9 プレストレスト・コンクリート・シェルにおけるケーブルの配置とプレストレス力との関係

抄録

The prestressing of the shell is introduced with an application of prestressing forces to shell concrete from stressed cables which are placed on the middle surface of the shell. The stressed cables apply prestressing forces on shell boundary and on shell surface. Thus there act the prestressing forces besides the external working forces. As a flexible cable is placed and stressed along a curve x=x(u^1(s), u^2(s)) drawn on a shell surface x=x(u^1, u^2), the cable stresses T are expressed by the equation: [numerical formula] Then, the prestressing forces applied to shell boundaries from both anchored ends (s=a,s=b) of the cable, are written as: [numerical formula] and [numerical formula] While the intensities p of the prestressing forces applied along the curve are expressed in the form:[numerical formula] where [numerical formula]: Christoffel symbol, [numerical formula] and H_<jk>=x_<j,k>・n. In the expressions above, we take u^1, u^2 as parameters on the surface, s as a parameter along the curve so that [numerical formula] in the equation x=x(u^1(s),u^2(s)), and each index i,j,k(=1,2) is used under conventions. In the expression for p with three terms, the first term represents the component of tensioning losses by Coulomb's frictions, that is tangential to the curve, the second represents the component tangential to the surface, that is perpendicular to the first, and the last represents the component normal to the surface, that is perpendicular to the others respectively. If the frictional losses are ignored, the intensities p are normal to the shell surface as cables are placed along geodesics on the surface, and are tangential as cables are placed along asymptotic curves on the surface. Especially, arranging cables according to anticlastic pairs of geodesics on the shell surface of negative curvature, they are related to a structural concept of the "Hangende Dach" constructions.