The authors developed a method of optimizing a greenhouse design with respect to the construction cost and a direct light transmission (Kurata and Tachibana, 1980). First the construction cost
Js was minimized. Then Inequality (1) was added to the constraints and the light transmission was maximized, where
Jsopt meant the minimum construction cost and the coefficient
k was named the coefficient of construction cost allowance.
In this report the dependence of the optimal designs on the coefficient of construction cost allowance, the design snow depth, the design wind velocity and the span was studied. Each of these parameters was changed stepwise and the optimizations were carried out while the rest of the parameters were fixed at the values shown in Table 1. The results are shown in Figs. 1-5. From these optimizations the following points became clear. Here the optimizations of the construction cost, the optimizations of the light transmission of NS-oriented and EW-oriented greenhouses are denoted C-, NS- and EW-optimizations, respectively.
1) The following features of the optimal designs already reported in the previous publication (Kurata
et al., 1980) also hold true in this study with few exceptions. The C- and NS-optimizations result in the symmetric designs, whereas by the EW-optimizations ridges are located nearer to the south walls. The rafters and posts by the C-optimization have members with larger depth and width if the moment of inertia is the same. The posts by the NS-optimization and the members facing the north by the EW-optimization have the same characteristic. On the contrary, the south post by the EW-optimization has short width.
2) The changes of the optimal EW-oriented greenhouses with the parameters are found comparatively complicated. This is due to the fact that different constraints become active with the change of the parameters. On the contrary, the C- and NS-optimizations show a relatively simple change.
3) By the NS-optimization the increase of the coefficient of construction cost allowance
k (mitigation of the cost restriction) results in longer posts and a steeper roof slope (Fig. 1). The EW-optimization shows a more complicated change with the change of
k-value, and the optimal designs can be classified in 4 phases. By the lightened cost restriction the optimal designs have larger memberson the north side so that the loads imposed on the greenhouse can be supported mainly by the north members. This enables the use of members on the south side which allow the high light transmission (Fig. 2).
4) With the increase of the design snow depth, the roof slope becomes steeper and the ratch measure decreases by every optimization undertaken in this study (Fig. 3).
5) The increase of the design wind velocity makes the roof slope more gentle by the EW-optimization (Fig. 4), whereas by the C- and NS-optimizations no change can be seen with the change of the wind velocity.
6) As the span increases, the ratch measure becomes shorter by every optimization. By the change of the span under 7m the C- and NS-optimizations show little change in the roof slope and the moment of inertia of each member. By the span above 9m both of them increase with the span. The EW-optimization shows an increase of the south roof slope with the span. In this optimization the moment of inertia of each member changes little by the span less than 9m. By the span of 11m members of larger moment of inertia are needed except for the south rafter (Fig. 5).
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