Question

Figure 4 shows an arrangement and dimensions of cylinder-frustrum-cylinder storage tank. It is supported by 4 hollow steel columns of length L. One end of each column is welded to the tank and provide a clamped support. The other end is free support rest on the ground. Figure 5 shows the cross- section shape of the column and its dimensions. The tank designed to store viscous liquid of mass density p kg/m². It is assumed that each column carries equal load and neglect the weight of the empty tank. a b Determine the maximum value H to avoid buckling in m. Evaluate the stress in the column when the load is equal to Pcrit in MPa. 03 m 1 H N 1 m V 2 m L Ø1 m Figure 4 k 120 mm 10 mm 90 mm 10 mm Figure 5

L = 5.2 m

p = 1040 Kg/m³

Common Data: [Young’s modulus, E=210 GN/m²]  [Poisson’s ratio, ν=0.33] [Yield stress σ₀ = 210 MN/m² ]

Answer 1

3rn 0 length of column (O) = 5200mm. (l) = 5.2 m. E 2108109 N/m2 0:33 oyt 210x 106 N/m2 p= 1040 kg/m 1 I'm . 2m 8 solution ܗܤܙܘܛܙ. Y K T :: Imin: Ix. 90 mm 3 3 Ironine 120x90% 100x70 12 Imin = 4.43 166 x006.. nue : Finding T2 E Imin Pes) ad Euter critical load for each column. le ļ one fined other (lele free) T12x 210x10 mm"), 4:43 1664 106 15200 Pa) 1358749

2 Total load = (Por) x4 as 4 collons 5434 998 N to we How find H the of will evaluate the volume cylinder fristum cylindur postion, V- Vit V2 + 13. # V2 1 *h* (x1++R2? +de1x12)] ****1* [0.5'41.524 6.5*0.45)] 3 V22 13:17 12 m i + 2 13 130 12 + 1 x V x2 32x H) CH 91H IGIT 12 V Total weight = r(specific weight) + volume. Sg x volume. 5434 998 1040 x 9.818 5434998 1917) thrin 74. 66 metres

H value of be less than to avoid buckling should or equal to 74-66 metres () Stress G) when load is equal to peritical, T: load dea ) cross cross section - Area) (120x90 – 100x70) L 3 roomma 1358749 3800 357.56 Mipa D. 357.56 MPa X