PSI - Issue 3

7

J.L. González et al. / Procedia Structural Integrity 3 (2017) 48–56 Author name / Structural Integrity Procedia 00 (2017) 000–000

54

FcL = 0 . 146 x 134 ks i = 19 . 6 k s i (7) According to the above result, the strength of the damaged ring is insufficient and therefore reinforcement is needed. To verify if the proposed reinforcement if sufficient, the buckling stress of the orthogonally stiffened ring is calculated as:

2

12(1 ) ecL xL r E F C    

2 ( / ) t b

(8)



 3





4.0 1 0.038

2

(9)

xL C

M 

 



/ r M b R t  

(10)

In the proposed design, R = 142” tr = 1” y b = 74.35”, thus substituting:

 6.24

74.35 / 142" 1" x

(11)

M

 

   3 4.0 1 0.038 6.24 2 

  15.59

(12)

xL C  

2

29000

ksi



73.9ksi

15.59

(1"/ 74.35")

F

x

x

(13)





xeL

2

12(1 0.3 ) 

Since F xeL is greater than F y the plastic buckling stress F cL should be calculated as:

 0.146×73.9ksi 10.8ksi

(14)

cL xeL F F   

To verify if the reinforcement is sufficient, F cL should be compared to fa, for which the compressive load in the damaged ring has to be introduced. From the original design data, the total compressive load P is estimated as 500 metric tons or 1,101,000 pounds; this value includes both dead and live loads. The equation to calculate f a is:

P

(15)

f

 

a

2

s s Rt N A  

Where N s is the number of vertical stringers (12) and A is the cross section area of each stringer (8” x 1” = 8 sq inch). Substituting values:

1101 2 142 lg 1 lg 12 8 lg kps p x p x p  

1.114ksi

(16)

f

 



a

2

The use ratio UR is defined as the applied stress over the buckling stress and its value should be less than 1.0 to have a sufficient reinforcement. Substituting values:

f

1.114 0.103 1.0 10.8 ksi ksi  

a cL

(17)

UR

 

F

Thus, the reinforcement is sufficient. Finally the stiffeners should satisfy the following requirement: