International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 07 Issue: 03 | Mar 2020 www.irjet.net p-ISSN: 2395-0072 © 2020, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 3203 An Investigation of Stresses induced in Curved Beams using MATLAB and Finite Element Analysis (FEA) S B Prakash 1 , Manoj PN 2 1,2 UG scholars, Department of Mechanical Engineering, NIE Mysuru ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - Curved beams find many applications such as Crane hook, Portable hydraulic inverter, Offset bar, S-link etc. For the proper functioning of curved beam, it should have high material properties to withstand stresses induced in it. When it is subjected to load, the bending stress developed in it should be within safety limits. This report deals with stress analysis of crane hook using MATLAB SOFTWARE. The same is done in ANSYS WORKBENCH (FEA). Finally, the results of both are compared and the cross section of the crane hook which induces minimum stress for the given load, cross sectional area and radius of curvature of the curved beam is identified and recognized as a optimal cross section for the crane hook. Key Words: Curved beams, Bending stress, Crane Hook, MATLAB and Ansys workbench. 1. INTRODUCTION If a beam is originally curved before applying any bending moment, then it is considered as curved beam. Its centroidal axis is not straight and is curved in the elevation hence it is said to be a curved beam. In Straight beam, the centroidal axis and the neutral axis coincide. But in curved beams, the neutral axis and the centroidal axis do not coincide and the neutral axis will be shifted towards the centre of curvature. Due to this shifting of the neutral axis towards the centre of curvature, the stress distribution in the curved beam will be non-linear.[3] 1.1 Classification of curved beams Curved beams can be classified into 2 sections: 1. Beams with small initial curvature. 2. Beams with large initial curvature. Though there is no clear distinct difference in the definition of both the sections; however, they are classified based on ratio of initial radius of curvature to the depth of the section. If this ratio exceeds number 10, then it belongs to classification of beams with small initial curvature, if it is the other way then it can be classified as beams with large initial curvature.[4] The bending stress equation for curved beams is given by Design Data Handbook.[1] M = Bending moment acting at the given section about the centroidal axis A = Area of cross-section e = Distance from the centroidal axis to the neutral axis =R –   R = Radius of curvature of the centroidal axis   = Radius of curvature of the neutral axis y = Distance between the neutral axis to the considered fibre at which bending stress is needed to be calculated Fig 1: Parameters of a curved beam 1.2 Applications of curved beams Curved beams find applications in many machine members, some of them are listed below: • C-clamps • Crane hook • Frames of presses • Chains, links & rings etc. Curved beams are widely used in Civil Engineering applications. In RCC buildings they are normally seen around recreation purpose buildings (centre), convention centres, cement silos etc. where circular beams serve the purpose in the form of ring beams. Curved beams are also used to support curved glass applications in high-end housing and other structures.[3]