Question

The column shown has a hollow rectangular cross-section. L=6 meters, the material is cold-drawn steel with E=207 GPa, and Sy=580 MPa. Assume end condition to be C=1; 010 Determine D=80mm 200mm 1. 2. 3. 4. Slenderness ratio Transition Slenderness ratio Short or long column? Why? Is the column safe if the axial load P shown is 1 MN? 100mm Column Cross-section bh3 For a rectangular cross-section I 12 X For a circular cross-section, I = 1 D4 64

Answer 1

solution giren L=6 m. E = 207 G Pan 207x10 N/mr. Sy = yield strength = 580 MPa = 5800106 N/my = constant of end conditions effective length (Le) = (x L - IXL. = 1x6=6m. Slendernere ration=? - 200mm. somm L-6m. A 1070 for type of buckling showh we have to consider y-y anis as axis of buckling We know that Slenderness ratio (4) rmin

where, rmin = radius of gyration about Y y asis. i.e. Moment of inertia of section is minimum about that axis itselt. I= Arr 7 Imin = A.Amin Imin - rmin A db3 T 64 5 I min- 12 where, d= 200 mm = 100 mm D = 80mm. . I min - 2ooking-lu, k soy) - Imin - 146,56047-37 mm armin Imin A A- Area of section (bd) - π DV = (100x200)480") 19 14,973-45175 mm

580x 100 N/m admin= 14656047-37 mmx? 14 973.45175 mm -farmin= 31.286 mm Now, stenderness ratio = le Amin 6m y = 31-286 mm 6x10² som 31.286mm - a=197.78 nave -Answer. @sol: Tansition slenderness ration * Transition Stenderness ration is the slenderness ratio when Eulers Critical stress (en is equals to half of the material yield Strenth(sy). Ser= Sy for x = x 2. Oor 2 for = 290x100 W N/m

we know that Euler's critical stress bert TE A” sy TT" X 207x10 290x10° rotor V TX207x127 103 290x106 A 704 4855 IST 83.933 • Answer, Short or AMI long column ? why? > is; Llo un supported length of column least lateral dimension it i short column, otherwise then long column. unsupported length = 6m = 6000mm 6000 Least lateral dimension = 100mm. 60>10 It is Long column 100 Ans

sol. - it P= I MN 6 = P = 10 N Area- 100 x 200) – (480") = 14973.45 mm. stress = 106N ✓ 14973.45 mm Tos N 14973.45x100 m .: stress = 66 784875.9 Nmr. But, Eulers critical stress == ITE ar TX207X10 N/m 191.78 -irer= 10.65281366x109 Wilm for= 10652873660 N/mr. istress induced due to IMN load is less than cr. Therefore Column is safe.