A tall fractionating column that is 14m long is made of a 30

A tall fractionating column that is 14m long is made of a 304.2mm ID standard steel pipe with weight of 74 kg/m and wall thickness of 9.5mm. During operation, the column is internally pressurized to 4.1 MPa and has a wind load of 600 N/m as shown.
(A) What is the state of stress at point A, on the windward side of pipe.
(B) Show all calculations and place the stresses on an equilibrated element.
(C) Determine if element is a planar state of stress and state the reason.
Please write neatly or type the solutions.

Could you draw the free body diagram and show the forces and moment acting in this problem. Please do the math as well.

Solution

Solution to Part A

Three types of loading is there on the fractionating column.

1) Stress due to internal pressure . t=9.5mm, D= 304.2, if D/t is more than 20, can be considered as thin walled cylinder.

2) stress due to wind load. this can be analysed treating the column as cantilever beam with uniformly distributed load. type of stress is TENSILE.

3) Streess due to self weight of the column. Type: Compressive stress.

State of Stress : Hoop Stress + (Bending stress on the outer Fibre- Compressive stress due to self weight)

Part(B)

Detailed Calculations given below

1) Stress due to internal pressure . t=9.5mm, D= 304.2, if D/t is more than 20, can be considered as thin walled cylinder. in this case D/t =32 and Hence can be analysed using the thin cylinder formula. Type of stress is TENSILE. the hoop stress: PD/2t N/mm2. here P= 4.1, D=304.2, t=9.5 and Hence Stress = 4.1 x 304.2/(2 x9.5) = 65.64 MPa

2) stress due to wind load. this can be analysed treating the column as cantilever beam with uniformly distributed load. type of stress is TENSILE. the uniformly distributed load w = 600N/m, the Maximum Bending Moment(BM) is at the point shown of the column: wL²/2, where L= 12m, hence Max BM = 600 x 12^2/2 = 43200Nm = 43200000 Nmm, Scection Modulus (Z) of the column Z= PI*(Do4-D4)/64/(Do/2) here Do is outer Diameter= 304.2+2x9.5=323.2, D=304.2; Substituting we get Z=713319 mm³ . Now the Tnesile Stress on the wind side BM/Z= 43200000/ 713319= 60.5 MPa.

3) Streess due to self weight of the column. Type: Compressive stress. Total column weight is = weight per unit length x lotal length = 74*14 = 1036Kg = 1036*9.8 = 10152N, total are of the cross section 9362mm². hecne the resulting compressive stress = 10152/9362= 1.08 MPa. this is too small compared to the other stresses. And HENCE neglected.

Part (C)

It is a planar stress as the all the sresses are in the same plane. (if meant to indicate PLANE STRESS or PLANE STRAIN case, the plane stress model can be used in the analysis of gently curved surfaces as this case is).