The total number of individual cases is 4- 9- 3- 3- 3 = 972 (not including X = 0 and eo = 0). For each case, calculations have been made with the general method according to 5.8.6 and with the simplified methods, i.e. the stiffness and curvature methods according to 5.8.7 and 5.8.8 respectively. The results are summarized in table A2-1 on the following two pages.

The vertical axes in the diagrams represent the ratio

Maximum first order moment according to simplified method Maximum first order moment according to general method

The moment ratio is given with the mean value m and with m+s and m-s respectively, where s is standard deviation. The mean value (and standard deviation) for a certain value of the independent variable includes all the values for the other variables. Thus, for one value of e.g. the slenderness, the mean value and standard deviation of the moment ratio represent 972/4 = 243 individual values; for one value of the eccentricity 972/9 = 108 values etc.

The horizontal axes represent the main variables: slenderness X, eccentricity eo/h, reinforcement ratio (both ro and p), concrete strength fck and effective creep ratio ^ef.

Interaction diagrams have also been prepared, covering all the above-mentioned cases and including the different methods and alternatives. However, to present all these diagrams would require too much space, and it would be difficult to obtain an overall view of the results.

Therefore, only two such diagrams will be shown to illustrate certain aspects.

12 In [1] the simplified methods are compared with the general method also for columns with circular cross section and with a different distribution of the first order moment. Although [1] deals with more refined versions of the stiffness and curvature methods, the main conclusion is that the same models, as for rectangular section and constant moment, can be used also for other cross sections and variations of the first order moment.

Table 5.A2-1. Summary of comparisons between simplified methods and general method

Table 5.A2-1, continued

Stiffness method. 5.8.7

Curvature method, 5.8.8

Expression (>.26) (simplified alternative)

Expression (5.22) (more accurate alternative)

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