Proving, inspecting and recording

Every buckling calculation in this book rested on assumptions about the real member: that it is the section on the drawing, as straight as assumed, held at its ends as assumed, braced where the drawing says, and loaded where the calculation says. Buckling is unforgiving of those assumptions being wrong, because the effective length is squared and imperfections are amplified. A stand that is calculated correctly but built with a missing strut, a leg bowed by 10 mm or slack bracing is not the stand that was calculated.

This chapter covers how the shop proves HT-8 was built as designed, how it watched the first fill, how a simple test can estimate a member’s buckling load without breaking it, how the stand is inspected in service, and how the whole is recorded. Its error is one that only inspection finds: a strut removed during maintenance and never replaced.

Checking what was built

This is an illustration. Before HT-8 left the shop and again after erection, the shop measured the quantities its calculations depended on.

Figure 1HT-8 erection checks against the design assumptions

Quantity	Design assumption	Measured	Result
Leg section	CHS 76.1 × 3.6, C350	76.1 mm by tape, wall 3.5 to 3.7 mm by ultrasonic gauge; mill certificate C350L0	accepted
Leg bow on each 2,000 mm segment	not more than 2 mm	0.9, 1.2, 1.8 and 2.6 mm on the worst segments of the four legs	one leg over; assessed below
Top frame centred over base	lean not more than 1 in 500, 8 mm	6 mm towards the north-east corner	accepted
Leg centreline under frame centreline	within 5 mm	2 to 4 mm	accepted
Mid-height struts	all four, welded all round	all four present; welds inspected visually	accepted
Diagonals	taut and locked	taut and locked after tensioning (Chapter 6)	accepted

The bowed leg

One leg segment was bowed by 2.6 mm against the 2 mm assumed. Rather than straighten it, the shop’s engineer re-ran the Chapter 5 check with the larger bow added to the 15 mm offset, an equivalent eccentricity of 17.6 mm, on the 2,000 mm segment under the gravity and wind load of 25.4 kN. The eccentric column tool gave a load factor to first yield of 4.02, against 4.30 for the design case and a requirement of 2. The bow was recorded and accepted. The calculation took ten minutes; straightening a leg in a finished frame would have taken a day and risked introducing a worse bow.

That is the purpose of stating the assumptions as numbers. A measured departure can be assessed against them quickly, instead of being argued about.

The lean

The top frame stood 6 mm off centre over 4,000 mm, a lean of 1 in 667. A leaning frame is a sway imperfection: the full gravity load of 78.7 kN, acting through a frame that leans by 6 mm in 4,000 mm, has a horizontal component of 78.7 × 6 ÷ 4,000 = 0.12 kN, which the bracing must resist. That is small beside the wind force of 3.52 kN the bracing was designed for, and the lean was accepted.

Watching the first fill

A staged first fill is a load test that costs nothing but time. The shop filled HT-8 in quarters, stopping at each stage to take readings.

Figure 2HT-8's staged first fill

1. Before fillingBaseline readingsplumb of top frame, string-line bow of each leg segment, diagonals checked by hand
2. 25% full, 1,900 LFirst holdno change in plumb or bow; base plates and grout checked
3. 50% full, 3,800 LSecond holdno change; diagonals still taut
4. 75% full, 5,700 LThird holdno change; tank shell and nozzles inspected for leaks
5. 100% full, 7,603 LFinal hold, 24 hourslean 6 mm, unchanged; bows unchanged within 0.2 mm reading accuracy

The expected changes were small. On a 2,000 mm braced segment, the full-tank leg load of 19.7 kN is 7.4% of the segment’s Euler load of 266.5 kN, so the amplification factor is 1 ÷ (1 − 0.074) = 1.08 and a 2 mm bow should grow by only 0.16 mm, below what a string line can show. If any bow had grown by several millimetres, it would have meant that the leg was behaving as a much longer member than designed, for instance because a strut connection had failed or the bracing was slack, and the fill would have been stopped and the tank drained.

Estimating a buckling load without reaching it

Sometimes it is worth testing a member to see how close to its predicted buckling load it really is, without loading it to failure. The classic method is the Southwell plot, published by R. V. Southwell in 1932. It uses the fact from Chapter 5 that an imperfect member’s extra deflection grows as the load approaches its critical load. Rearranged, that relationship gives a straight line:

Figure 3The Southwell plot

δ ÷ P = δ ÷ P_cr + δ₀ ÷ P_cr

Plot δ ÷ P (vertical) against δ (horizontal): the slope is 1 ÷ P_cr

δ

extra lateral deflection at mid-length, measured, mm

P

applied axial load, kN

P_cr

critical load of the member as built and as held, kN

δ₀

initial imperfection, found from the intercept, mm

This is an illustration. When the shop considered a lighter option for HT-8’s mid-height struts, CHS 33.7 × 2.6, it tested one 2,200 mm length in its press, pinned at both ends through clevises, with a dial gauge at mid-length. The tube’s predicted Euler load was 12.61 kN, with a slenderness of 199. The press was stopped at 7 kN, a little over half the prediction.

Figure 4Southwell test of a CHS 33.7 × 2.6 strut, 2,200 mm, pinned

Load	Extra deflection at mid-length, mm	δ ÷ P, mm/kN
2 kN	0.67	0.335
3 kN	1.12	0.373
4 kN	1.71	0.428
5 kN	2.50	0.500
6 kN	3.60	0.600
7 kN	5.25	0.750

The test gave a critical load of 11.0 kN, 13% below the 12.61 kN prediction, and showed the strut had an initial bow of about 3 mm, more than the 2.2 mm (1 in 1,000) the shop assumes. Measuring the tube afterwards found its wall averaged 2.4 mm instead of 2.6 mm, within the product tolerance, which alone lowers the Euler load to about 11.9 kN; the rest was put down to the clevises not being perfectly free to rotate and to the test rig’s own flexibility. The shop decided to keep the 48.3 × 3.2 struts, and kept the test result as a reminder that predicted buckling loads are upper bounds until proven.

A Southwell test has to be done carefully. The load must be applied slowly and held while readings are taken, the gauge must measure deflection in the plane the member will buckle in, the test must stop well short of the predicted load, and the test rig must be guarded so that a member that buckles unexpectedly cannot hurt anyone.

Inspection in service

The buckling capacity of HT-8 can be lost after commissioning without anything being overloaded. The shop recommended, and the plant adopted, an annual inspection of the stand with these items:

Figure 5Annual inspection of HT-8's stand

• Do: Legs sighted for bends and dentsChapters 3 and 5
• Do: Base plates, bolts and grout checked; corrosion at the leg baseswater pooling at bases thins the wall where it cannot be seen
• Do: Diagonals taut, turnbuckles lockedChapter 6
• Ask: Every member on the drawing present, counted against the drawingstruts, diagonals and portal members
• Do: Nothing new attached to the legs or frameadded loads and offset brackets need a design check
• Do: Vent clear and mesh cleanChapter 9
• Do: Service temperature unchanged since the last design reviewChapter 8

Corrosion at the leg bases

The base of a tank stand leg is where its capacity is most quietly lost. Water runs down the legs, pools on the base plate around the tube and wets the bottom of the wall for days after every rain or washdown. A tube sealed at its base with no drain hole can also fill with condensation and rust from the inside, where nobody can see it.

This is an illustration. Suppose an inspection found HT-8’s leg wall reduced from 3.6 mm to 2.4 mm over the bottom 150 mm. The overall buckling of the leg would hardly change, because a short, thin band at the very end of a 2,000 mm segment has little effect on the segment’s bending stiffness. But the local section would be weaker. Its area would fall from 820 mm² to 556 mm², so the stress under the gravity and wind load would rise from 31.0 to 45.8 MPa, and the wall’s diameter-to-thickness ratio would rise from 21 to 32. Neither figure is alarming yet, but corrosion rarely stops at a uniform 1.2 mm: it pits, and a pit through the wall at the base is a crack starter and a weak point in exactly the place where the leg’s load, offset and any base fixity moments are concentrated.

For that reason the shop specifies HT-8’s legs with sealed tops and small drain holes at the base, the base plates with a slight fall away from the tube, and the inspection measures the wall at the base with an ultrasonic gauge every year. A reading below 3.0 mm triggers a design check; a reading below 2.4 mm, or any through-pitting, triggers repair before the tank is refilled.

The error: a strut that never came back

This is an illustration. Two years after commissioning, a contractor replacing the transfer pump found one of HT-8’s mid-height struts in the way of the new pump’s discharge pipe. The contractor cut the strut out at both ends with a grinder, installed the pump and left, intending to have the strut refitted with a new bracket. The tank was full at the time, and stayed full.

The strut was not refitted. Its absence was not noticed by operators, because the stand looked no different and nothing moved. It was found at the next annual inspection, eleven months later, when the inspector counted the members against the drawing.

With the strut gone, two legs were unbraced at mid-height in one direction. Chapter 5’s exercise had already worked out what that meant: on 4,000 mm instead of 2,000 mm, each of those legs had a buckling factor of 3.39 under the full tank, falling to a load factor to first yield of about 2 with the wind and the 15 mm offset. The stand had been running for eleven months with half of its designed margin gone on two legs, and with the diagonals of that face, which relied on the strut, not acting as designed.

Figure 6One HT-8 leg with and without its mid-height strut

Strut in place, 2,000 mm braced segment10.66×

Strut removed, 4,000 mm3.39×

Shop's required factor2.5×

The strut was refitted the following week with a new connection that cleared the discharge pipe, designed and checked by the shop. The plant made two changes to its permit-to-work system: removing or modifying any structural member now requires a permit signed off by the site’s engineering lead, and the permit cannot be closed until the member is reinstated or a design change approved. The inspector’s member count was added to the checklist above as a permanent item.

The member register

The shop now keeps a short register for every structure it designs with members in compression. It is one page for HT-8.

Figure 7Extract from HT-8's compression member register

Member	Section	Effective length, mm and K	Slenderness	Design load, kN	Factor	Key assumptions
Legs, each segment	CHS 76.1 × 3.6, C350	2,000, K = 1.0	77.9	25.4 with wind	8.24 buckling; 4.30 first yield	struts and diagonals present; offset ≤ 15 mm; bow ≤ 2 mm
Mid-height struts	CHS 48.3 × 3.2, C350	2,200, K = 1.0	137.6	2.0	23.6	welded all round both ends
Diagonals	16 mm round bar	tension only	n/a	2.4	tension check in design note	taut and locked; both of each pair present
Outlet pipe	60.3 × 2.77, 316	2,660, K = 0.7	130.6	thermal	see Chapter 8	flexible connector and anchor fitted
Tank shell	3 mm 316 on 2,206 mm	short shell	D ÷ t = 735	vacuum	not designed for vacuum	vent must be open; no vacuum service

The last column is the important one. Each assumption is something that can be seen, measured or counted on site, so that anyone inspecting the stand can tell whether the calculation still describes it.

What the design note must contain

A buckling check that nobody else can follow cannot be checked, and an unchecked buckling check is a guess. The shop’s design note for HT-8 runs to a few pages, and every compression member’s check in it states:

• the load and where it comes from, including every load case combined, with the reference used for wind;
• the section and its properties, with their source (a calculation, a KEVOS® tool’s output with its inputs, or a maker’s table);
• the effective length in each direction and the reason for each K;
• the method (Euler, Johnson, Rankine–Gordon, secant or a code curve) and why it applies at that slenderness;
• the imperfection and offset assumed, and the fabrication tolerance that will make them true;
• the factor obtained and the factor required;
• what the check does not cover, such as connections, local effects or loads not yet known.

The note is checked by a second person, who repeats the key numbers independently. For a structure that must comply with the Building Code or a standard, such as AS 4100 for its design or AS/NZS 5131 for the fabrication and erection of structural steelwork, the note is the place to show how each requirement is met, and the design must be done or checked by someone competent to sign it.

Bringing it together

The eleven chapters of this book follow one stand and the equipment around it from the first sketch to the annual inspection. The story they tell is consistent. Buckling is decided by stiffness and length, not strength. The effective length, set by how a member is held and braced, matters more than anything else, because it is squared. Real members are crooked and loaded off-centre, and those imperfections grow as the load approaches the critical load. Bracing must be stiff, strong and taut. Machines can push their own members harder than the job needs. Heat can load a member that carries nothing else. Thin shells buckle at pressures far below what their thickness suggests, unless their ends hold them round. Temporary frames are often mechanisms in one direction. And every calculation is only as good as the member that was built and the member that is still there years later.

Exercise: a new pump bracket

This is an illustration. The plant asks to bolt a bracket to one of HT-8’s legs, 1,000 mm above the base plate, to support a 60 kg valve on a 300 mm arm.

1. What vertical load and what moment does the bracket put on the leg?
2. Why does this need a design check even though 0.6 kN is small beside the leg’s 19.7 kN?
3. Which register assumption does it affect?
4. What would you ask the plant to do?

Worked answer.

1. Load 60 × 9.81 = 0.59 kN; moment 0.59 × 0.3 = 0.18 kN·m, applied part-way up the lower 2,000 mm segment.
2. Because the load is offset by 300 mm, twenty times the 15 mm offset the leg was designed for. The moment is amplified like any other bending in a compression member (Chapter 5), it adds to the bending from the existing offset, and the bracket’s bolts or welds may damage the leg’s wall. A small load with a large offset can matter more than a large load on the centreline.
3. Offset ≤ 15 mm and “nothing new attached to the legs”.
4. Support the valve from its own stand or from the pipework, not from the leg. If that is impossible, ask the shop to check the leg with the bracket’s moment added, and to design a clamp that does not need welding or drilling the leg. Either way, record the change in the register.