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15.08.2018 Солнце в сеть

Производство оборудования и технологии

Collapse Pressure Calculations According to Krug and Marx (1980)

Krug and Marx (1980), and Krug (1982) conducted 160 collapse pressure tests on casings with d0/t ratios between 10 and 40 and L/d0 ratios between 2 and 12. In the evaluation they took only the collapse strength in the elasto-plastic transition range into account and made the following observations:

1. Calculated values of average collapse strength in accordance with API pro­cedures are too high. In part this ran be attributed to the use of short specimens. Overall, the results exhibit favorable and uniform scattering in which dependence on steel grade is always reflected.

Fig. 2.15: Collapse strength of grade C-95 steel. Comparison between API and Clinedinst formulas. (After Krug. 1982: courtesy of 1ТЕ-ТГ Clausthal.)

2. At low values of collapse pressure (up to about 15.000 psi), the average collapse strength according to Clinedinst (1977) exhibits good agreement with the test results. At high values of collapse pressure, the calculation for high-strength steel once again yields values which are too high — irrespective of d0jt ratio.

3. For calculation of average collapse values, the API method clearly provides better results. In comparison to the API method, however, the analytical method of Clinedinst (1977) offers the advantage that the calculated value of collapse strength is dependent only on yield strength besides d0/t ratio: this requires less elaborate calculation.

To simplify calculations Krug and Marx (1980) generalized Clinedinst’s formula by introducing the parameters a. b and c. the values of which are obtained ex­perimentally from collapse tests:

pp = a (do/0b~CCT0 2 (2.147)

They then applied a statistical approach to obtain the equation for average col­lapse pressure for the elastoplastic range which provides the optimum agreement with the test results.

where the units of (T0.2 are N/mm2.




1000 lbs/in’

с <552






• 758-862


* 862-965


* >965


* •*•





200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

Pcoic. bar

Fig. 2.16: Comparison between measured collapse pressure and average collapse strength according to pPav. (After Krug and Marx. 1980: courtesy of ITE-TU Clausthal.)

A comparison between the measured values of the collapse pressure and those calculated for the collapse strength using Eq. 2.148 is presented in Fig. 2.16. For the purpose of specifying a minimum pressure for collapse strength. pPm, n. defined as 85% of the average collapse strength, pPal. in psi, is introduced:


9.0924 x 105

Ppmm —

(d0/t) 1-929-3.823X10-4 <70.2

where the units of op.2 are N/mm2.

In Figs. 2.17 and 2.18, a comparison is made between the collapse strength pPav or pPm,„ and the values calculated using the API and Clinedinst (1977) methods for steel grade C-95.

Fig. 2.17: Comparison of the average collapse strength determined in the test Ppav- with that calculated by the methods of API (P2) and Clinedinst (P3). (After Krug and Marx. 1980; courtesy of ITE-Tl’ Clausthal.)

The formulas are as follows (note that it is the smaller value of Pi that is decisive):

cfd Eq. 2.138 cf Eq. 2.144 cf Eq. 2.139 cf Eq. 2.140 cf Eq. 2.145

Pi =


Рз =



— В





P4 =

(d0/f )2.096 — 4.976×10—<<70 2

‘ A




11.230 x 105

(d0/f)2’°96-4.976x!0-<j0 2

d0/t 14.434 x 105

— В


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