All the struts shown in Figure B1 have a same diameter solid circular cross sect
ID: 1853267 • Letter: A
Question
All the struts shown in Figure B1 have a same diameter solid circular cross section. In case (i), both ends are pin-jointed. In case (ii), one end is fixed and one end is pin-jointed. In case (iii), both ends are fixed. Determine which strut in Figure B1 can carry the largest critical buckling load. Explain the assumptions and limitations of the Euler formula for the buckling loads of struts. Show on a suitable diagram how the results of a practical test compare with the results predicted by the Euler formula.Explanation / Answer
In science, buckling is a mathematical instability, leading to a failure mode. Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium. At a certain stage under an increasing load, further load is able to be sustained in one of two states of equilibrium: an undeformed state or a laterally-deformed state. In practice, buckling is characterized by a sudden failure of a structural member subjected to high compressive stress, where the actual compressive stress at the point of failure is less than the ultimate compressive stresses that the material is capable of withstanding. For example, during earthquakes, reinforced concrete members may experience lateral deformation of the longitudinal reinforcing bars. This mode of failure is also described as failure due to elastic instability. Mathematical analysis of buckling makes use of an axial load eccentricity that introduces a moment, which does not form part of the primary forces to which the member is subjected. When load is constantly being applied on a member, such as column, it will ultimately become large enough to cause the member to become unstable. Further load will cause significant and somewhat unpredictable deformations, possibly leading to complete loss of load-carrying capacity. The member is said to have buckled, to have deformed.