Prestressing in concrete structures
Since the rise of prestressing in concrete, architects and structural engineers have been keen to experiment with innovative and unique building and bridge forms. Prestressing most simply can be expressed generally as improving the behaviour of traditional reinforced concrete designs by applying a tensile force to the reinforcing steel within the concrete. The major benefit is to prevent cracking of concrete by counteracting the inherent low tensile strength of concrete. To motivate some examples of the use of prestressing in both buildings and bridges are among others:
- the Sydney Opera House with it's iconic billowing sails:
Figure 1: Source: https://www.biennaleofsydney.art/venues/sydney-opera-house/
- the Giesel Library of the USC San Diego with it's inverted pyramid structure
Figure 2: Source: http://architectuul.com/architecture/geisel-library
- the Laguna Bridge in Brazil???
As you can see not only are unique and striking architectural forms possible but also beneficial structural mechanics can be achieved using prestressing in concrete. But the design of prestressed structural members is often regarded as difficult and best left to so-called experts and so the remainder of this article is to share the design philosophy behind structural mechanics of prestressed concrete members.
How do structural engineers define prestressing?
Prestressing in relation to structural concrete is define as:
the creation of internal stresses in a structure to improve its performance such that these stresses counteract the stresses caused by application of a external load.
Since concrete is durable and strong in compression but weak and susceptible in tension, prestressed concrete improves the performance of the concrete member with regard to it's resistance to tension (i.e. reduce cracking). This is beneficial since often a limiting design case of many ordinary reinforced concrete members is cracking in tension. So the reason to apply prestressing is quite obvious in terms of the benefits to take advantage of but how is this prestressing effect included in structural analysis/design?
Structural engineers include the prestressing effect in our calculations by introducing a effective prestressing force acting on the concrete member. The effective prestressing force is defined as:
the force in the prestressing steel when the concrete stress at the level of the prestressing steel has the value of zero.
This force represents the internal stresses (or internal restraint) that originates from the tensioning of the prestressing steel in relation to the concrete. Here it is useful to also differentiate between pre- and post-tensioning of structural concrete members. The difference is that in pre-tensioned members the prestressing is applied before the concrete has hardened while in post-tensioned members the prestressing is applied by a force after the concrete has already hardened.
This difference in pre- and post-tensioning introduces the concept of a tendon force. The tendon force is simply defined as:
the actual force in the prestressing steel for any load case under consideration.
So the tendon force is the force in the prestressing steel once a load is applied on the concrete member whereas the *effective prestressing force is determined prior to the effect of external load on the member. To solidify this concept a example of how this affects the design calculations by comparing the design of a simply-supported concrete beam for both a ordinary reinforced and prestressed member.