Vertical distance between supports and how the column is connected to those supports. The length L in the formula TEI is the distance between points of zero moment. For a pin-supported column, this is the full height of the column.
A column has a 4.7 cm by 8.8 cm rectangular cross section and a height of 4 m. The column is fixed at both ends and has a lateral support at mid-height for the weak axis. The material has E = 200 GPa and σ = 250 MPa.
Part A - Yielding
For a column that is not pinned at both ends, the points of zero moment are not at the supports. The equation for the critical load can be modified to use an effective length L_eff = KL, where K depends on the support conditions. For a column fixed at both ends, K = 0.5. For a column fixed at one end and pinned at the other, K = 0.7 (Figure 1). The equation for the critical load then becomes:
C
EI P_a = (K*L_eff)^2
P_yield = Value
Units
A column can also have lateral supports along its height. A lateral support prevents lateral movement in one direction, which reduces the effective length, L_c.
Part B - Strong axis buckling
The design is to have a factor of safety for buckling S_s = 2.5. What is the maximum load based on buckling in the strong axis of the column? Express your answer with appropriate units to three significant figures.
A factor of safety is used to account for uncertainties in material.
Figure 1
Part C - Weak axis buckling
The design is to have a factor of safety for buckling F_s = 2.5. What is the maximum load based on buckling in the weak axis of the column? Express your answer with appropriate units to three significant figures.
