고체역학 (Gere) — Axially Loaded Members: Problem 2.3-10

2.3-10 A two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load \( P_1 \) equals 400 kN, and the second-floor load \( P_2 \) equals 720 kN. Each column has a length \( L = 3.75 \) m. The cross-sectional areas of the first- and second-floor columns are 11,000 mm\(^2\) and 3900 mm\(^2\), respectively. (a) Assuming that \( E = 206 \) GPa, determine the total shortening \( \delta_{AC} \) of the two columns due to the combined action of the loads \( P_1 \) and \( P_2 \). (b) How much additional load \( P_0 \) can be placed at the top of the column (point C) if the total shortening \( \delta_{AC} \) is not to exceed 4.0 mm?