Finite Element Analysis Of A Fixed-Free End Steel Column

Finite Element Analysis of Structures-Assignment 1Gennaro DeMarco a1705640March 20191 TheoryWe are asked consider a 1 metre column of structural steel, with solid square cross-section 10mm x 10mm, as depicted in Figure 1. The column is xed at the baseand free at the top in which a vertical load of +1000N is applied, as well as amoment of +1 Nm about the z-axis. Figure 1: CaptionAs specied by ANSYS Workbench, structural steel exhibits a Young's modulusof 200 GPa.1.1 Axial DeectionTo determine the axial deection of the column at various y locations, simplestress/strain theory can be applied. Thus, we know that axial stress is expressedas:= F A(1)1For axial force, F, and cross sectional area. Furthermore, axial strain is dened asthe axial deection divided by the total original length:= Ly Ly (2)Therefore, the axial deection can be determined for any value of Ly by substitut-ing equations (1) and (2) into Hooke's Law and rearranging.= E (3)) F A=ELy Ly) Ly= F Ly E A(4)Hence by applying equation (4) the axial deection can be calculated for thedesired points in the y direction: Ly = 0.25, 0.5 and 1 m. ForLy = 1 m:L y = 1000 mmF = 1000 NE = 200 e3 MPaA