To use the formula for the critical load. i. e., the euler buckling load, for pin-supported columns to calculate various parameters of columns. ideally, a column that is perfectly straight and has an axial load applied exactly at the centroid of its cross section will not yield until the internal normal stress reaches the yield stress of the material. real world columns, however, are subject to small asymmetries, whether due to irregularities of shape or just lateral vibrations. when the axial load is large enough relative to the length of the column, such asymmetries cause the column to become unstable and buckle. it bends and continues bending until it fails. the load required to cause buckling depends on how the column is attached to its supports. the maximum or critical load for a column of length l that is pin supported at both ends is p_ct = pi^2 ei/l^2. a factor of safety is used to account for uncertainties in material properties and dimensions the factor of safety is the ratio of the failure load to the allowable load, or the ratio of the maximum design load to the maximum expected load. a column is made from a rectangular bar whose cross section is 5.5 cm by 8.7 cm. if the height of the column is 2 m, what is the maximum load it can support? the material has e = 200 gpa and sigma_y = 250 mpa. express your answer with appropriate units to three significant figures. a circular column with diameter 9.2 cm is to support a vertical load of 700 kn. what is the maximum length the column can have if it is pin supported at both ends? the material has e = 200 gpa. assume the material does not yield. express your answer with appropriate units to three significant figures. a solid circular steel column with a height of 2.4 m needs to support a vertical load of 960 kn. what is the minimum diameter required if the factor of safety for buckling is fs = 2.5 and the material has e = 200 gpa? assume the material does not yield. express your answer with appropriate units to three significant figures.