GENERAL The Design Aids section contains the downloadable software program for the determination of the compliance function J (primary function) and of the derived functions R, x, R*, as well as of the aging coefficient c of the AAEM method, for three creep prediction models, including the user interface necessary for setting input data and handling output results. The basic guidelines for the use of the program are presented in the following. For further detail refer to [Sassone and Chiorino 2005]. STRUCTURE OF THE PROGRAM The Creep Beta 1.0 program is a C++ stand-alone compiled application, complete with all the interfaces and data output features permitting the creation of a user friendly tool for a quick computation and printing of the basic functions required for creep analysis. The main interface window 1 provides a graphic screen where the computed diagrams of the different functions are drawn. All the parameters of the graphic screen can be edited by the user. Through this window it is possible to select the creep prediction model and the function to be calculated (compliance J , relaxation R, redistribution x or aging coefficient c). A separate window is available for the determination of the reduced relaxation functions R*. The other selections concern: scaling, boundary and type of coordinates (linear or logarithmic), the type of integration rule for the numerical solver of the integral equation (rectangle or trapezoidal), the amplitude of the initial step and number of time steps. The button options permits the choice of a dimensional or dimensionless format for J, R and R*. Through the creep models window 2 it is possible to insert all the values of the parameters required by each model; this windows permits also the calculation of one spot value of the compliance function J for given values of time parameters t and t0 . Window, opening upon the selection of the required function, permits the choice of the total number of curves to be calculated and plotted, of the final time t and of the initial times t0 (and t1 for the redistribution function x(t,t0,t1)). The dimensionless versions are obtained dividing the compliance Jmes">J by the initial (nominal elastic) value of the strain due to a unit stress at 28 days [1/Ec28], and the relaxation functions R and R* by the initial (nominal elastic) value of the stress due to a unit strain at 28 days [Ec28 ], i.e. : J (t,t) Ec28 ; R(t, t )/Ec28 ; R*(t, t ) /Ec28 .
OUTPUT The output consists of text files of the numerical values of results and graphic bitmap files of the charts. For printing the charts as shown in the window use the file button. NUMERICAL APPROXIMATION Two options are available for the approximation of the integrals with finite sums: the trapezoidal rule and the rectangle rule. The second option allows a quicker solution and usually leads to acceptable approximations if the number of time steps is not too small. However, computation time is not significant even when adopting the trapezoidal rule: of the order of seconds for the entire family of curves appearing on one window. The selection of the most convenient progressions of time steps, in terms of amplitude of the first time interval and rate of the geometrical progression, can be easily performed – thanks to the rapidity of the process – verifying the influence of the refinement of the adopted subdivision of the time scale on the numerical results of the computed function through repeated trials. The following values are normally adequate for accuracy in the results up to third digit for all the models: amplitude of the first time interval: D t2 = t2 - t1 = 0.01 day = 864 s, number of step per decade: m = 80, number of steps for 105 days: @ 550. CREEP MODELS The following models have been embedded in the program: CEB MC90 [CEB 1993] GL2000 [Gardner and Lockman 2001] B3 [Bazant and Baweja 2000]. Their formulations are presented in Appendix 2 of [Sassone and Chiorino 2005], together with the input data required by each model. EQUIVALENT CONDITIONS FOR A COMPARISON OF DIFFERENT MODELS For a comparison of the predictions of the different models, equivalent conditions can be established setting at the same values identical or equivalent parameters. Some minor problems arise in this selection. Reference can be done to [Sassone and Chiorino 2005] for a detailed discussion.
INITIAL (NOMINAL ELASTIC) VALUES OF STRAINS AND STRESSES In creep prediction models the compliance function J(t,t0) is normally conventionally separated into an initial age-dependent strain due to unit stress J(t0+D,t0) with D = t - t0 small, which is treated as instantaneous and elastic (nominal elastic strain), and represented as the inverse of a nominal elastic modulusEc(t0) , and a creep strain C(t ,t0), i.e.: By analogy, in the relaxation function the initial age dependent stress response due to a unit imposed strain for D = t - t0 small is treated as instantaneous and elastic, i.e.: This conventional separation is included directly in the formulations of the model for CEB MC90 and GL2000 models. For CEB MC 90 it is accompanied by the indication that the “corresponding modulus of elasticity “is defined as the tangent modulus at the origin of the stress-strain diagram”, and that “it is approximately equal to the slope of the secant of the unloading branch for rapid unloading and does not include initial plastic deformation”. As for the stress rate an indication of 1MPa/s is given [CEB 1993]. For GL2000 no specific indication is given on the stress duration for measuring the initial strain and the corresponding elastic modulus Ecmt0. In model B3 this conventional separation is not operated. The formulation of the model evidences an instantaneous strain due to unit stress, termed q1, which is age independent and represents the inverse of an asymptotic modulus for load durations t – t0 = 0. To be able to compare the graphical outputs of functions J and R of model B3 with those of the other models, a conventional value of D = 10 seconds has been adopted. It must be noted that the graphical representation of the relaxation curves requires selecting a conventional initial (nominal elastic) stress due to the unit imposed strain. For the same reasons the first curve of the redistribution function x for t1 = t0+. must be referred to a conventional change of statical system 10 sec after the instantaneous application of loads.