Anticlastic

Principal radii of curvature r ₁ and r ₂

As anticlastically ( Greek preposition anti : against) to the opposite direction referred curved shells or folded structures , z. B. a hyperbolic paraboloid , saddle surfaces or a rotational hyperboloid . They have a negative degree of curvature

${\displaystyle \kappa ={\frac {1}{\mathrm {r} _{1}\cdot r_{2}}}<0}$,

because the two main radii of curvature r ₁ and r _{2 are} on different sides. In contrast, a synclastic shell is curved in the same direction and has a positive amount of curvature.

Domes and shells belong to the planar structures and have a three-dimensional load - bearing behavior, as there is a third direction due to the curvature . Slabs and panes, on the other hand, are flat 2D structures.