# An-Najah National University

## An-Najah Blogs

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• Sunday, March 14, 1999
• The 1st-MINIA INTERNATIONAL CONFERENCE FOR ADVANCED TRENDS IN ENGINEERING
• Finite Element Analysis of Reinforced Concrete Cross-vault Shells

By Shuhrat Hani Tawfq Arafat

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Civil Engineering Department AN-Najah National university 1998

ABSTRACT

Thousands of years ago, man had discovered the idea of using vault systems, built in stone to cover large areas. The Romans used the vault system widely especially in the construction of roofs of thermae.

One vault system is that     system which is constructed by two intersecting cylindrical vaults known as cross-vault system.

Muslims also used this system especially to cover large areas of the holly places (mosques) and it became a tradition in the construction of mosques for hundreds of years. In modern architecture, shell structures occupy a place of increasing importance because of their strength, economy, and architectural form.

At the end of previous century and the beginning of this century, some scholars started to study the distribution of stresses in plates and shells. Their studies showed that in most cases the shells are under compression.

The vast use of concrete nowadays, which has good strength under compression and weak strength under tension, encourages the use of concrete as a new material for the old structural conception of shells.

Prior to the 1970s engineers used the membrane theory to analyze cross-vault shells. Based on a statically determinate analysis neglecting bending stresses, this theory gives uniform in- plane shearing stress resultants on all element sections parallel to the edges. At 45° from the boundaries these forces resolve into the principal compressive stresses resultants in the convex parabolas implying that the hyperbolic shell carries the vertical load through arch action.

In this paper , the Finite Element Linear Analysis is used to study the stress distribution in cross vault shell model and finding the best geometry of this type of structures that leads to the minimum tensile stresses at the surface of the shell, and puts all elements in that surface under compression

The Finite element analysis is made using an available and widely used software program called STAAD III and a triangular three noded element is assumed in the analysis.

Finite element analysis have shown that the shape of the cross-vault shell is very proper in getting compressive stresses only and membrane theory assumption for the behavior of cross vault shells is incorrect at certain sections, and the junction between  two shell surface leads to a large stress concentration So, this paper proposes a des. Based on these observations in which small crown beams at the shell junctions introduced and material is added near the supports to reduce high stress concentryti that results at this corner and free edges for the shell.

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