Question

O The column shown has a hollow rectangular cross-section. I=6 meters, the material is cold-drawn steel with E=207 GPa, and Sy=580 MPa. Assume end condition to be C=1; Determine 1. Slenderness ratio 2. Transition Slenderness ratio 200mm 3. Short or long column? Why? 4. Is the column safe if the axial load P shown is 1 MN? D80mm 100mm Column Cross-section bh? For a rectangular cross-section I 12 For a circular cross-section, I = +04 64

Answer 1

2, 200mm =b De sono 100mm =h I (min) should be about N-A. Cas shown in fig.): Imin = I rectangle) - I (circle) bh ble TOY 64 200 * 1003 I 804 [ 2 64 = 16666666.67 2010619.298 Imin 146560 47.37 mmy Area of crow-section - b*ha TD2 4 2 Tloo 200 * 1oo 9 14973.45175 mm² A A.K² - Imin K = Radius of gyration, k= Imin VA 114 65 6047.37 14973-45175 k=31.29 mm

Leffective = Length of Column for Cus Leff = d = 6 metres or Lap dels Gooo mm 1- Slenderners ratio : k S 6000 31.29 191.7546 Answer 2- Transition Slendernes ratio: - It is the ratio where Euler load Stress (SCR) becomes equals to half of th yield stres. It is given by : Stron = 272E Sy 2 x 2207*103 580 "E=2074/0² mpa Sy = 580 mpa Strans 83.93 Westen 34 which is than 96 S=191.75 greater hence it is a long column and will fall majorly by buckling

According to Enter equation for long column Por T2E Tmin Left ? Por= 2 * 207* 103 * 14656 047.37 60002 Por 831733.9903 Newton as Para 0.84 MN] Pappied sie IMN > Por hence column. is not safe.
i tried to make the explanation as simple as possible.plz Upvote to motivate me to right such answers in future too.