram,

Drawing by Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Figure-02: Cross-section of a Eccentric Pre-stressed Beam with its all respective stress diagram

In this Figure-02, the pre-stressing force F is applied with a value of eccentricity. That means F is applied to the beam not at the centroid of its cross-section. This pre-stressing force F will be applied at the distance below the centroid of the beam. Under this condition Beam will be subjected to a uniform compressive stress (-F/A) along its length (shown in Figure-a). Though a eccentrically pre-stressing force is applied here, the effect of eccentrically pre-stressing force will very symmetrically from a tensile stress at top (+Fey/I) to a compressive stress at bottom (-Fey/I) of the beam (shown in Figure-b). A concentrated downward force P has also applied at the mid span of this cross section. The effect of this concentrated downward force P will be the maximum at the mid span and the stress due to P at mid span will vary symmetrically from a compressive stress at top (-My/I) and tensile stress at bottom (+My/I) of the beam (shown in Figure-c). Now the combination of Figure-a), Figure-b) & Figure-c) will be the minimum compressive stress at top and maximum compressive stress at bottom (shown in Figure-d).

Pre-stressing Methods:

A tensile force should be applied to the steel strands or, cables (pre-stressing elements) to induce the required compressive stress in concrete. Thus the pre-stressing force which is a tensile force in pre-stressing element produces a compressive stress in the surrounding concrete.

The tension in pre-stressing elements can be applied in two different ways or two different methods of pre-stressing which are,

            ------Pre-tensioning Method,

            ------Post-tensioning Method.

Pre-tensioning Method:

Pre-tensioning is that type of pre-stressing method by which pre-stressed force is applied before casting of a Girder. By this process, at first pre-stressed force is applied, then shuttering  process of a girder is performed & at last casting/curing process is completed.

In Pre-tensioning Method, pre-stressing element is tensioned before the surrounding concrete is cast or poured. Thereafter the surrounding concrete is cast with the pre-stressing elements in direct contact with the concrete. Therefore pre-tensioning method, the stress is transferred from pre-stressing element to concrete throughout the length of the pre-stressing elements and there is no relative movement between pre-stressing element and the surrounding concrete.
Figure-03 indicates the cross section & elevation of a I-girder with pre-tensioning method,

Drawing by Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Figure-03: Cross section & elevation of a I-girder with Pre-tensioning Method

Post-tensioning Method:

Post-tensioning is that type of pre-stressing method by which pre-stressed force is applied after casting of a Girder. By this process, at first shuttering  process, casting/curing process of a Girder is complete then pre-stressed force is applied.

In Post-tensioning Method, pre-stressing element is tensioned after the surrounding concrete is cast and cured. In post-tensioning, concrete is essentially cast cured after the pre-stressing elements with some sheathing or just the duct to carry the pre-stressing elements are laid out with desired profile. Thereafter the pre-stressing elements are tensioned and that tensioned is preserved by anchoring the one end and jacking at the other end of the elements. Since a separator is provided between the pre-stressing element and surrounding concrete (by means of either sheathing or, duct hole) throughout the length of the element, relative movement between the pre-stressing element and surrounding concrete takes place. Pre-stressing force is transferred from the pre-stressing element to the concrete only at the ends of the pre-stressing element by means of anchorage device. Therefore, in post-tensioning method, the effectiveness of pre-stressing elements depends on the effectiveness of the anchorage devices used at their ends.
Figure-04 indicates the cross section & elevation of a I-girder with post-tensioning method,

Drawing by Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Figure: 04 Cross section & elevation of a I-girder with Post-tensioning Method

Figure-05, indicates the cross section & elevation of a segmental girder / box girder with post-tensioning method,

Drawing by Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Figure: 05 Cross section & segmental girder with Post-tensioning Method

To Be Continued.......... .......... .......... .......... .......... ..........