An Exact Static Analysis of Rigidly-Jointed Coplanar Beam Structures Subject to Distributed Loading

Abstract

A simple matrix-displacement method is presented here to facilitate the static analysis of rigidly-jointed coplanar beam frames. The geometric arrangement of the frame, the boundary conditions, the material properties, and the external loading, are allowed complete generality, thereby enabling a large range of 2D structures to be modelled. Point loads, self-weight, inertial and distributed loads may all be accommodated in the analysis; emphasis is placed on the inclusion of the distributed loads, since these prove a more significant challenge to represent accurately in a matrix-displacement type of analysis. The chief novelty of this work is that for such structures exact solutions may be obtained with great ease for the displacement, reactions, and the individual member bending moment, shear force, and axial force, through the inclusion of suitable serendipity functions in the element formulation. The computational effort is the minimum possible for this class of problem, requiring the solution to just 3S simultaneous equations, where S represents the total number of junctions or nodes used to define the frame. Such solutions can easily be implemented using desktop computing, and five examples of increasing complexity are presented herein to demonstrate the efficacy of the method.

Key Words:

• Beam frames
• distributed loads
• exact solutions
• serendipity functions

Additional information

Notes on contributors

N S Bardell

Dr Nicholas Bardell is currently a Technical Specialist at GKN Aerospace Engineering Services based in Port Melbourne, Victoria, where he has worked for the past 10 years on a variety of civil and military aircraft projects. Prior to this, he worked in the UK as a stress analyst for BAe, Rolls-Royce, Aerostructures Hamble, and as a Lecturer in Aircraft Structures in the Department of Aeronautics and Astronautics at the University of Southampton. His professional affiliations include RPEQ, MRAeS and CEng. He has published over 45 papers on various aspects of structural analysis and modelling.

N E M Frazer

Norman Frazer is a Technical Specialist at GKN Aerospace Engineering Services based in Port Melbourne, Victoria. He has been employed there for more than 10 years where he has worked on a variety of civil and military aircraft projects. Prior to this, he worked as a stress analyst for Tenix Defence Aero Division (Melbourne), Boeing Commercial Aircraft (USA) and Hawker DeHavilland (Bankstown, NSW) on various Airbus, Boeing, McDonnell Douglas, Lockheed and Sikorsky projects. During the 1980s he was employed by the Airworthiness Division of the Civil Aviation Authority and held a CAR35 Design Authority at Bankstown Airport in the disciplines of aircraft modification, weights, flight test and flight manual amendments. His experience spans 30 years of aeronautical engineering employment subsequent to his B. Aero E. (Hons) from the University of New South Wales.