Determination of Collapse Strength Under Biaxial Load Using the Modified Approach
From the previous section it can be concluded that additional axial loads do not exert any immediate influence on the collapse strength. The sum of the tangential stresses induced by external pressure and axial tension is alone decisive in determining collapse behavior and collapse strength. If the collapse strength is to be calculated for a casing specimen subjected to combined stresses then the load limit, decreased by the axial tension (reduced yield strength), must be calculated first.
|
0 |
|
0.2 |
|
0.3 |
|
0.4 |
|
0.5 |
13 3/8” X 0.480” N-80 d0/t = 27.87
9 5/8” x 0.472” P-110 d0/t = 20.39
T x 0.408” N-80
d0/t = 17.16
|
0.6 |
|
<7q <70.2 |
4 1/2" x 0.337′ N-80 do/t = 13.35
Fig. 2.23: Combined stress due to external pressure and tension: comparison between results obtained using the API Bui. 5C3 (1989) formulas and those of Krug and Marx (1980) and Krug (1982). (Courtesy ITE — PU Clausthal.)
From a series of test results, Krug and Marx (1980) proposed that the reduced yield strength, <rre^, due to the axial tension must be first determined to calculate the collapse strength under biaxial load. The reduced yield strength can be obtained using Eq. 2.163 as follows:
where:
(To.2 = reference value of the stress (0.2% strain limit).
The minimal collapse strength for different ranges can then be found using the following equations:
1. For elastic range (Clinedinst. 1977):
= К/ОК/»-
|
90.92 x 104 (do/ty |
2. For plastic transition range:
TOC o "1-5" h z T) — (9 107′
i Pmin fj /^1.929—3.823X 10’4 агЫ v~* ‘
3. For yield range (Barlow, referenced in Goodman. 1914):
290 M ICON
p, = ~djr (1I6M
where the units of crre^ are N/mrn2, and d0 and t are in inches.
In each case, the lowest value of the external pressure corresponds to the collapse resistance under combined stress.
A comparison between the minimal collapse strength under combined stress, as calculated in accordance with the API method and the values obtained using the method, of Krug and Marx (1980). is presented in Fig. 2.23. The sudden changes in slope in each curve are caused by the use of reduced yield strength and correspond to the transition to a different collapse range (refer to the following test data). The advantage offered by the method of calculation utilizing the reduced yield strength is especially evident with increasing d0/t ratio.
|
Table 2.5: Comparison between calculated minimal collapse values under combined stress using the API method and the Krug and Marx (1980) method.
|