Isaac Scientific Publishing
Modern Civil and Structural Engineering
MCSE > Volume 1, Number 1, June 2017

Aprismatic Beams – A Mathematical Model and Application to a One Kilometre Arch Bridge

Download PDF  (561.4 KB)PP. 27-43,  Pub. Date:June 15, 2017

John Nichols
Department of Construction Science, College of Architecture, Texas A&M University, College Station, United States
Design engineers, like all humans, are driven by Nash game theory to maximize return and hence simplify design. A determination of the optimal shape of beams to maximize strength and minimize costs has been an area of significant research since the 1970’s. However, real cost constraints in the market place usually see the selection of standard beams with invariant inertia tensor properties being used for most buildings throughout the world. The more challenging problem is the development of a beam of varying cross sectional area, this type of beam provides savings in terms of the quantity of steel and the mass of the ultimate building or bridge without degrading safety and can when manufactured in quantity to reduce costs. The purpose of the paper is to outline the mathematical development of aprismatic beams for everyday use in engineering to reduce material usage and hence human impact on the global environment. An example is provided using a 1 km arch bridge.
Aprismatic, beams, Finite elements, arch bridge
  • [1]  W. Little, et al., The Shorter Oxford English Dictionary on Historical Principles. 1973, Oxford: Clarendon Press.
  • [2]  S. Timoshenko and J.N. Goodier, Theory of Elasticity. 1951, New York, NY: McGraw-Hill Book Company Inc.
  • [3]  A. Sudhakar, et al., Computer Program: ULARC: Sample Elasto-plastic Analysis of Plane Frames. Sudhakar 1972 ed. 1972, Berkeley: UCB.
  • [4]  J.M. Nichols, The degrading effective stiffness of masonry finite element model: amendments to allow for a non-symmetric damage element, in Australian Masonry Conference. 2004: Newcastle, Australia.
  • [5]  J.L. Meek, Matrix Structural Analysis. 1971, NY: McGraw.
  • [6]  J.F. Nash Jr., Essays on Game Theory. 1996, Cheltenham, UK: Edward Elgar Publishing Limited.
  • [7]  H.B. Harrison, Computer Methods in Structural Analysis. 1973, Englewood Cliffs, NJ: Prentice.
  • [8]  W.J. Lewis, Mathematical model of a moment-less arch. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 2016. 472(2190).
  • [9]  A.K. Tomor, J.M. Nichols, and A. Benedetti, Identifying the condition of masonry arch bridges using CX1 accelerometer in Eighth International Conference on Arch Bridges. 2016: Wroclaw, Poland.
  • [10]  I.O. Baker, Treatise on Masonry Construction. Baker 1914 ed. 1914, New York: Wiley. xiv+745.
  • [11]  T.G. Hughes, G.N. Pande, and C. Sicilia. William Edwards Bridge, Pontypridd. in The South Wales Institute of Engineers. 1998. University of Glamorgan, Pontypridd.
  • [12]  J.M. Nichols, A Modal Study of the Pont-Y-Prydd Bridge using the Variance Method. Masonry International, 2013. 26(2): p. 23-33.
  • [13]  A. Benedetti, et al., Taro Bridge in Parma: Studies on a 19th century masonry bridge. 2017, UNIBO: Bologna, Italy.
  • [14]  A. Tomor, Methodology for fatigue life expectancy of masonry arch bridges. 2014, International Union of Railways (Research Report): Paris.
  • [15]  Strand7 Pty. Ltd., Strand 7 Manual. 2009, Perth: Strand7 Pty.Ltd.
  • [16]  A. Taliercio, Closed-form expressions for the macroscopic flexural rigidity coefficients of periodic brickwork. Mechanics Research Communications, 2016. 72: p. 24-32.
  • [17]  American Institute of Steel Construction (AISC), Steel Construction Manual 14th Edition. 3rd ed., ed. 2011, Chicago, IL.: AISC.
  • [18]  R.E. Melchers, Structural Reliability. 1987, Chichester: Ellis Horword Limited.
  • [19]  O. Schenk and K. Gartner, PARDISO: Parallel Sparse Direct and Multi - Recursive Iterative Linear Solvers. 2014, Switzerland: Institute of Computational Science, USI Lugano.
  • [20]  E. Polizzi, A High-Performance Numerical Library for Solving Eigenvalue Problems: {FEAST} Solver v2.0 User's Guide. 2012, Switzerland:
  • [21]  H.P. Gavin, Numerical integration for structural dynamics (541 Course Notes). Durham, NC. : Department of Civil and Environmental Engineering, Duke University.
  • [22]  G.L. Squires, Practical Physics. Squires 2001 ed. 2001, Cambridge ; New York: Cambridge University Press.
  • [23]  J. Wang, C. Melbourne, and A. Tomor, The Theoretical Basis of the MEXE Method for masonry arch bridge assessment, in Eighth International Masonry Conference, W. Jager, Editor. 2010, IMS: Dresden. p. 207-216.
  • [24]  Intel Corporation, Intel? Fortran Compiler 16.0 User and Reference Guide 2016, Santa Clara, California: Intel Corporation.
  • [25]  J.M. Nichols, A Failure Analysis of a 17th Century Welsh Bridge using Abaqus, in 10th Canadian Masonry Symposium. 2005: Banff, Alberta.
  • [26]  H. Svensson, Cable Stayed Bridges 40 years of Experience Worldwide. 2012, Weinheim, Deutschland: Ernst and Sohn.
Copyright © 2017 Isaac Scientific Publishing Co. All rights reserved.