Buckling of Columns

Buckling of columns. INTRODUCTION Slender collutions are subject to a type of behavior known as buckling. As long as the load cllsuch a member. However, once a certain critical Load is large de formations, which in turn cause the member to suddenly bows out sideways. This bending gives rise to large defamations which in turn cause the member to collapse. The load a which backling occurs is thus a design criterion for compression members. Tension members as well as short stocky columns fail when the stress in the member rearnes a certain limiting strength of the Material Once this limiting strength of the material is known, IE IS a relatively simple matter to determine the load-carrying capacity Capacity of the member. Buckling occurs depends on a variety of eactors, including the dimensions of the member, the way in which the monter is Supported, and the properties of the materid out Of wich the member is made The determination of the burkling stress is thus a relatively complex Problem. It is the Solution of this Problem that will be our main concern in this book. IF, ckiing does not take place because a certain strength of the Thakrial is exceeded then why, one may ask, does a compression member Suddenly bucke? Athough it is not possible to answer this question directly on can make certain observations about the buckling Phenomenon and thus explain at least partially what is taking Place Olle such closervation, Which elucidates in a excellent manner the Phenomenon of bockling, is given in the on Structure In Architecture. METHOD OF NEUTRAL EQUILIBRIUM The concept of Stability is Frequently explained by cons; derinlg the equilibrium of a tiged ball in various, as dericled in Fig. (Stability of equilibriom) Although the ball is in equilibrium in each Position shown, a dose examination reveals the existence of Important differences among the three siluations, If the ball in farm (A) is dis placed slightly Flom its original Position of equilibrium, it will return to that. Position Subrequent to the removal of the disturlang Force. A body that behaves in this manner is said to be in a state of stable equilibrium. By comparison, the ball in part (B) If it is displaced slightly from its position of rest, does not return, but instead Contillues to move father away from the original equilibrium Position. The equilibrium of the ball in Part (b) is a very precarious one. It is called unstable equilibrium. Part(c) depicts Yet another Possible type of quilibrium. Here the ball, after being dis placed Slightly, neither refums to its original Position nor contlilves to move Father away. Instead, it remains at the position folwich the Small disturbance has Mov it. This behavior is referred to as neutural equilibrium. The ball in Fig. 1-2 is in quiliorcom at any Point along line ABC. in the (stability surface) region between A and B the equilibrium B stable, an in the region between B and C it is unstable. Alfollit B, the transition between the tho regions, the ballis il a state of neutral equilibriom. in Article lil it was pointed out that a column buckles at a certain load becave the strought configuration becomes unstable at that lead. The behavior of the column is thus very similar to that of the ball in Fig. 1-2 The straight configuration of the column is stable at Sihall loads, but it is unstable at large loads If it is assumad tinot a state of neutral equilibrium exists at the transition From stable to unstable equilibrium inthe column, similar to that Present for the ball iny Fig. 1-2 then the load at wich the straght Configuration of the column ceases to be stable is the lond at which neutral equilibrium is possible. This load in usually referred to as the critical load