1. The problem statement, all variables and given/known data This seems to a reasonably basic question to go through but yet I seem to have a bit of a mental block on it. so any help in the right direction would be great.. An I-beam is 10mm thick on the web and flange, is 6m high and has a Young's modulus of 200 GN/m2. The design must be optimized to carry 92KN down the neutral axis of the section. Given the the depth of the section, d, must be half the breadth, b, calculate the minimum section requirements when: 2. Relevant equations 1, The upper end is free 2, The upper end is pinned and constrained to move vertically 3. The attempt at a solution To do this problem I used the critical pressure equation and derived it for I: Pcr=2π2 EI/L^2 I= (P_cr.L^2)/(2π^2.E) I= (92〖x10〗^3×〖6x10〗^3)/(19.74×〖200x10〗^9 ) I=0.838 Now this is where I get stuck as I don't know how to input I value to calculate the breadth and depth of the I-beam section. Putting it into the 2nd moment of area equation for an I-beam gets very messy. So what do I do from here? I know the answer for depth, d=79mm, and when calculated for a rectangular cross section (I=bd^3/12) d=150mm, almost exactly twice. How do I correct this from a rectangle to an I-beam equation?