BUCKLING OF SLENDER CRACKED FIXED-FREE ENDED COLUMNS EXPOSED TO TWO CRACKS UNDER CONCENTRIC VERTICAL LOADS

Abstract

two cracks under concentric vertical load. The case which was studied is for columnsfixed at one end and free at the other. The equation includes a set of sine –cosinefunctions but the main variables are buckling load parameter, depth of crack andpositions of cracks. The main source of derivation is the elastic buckling theory using atransfer matrix method by representing cracks by a massless rotational springs. Thegoverned equation was solved by a visual basic program and trial and error method toreach the most accurate result. The equation is checked for perfect columns to see itsvalidity and it gave hundred percent comparison. The results show that the bucklingload is reduced generally by different ratios depending on the position of the cracks andtheir depths. The effect of the crack depth ratio is severely affecting the buckling loadespecially between (0.15-0.20) ratios. The effect of position of cracks is also studied andit is found that the maximum decrease in buckling load was at position ratios β1 and β2equal to 0.9 and 1.0 respectively. .