Geometric and Economic Considerations in the Design of Flat Storage Systems

The geometric shape of flat storage systems for grain influences economic feasibility. Total cost per unit volume first decreases and then increases as vertical wall height increases. For a given wall height and length, cost per unit volume decreases as facility width approaches length. INTRODUCTION The term "flat storage" generally refers to rectangular-shaped structures with relatively low heightto-width ratios. Flat storage systems are often multipurpose structures that utilize permanent floors capable of supporting the weight of a truck or tractor. Generally, portable conveying equipment is used for filling and emptying these types of facilities, and ducttype aeration systems are employed, most often above the floor. Usually, grain is not placed directly against the wall of the building but against a portable structure indented from the edge of the facility. At the farm level, flat storage systems are often viewed as being "temporary," "stop gap," or "last choice" storage measures rather than as permanent "first choice" types of facilities. However, flat storage is often used commercially by utilizing a relatively large floor area with the grain being covered by plastic rather than a conventional roof (Siebenmorgen et al., 1986; Loewer et al., 1988). The objectives of this paper are to: 1. Present geometric design considerations for flat storage facilities. 2. Describe the influence of geometric configurations on cost of construction. DESIGN CONSIDERATIONS The capacity of a flat storage system (Fig. 1) may be computed by adding together the several geometric shapes that compose a pile of grain while recognizing that the grain slopes may not be uniform. Either length or width of the pile will be the limiting factor as to grain height. The following equation may be used to determine grain volume: B = C * [(L*W*V) + (W*TAN(t))/6 + ((L-W)*W*TAN(t))/4] [1] Article was submitted for publication in July, 1988; reviewed and approved for publication by the Structures and Environment Div. of ASAE in October, 1988. Presented as ASAE Paper No. 86-6053. Published with the approval of the Director, Arkansas Agricultural Experiment Station. The authors are: O. J. LOEWER, Professor and Head, I. L. BERRY, Professor, and T. J. SIEBENMORGEN, Assistant Professor, agricultural Engineering Dept., University of Arkansas, Fayetteville. where B = volumetric capacity for rectangular flat storage C = conversion factor (one for SI units, 0.8 for bu if L, W and V in ft) L = length of structure, where L > = W W = width of structure t = angle of repose for the type of grain being stored, degrees V = usable wall height. The " shape" of the grain pile used in equation [1] is composed of a rectangular solid, a triangular solid and two rectangular pyramids (Fig. 1). The base formed when the two rectangular pyramids are placed together forms a square. The slope of the grain is referred to as the angle of repose. If the structure is filled uniformly, the longitudinal measurement of the base of each rectangular pyramid is one half of the width of the structure (assuming the width is less than or equal to the length). This is because the width governs the height that the grain may be placed in the structure. Therefore, the length of the triangular solid is the length of the facility minus its width. The dimensions and volumes of the different sections may be computed as follows: H = TAN(t) * (W/2) [2]