Question

Three storey building A three-storey steel column in a building supports roof and floor loads as shown in the figure below. The storey height His 3 m, the cross-sectional area A of the column is 7500 mm2, and the modulus of elasticity of the steel is 200 GPa. Calculate the magnitude of the total shortening of the column, assuming P, = 1832 kN and P2 = 1681 kN, and P3 = 2196 kN. provide your answer in mm and to two decimal points. Answer:

Answer 1

balution to one above problem given data- A Area 7900 mm (E) Modulus of elasticity 200 Gpa = 200 x 109 N/m² IN/mm² 100 N/m² E = 2008 03 N/mm² Height H= 3m 3x10 mm loads P = 1832 IN P2 = 1681 KN P3 = 2196 KN To find? Total shortening length. Solution JL = PL AE mm JL - Change in longon P load lingon of member mm A Area mm² E Youngs modules 11 N/mm²

or total Piri AE + + P2 L₂ Az Ez P 3 L3 Az Ez E, = F2 = Ez =E A = Az = A3=A L = L2=L3=H H [Pit Pz+P3 AE 3x43 [1832x03 + 1681x03 + 7500 x 200 x1GB 2196x 03 3x10² 1632 +1631 +2126] 7 1500 x 200 3 x 0²x 5709 7500 x 200 11. 418 mm dh Total Resuita 11.418 mm Total Shortneing dengan