Wind-Induced Dynamic Responses of Structures with Outrigger Systems
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Analysis of high‐rise braced frames with outriggers
A graphical method of analysis for the preliminary design of tall building structures comprising braced frames with outrigger trusses subjected to horizontal loading is presented. For this method of analysis it is necessary to determine five stifnesses for the uniform structure: bending and racking shear stiffnesses of the braced frame and outriggers in addition to a stiffness parameter representing the axial lengthening and shortening of the exterior columns. The analysis allows a simple procedure for obtaining the optimum location of the outrigger up the height of the structure and a rapid assessment of the impact of the outrigger on the behaviour of the high‐rise structure. It is concluded that all five stiffnesses should be included in the preliminary analysis of a proposed tall building structure as the reductions in horizontal deflections and bending moments of the braced frame are influenced by all stiffness parameters. Copyright © 2003 John Wiley & Sons, Ltd.
How to do a p-descent on an elliptic curve
In this paper, we describe an algorithm that reduces the computation of the (full) p-Selmer group of an elliptic curve E over a number field to standard number field computations such as determining the (p-torsion of) the S-class group and a basis of the S-units modulo pth powers for a suitable set S of primes. In particular, we give a result reducing this set S of 'bad primes' to a very small set, which in many cases only contains the primes above p. As of today, this provides a feasible algorithm for performing a full 3-descent on an elliptic curve over Q, but the range of our algorithm will certainly be enlarged by future improvements in computational algebraic number theory. When the Galois module structure of E[p] is favorable, simplifications are possible and p-descents for larger p are accessible even today. To demonstrate how the method works, several worked examples are included.