This post is to clarify an issue that occasionally confuses the readers, particularly when they are starting to understand what UHPC is.
This issue is with regards to the stiffness of UHPC. Sometimes it is possible to see UHPC elements that have a noticeable deflection while they are being handled or manipulated. This leads some people to think that UHPC is more flexible than other materials, as they are not used to appreciate such deflections in, for example, ordinary concrete precast elements.
However, the elastic modulus of UHPC is high compared with ordinary concrete. The figure below (Camacho, 2012) shows the typical range of elastic modulus of different mixtures of UHPC developed by dozens of researchers. It can be seen that it varies between 40 GPa and 55 GPa, while for ordinary concrete it is generally between 32 GPa and 38 GPa, about 30% lower.
Then, the stiffness of UHPC as material is higher than the stiffness of ordinary concrete, meaning that if both materials are submitted to certain stress under tension or compression and in the elastic range, the strain in UHPC is lower than in ordinary concrete.
If UHPC is stiffer, why the deflection in certain UHPC elements is so obvious compared to ordinary concrete? Well, to answer this we need to evaluate the bending stiffness of the beam. (relation between a bending moment applied in an edge of the beam and the rotation angle that it generates).This parameter is obtained as:
Being I z the inertia of the section of the element with length L. Inertia varies in accordance with the third power of the depth. This implies that if we reduce the depth of a rectangular beam a 20%, we reduce its inertia a 50%, even maintaining the width.
But why would a designer reduce the inertia? In general, this is not a goal, it is a consequence of the design of the element: Minimizing the use of material to reach a competitive design implies a reduction of the inertia that will decrease the stiffness, and the engineer should evaluate if this can be afforded or should be avoided (excessive deflection, vibrations…).
Compared to ordinary concrete, UHPC has an advantage as even under significant deflection macrocracks do not appear. Thus, the design can be conditioned by vibrations or deflection under service limit state, but not by certain crack width. Vibrations and deflection are limiting under service, but generally not during the manipulation and commissioning of the precast elements, and for this reason we can see impressive pictures of curved elements while they are being manipulated.
There are very specific cases where reaching a limited stiffness is a goal. One are the Formex® rafts, which should behave as a blanket that adapts to the ocean waves to minimize the pulls in the mussel ropes. This design, patented by RDC, has beams with the same stiffness as the wooden beams used in traditional rafts. The lower depth of the UHPC beams compensates the higher elastic modulus of UHPC to provide the same stiffness as the wooden beams, assuring that both have a comparable response on the water:
Thus, in these floating farms UHPC beams are used mainly due to their longer lifespan and their minimum maintenance costs. However, there is a significant benefit in terms of structural performance: The fact that all UHPC beams are similar assures that all of them have a similar structural contribution, while wood properties are highly variable, so the stiffer beams are overloaded.
Concluding, UHPC is stiffer than ordinary concrete, but with it we can design more flexible structures. This is one of the paradoxes of UHPC.
It is also denser than ordinary concrete, but we can design much lighter structures with it.
It is also more expensive per cubic meter than ordinary concrete, but in many cases, we can design more economic structures with it.
This shows how relevant is to carry out an efficient design, which in the end is simply the process to go from the material to the structure.