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The prestressed composite space truss (PCST) is a new kind of space structure composed of steel cables, steel tubes and reinforced concrete ribbed slabs. The prestressed steel cables are arranged in one direction or two directions within the plane of the bottom chord of the composite space truss. There are two main forms of PCST in practice; one is prestressed square on square offset composite space truss (PSSCST), the other is prestressed diagonal on square composite space truss (PDSCST). In this paper, the static behaviour of PDSCST is analyzed in detail using the linear finite element method. The first 10 natural frequencies of a PDSCST are calculated using the subspace iteration method and are found to be really close together, and all of the corresponding mode shapes are vertical vibrations. A simplified formula for calculating the first period is obtained by a linear regression method. The initial tension values in the cables to be applied during construction are calculated by the Release Tension Method which can also take into account the influence of different tensioning sequences. Finally, both the static behaviour of a PDSCST and the influence of different tensioning sequences are studied on a physical model test.