Abstract
In this paper, horizontal and largest vertical deflections have been calculated for uniformly distributed loaded, simply supported beams made of Ludwick type nonlinear material. Curvature expression for elastic curve had been defined according to two different arc length functions. Variations of horizontal and vertical deflections are tabulated depending on arc length functions, material, cross section and loading conditions.
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Abbreviations
- w :
-
Unit-distributed load
- Δ:
-
Horizontal deflection
- δ v :
-
Vertical deflection
- L :
-
Beam length
- x 0 :
-
Arc length
- M:
-
Moment
- σ :
-
Normal stress
- ε :
-
Strain
- B:
-
Coefficient of material property; Young’s modulus of elasticity for linear elastic materials
- n :
-
Material dependent constants
- κ :
-
Curvature
- Γ:
-
Euler gamma function
- h :
-
Height of the cross section
- b :
-
Width of the cross section
- 2F1:
-
Hypergeometric function
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Eren, I. Analyses of Large Deflections of Simply Supported Nonlinear Beams, for Various Arc Length Functions. Arab J Sci Eng 38, 947–952 (2013). https://doi.org/10.1007/s13369-012-0375-2
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DOI: https://doi.org/10.1007/s13369-012-0375-2