Scaling laws for static displacement of linearly elastic cracked beam by energy method

Abstract Experimental studies on the problem of crack identification can be simplified and enhanced through the concept of structural similarity since the behaviors of a full-scale structure can be investigated using a reduced-scale model. The structural similarity of a rectangular cross-section beam with a through-thickness edge crack and elastically supported was investigated. The beam was subjected to concentrated forces perpendicular to its longitudinal axis and concentrated bending moments. Complete similarity conditions and scaling laws for static deflection and slope of the cracked beam were derived using the principle of conservation of energy and the strain energy release rate approach within the framework of linear elastic fracture mechanics. Accuracy of the derived complete similarity conditions and scaling laws were experimentally and numerically verified. The concept of incorporating the similarity theory to problems of structural health monitoring was explained.

[1]  Andrew D. Dimarogonas,et al.  Vibration of cracked structures: A state of the art review , 1996 .

[2]  B. Muñoz-Abella,et al.  Static behaviour of a shaft with an elliptical crack , 2011 .

[3]  Masoud Sanayei,et al.  Damage assessment of structures using static test data , 1991 .

[4]  Cristiano P. Coutinho,et al.  Reduced scale models based on similitude theory: A review up to 2015 , 2016 .

[5]  Al Emran Ismail,et al.  Stress intensity factors of three parallel edge cracks under bending moments , 2013 .

[6]  Andrew D. Dimarogonas,et al.  A CONTINUOUS CRACKED BEAM VIBRATION THEORY , 1998 .

[7]  Sung-Kon Kim,et al.  Experimental investigation of local damage detection on a 1/15 scale model of a suspension bridge deck , 2003 .

[8]  Z. P. Bažant,et al.  Size effect on structural strength: a review , 1999 .

[9]  Antonino Morassi,et al.  Detecting Multiple Open Cracks in Elastic Beams by Static Tests , 2011 .

[10]  S. Caddemi,et al.  Crack detection in elastic beams by static measurements , 2007 .

[11]  J. Kasivitamnuay,et al.  Scaling laws for displacement of elastic beam by energy method , 2017 .

[12]  Ahmad Shooshtari,et al.  Analysis of cracked skeletal structures by utilizing a cracked beam-column element , 2016 .

[13]  Andrea Carpinteri,et al.  Size effect in S–N curves: A fractal approach to finite-life fatigue strength , 2009 .

[14]  V. Nguyen,et al.  Static load testing with temperature compensation for structural health monitoring of bridges , 2016 .

[15]  A. Meghdari,et al.  A linear theory for bending stress-strain analysis of a beam with an edge crack , 2008 .

[16]  Zdeněk P. Bažant,et al.  Size effect in Paris law and fatigue lifetimes for quasibrittle materials: Modified theory, experiments and micro-modeling , 2016 .

[17]  Johann Petit,et al.  AN INVESTIGATION OF STRESS INTENSITY FACTORS FOR TWO UNEQUAL PARALLEL CRACKS IN A FINITE WIDTH PLATE , 1992 .

[18]  J.-S. Jiang,et al.  The dynamic behaviour and crack detection of a beam with a crack , 1990 .

[19]  Ganggang Sha,et al.  Structural damage identification using damping: a compendium of uses and features , 2017 .

[20]  Amin Zare,et al.  On the application of modified cuckoo optimization algorithm to the crack detection problem of cantilever Euler-Bernoulli beam , 2015 .

[21]  Yong Guo,et al.  Model test on scale effect of the frequency decreases of the reinforce concrete beam due to moment cracks , 2015 .

[22]  G. I. Barenblatt,et al.  Scaling Phenomena in Fatigue and Fracture , 2004 .

[23]  S. Naik.  Crack Detection in Pipes Using Static Deflection Measurements , 2012 .

[24]  A. Barr,et al.  One-dimensional theory of cracked Bernoulli-Euler beams , 1984 .

[25]  David Kennedy,et al.  Free vibration analysis of beams and frames with multiple cracks for damage detection , 2014 .

[26]  Yifan Huang,et al.  Stress intensity factor for clamped SENT specimen containing non-straight crack front and side grooves , 2018 .

[27]  Anthony G. Atkins,et al.  The laws of similitude and crack propagation , 1974 .

[28]  Qiuwei Yang,et al.  Damage localization for beam structure by moving load , 2017 .

[29]  Wei-Xin Ren,et al.  Damage detection of beam structures using quasi-static moving load induced displacement response , 2017 .

[30]  N. Khaji,et al.  Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions , 2009 .

[31]  A. Carpinteri.  Decrease of apparent tensile and bending strength with specimen size: two different explanations based on fracture mechanics , 1989 .

[32]  Jirapong Kasivitamnuay,et al.  Application of an Energy Theorem to Derive a Scaling law for Structural Behaviors , 2005 .

[33]  Jia-Jang Wu,et al.  The complete-similitude scale models for predicting the vibration characteristics of the elastically restrained flat plates subjected to dynamic loads , 2003 .

[34]  J. R. Radbill,et al.  Similitude and Approximation Theory , 1986 .

[35]  Shapour Moradi,et al.  On the application of bees algorithm to the problem of crack detection of beam-type structures , 2011 .

[36]  Pairod Singhatanadgid,et al.  A Scaling Law for Vibration Response of Laminated Doubly Curved Shallow Shells by Energy Approach , 2009 .