This software was part of my dissertation at Imperial College.

General information

It was completed in July 2000 during my MSc studies under the supervision of the director of the post graduate studies, prof. G.L. England. It refers to analytic and arithmetic methods for the calculation of short and long term deformation and stressing of concrete because of time-dependent phenomena, such as creep and shrinkage. I applied these arithmetic methods in slender cylindrical concrete piers, which are deformed because of the solar heating and the continuous movement of the sun.

The computer program, called myCreep, was developed using Microsoft Visual Basic version 6 (SP3), for Microsoft Windows 95/98/2000/NT based systems. It consists of 3781 lines of source code. The program is user-friendly and most of the results can be plotted automatically, so that the user can check visually the validity of the calculations. The program is also capable of editing the various diagrams directly, but it is possible to input data using a spreadsheet, e.g. Microsoft Excel. In this way, the user can easily use as many points as desired.

myCreep can calculate the thermoelastic solution at a specified time of the day. This is important, because in this way the user can check if the discretization of the structure is sufficient. Finally, myCreep is able to calculate the creep solution based on the analysis presented in the thesis; it can also store the deflection profiles of the pier at a specified time interval.

Data

Two kinds of data are fed into the computer program:

• Variables: These are discrete variables which either refer to the whole structure or are assumed to be common within the structure, e.g. the dimensions of the pier, the coefficient of thermal expansion, the reference temperature, the number of rings, sectors, slices, etc.
• Diagrams: The computer program also uses diagrams which provide complete freedom to the user. There are various diagrams invoked in the analysis, such as the position of the sun as a function of time, the ambient temperature as a function of time, etc. The diagrams are defined as a series of discrete points, i.e. pairs of x - y values. The variation of the diagrams between adjacent discrete points is assumed to be linear; however, there are but practical limitations to the number of the points invoked in the definition of a diagram.

Example

A slender pier was analysed as an example; the results included the short and long term deformation, the pier profile in all directions, the stresses of all elements etc after 50 years. The calculation step was 15 minutes. The data used in this example are:

• Height: 150 m
• Internal radius: 3.5 m
• External radius: 4 m
• Compressive force: 20 MN
• Unit load: 25 KN/m³
• Elastic modulus: 35 GPa
• Reference temperature: 10 ^oC
• Coefficient of thermal expansion: 10 x 10^-6 /^oC
• The structure was divided into 4 rings, 40 sectors and 100 slices

The following data were also used for the creep analysis:

• Time interval: a quarter of an hour (0.25 hours)
• Starting date: 1/1/2000
• Ending date: 1/1/2050
• Deflection profiles were stored every 5 years.

The analysis lasted almost 12 hours using a Pentium III 500 MHz computer system. The details of the input data as well as the results are provided in the thesis. 

Comments on the results

Some comments can be made based on the results:

• As expected, the deflection profiles are sparser at the beginning of the analysis when the creep rate is greater. However, as time passes and creep rate reduces, the deflection profiles become increasingly dense.
• It is important to note that, while creep deflections are generally towards South, thermoelastic deflections are generally towards North. This is so because the southern part of the pier is generally hotter; therefore it creeps more, causing the pier to deflect in a Southern direction. However, the thermoelastic deflection of the tip is against the sun, i.e. in a Northern direction.
• The deflection of the tip of the pier along the X and Y axes because of creep alone were found to be ~-1.06 cm and ~2.33 cm, respectively, after 50 years. Therefore, the overall deflection is ~2.56 cm. We can compare this value with the thermoelastic deflection in the summer, at the hotter time of the day i.e. at 15:00 hours. In this case, the overall deflection is ~12.18 cm. Therefore, in this case, the creep deflection is ~21% of the thermoelastic deflection. However, for the hotter time of the day in winter, the creep deflection is greater than the thermoelastic deflection. Of course, these deflections are not based on experimental data and they are not in the same direction; therefore, they cannot be directly compared. The purpose of the comparison was to obtain the relative magnitude of these values.
• As far as the horizontal creep deflections are concerned, the critical factor is not the magnitude of the temperatures but the difference between the ambient temperature and the surface temperature. This means that the critical factor is sunshine, which heats concrete above the ambient temperature. The corresponding diagrams used in this example were not conservative; bearing in mind that, for example, some areas in the Mediterranean have as many as 320 days of sunshine per year, it is obvious that in these cases creep deflections may be significantly greater. 

[myCreep :  executable]