This is a question that has puzzled stack designers since the beginning of time, is it Breach or Breech? Lets look at the definition for each according to Dictionary.com:

**Breech** – *The lower, rear part of the trunk of the body. In an ordnance, the rear part of the bore of a gun, especially the opening and associated mechanism that permits insertion of a projectile. *

**Breach** – *The act or result of breaking; break or rupture. A gap made in a wall or fortification. To make a breach or opening in.*

According to the definitions, it seems that BREACH is the most accurate for the context of an opening in a cylidndrical shell; however, I have been using breech to describe this situation for my entire career. The book “Tubular Steel Structures” by Troitsky uses the term breech, and ASME STS-1 uses breech. Consulting with colleages they have stated that they believe that the industry has used breech and breach interchangeably, so that either is acceptable.

At the end of the day, we at Meca have decided that breach is more consistent with the definitions and so moving forward we will use breach; however, don’t be surprised if you see breech in various locations in our website and software, it’s going to take a while to locate and update all references.

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]]>ASCE 7-05 was based upon wind speeds used for Allowable Stress Design (ASD). Then starting with ASCE 7-10, the wind basis was changed to be Ultimate design. Ultimate wind speeds are higher than ASD wind speeds. For example, in Dallas, Texas an ASD wind speed would be 90 mph and a comparable Ultimate wind speed would be 105 mph (Category II). The wind speed is one of the parameters used to calculate the flexible gust factor. The gust factor calculation is unchanged from ASCE 7-05 to ASCE 7-16, and so if the wind speeds increase, then the gust factor increases. Can this be correct, why would the gust factor increase? I had this very question, and got this excellent explanation from a very knowledgeable member of the ASCE 7 committee:

__When ASCE 7 adopted ultimate wind speeds as the design basis, the flexible gust factor Gf increased. Some practitioners questioned this, thinking it was simply some sort of “coefficient” that shouldn’t vary with wind speed. But this is not the case, and it was quite intentional that Gf should increase. In fact, previously Gf was based on the service (~50-yr speed), accounting for the increased dynamic response at this speed; then the ultimate response under the ultimate wind speed was estimated by multiplying by the nominal square of the wind speed factor, 1.6. This was not theoretical sound, since the dynamic response factor increases with speed faster than the speed squared. Thus multiplying the dynamically-magnified load by 1.6 results in an unconservative dynamic load under the ultimate wind speed. In fact this is one of the reasons why the ultimate wind speed is the preferred “starting place.”__

This excellent explanation makes it clear that the flexible gust factor does increase and it was intentional. Now is this going to increase our wind forces acting on the structure?

You have to determine if the structure is rigid or flexible, and that can be the hardest part on some structures. If you determine it’s flexible, you then have to determine the natural frequency and structural damping, both of which play a HUGE role in the calculation of the flexible gust factor. If you do specify that the structure is flexible and enter the natural frequency and damping, then MecaWind is going to automatically calculate the flexible gust factor.

Yes, this software will handle the entire process automatically. If you select ASME STS-1 as your design code, then the software is going to calculate the frequency and calculate the flexible gust factor automatically. You will need to enter or select a proper structural damping value, since that plays a major role in the gust factor calculation; however, there is some guidance on this within the software for some common scenarios. Select the structural damping and MecaStack will do the rest as far as calculating the flexible gust factor.

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]]>What it does is summarize all of the pressures for components and cladding (C&C) over all applicable zones and areas. As an example, lets look at a building which demonstrates this feature:

ASCE 7-16, 150 mph, Exp. C, Cat. III

Enclosed Building w/ Hipped Roof (Slope=18.4 Deg)

Width = 50 ft, Length = 100 ft

To the right is the C&C Zone Summary for this building. In one table, we have max and min pressures for all possible C&C areas and zones. This was created by clicking 2 checkboxes.

Let’s illustrate how the table is created using the same building stated previously. We are using Ch 30 Part 1, and so we are followign Fig 30.3-1 for the walls. Since it’s a Hipped roof with a slope of 18.4 deg, Fig 30.3-2E would be used for the roof and 30.3-2F for the overhang. Our h/B = 0.48, and so we are using the h/B<=0.5 for both Fig 30.3-2E and F. Looking at all three of these figures, we determine the Effective Area’s where each curve changes the value of GCp and we summarize them in the table below. The “Unique Areas” is the combination of unique areas from all three figures.

Fig 30.3-1 |
Fig 30.3-2E |
Fig 30.3-2F |
Unique Areas |

10 | 10 | 10 | 10 |

20 | 20 | ||

100 | 100 | 100 | |

200 | 200 | 200 | |

500 | 500 |

These “Unique Areas” are the exact same values that appeared in the C&C Summary chart, we display the pressures for each of these Unique Areas for EACH zone.

Two (2) pressures are listed for each cell, these represent the maximum and minimum pressure calcualted. The ASCE 7 convention is that Positive pressures are acting toward the surface and negative pressures are acting away from the surface.

The first column is <= 10 sq ft, which means that any area that is less than this value use this column of pressures.

The last columnn is > 500 sq ft, which means that any area that is > 500 sq ft will use the values in the columns.

For all values that fall between the first and last column things get a little more complicated. The Figures are not linear, they are linear on the vertical scale and logarithmic on the horizontal. There are a couple options depending upon how accurate you wish to be in your calculations:

1) Simple – If you have an area that falls between two columns, then just take the pressures that are the highest. This will always be the one to the left, which has a lower area.

2) Accurate – If you want to interpolate then you must use Logarithm for the Area values. For example, if we want to get Zone 4 value at 100 sq ft, we would calcualte as follows (Using A = 10 sq ft and 500 sq ft as upper and lower bounds):

Zone 4 @ 500 sq ft ==> Pu=24.26, Au = 500

Zone 4 @ 10 sq ft ==> Pl=32.53, Al = 10

What is Px for Zone 4 @ 100 sq ft?

Px = [(Pu-Pl) / (Ln(Au)-Ln(Al) ]*(Ln(Ax)-Ln(Al)) + Pl

Px = [(24.26-32.53)/(Ln(500)-Ln(10))]*(Ln(100)-Ln(10))+32.53 = **27.66 psf**

Which exactly agrees with the value that was shown in our table.

3) Approximate – The above interpolation is a little complicated, what if we just used linear interpolation?

Px = [(Pu-Pl) / (Au-Al)]*(Ax-Al) + Pl

Px = [(24.26-32.53)/(500-10)]*(100-10)+32.53 = **31.0 psf**

It’s not very accurate, but at least it’s conservative.

When calculating your effective areas, don’t forgot to consider the definition of the Effective area, which includes what we refer to as the One-Third rule. When you enter the dimensions into MecaWind this is taken into account by the software automatically; however, if you choose instead to use the C&C summary table, then you must take this into consideration with any area that you use to extract values from the C&C Summary manually. As a reminder the One-Third Rule is stated below.

**The effective area is the span length multiplied by an effective width that need not be less than one-third the span length. **

The C&C Summary is a very easy way to get pressures across all zones and all areas with just two clicks. We explained above how the data is generated, and how you can interpret the data. When you have an area betwen two columns, it’s simplest to just take the higher pressures and be conservative. I have demonstrated one summary table here, and all of the other summary tables follow the same basic approach.

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]]>By adding guy wires we can reduce the likelihood of vortex shedding by a couple of different methods:

1) A guy wire supported stack has a recommended structural damping of 0.006. Depending upon the stack, a self supported stack could have structural damping of only 0.002, and so adding guy wires can triple that value. Often this alone is enough to solve the problem.

2) The addition of guy wires increases the stiffness, and this will change the frequency and the critical wind speed.

3) Guy wires can help resist the lateral loads due to vortex shedding, bringing the stresses to an acceptable level.

To illustrate this technique of lowering the Vc, lets use a real example. If we have a stack that is 100 ft [30.48 m] tall, 2 ft [0.6 m] OD at the top and then transitions to 4 ft [1.2 m] OD at the bottom. The entire stack is 0.25 in [6.35 mm] thick. Using the MecaStack software, we get the following dynamic results

**Mode # Freq (Hz) Vc (mph) Vc (m/s) **1 1.6 11.3 5.1

2 5.8 39.5 17.7

Both modes show that there are high amplitude vibrations due to vortex shedding.

Now lets look at the same stack after adding 1/2″ [12 mm] diameter wire rope guy wires. By adding these guy wires we do the following:

* Increase Structural Damping from 0.002 to 0.006

* Increase the frequency

* Increase the lateral resistance to loads

All of these combined resolves our vortex shedding problems for mode 1 and mode 2. The results are shown below, and the stack is now passing both modes.

I have a confession to make, I don’t completely trust the calculations that predict vortex shedding on guy wire supported stacks. The Euro standards do the most detailed job of giving guidance in this area, but most of the other codes don’t give much guidance at all. As a result, most of the stack codes in MecaStack just analyze a guyed stack the same way we would analyze a self supported stack; however, taking into consideration the increased structural damping and stiffness provided by the guy wires. The good news is that there have been very few instances where guyed stacks actually vibrate, and even in the rare cases where I have personally been involved, the calculations still indicated that there was no problem. The best advise that I can offer is to avoid the situations which I have seen that led to wind induced vibration:

1) Top guy wire too far down from top of the stack. I try to keep the top guy wire as close as reasonably possible to the top of the stack, usually a few feet or couple of meters.

2) Structural bridge strand was used in all cases where I have witnessed vibration. I think it is very stiff and provides little damping. Bridge strand can be used, but the combination of a guy wire that is far from the top and the use of bridge strand is a dangerous combination.

Our MecaStack software does consider vortex shedding, but since the codes don’t do a great job at addressing this for guy wire supported stacks you should apply good engineering judgement.

If you have a big stack, then you are going to need big guy wires. There might be a tendency to think that the stack is already strong, so it just needs a little help from the guy wires. I think of it this way, imagine attaching guy wires to a mountain to provide support. If you attach a small diameter guy wire to the moutain, do we really expect the guy wire to take any of the lateral load? You would need a VERY big guy wire to compete with the high stiffness of the mountain, otherwise all lateral loads would just go to the mountain. The same is true of stacks, Big Stacks require Big Guy Wires.

Adding guy wires to a stack to address vortex shedding isn’t very common, but it is often a valid solution. I’ve only personally seen this done a couple of times in my career. Usually a stack is self supported (free standing) for a reason, because there isn’t enough space for guy wires; however, when there is space for guy wires, it is a possible solution.

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]]>The first notable thing is that in ASCE 7-05 and earlier, there is only one return period for the entire standard. Starting in ASCE 7-10 and later versions, there is a different return period for each category.

In ASCE 7-05 and earlier, we used a single wind speed for a single location, and then we accounted for the “structural category” by using importance factors. For example, if it was an essential building such as a hospital then we would use Category IV, and then the importance factor would be 1.15. This would multiply the wind velocity by 1.15, and would significantly increase the wind loads.

Starting in ASCE 7-10, there were different wind maps for each structural category. The importance factor was eliminated and the higher categories used a higher wind speed than the lower categories. If we are looking up a wind speed for a location, we must also know the category of the structure, because the wind maps change for each category.

The wind speeds in ASCE 7-10 and later are considered “Ultimate” wind speeds, where as the wind speeds in ASCE 7-05 and earlier are Allowable Stress Design (ASD) wind speeds. The Ultimate indicates that the wind pressures calculated are to be used with the Ultimate (Strength) load combinations provided in ASCE 7-16 Sec 2.3, whereas in ASCE 7-05 we used the wind pressures in the Allowable Stress Design (ASD) combinations. This can all become a little confusing, and so we have worked an example in this document to illustrate. In this example, I use the same wind speeds that I mentioned at the begining of this article. This shows that even though we used 90 mph with ASCE 7-05 and 115 mph with ASCE 7-10, that the final pressures are actually quite similar when we take all other factors into consideration. There are areas of the US (Typically along the coasts) where the pressures won’t match so closely, but in much of the US both codes (ASCE 7-05 and ASCE 7-10) will give similar results if applied correctly.

If you are using ASCE 7 for design, then you simply look up your location in the latest version to determine what wind speed to use for design. There are instances where you may be trying to convert from a wind speed provided in another country to that of ASCE 7, or vice versa. In these instances we have created a free wind conversion tool to help with that conversion from one code to another. To receive it, you simply need to sign up for our newsletter, and one of the emails in that welcome sequence of emails provides the link to download this free tool.

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]]>I’ll bet “Slow Down” isn’t an expression you hear much in your business. I dream of a day when a customer tells me, “Slow down, we really don’t care when you finish your design.” I can’t get you more time on your deadline, but I can tell you one instance that slowing down will actually make your customer happy.

We calculate critical wind speed (Vc) for a stack, and this is the wind speed at which the stack can experience wind induced vibration. The stack design codes provide an upper limit, and when the critical wind speed is above this limit then we no longer have to consider vortex shedding. Unfortunately there is no corresponding lower limit for critical wind speed, where below this limit we would be able to ignore vortex shedding; however, practically there usually is a lower limit where below that point vortex shedding loads become negligible. I’ll refer to this as a “Virtual Lower Limit” (VLL).

Early in my career we used a rule of thumb that indicated if the critical wind speed (Vc) was less than 15 mph [6.7 m/s] then the energy in the wind was small, and we could ignore vortex shedding. Although this rule of thumb served us well for many years, it isn’t always correct; however, in many cases it is a good target for a VLL. The actual value may be higher or lower on your particular stack, but on average I think 15 mph [6.7 m/s] is a good initial guess.

I don’t have an equation used to calcualte this value, but it’s a trial and error solution. I use our software, MecaStack, and I make changes to my stack to lower the critical wind speed (Vc) and then I try to find the point at which the vortex shedding deflection and loads are negligible.

From a dynamic standpoint, we can reduce our complicated stack into the simplified system as shown, with a beam of stiffness “K” and a mass “M” at the top. Visualize hitting the mass with a big hammer. The mass will start oscillating from side to side. We can also calculate the frequency of oscillation with the “K” and “M” values. The critical wind speed (Vc) is directly proportional to the frequency. The math is simple:

f = (K / M)^0.5

Vc = f * D / S

D = Average Outer Diameter of Top 1/3 of stack

S = Strouhal number which is usually 0.2

We can see from this simple equation that to decrease Vc, we simply need to either decrease D or decrease f. We can decrease f by either decreasing stiffness (K) or increasing mass (M). This gives us several options to decrease Vc.

1) Decrease the outer diameter of the top 1/3 of the stack.

2) Decrease the frequency of the stack, which can be done multiple ways:

a) Increase the mass, and most importantly the mass near the top. Sometimes this is as simple as increasing the thickness on the cylinders near the top and/or adding some other mass to the top of the stack. Changes to the top have the biggest impact to the frequency.

b) Decrease the diameter of the stack, which will decrease the stiffness (K). For the biggest impact, decreases in the diameter at the base of the stack will have a far bigger impact on the frequency than changes in the diameter at the top.

c) Decrease the thickness of the stack, which will decrease the stiffness (K). For the biggest impact, decreases in the thickness at the base of the stack will have far more impact on the frequency than changes in the thickness at the top (which also decreases mass, and increases the frequency).

To illustrate this technique of lowering the Vc, lets use a real example. If we have a stack that is 100 ft [30.48 m] tall, 2 ft [0.6 m] OD at the top and then transitions to 4 ft [1.2 m] OD at the bottom. The entire stack is 0.25 in [6.35 mm] thick. Using the MecaStack software, we get the following dynamic results

**Mode # Freq (Hz) Vc (mph) Vc (m/s)**1 1.6 11.3 5.1

2 5.8 39.5 17.7

Both modes show that there are high amplitude vibrations due to vortex shedding. Even though mode 1 is already less than our previous VLL of 15 mph [6.7 m/s] that was previously mentioned (I also mentioned previously that this is not an absolute limit but rather just a rule of thumb).

Now lets make a change to the stack so that the Vc is lowered. To do this we want to lower the frequency, which in turn will lower the Vc. We do this by changing the top 10 ft [3.04 m] of the stack from 0.25 in [6.35 mm] to 0.5 in [12 mm]. This additional mass at the top of the stack will lower the natural frequency of the stack, which in turn will lower the Vc.

**Mode # Freq (Hz) Vc (mph) Vc (m/s) **1 1.4 9.6 4.3

2 5.3 35.9 16.0

The first mode Vc has been lowered to 9.6 mph, but we also ended up lowering the mode 2 Vc to 35.9 mph. This is an unavoidable consequence, when you lower the frequency for one mode you are going to lower the critical wind speed for all modes; however, we got fortunate in this stack in that we changed the dynamic behavior for mode 1 and mode 2 benefited also. The mode 2 critical wind speed decreased, which in this case isn’t necessarily a positive thing, but the mass distribution and frequency changed and now the deflection estimate is much lower for vortex shedding for mode 2. This won’t always be the case, it’s just something you have to evaluate by trial & error to determine the net result on a specific stack.

This can be a complicated problem to solve. You can add mass to the top, and lower the critical wind speed for mode 1; however, you also will lower the mode 2 critical wind speed also, and sometimes this can make mode 2 better and other times it will make it worse. You could end up being like a dog chasing its tail. Sometimes the design comes together easily, and other times you just go in circles.

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]]>The short answer is no. There is a section covering tornadoes, and this section consist of the following sentence:

ASCE 7-16 Para 26.14 Tornado Lmitation

“Tornadoes have not been considered in the wind load provisions. “

Well that was simple, so I guess this is where the article ends? Not exactly, in the commentary of ASCE 7-16, Para C26.14 there is some more guidance on the topic. There is quite a bit of additional guidance in this section, and I will pull out the highlights in this article.

After a tornado, the meteorologists usually determine the magnitude of the tornado by specifying an EF number. The smallest tornado’s are EF0 and the largest are EF5. The EF value is the “Enhanced Fujita” scale, and it determines the range of wind speeds.

In the central United States the probability of a specific location experiencing an EF0 or EF1 rated tornado, is on the order of 4,000 years. ASCE 7 commentary recommends that if you are designing a Category IV (Essential) structure, that it would be prudent to use the EF1 wind speeds for design, since it would normally be a minimal increase in wind speed.

The probability of a site experiencing an EF4 or EF5 tornado are on the order of 10,000,000 years. According to the National Weather Service (NWS) between 1950 and 2013 there were 56,221 recorded tornadoes. Of these, only 4% were rated as EF3 and 1% were EF4-EF5; therefore the chances of experiencing an EF3 or higher is very remote.

Studies have found that tornadoes are more likely to generate wind borne debris compared to non-tornadic winds of the same speed. The momentum of wind-borne debris generated by EF3 speeds may exceed the impact test criteria adopted from hurricane opening protection.

ASCE 7 has provided a comparison to compare various wind speeds due to tornadoes in Table 26.14-3. You can see that even for lower tornadic wind velocity, larger roof and wall pressures are generated rather than a straight line wind of the same or greater speed.

ASCE 7 doesn’t include provisions in the main standard for calculating wind pressures for tornadoes; however, there are some provisions provided in the ASCE 7-16 Commentary C26.14. If you refer to that section you will find some guidance on how to estimate wind pressures for tornadoes.

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]]>We calculate critical wind speed (Vc) for a stack, and this is the wind speed at which the stack can experience wind induced vibration. The stack design codes provide an upper limit and when the critical wind speed is above this limit, then we no longer have to consider vortex shedding. The basic logic is that if the Vc is higher than any wind speed we expect to ever see on the stack, then it’s only logical that we can assume that vortex shedding will never occur.

For example, I’m located in Broken Arrow, Oklahoma, and here the design wind speed per ASCE 7-16 for Category II structures is 110 mph. I decide to design a steel stack for my back yard just to irritate my neighbors, and this stack happens to have a critical wind speed of 180 mph. That means at 180 mph the stack could experience vortex shedding; however, this is much higher than 110 mph for my region, and so it’s highly unlikely that my stack will ever see 180 mph in it’s life. Therefore, it’s not necessary that I even consider vortex shedding. The actual numbers we compare for with the upper limit aren’t quite this simplistic, but that is the basic concept.

We can use this concept to our advantage in certain situations. Now if your critical wind speed is 25 mph and your design wind speed is 100 mph, then this concept isn’t going to help you. The additional steel necessary to increase your critical wind speed from 25 mph to well above 100 mph is enormous. Where this concept comes into play is when your critical wind speed is maybe 5% to 10% less than the upper limit.

Another time we could use more speed is if we have problems with higher modes. Your mode 1 critical wind speed may only be 20 mph; however, your mode 2 critical wind speed might be just below your upper limit. In this case you could increase the stiffness of the stack and raise mode 2 above the upper limit, and then you only have to address mode 1.

From a dynamic standpoint, we can reduce our complicated stack into the simplified system shown to the right, with a beam of stiffness “K” and a mass “M” at the top. Visualize hitting the mass with a big hammer, the mass will start oscillating from side to side. We can also calculate the frequency of oscillation with the “K” and “M” values. The critical wind speed (Vc) is directly proportional to the frequency. The math is simple:

f = (K / M)^0.5

Vc = f * D / S

D = Average Outer Diameter of Top 1/3 of stack

S = Strouhal number which is usually 0.2

We can see from this simple equation that to increase Vc, we simply need to either increase D or increase f. We can increase f by either increasing stiffness (K) or decreasing mass (M). This gives us several options to increase Vc.

1) Increase the outer diameter of the top 1/3 of the stack.

2) Increase the frequency of the stack, which can be done multiple ways:

a) Decrease the mass, and most importantly the mass near the top. This isn’t always a feasible option, but if it’s possible to reduce the mass near the top it can help increase the frequency.

b) Increase the diameter of the stack, which will increase the stiffness (K). For the biggest impact, increases in diameter at the base of the stack will have a far bigger impact on the frequency than changes in diameter at the top.

c) Increase the thickness of the stack, which will increase the stiffness (K). For the biggest impact, increases in the thickness at the base of the stack will have far more impact on the frequency than changes in the thickness at the top (which also increases mass, and lowers the frequency).

To illustrate this trick lets use a real example. If we have a stack that is 100 ft [30.48 m] tall, 10 ft [3.048 m] OD and 0.25 in [6.35 mm] thick, then MecaStack will give a natural frequency of 3.3 Hz. This corresponds to a critical wind speed of 111.7 mph. The upper limit for vortex shedding is 115.7 mph. This means that if we can increase the Vc from 111.7 mph to something greater than 115.7 mph then we will no longer need to consider vortex shedding.

The easiest way to increase Vc is to increase the stiffness. This can be done by making the stack lighter, or making it more rigid. We can have the biggest impact by increasing the diameter, but increasing thickness can also have an impact. Generally changes at the bottom of the stack have a bigger impact than changes at the top of the stack.

Let’s just make a simple change of increasing the bottom 10 ft [3.048 m] from 0.25 in [6.35 mm] to 0.375 in [9.5 mm]. These results are shown below, and we are able to increase Vc > Vupr, eliminating the need to check vortex shedding. This change would generally be far less expensive than adding a damping solution or adding helical strakes, and it’s far simpler.

Increasing speed isn’t going to work in all instances, but there are many instances where this approach will work and save you time and money. The size and stiffness of stacks vary widely, and so the amount of additional steel needed to raise Vc above Vupr will vary widely. Sometimes just adding a small amount of steel can get you out of the danger zone, and other times it can take a tremendous amount of steel just to raise the Vc by 0.5 mph [0.2 m/s]. You just have to try and see if it will work on your stack.

If we can be of assistance, please don’t hesitate to contact us at support@mecaenterprises.com

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