Stability of concrete beam-columns under follower forces

Abstract

An axial follower force acting on the free end of a beam-column is known to remain tangential to its elastica at that point. Elastic beam-columns exhibit infinitely high buckling resistance to static compressive follower load. Loss of their dynamic stability is known to occur at critical follower loads, by flutter characterized by vanishing lateral displacement and infinitely high natural frequency. Classical theory deals with physically linear nonconservative beam-columns. Physical nonlinearity exhibited by concrete beam-columns under service loads is caused by the closing and reopening of the extant transverse cracks. In this Paper, analytical expressions for the lateral displacement and lateral stiffness of such concrete beam-columns are derived. Using these expressions, the stability of physically nonlinear elastic flanged concrete beam-columns under the action of a follower compressive axial force and a lateral force is investigated. The significance of the analytical approach and the theoretical predictions is discussed.

Stability analysis of Beck's column over a fractional-order hereditary foundation

“…Stability analysis of a cantilevered column subjected to constant intensity follower force applied to its free end is known as Beck's problem [1]. Since the first introduction [2], the problem has been investigated by several authors [3,4] for different engineering application [5][6][7][8][9][10][11][12][13][14][15][16]. Models of follower agencies involves rocket thrust [17,18], MEMS [19], spine biomechanical problems [20,21], civil engineering application.…”