**Introduction**

The intention of the Tee area figures is to provide a calculation method and understanding which allows to make calculations for standard EN 10253, ASME B16.9 and custom Tees. The area figures are supposed to be close to the EN 10253 dimensions as possible. It is not the intention to validate the EN 10253 approach. However we provide feedback on the statements made in above emails

The statements from the above emails is listed below in ‘*Italics’* and the reply in regular font.

**About EN 10253**

*‘The left figure on page 2 shows the lengths correctly according to EN 10253-2. The calculation of the areas in EN 10253-2 is done using the red lines in the left figure. The figure on the right side is not in line with EN 10253-2. I have no idea why the areas calculated with these limits are compared with the areas according to EN 10253-2. The difference between the areas are not caused by details at the taper area, they are caused by different positions of the red lines (lengths l_s and l_b) in the left and right figure.’*

This is unfortunately not the case, the formulas use the l_b_acc and l_s_acc from the figure at the right. Below are some formulas from the EN 10253-2 B.3 standard:

The formulas clearly use l_b_acc and l_s_acc, not l_b and l_s.

*‘Starting with l_s and l_b from the new point half way the outside arc of the crotch is in my opinion a good idea and gives reasonable results.’*

Acknowledged

*‘I disagree with the calculation of l_b = 117.553 mm on page 3. In my opinion, the wall thickness in the tapering zone of 16.3904 mm used for its calculation is not representative for the wall thickness of the branch. I agree to limit the length with the height of the branch H00 - D00 / 2.’*

In your approach it would not make any difference whether there would be tapering, and reducing the amount of material in the branch, or not. This would not logical and would be unacceptable to some of our customers who regularly orders large, thick custom made tees. The dependence on the tapering position and shape is giving proper results for custom and standard Tees. It allows also the calculation of the thick type A Tees which are tapered to match the connecting pipe.

*‘I propose to use examples where the lengths l_s and l_b end before the tapering starts and include W00 - D10 / 2 and H00 - D00 / 2 as maximum in the formulas for l_s and l_b.’*

It is unfortunately not always the case that l_s and l_b end before the tapering starts. For the thick Tees it is frequently that the limit will end somewhere in the tapering zone or even goes beyond the tapering up to the end of the Tees. In this last case you will have the limit as you state above at Tee boundary limits.

**About EN 13480-3 proposal**

*‘I agree to your proposal to start the distance for limits at the 45 degrees point at the crotch outside arc.’*

Noted.

*‘I do not agree with the proposal to use the wall thickness and diameter in the tapering area for the calculation of the reinforcing lengths as these values are not representative for the wall thickness of run and branch of the tee. Of course, the reinforcing lengths have to be limited by the dimensions F and G of the tee.’*

The same answers applies as above for the similar statement, For clarity it is repeated here. In your approach it would not make any difference whether there would be tapering, and reducing the amount of material in the branch, or not. This would not logical and would be unacceptable to some of our customers who regularly orders large, thick custom made tees. The dependence on the tapering position and shape is giving proper results for custom and standard Tees. It allows also the calculation of the thick type A Tees which are tapered to match the connecting pipe.

*‘The proposed figures 8.3.9-4 “Detail of limit start point”, 8.3.9-5 “Thin wall tee, Dm and dm diameter definition” and 8.3.9-6 “Thin wall tee, detail of analysis wall thickness defini**ti**on“ are acceptable to me. The figures 8.3.9-3 “Thick wall tee, reinforcement inside“ and 8.3.9-5 “Thick wall tee, reinforcement inside and outside” (figure number used twice) would be acceptable if the reinforcing lengths end before the tapering zones start.’*

The second figure 8.3.9-5 Thick wall tee, reinforcement inside and outside should have had the number 8.3.9-7. It is not logical to state that the limits l_s and l_b should end before the tapering starts. Depending the shape and dimensions of the Tee the tapering, the tapering angle and the tapering location will have influence on the material area and pressure area. The ASME even prefers an inside and outside tapering with an offset. This offset would look like this (at the run side):

Figure: tapering at run side with offset as per ASME

In above figure the tapering at the run side has an offset at the outside compared with the tapering at the inside. For thick wall Tees this is the preferred design according the ASME.

*‘I was surprised by the large differences shown in the tables on page 2 and on page 3 for small tees (diameters 21.3 and 26.9) for wall thickness series 8. After doing some calculations, I realized that a different formula applies for the calculations for pipes of these dimensions. In EN 13480-3:2017, for Do/Di > 1.7 Lame’s equation (6.1-4) appliers, while for smaller wall thicknesses the boiler formula (6.1-1) applies. The boiler formula uses the same principle as is used for the calculation of branch connections in formulas (8.4.3-3), (8.4.3-6) and (8.4.3-7). For branch connections (tees), the same formulas are used for all thicknesses. I assume that this circumstance is somehow the reason for this effect.’*

Your conclusion might have an effect, we did not check this cause. For us it was sufficient that the detail calculation would show that the series 8 small size Tees are in actual fact stronger than is assumed in the EN 10253.

*‘On page 10 and 11 a table “EN 10253-2 Tee type B - MAWP [MPa] based on X = 1 factor” is shown, but the values are different even though the dimensions are the same. A pressure factor X = 1 means that the pressure resistance corresponds to that of a pipe. I would therefore assume that these tables list the calculation pressure as per EN 13480-3 paragraph 6.1. But why are there differences between these two tables? What material (and temperature) and design stress f was used for the calculations?’*

The number of tables might be a bit confusing and perhaps do not clearly state what should be compared with what.

Page 9 and 10 show the results of the type A comparison. The page 9 was the original proposal result and the page 10 with the modified approach at 45^{O} starting point. The page 10 right bottom table shows the results as compared with the EN 10253 and everything is green. This means that the proposed area definition with limits starting at 45^{o} have good and sometime a bit stronger result

Page 11 and 12 are the same but for type B. Except for a few yellow but very close to EN 10253 the results at the right bottom table at page 12 are acceptable.

The pressure and temperature are 2.5 MPa and 220 Celsius but they do have any impact on the comparison.