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The tower analysis will consider the forces and moments caused by a variety of factors: vessel material, liquid, packing, insulation weight, wind and seismic loadings, attachment weights, bending due to eccentric attachments, and applied horizontal forces. The calculations are based on common industry methods that have been proven, both in theory and practice. The tower analysis stress and deflection calculations are based on static design methods and are not adequate for tall vertical vessels that are subject to wind-induced vibration. These vessels must be designed to meet static requirements and then be designed to withstand dynamic loading (wind-induced vibration) or redesigned to prevent it from occurring.

Tower Analysis Basics

Before you proceed with reviewing the tower analysis, check to make sure your component order is correct one more time (top head, shells-cones, bottom head, skirt, base plate). Also check to make sure that your attachments, wind load diameters, liquid, insulation, and packing all match up with the correct elevations for the tower portions they are a part of. DesignCalcs will automatically perform a tower analysis for you that incorporates all of these items. You will see the tower analysis in the reports. Note that the base plate calculations will take information from the tower analysis; you can see this in the base plate report. Below is a basic introduction to the way that the tower analysis works.

Definitions

Section: A portion or length of the tower in which the general design parameters defined in Section Boundaries are constant.

Section Boundaries: An elevation where a change occurs in one or more of the following:

  • Section Type (e.g., head, cylindrical shell, conical section, skirt, etc.)
  • Design Pressure
  • Material Type
  • Inside Diameter
  • Nominal Wall Thickness
  • Corrosion Allowance
  • Insulation Thickness
  • Insulation Density
  • Liquid Density
  • Packing Density
  • Wind Load Diameter
  • Wind Pressure
  • Circumferential Weld Joint Efficiency

Segment: A section or a portion of a section used for calculation purposes.

Node: A node exists at the top and bottom of every segment. Nodes are placed at section boundaries and at attachment locations.

Methodology

The tower methodology is the work of a professional engineering firm contracted to provide these calculations to CEI. The method used relies on many of today’s popular vessel manuals, including AISC, Bednar, Megesy, and Moss. The calculations have been refined and perfected over time.

This section provides a basic outline of the steps and calculations that the tower analysis performs to check the skirt and vessel reactions for adequacy. They are provided here in a logical order reflective of the report and mathematics. These steps are performed for each calculation case of the tower analysis (for example, Operating Pressurized Sustained Case and Empty Unpressurized Occasional Loadings Seismic Case 5 are two different calculation cases).

  1. Determine properties for the tower components
    1. Divide the vessel into sections and segments
    2. Look for cylinder lengths longer than 20% of the vessel total length and divide in half (repeat as necessary)
    3. Calculate the weight of each segment
    4. Calculate the First Natural Period of Vibration (FNPV) for the vessel per Rayleigh's Method
       
  2. Determine wind loading
    1. Calculating the wind pressure at the midpoint of each segment from the wind code chosen.
    2. Calculating the wind force on each segment.
    3. Calculating the moment at the bottom of each segment from the shear at the top of the segment and the wind force on the segment.
    4. Calculating the bending stress at the bottom of each segment due to the moment at the bottom of the segment.
       
  3. Determine seismic loading
    1. Calculating the total seismic shear force on the vessel based on the seismic code selected.
    2. Calculating the seismic shear distribution based on the seismic code selected.
    3. Calculating the moment at the bottom of each segment from the shear at the top of the segment and the seismic shear on the segment.
    4. Calculating the bending stress at the bottom of each segment due to the moment at the bottom of the segment.
       
  4. Determine sustained loadings
    1. Calculating the stress in each segment due to internal pressure.
    2. Calculating the stress in each segment due to external pressure.
    3. Calculating the stress at the bottom of each segment due to weight.
       
  5. Perform stress superposition
    1. Calculating the maximum tensile stress in each segment as follows:
    2. Calculating the maximum compressive stress in each segment as:
    3. Calculating the allowable tensile stress for each segment as the Section II, D allowable tensile stress multiplied by the girth seam efficiency.
    4. Calculating the allowable compressive stress for each segment per UG-23(b) from Section VIII, Division 1
    5. Calculating the critical buckling stress for each segment per engineering firms recommendations. This is nearly always redundant with compressive stress.
       
  6. Compare stresses: If the maximum tensile stress is less than the allowable tensile stress for each segment and the maximum compressive stress less than the smaller of the allowable compressive stress or the critical buckling stress, the tower design is acceptable.

Review

The calculated stresses are divided by the allowable stresses to determine stress ratios that allow for a much more rapid review process. The stress ratios must be less than or equal to 1 for all cases for a design to be passing. In addition, ratios greater than 1 are bolded to stand out in the report.

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