PSI - Issue 2_B

Sang-Hyun Kim et al. / Procedia Structural Integrity 2 (2016) 2583–2590 Author name / Structural Integrity Procedia 00 (2016) 000–000

2588

6

Fig. 4 Mesh sensitivity results (a) internal pressure (b) in-plane bending

4. Limit pressure Closed form limit load solution for branch pipe under internal pressure which is obtained by FE analysis results (K-H Lee, Y-J Kim, 2009) are below:

Q h h

            

            



 0.5

2

2

0.25 0.5

1 1 0.79 1 / (2 ) ln 1 / (2 ) t r t r    

h

  

2

  

(8)

P

o

2

min





1 / (2 ) 1 / (2 ) T R T R  

  

  

1 / (2 ) 1 / (2 ) T R T R 

 

  

3

ln



y

ln

 

2

3

Where,

2

0.297

4

0.0505



2       R T

2       R T

r

t

r

  

     

  

  

  

0.4603 0.1525 

1 1.015

0.52 1.127 

Q

 

 



R

T

R

4

2

  

   

1 3

3

1

r       R

r       R



1  

;

1  

;

f

f

k



1

2

3

2 16 

  t T

1



2

2

2

 

  

2         

2      2   R f

t

r

R t

r

r       R

  

  

1 0.145 

1     

;

0.175

1

0.3185

h

k

f

h

k

f





 

2

2

1

1

2

2

r

R T

r

R T



Limit pressure results which obtained by m  tangent method for branch pipes for various r/R and R/T are presented at Fig. 5. Fig. 5 compares limit pressure using m  tangent method with eq. (8), where the m  results are normalized with respect to prediction using eq.(8). m  results are under estimate the limit loads for various geometry. Limit pressure is increasing with increasing R/T. for thin wall branch pipes (R/T=20), limit pressure getting close to eq. (8).