Introduction
This document is for discussion, comments and suggestions. The purpose is to compare and validate the EN 102532/4 strength calculation in B.4.4 and B.5.3 with the EN 134803 Clause 8. The EN 102532/4 indicate that the calculations are based on the EN 134803. This document highlights possible differences.
Description
The EN 134803 clause 8 gives the calculation for openings. The clause includes openings in various closures like cylindrical shell, cones, spheres and dished ends. The methods for calculation have a similarities with the EN 134453. The clause 8 in EN 134803 also includes piping specific components like a Ytype branch, an oblique branch and forged tees. The subject of this article is the calculation method for tees with focus on the material and pressure area.
The basic approach of EN calculations for openings is the comparison of the strength of the material within defined limits and the pressure area force within the same limits. The concept is illustrated in below figure for pipe branch.
Image: Figure 8.4.31 material area versus pressure area
The Ap is the pressure area and the Afb + Afs + Afpl is the material area. The maximum force for the material, which is the allowable stress times the material surface area should be equal or stronger than the force resulting from the pressure within the pressure area.
The formula which takes different materials of the above branch connection into account is:
Image: formula 8.4.37 material area versus pressure area
The fs, fb and fpl are the allowable stresses for the respectively run pipe, branch pipe and the reinforcement plate. These stresses are reduced by half the internal pressure pc before multiplied with the related material area, Afs, Afb and Afpl. The comparison is made with the internal pressure pc times the pressure area Ap
The limits ls and lb for the material and pressure are defined in the following formulas:
Image: formula 8.4.12 reinforcement limit in run pipe direction
The formula defines the reinforcement limit ls in run pipe direction as the square root of the equivalent run pipe diameter Deq times the analysis thickness of the run pipe eas
Image: formula 8.4.31 reinforcement limit in the branch pipe direction
The branch pipe limit follow the same approach as the run pipe limit, the square root of the branch pipe equivalent diameter deqb times the thickness of the branch pipe eab.
The tee figures in the EN 134803 Clause 8.3 are as follows:
Image: Figure 8.3.91 Forged tee with machined bore
Image: Figure 8.3.92 Die forged tee
Unfortunately the limits for the pressure area and the material area are not indicated but the same rules apply for the tee as for the other and above illustrated branch opening.
Validation calculation tee type A according EN 102532 B.4.4
Example calculations have been made for the tees as defined in the EN 102532 B.4.4 tee fitting type A and B.5.3 tee fitting type B with RedBag E80 software, further referenced as E80. The exact dimensions have been used and the areas have been verified in a CAD application.
The below image is to scale:
Image: EN 102532 B4.4 example calculation tee type A
The EN 102532 (similar in EN 102534) use a simplified approach to determine the limits ls and lb. The ls and lb cannot always be calculated directly for example when the reinforcement limit is in the crotch. In the crotch area the Deq and eas, for example, vary depending the position of the limit. This is illustrated in below image.
Image: reinforcement limits in the crotch
The above detailed approach, as used in the E80 software, the ls and lb formulas result in the following:
F.8.4.12 
ls = 
77.5394 [mm] 
= (D_eqa * e_asa) ^ 0.5 
= (808.755 * 7.43408) ^ 0.5 

F.8.4.31 
lb = 
55.9856 [mm] 
= (d_eqba * e_aba)^0.5 
= (518.63 * 6.04359) ^ 0.5 
The areas according these limits are as listed below:
Before F.8.4.33 
Ap = 
150160 [mm2] 
= From area helper 
= 150160 

Before F.8.4.33 
Aft = 
653.592 [mm2] 
= From area helper 
= 653.592 
The comparison of the above values with the EN 10253 B.4.4 gives
EN 134803 (E80) 
EN 102532 B4.4 tee 

ls 
77.5394 [mm] 
(ls = 78.49 mm) 
ls’ = 98.88 mm 
lb 
55.9856 [mm] 
(lb = 52.63 mm) 
lb’ = 73.21 mm 
Ap 
150160 [mm2] 
Ap = 163038 mm2 

Aft 
653.592 [mm2] 
Af = 921.7 mm2 
The differences in Ap and Af are significant:
 Ap / Af = 150160 / 653.592 = 229.74  for the E80 iterative approach
 Ap / Af = 163038 / 921.7 = 176.89  according the EN 102532/4 calculation.
The wall thickness of a pipe Tx with the same strength in EN 102532 is defined in B.7 as:
Image: formula EN102532 B.7 for equivalent wall thickness of pipe
 Tx = 813/(2 * (229.74 + 1)) = 1.762 mm  for the E80 iterative approach
 Tx = 813/(2 * (176.89 + 1)) = 2.285 mm  according the EN 102532/4 calculation.
The result of the pressure factor gives similar differences. The formula for the pressure factor X with different ends is as follows:
Image: formula EN102532 B.5 pressure factor
The E80 result for the pressure factor is:
 X = ((1.762 / 813) / min(7.65 / 813; 5.513 / 508)) * ((1  min(7.65 / 813; 5.513 / 508)) / (1  (1.762 / 813))) * 100 = 22.865%
The result for the EN 10253 method is:
 X = ((2.285 / 813) / min(7.65 / 813; 5.513 / 508)) * ((1  min(7.65 / 813; 5.513 / 508)) / (1  (2.285 / 813))) * 100 = 29.672%
The MAWP for the tee with the relevant pipe, with the wall thickness of the run of the tee, gives the actual strength comparison:
 MAWP_tee / MAWP_pipe = 0.467328 / 2.04418 = 0.228614 * 100% = 22.8614%
The summary report of the E80 calculations and the tee CAD drawings are available upon request.
Validation calculation tee type B according EN 102532 B.5.3
The tee in B.5.3 looks like below image, image is to scale:
Image: EN 102532 B5.3 tee type B
The limits for above tee type B are:
F.8.4.12 
ls = 
121.236 [mm] 
= (D_eqa * e_asa) ^ 0.5 
= (794.5 * 18.5) ^ 0.5 

F.8.4.31 
lb = 
82.9188 [mm] 
= (d_eqba * e_aba)^0.5 
= (495.641 * 13.872) ^ 0.5 
The areas according these limits for type B are as listed below:
Before F.8.4.33 
Ap = 
172609 [mm2] 
= From area helper 
= 172609 

Before_F.8.4.33 
Aft = 
2914.93 [mm2] 
= From area helper 
= 2914.93 
The comparison of the above values with the EN 10253 B.5.3 gives
EN 134803 (E80) 
EN 102532 B5.3 tee 

ls 
121.236 [mm] 
(ls = 121.24 mm) 
ls’ = 141.62 mm 
lb 
82.9188 [mm] 
(lb = 81.89 mm) 
lb’ = 102.28 mm 
Ap 
172609 [mm2] 
Ap = 185179 mm2 

Aft 
2914.93 [mm2] 
Af = 3556.5 mm2 
The differences in Ap and Af are:
 Ap / Af = 172609 / 2914.96 = 59.21  for the E80 iterative approach
 Ap / Af = 185179 / 3556.5 = 52.07  according the EN 102532/4 calculation.
The wall thickness for a tee needs to satisfy the EN 102532/4 equation B.47:
Image: formula EN 102532/4 B.47 acceptance criteria for type B tees
The acceptance criteria is:
 max((813  2 * 7.65) / (2 * 7.65); (508  2 * 5.513) / (2 * 5.513)) = 52.137
and the results are:
 59.21 <= 52.137  fail, for the E80 iterative approach
 52.07 <= 52.137 accept, according the EN 102532/4 calculation.
Conclusions
This documents compares the area calculation method for the EN 134803 and the EN 102532/4 standards. The detailed area calculation and CAD validation show significant difference with the EN 10253 2/4 method. These difference can be more than 10% and have impact on the acceptance of tees.
Note: the EN 102532 states in B.5.3, “Under certain circumstances, the calculation may need to be repeated using an improved assumption of the wall thickness.”
Below: detail drawing of EN 102532 B.4.4 type A tee