Tower With Combined Loads
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This tower sample focuses on the combination of wind, seismic and external pressure loads. The calculations are done in Compress, and the drawing is made in SolidWorks. Download both at the bottom of the page. Tower dimensions and calculations found in the calculation set and on the drawing are discussed throughout this sample.
This vessel is calculated using the Compress pressure vessel code program by Codeware Inc. Compress is our favorite program for tower design. Its extensive library of available calculation methods makes it useful for many vessel design tasks. The report is longer than other programs, but often is easier to read and includes extensive references, and illustrates most of the calculation steps allowing the methods to be checked.
The drawing is created in SolidWorks. By default, we use SolidWorks to create vessel drawings. Use of solid modeling is like building the vessel once in advance before it hits the shop floor. Solid modeling often takes more time than 2D CAD, but it also shows many design errors or issues in advance. The extra time can easily pay off during construction.
Internal + External Pressure Calculations
Each shell section is calculated for internal and external pressure loads. For some of the sections internal pressure governs, for others external. Internal pressure calculations are based on diameter and thickness (+ angle for cones). Calculations are found in the ASME VIII-1 code book. In the sample calculation, look for the Appendix 1-1 calculations for the Cylinders and App 1-4(e) for the cones. The external pressure calculations also use the diameter, thickness, and adds the use of the section length. Long shapes collapse easier than short shapes of the same section, and the code rules account for this. Look for UG-28(c) calculations for the cylinders and UG-33(f) for the cones.
|Section||Di||t nom||t req int||t req ext|
|Upper Cone||36.25 -> 120.25||0.875||0.6249||0.4673|
|Lower Cone||120.25 -> 84||0.875||0.6041||0.5074|
Required thickness based on internal and external pressure only. Some sections are governed by the internal pressure design (Upper Cone and Lower Cone) and some by external pressure (Upper Section, Middle Shell and Lower Shell). Wind and seismic loads have not been added yet.
IBC Seismic Calculations
This tower is designed to support IBC wind and seismic loads as programmed into Compress. Response modification factor “R” is the input users get wrong most often. From Earthquake-Resistant Design Concepts, FEMA P-749 / December 2010
R is a response modification factor that accounts for the ability of some seismic-force-resisting systems to respond to earthquake shaking in a ductile manner without loss of load-carrying capacity. R values generally range from 1 for systems that have no ability to provide ductile response to 8 for systems that are capable of highly ductile response. The R factor is used to reduce the required design strength for a structure.
The tower material is assumed to have ductility, but has limited ability to absorb energy by yielding without also collapsing. The goal is not always to prevent damage, but to prevent loss of life. ASCE 7-05 Table 15.4.-2 “Seismic coefficients for nonbuilding structures not similar to buildings” provides the correct value to use for a tower (this table is linked below):
Table 15.4-2: All other steel and reinforced concrete distributed mass cantilever structures not covered herein including stacks, chimneys, silos, and skirt-supported vertical vessels that are not similar to buildings. R=3
Or, with the unnecessary words removed:
Skirt-supported vertical vessels, R=3
Other factors required to do the seismic calculations are included in the table below. Typically, all except the R factor are provided by the end user.
|Factor||For this vessel|
|Importance Factor, I||1.0|
|Spectral Response Acceleration at short periods, Sa||200% of g|
|Spectral Response Acceleration at period of 1 second, S1||100% of g|
|Response Modification Coefficient from Table 15.4-2, R||3 – see text above|
|Acceleration Based Site Coefficient, Fa||1|
|Velocity-based Site Coefficient, Fv||1|
|Long-period Transition Period, TL||3|
|Redundancy factor, ρ||1|
|Occupancy Category (Table 1-1)||1|
From these inputs the base shear can be calculated. See pages 135 and following for the actual calculations. Some points of interest:
- The seismic spec provides Sa – seismic load at short period and at S1 – seismic load at 1 second. The calculated period is 0.447 seconds (page 116) Again from Earthquake-Resistant Design Concepts, Figure 30, The generalized period vs acceleration graph looks like this:
- For this and most towers, the period of vibration is between Ts and 1.0 second.
- Using Sa, S1 and R, the calculated acceleration is 44% of g. The R factor of 3 lowers the amount of base shear that the tower has to experience on the assumption that 2/3 of the seismic energy applied to the base of the tower gets absorbed internally – converted to heat – during a seismic event. If the tower did not have this ability – for example if the skirt was built from brick and R=1 – then the calculated base acceleration would be 133% of g (see page 120 cs=0.444)
- Consider the seismic load to be a random shaking in all 3 dimensions. A vertical load term is calculated (page 119, 1.1867 and 0.4133)
- The calculated base shear is 44% of the weight of the vessel (page 138 cs=0.44). This is reduced to 70% to account for the increased stresses allowed for occasional loads by the ASME codes. At this point the seismic and operating loads can be combined and compared to the ASME allowable operating stresses. Throughout the calculation set both combined and operating loads are checked individually to make sure neither is excessive.
External Pressure + Seismic Loads = Combined Loads
Previously, each section was calculated for internal and external pressure on its own. Now wind and seismic loading is added. The VIII-1 code rules do not cover the combined load. There are many ways available, and Compress uses the methods of Bergman and Calif, ASME 54-A-104, 1954 An interesting off topic note from the paper:
The codes furnish the designer with a list of approved materials and the maximum stress values in tension permitted over their usable range of temperatures. The design rules in the codes are limited to vessels of cylindrical or spherical shape under internal or external pressure, and to heads and nozzle attachments for such vessels. Rules for more complicated types of construction and for loadings other than that due to pressure are beyond the scope of the code. To include such rules would turn the code into a design handbook. And it would restrict the designer in working out his design in accordance with acceptable engineering principles. The code requires that he “shall provide details of construction that will be as safe as those provided by the rules of the code.”
Today as in 1954, the code book contains explicit rules covering the design of basic vessel components, and also today, there are no rules for combining loads. However, many would argue that their fears of turning the VIII-1 code into a design handbook have come true. Many more mandatory sections exist than in Bergman and Calif’s day. When designs do not fall within the scope of code rules, reviewers can insist on design changes to make code rules applicable, and thus mandatory. This is a particular concern in Canada when designs need to be approved by multiple reviewers for different provincial jurisdictions. To be innovative, vessels need to be designed under the more flexible VIII-2 code, when the jurisdictions allow. The method of Bergman and Calif combines the seismic load with the external pressure to create a new, increased equivalent external pressure for the wind and seismic conditions. (Look for “External Pressure + Weight + Seismic Loading Check Bergman, ASME paper 54-A-104” in the calculation sets). The method calculates a new effective external pressure for the vessel section. Because the combined load is an occasional load, the combined limit is higher and the calculated thickness at external pressure might be higher than the combined load required. This chart shows the new effective pressures and from that, the combined load required thickness:
|Section||Di||t nom||Ratio * Pe||Ratio * Pe||t req int||t req ext||t combined|
|Upper Cone||36.25 -> 120.25||0.875||15.05||15.07||0.6249||0.4673||0.3708|
|Lower Cone||120.25 -> 84||0.875||15.13||15.27||0.6041||0.5074||0.3911|
|Support Skirt||86||0.750||0.7267||Required t|
Combined load is the governing load case the Lower Shell. Wind load does not govern the design. Combined loads now govern the lower shell, but the same nominal thickness still works.
Junctions – Creating Lines of Support
Two things need to happen at the junctions between the cones and shells: 1) the discontinuity stresses created by the change in shape between cones and shells must be kept within the limits specified by the code, and 2) the junction has to be strong enough to act as a line of support. When the shape of a shell changes, local discontinuity stresses are created. All of the cone to shell junctions are discontinuities. The code uses a simple “area replacement” method to determine if the junction is strong enough to withstand the discontinuity loads. All the junctions pass without the need for additional area. [Look for the Appendix 1-5(d & e) calculations for the cones, comparing required with actual area.]
Without any lines of support, the external pressure and combined load calculations would be based on the entire pressurized length of the vessel. The longer the section, the thicker the material needs to be for these loads. The required thickness for this tower would be much larger. The lines of support on this tower are made up of rings rolled the hard way welded to the shells close to the cone to shell junctions. The supports isolate each cone and shell section – they can be calculated individually. The junction’s ability to act as a line of support is judged on the combined moment of inertia of the connecting shells and any reinforcing present. [Again look for the Appendix 1-5(d & e) calculations for the cones, this time looking for I’s and I’]:
|Internal Pressure||External Pressure|
|Junction||Ring||Area Req||Actual||Area Req||Actual||I Req||I Actual|
|Upper Cone Small End||3/8 x 2||0.4183||1.2656||0.1751||1.1393||0.5699||0.7887|
|Upper Cone Large End||1/2 x 5||Pass||0.7047||8.2255||27.1189||32.6292|
|Lower Cone Large End||5/8 x 6||Pass||0.5326||7.9363||32.529||44.6851|
|Lower Cone Small End||1/2 x 5||0.1524||2.0393||0.9225||1.7468||10.4426||16.2853|
Every junction passes the requirements for area replacement without additional reinforcement. Rolled rings have been added to every junction to also pass as lines of support. Internal and external pressure calculations are also run on the heads and the nozzles, but they are beyond the scope of this article.
Downloads (pdf format):
More Information on Seismic Response Factors:
- Purchase: ASCE 7-05 Minimum Design Loads for Buildings and Other Structures(Link goes to 7-10 which replaces 7-05)
- ASCE Standard 7-05 Table 15.4-1
- From Earthquake-Resistant Design Concepts, FEMA P-749 / December 2010 – see chapter 5. https://c.ymcdn.com/sites/www.nibs.org/resource/resmgr/BSSC/FEMA_P-749.pdf
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