New load combination approach brings API 650 into line with ASCE 7

API Standard 650 specifies loads for petroleum storage tanks, including the open top and cone roof tanks such as those shown here at Plantation Pipe Line's tank farm in Baton Rouge, LA. (Photographer: Robert Ferry, the TGB Partnership; photograph from Plantation Pipe Line Co.)

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Although the new load-combination design methods (discussed in this concluding article) will not typically result in drastic changes to tank components, the new approach allows API 650 to align with the standardized ASCE 7 strength-design methods and changes in the future easier as ASCE and other codes evolve.

Although the ASCE 7 methods for combining loads have been applied to most tank loads, ASCE 7 does not cover certain other specific design issues and failure modes, such as design of the frangible roofs for venting of excess internal pressure, settlement, thermal loads, and design of internal floating roofs.

Safety factors

Load combinations are written by providing factors on loads when certain combinations are considered, for example, 1.2D + 1.6L, used for the dead (D) and live (L) load combination in strength design.

Load combinations cannot be rationally set, however, unless safety factors as well as load factors are considered. As noted in Part 1 last week, factors on strength (safety factors) and factors on loads are simply opposite sides of the same coin.

Therefore, let's first examine 650's safety factors.

Some failures have more serious consequences than others. For example, shell rupture due to stress from stored liquid would spill the tank contents, while wind damaging the tank roof would not.

API 650 accounts for this by setting safety factors commensurate with failure consequences. For example, API 650 3.6.2.1 prescribes a safety factor of 2.5 for shell rupture due to pressure from a full tank of stored liquid, while the API 650 3.11.2 safety factor for wind overturning an empty tank is 1.5.

Safety factors can be used to address tank wind overturning stability. For a full tank, a safety factor of 2.5 is appropriate because overturning would presumably rupture the tank and spill its entire contents.

For liquid levels between empty and full, a safety factor proportionate to the liquid level can be rationalized. For example, the safety factor required for a half-full tank is the average of the safety factors for empty and full tanks, or (1.5 + 2.5)/2 = 2.0 (Table 1).

Hydrotest loads (Ht), because they are infrequent (only at initial construction of the tank and after major repairs) and closely controlled, have lower safety factors than stored product (Table 2).

API 650 allows a one-third increase in allowable stresses (effectively decreasing the safety factor to three quarters of its normal value) for some components (e.g., anchor bolts and foundations) under wind or seismic load. This increase is not applied in all cases involving these loads, however.

It is not applied, for example, in the overturning stability check in Section 3.11.2 or explicitly included in the wind load checks on tank shell and wind girder. The reason for the increase is not given in API 650 and ASCE 7 prohibits it, except in two cases:

1. In allowable stress design, when more than one transient load (i.e., other than dead load) acts at the same time, the sum of the transient loads may be factored by 3/4. This has nearly the same effect as increasing the allowable stress by 1/3 because 1 + 1/3 = 4/3, the reciprocal of 3/4. (It's not exactly the same because stresses from dead loads are not reduced.)

The purpose of increasing the allowable stress is to account for the fact that it's unlikely that the wind and another transient load will both attain their maximum value simultaneously. Therefore, no allowable stress increase should be applied when only wind and dead load act.

2. Where "it can be demonstrated that such an increase is justified by structural behavior caused by rate or duration of load," increases may be used (ASCE 7 Section 2.4.1). This refers to materials with a significant difference in strength for short-term loads vs. long-term loads. This is true for wood (which has about one half the strength for a load applied for 10 years vs. its strength for a short duration load) but not steel used to build tanks.

Other reasons have been offered for an allowable stress increase for wind. One is that "wind is a comparatively rare occurrence." But the wind load has the same probability of occurring as the snow load (that is, once in 50 years). Another is that wind is "intermittent," "transient," or of "short duration." But this effect is accounted for by the gust factor (which is less than 1).

Yet another is that for some structures the direction of the maximum wind may not coincide with the direction in which the building is most vulnerable. For example, a rectangular building is most vulnerable when the wind is perpendicular to one face. This is the directionality factor discussed in the section on wind loads above.

A blanket 1/3 allowable stress increase for wind cannot be justified based on the principles of ASCE 7. A lower safety factor is, however, reasonable when failure would not have serious consequences. If, for example, an empty tank's anchors fail, no contents will be spilled, even though the tank might suffer significant damage, because there is nothing (or very little) in the tank to spill.

An anchor allowable stress of 80% of the yield strength as in E.6.2.3 for seismic loads represents a relatively low safety factor of 1.25. A low safety factor on anchor yielding is appropriate for a seismic load on a tank because, to avoid rupturing the tank, it is preferable to have the anchor yield before the anchor attachment to the shell fails.

Similarly, API 650 Section 3.10.3.4 provides for reduced safety factors (as low as 1.34) for cone-roof column buckling in limited cases (yield strength does not exceed 36 ksi, slenderness between 120 and 180). The reason for the limits is questionable because buckling of any column would probably not cause product release, but reduced safety factors for columns are consistent with the consequence of failure.

Load combinations

Although safety factors can account for the varying consequences of failure, factors on loads in load combinations can address the varying likelihood of loads acting concurrently. Different loads are likely to coincide at some time during the life of the tank. If a tank operates with external pressure, for example, it's likely that wind will blow on the tank while external pressure is acting. It's unlikely, however, that the external pressure and wind loads will be at their design values at the same time.

The new API 650 load combinations are based on the premise that a consistent level of risk is desired for all load combinations that may occur in the life of the structure. For example, the load combinations have been determined so that the risk of failure from a combination of hydrostatic pressure due to stored liquid and internal pressure will be the same as the risk of failure from a combination of wind and external pressure.

No load combination, however severe, will ensure that collapse will never occur because there is always a probability, however small, that the design loads will be exceeded or the strength overestimated. The assumption on which the new API 650 load combinations is based is that the risk of failure for any combination of loads is no more or less than for any other.

API recognized, however, that tanks built to recent API 650 editions have performed satisfactorily. While the intent was to align tank performance based on constant risk for components, therefore, some load combinations were adjusted to account for satisfactory historical performance.

Click here to view Load combinations and calculations in pdf.

This uniform reliability (or risk, to the pessimist) can be accomplished by adapting load combinations from ASCE 7. This has two sets of load combinations, one intended for strength design (in Section 2.3) and one for allowable stress design (in Section 2.4).

The ASCE 7 strength-design load combinations are based on statistical studies, whereas the allowable-stress-design load combinations are estimates without much justification.

Therefore, ASCE's strength-design load combinations (Section 2.3.2; see Section A, first set of load combinations in the accompanying box were used to develop the API load combinations.

A 0.5 factor is allowed by ASCE 7 2.3.2 Note 1 when the live load is less than 100 psf (0.69 psi). The live load for tanks is internal pressure (limited to 2.5 psi in 650 Appendix F) or external pressure (limited to 5.2 psf). Since internal pressures greater than 0.69 psi are rare in API 650 tanks, the 0.5 factor is used.

These combinations are modified for tanks because tanks experience slightly different loads than buildings. The ASCE 7 rain load (R) and self-straining load such as thermal (T) are not applied in API 650.

Also in Section B, the pressure load P replaces the live load L in combinations stressing the tank. Fluid load F is added (where underlined) to the ASCE load combinations in which it is implied but not stated. Load Combinations 6 and 7 from the initial set of combinations (Section A) are overturning stability checks, but ASCE 7 does not address fluid loads in these checks.

Because API 650 Appendix E on seismic loads is currently being revised, the seismic overturning load combination is left for that study to determine. The overturning check for wind is addressed presently. Therefore, Combinations 6 and 7 are not considered further.

The resulting, revised load combinations appear as the second set (Section B).

Stresses in the structure from these revised load combinations are not to exceed the design stresses of the members. The ASCE 7 strength-design load combinations assign higher design stresses (fS) to members than does API 650's allowable-stress design method.

Both methods require the same size members with the same level of safety, however, if the strength-design load factors are appropriately reduced when used with API 650's allowable stress methodology. The reduction factor is determined from the load combination for fluid load F (Combination 1 with dead load DL negligible for this case), as shown in Table 3.

From the API 650 line in Table 3, F = γ API ^L and from the ASCE 7 line, 1.4F = γASCE ^L. Therefore, F /(1.4F) = γAPI ^L /(γASCE ^L), and γAPI = γASCE /1.4.

This means that dividing the ASCE load factors by 1.4 gives the API load combinations shown in Section C in the accompanying box.

Next, internal pressure (Pi) is substituted for P in each of the combinations, and external pressure (Pe) is substituted in each. (See Section D of the accompanying box.)

Discarding load combinations that counteract gives the revised set of load combinations shown in Section E of the accompanying box. The next, Section F, of the box shows the resulting combinations.

Grouping the combinations according to the tank component they affect yields Section G of the box.

Several simplifying adjustments were then made:

• The dead load factor can be rounded up to 1.0 from 0.9 with little effect on design because dead load stresses are generally small (the 20-psf minimum roof live load is much larger than the weight of common roof plate [7.6 psf]).
• The 1.1 factor on pressure, wind, and roof loads and the 0.9 factor on fluid loads can be rounded to 1.0 for simplicity. For wind, this is actually less of an approximation than it appears because ASCE rounded up the 1.6 ASCE load factor on wind from 1.53, and the 18-psf wind pressure is conservative. Also, this makes the new combinations consistent with 650's previous load combinations.
• ASCE 7's seismic load E is formulated for use with strength design and is about 1.5 times the API 650 allowable stress seismic load E_API. So E = 1.5 E_API ; since a 0.7 factor appears in all the terms of the combinations in the accompanying box involving E, they become 0.7(1.5 E_API) = 1.0 E_API in the combinations with seismic load. The dead and fluid load factors can be rounded from 0.9 to 1.0 so that 650 Appendix E need not be changed.

Making these adjustments and eliminating redundant combinations yields the final Section H of the box.

These load combinations are similar to those API.650 previously specified or implied, but they provide combinations that had been unspecified. For example, for seismic loads API 650 E.3.1 specified that the weight of the roof include "a portion of the snow load, if any, specified by the purchaser" but gave no method for determining this portion.

Based on ASCE 7 load-combination methodology, API 650 now specifies that 10% of the snow load be combined with the seismic load to maintain a level of reliability for seismic loads consistent with other loads.

Wind-overturning stability checks

ASCE's load combinations combine the design value of a given load with the arbitrary-point-in-time (APT) value of other loads. For fluid and wind loads there are two cases:

1. Design fluid load (for overturning, the design fluid condition is an empty tank) and APT wind load.

2. Design wind load and APT fluid load.

For Case 1, the APT wind load is determined by dividing ASCE 7 load Combination 3 (which provides the APT wind load while live loads are at their maximum) by 1.4, as was done for the other ASCE load combinations: (1.2D + 0.8W)/1.4 = 0.9D + 0.6W. Therefore, 60% of the wind load is combined with dead load for an empty tank.

For Case 2, the APT fluid load is estimated as a 1/2 full tank because fluid loads range from empty to full. This is reasonable because, although liquid levels rarely reach the full design liquid level, tanks are also rarely empty because environmental regulations discourage landing floating roofs on their legs and it's difficult to empty a tank completely.

The safety factor on overturning of an empty tank remains 1.5 as previously used in API 650, rather than 1/0.6 = 1.67 as given by ASCE 7 in its allowable-stress-design load combinations (Section 2.4.1(7)).

API was reluctant to increase the safety factor and anchoring costs because tank uplift has not historically caused problems. This slightly lower safety factor is offset by API 650 excluding any portion of the weight of the tank bottom in the counteracting dead load. The resulting API 650 wording appears in an accompanying box.

Fig. 1 summarizes API's former and new approaches to wind overturning and also shows the safety factors and the change in roof wind pressures.

The weight of the portion of the liquid contents (if any) that is able to act with the shell against overturning before the bottom yields is given in API 650 E.4.1 for a full tank. The weight of the tank contents that can be used to resist uplift given in the new API Section 3.11 is based on E.4.1 with G = 0.7 and height as 0.5H and is also shown in the previously mentioned box.

Combined gravity loads

The load combinations given previously contain two cases for gravity loads on the roof:

D_L + (L_r or S) + 0.4P_e

D_L + P_e + 0.4(L_r or S)

For ground snow loads of 20 psf or less and a 1-in. water column (w.c.) external pressure (a common case for tanks in the US):

D_L + (L_r or S) + 0.4P_e =

D_L + 20 + 0.4(5.2) = D_L + 22.1 psf

D_L + P_e + 0.4(L_r or S) =

D_L + 5.2 + 0.4(20) = D_L + 13.2 psf

Because the first combination is greater, 22.1 psf is applied to the tank. Previously, API conservatively assumed the maximum roof live load occurred at exactly the same time as the design external pressure, giving a 20 + 5.2 = 25-psf load.

Combinations with pressure

There are five load combinations involving internal or external pressure:

D_L + W + 0.4Pi

D_L + P_i

D_L + W + 0.4P_e

D_L +(L_r or S) + 0.4P_e

D_L + P_e + 0.4(L_r or S)

To derive these load combinations, internal and external pressures were treated as live loads. It's not clear, however, how closely the statistical variation of live loads in buildings matches that of pressures on tanks.

Another approach is to use the arbitrary point in time values for pressures when they are combined with design values of other loads such as wind.

The APT value for pressure is the operating pressure, which is lower than the design pressure by some margin. API 650, however, does not specify this margin.

In order to address the issue, API 650's new load combination appendix suggests increasing the 0.4 factor on pressures if the ratio of operating pressure to design pressure exceeds 0.4.

If the design pressure exceeds 0.69 psi, applying the ASCE load combinations gives a 0.7 load factor on pressure, since ASCE prescribes a higher load factor when the live load exceeds 100 psf (0.69 psi).

API 650 summarizes the resulting load combinations in an appendix, the exact wording of which is shown in a final box.

References

1.American Petroleum Institute, API Standard 650, Welded Steel Tanks for Oil Storage, 10th Edition, Addendum 2, November 2001, Washington.

2.American Society of Civil Engineers, ASCE 7-02, Minimum Design Loads for Buildings and Other Structures, Reston, Va., 2003.

3.American Society of Civil Engineers, ASCE 7-95, Minimum Design Loads for Buildings and Other Structures, Reston, Va., 1996.

4.McGrath, Raymund V., Proceedings of the American Petroleum Institute, Section III—Refining, Vol. 43, pp. 458-69, New York, 1963.