Question:
What is the maximum modulus of elasticity that can be achieved with lightweight HPC?
Answer:
The modulus of elasticity (MOE) of lightweight high performance concrete (HPC) is affected by numerous variables including concrete compressive strength; concrete density; lightweight aggregate (LWA) type, size, and content; fine aggregate roperties; air content; concrete age; and method of curing. To consider each factor in calculating MOE is difficult and impractical. Therefore, a implified equation
is used.
Current Method
The AASHTO Standard and LRFD Specifications provide the following equation for the calculation of MOE, Ec, for concrete densities, wc, from 90 to 155 lb/cu ft (1.44 to 2.48 Mg/cu m):
Using the equation, a designer might believe that MOE values of over 4000 ksi (27.6 GPa) are possible for lightweight HPC having a density of 120 lb/cu ft (1.92 Mg/cu m) and a strength of 10,000 psi (69 MPa).
Experimental Results
The figures provide a sampling of experimental MOE results for shale, clay, and slate aggregates and indicate that MOE values for lightweight HPC seldom reach the levels suggested by the equation.
The figures show a large variation in MOE for a given strength or density. The figures also show that it is not always possible to identify a particular type of LWA as being superior to another one for MOE values across the spectrum of strengths and densities depicted. This suggests that the use of a generally applicable equation to predict MOE based only on strength and density is not very precise.
The Maximum MOE
The best answer to the original question does not involve an equation. The only guaranteed method is to conduct an experimental study based on the same concrete mixture proportions and constituent materials planned for the project. The study will produce a range of MOE values from which the designer may choose. Local lightweight aggregate suppliers will be able to provide starting points. However, subtle changes in regionally available fine aggregate, as well as the other factors mentioned above, can affect the MOE.
Answer contributed by Karl F. Meyer, United States Military Academy, West Point, NY. He may be contacted at [email protected].