Recommendations on the design of steel linings for penstocks By S. Jacobsen Consulting Engineer*
T
he recent design and construction of several highhead hydro powerplants with large steel linings has shown that some designers of such steel linings are unaware of dangers which can be associated with application of the well known Amstutz formulae. These problems arc discussed, and design recommendations afC put forward.
Since 1957, when the author began working on hydropower plants, there have been several buckling accidents in Switzerland, some because of false buckling calculations, others caused by drainage systems not functioning. Fortunately, nobody was killed or injured, but repair works and loss in energy production demonstrated to owners that it does not pay to over~economize on the design of steel linings. Correct design is always the most important element. Steel-lined tunnels are periodically dewatered for inspec~ °Rebberf,!,SIrasse 50A, 5430 WeUinjl;ell, Switzerland.
44
tion purposes, and the safe design of the linings may be critical for the safety of the inspection personneL This article follows on from several previous papers by the author published in this journal (see Waler Power & Dam Construction January and December 1974, December 1977, and May 1983), To demonstrate the design problems which can arise, the example will be taken of one of the largest penstocks cver built. This penstock has a stcel lining with a diameter of 6.8 m. Just downstream of the lower bend in the horizontal section, the internal design head is specified as 448 m water column including water hammer and considering 20 per cent rock contribution. The authors of the specification have assumed a maximum external pressure equal to 230 m water column at this point. This example will now be worked through to compare the Amstutz and Jacobsen methods for calculation of the pen~ stock design to; withstand the external buckling pressure.
Water Power & Dam Construction April 1990
The most important data for this example are 0.5 x yield stress or • allowable stress for internal pressure: 0.4 x tensile strength (whichever is smaller); • welding efficiency for field wclding:O.9; 2; • safety factor against buckling: • rock contribution: 0 or 20 per cent; • initial gap between liner and 0.001 x radius; and, concrete: • allowance for corrosion: I mm. The supplier of the penstock will normally select a high strength quenched and tempered steel to keep the plate thickness as small as possible. In this case, the yield stress of the steel would be 700 N/mm 2 (MPa). For a penstock without stiffeners, a lining thickness of 68 mm would be required. However, such a plate thickness would cause problems and high costs in its manufacture, transportation and erection. As a result, the supplier will look for a solution to reduce the nominal wall thickness. As a 49 mm thickness would be sufficient to meet the internal pressure in this example, the designer will probably select this thickness for the liner and then provide stiffeners welded to the outside of the liner to sustain the external pressure. In this case the stiffener would be flat in profile (the most economical cross section, providing a ring with a sufficient moment of inertia); its dimensions would be 250 mm wide and 25 mm thick, and rings would be spaced 3000 mm apart. If the suppliers of the penstock were free to choose the method of calculation for the external buckling pressure, they would probably use the Amstutz theory (Water Power November 1970). This is because this theory has been used extensively in the past, and, perhaps more important for the contractor, the Amstutz method tends to give lighter stiffener rings than the alternative theory propounded by the author. To calculate the critical external load of a ring-stiffened pipe, Amstutz recommends an effective width of the ring girder equal to 30 t (where t is the thickness of the lining). I~ the cl'tse of this example, the properties of the ring section would be: effective width ~ (49-1) X 30 cross section (F) =: 1440 x 48 + 250 x 25 radius of ring moment of inertia of ring distance from neutral axis to outside ring
1440 mm 75370 mm' 3437.36 mm 173073117 mm' =
261.644 mm
We can now calculate the Amstutz figures as shown below:
The critical Amstutz buckling stress (aN) is 320.02 N/mm 2 ' and the critical external pressure =: 4.647 N/mm 2• The actual external pressure is 230 m water column (:::::: 2.255 N/mm 2) and thus the safety factor is 4.64712.225 46
~
2.06
The effective width "'" 30 { is more or less selected 'l! random. " It is common to use the formula 1.556 x \i"r~ t (where r is the pipe radius) for the effective width in curved beam~ wi.th wi~e flanges (as used in the Jacobsen formulae), App'. lyIng thIS more correct effective width (631 mm for [his example), .the critical external pressure, according to Arnstutz, YIelds 6.465 N/mm 2 and the corresponding facer of safety is 6.46512.255 "'" 2.87
However, if one calculates the same with the Jacobsep method (see Internalionai Waler Power & Dam Constr·uc~ lion June 1983) we arrive at a safety factor of onlv 1A. What is the reason for the lack of agreement between these results? Arnstutz loads the stiffener ring only within the effective width. In the first calculation, the loading width was 30 t :c1440 mm, but in the second calculation it \vas only 631 mm. Therefore, the Amstutz values are independent ~f the dis· tance of the rings. Thus, the critical Amstutz pressure is the same for narrow or widely spaced ring stiffeners. In the Jacobsen formulae, the stiffener ring must sustain the total external load acting on the lining wall. Amstutz knew about this shortcoming in his philosophy, The present author wrote the English version of his theorv (Wafer Power, November 1970) and discussed it with him" but Amstutz died shortly after this, and so did not have a~ opportunity to correct his article. At the end of this article an algorithm of the author's buckling theory is given (Wafer Power & Dam Construction, June !983) written in the Pascal programming langu~ge. ThiS program can be run on a PC using a Pascal compl1er*. The program gives the critical external loads for buckling of the stiffener rings and for buckling of the shell between the rings. Also, the shear force in the stiffener rinil is computed for the welding seam design. If the dimension~ of the rings are set to zero, the program will calculate an unstiffened lining. The stiffener may be a flat profile (like the ab~ve example) or may have an additional flange (T -profde). Sometimes it is economical to use a channel profile stiffener with the two tips welded to the pipe. The program was written with the dimensions Nand mm. It will, of course, also run with other dimensions, but then all input figures, and the E¥modulus must be chanced accordingly. , ( : 0
Recommendations for the designer • As far as the author is aware, no steel lining has been damaged as a result of internal pressure. If steel must be saved, it should be remembered that external pressure is far more dangerous than internal pressure. • Dr~inage systems should not be trusted. Especially if there IS a steady flow through the system, it may be unsafe after years of operation, Depending on how much water is entering the system and how much is leaving, actual external pressure is still unknown. If there is already a draina?e system, it should be closed during norma! operatIOn (when the penstock is under pressure). • The welding efficiency factor should be forgotten. This antiquated provision may increase the wall thicknesses to
>2 Water Power & Dam Construction April 1990
dimensions where welding aClUally becomes problematic • Pcnstock welding must be of excellent qua!it y in any case. • Welding:; should also be checked during production and ereclion, not only by non-deSlructive tesling (run off plates with Charpy notch specimens should be used), • Norma! Welding Procedure Tests and Welder Qualification TcSl~ are usually of little value. A responsible DCnS[ock sUDPlicr will in any case carry out procedure tests to ensure that the production of the pipe cans may start and proceed according to the construction programme. • AU welders and welding operators assigned to work should not only have passed a qualification test of. for example, ASME Section IX. More important is that they should have passed a test which simulates production welding with respect to material and thickness of plate and elecll"odcs, groove preparation and welding procedure. The
welding operators should pass a corresponding qualification test, operating the same type of welding machine which is going to be used during production. • Testing of the welding coupons should comprise nondestructive examination, but more imponan: are destructive tests: impacl tests (Charpy V-notch), bending tests, hardness tests, tensile tests and so on. • An allowance in thickness of I mm or more for corrosion resistance is not necessary with today's painting systems. They are good for 10-20 years' operation if abrasion is not too severe. The responsible owners will have the corrosion protection system repaired before corrosion of the steel surface begins. • Contact grouting needs time and is costly_ Especially cleaning works and dosing of the grouting holes at the end arc tedious. It is recommended to limit contact grouting to a minimum, mainly in the horizonial sections.
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Water Power & Dam Construction April 1990
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47
