Design of Domes

INTRODUCTION The domes on the circular-shaped base have a large usage – silos, tanks, warehouses for bulk materials, sportive facilities and exhibition halls. They are light, beautiful and can cover big spans, providing free space without intermediate columns. The steel domes are successfully applied on the spans with diameter D ≤ 50,0 m. A major part of the domes are used to cover steel tanks for oil storage. Traditionally their construction is composed by radial elements (girders), ring-shaped elements (rings) and roof cover plates (Fig. 1). 

Fig. 1 Structure of the self-supporting roof а) basic elements b) design scheme 

1 LOADS AND LOAD COMBINATIONS The calculation of roof domes during the exploitation usually is done for two load combinations. In the first of them the summarized loading q1 operates from top to the bottom. In the second one the loading on the roof q2 operates from the bottom to the top: 

2 FORCES IN THE DOME’S ELEMENTS Spatial steel domes with radial girders and circular elements are many times undetermined spatial systems, which forces into elements difficultly can be calculated through manual solution. The precise calculation of forces in elements of steel structure of dome is done with use of suitable software, considering the stiffness of the elements and flexibility of the joints. Preliminary design of the elements of the steel structure of dome roofs could be done to obtain the cross section and type of the elements that are defined in the FEA model. Here will be shown two approaches to receive these steel sections.

 2.1 Forces in the elements of dome, according to procedures of E. Лессиг [2] 

The shown there methodology is used from Bulgarian engineers for a long time. Of course, it is applied for a lot of dome roofs of steel tanks that are in service now. Calculations of the section of elements of spherical domes with radial girders and circular elements are done on the base of pin - joint system. Characteristic feature of the methodology is that effective length of compressed elements is equal to real geometrical length (distance between pin joints) . The biggest axial force Si (pressure in combination q1 and tension in q2) in the dome’s radial girders is done when a full design load operates on its whole surface. The efforts in the girder immediately upon the i-th joint are calculated according to the formula: 

S1=A1q/nSinX