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Structural Engineering and Mechanics
  Volume 19, Number 4, March10 2005, pages 413-423

Large deflections of variable-arc-length beams under uniform self weight: Analytical and experimental
Tawich Pulngern, Marvin W. Halling and Somchai Chucheepsakul

    This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.
Key Words
    large sag deflection; variable-arc-length beams; uniformly distributed self weight; finite-element solution; shooting method; experimental studies.
Tawich Pulngern
Department of Civil Engineering, King Mongkut

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