A hyper triangular finite element based on shallow shell formulation is developed in this paper. The element has six degrees of freedom. five of which are the essential external degrees of freedom and the additional sixth is associated with the in-plane rotation of shell. The displacement fields of the element satisfy the exact requirement of rigid body modes of motion. The element is based on independent strain assumptions insofar as it is allowed by the compatibility equations.

The essential feature of the resulting displacement functions is that the in-plane displacements are represented by higher order polynomial terms. This is achieved without having to introduce additional and unnecessary internal nodal degrees of freedom.

A hyperbolic paraboloid shell roof for which a previous solution exists is first analysed to validate the program and to compare the results. The element is then used in the analysis of a complex type of hyperbolic paraboloid roof which is normally referred to as the gable roof. It is usually made up of a combination of four hyper shells together with crown and edge beams. The shell is supported at its four low corners by pin supported. The discontinuities in the geometrical form of the roof are dealt with by co-ordinate transformation and the stiffening beams are represented by three-dimensional exact beam elements having all the essential six external degrees of freedom.

Distributions of normal deflection and components of stresses are obtained for the surface of the shell roof. An investigation of the effect of varying size of the crown beams on the deflection and components of stress is also considered. The details given will provide designers with necessary information for implementation of a practical shell roof of this form.

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