A bending theory for beams with vertical edge crack

• Published in: International journal of mechanical sciences Vol. 52; no. 7; pp. 904 - 913
• Main Authors: Ebrahimi, A., Behzad, M., Meghdari, A.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.2010; Elsevier
• Subjects: Beams (structural); Bending; Cracked beam; Decay rate; Differential equations; Displacement; Edge cracks; Exact sciences and technology; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Load–deflection; Mathematical analysis; Mathematical models; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Stress–strain; Structural and continuum mechanics; Vertical crack; Stress–strain; Bending; Load–deflection; Vertical crack; Cracked beam; Stress analysis; Stress strain relation; Rupture; Bernoulli Euler model; Exponential stability; Equilibrium equation; Modeling; Edge crack; Finite element method; Stress-strain; Transverse crack; Load-deflection; Crack tip
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2010.03.004

In this paper a linear continuous theory for bending analysis of beams with an edge crack perpendicular to the neutral plane subject to bending has been developed. The model assumes that the displacement field is a superposition of the classical Euler–Bernoulli beam's displacement and of a displacement due to the crack. It is assumed that in bending the additional displacement due to crack decreases exponentially with distance from the crack tip. The strain and stress fields have been calculated using this displacement field and the bending equation has been obtained using equilibrium equations. Using a fracture mechanics approach the exponential decay rate has been calculated. There is a good agreement between the analytical results from solving the differential equation of cracked beam and those obtained by finite element method.