Flexibility Analysis of Piping (Part-1)

Purpose of Stress Analysis

The designer after careful consideration, prepares most economic layout he can undertake within parameters available to him only to find that further alterations, dictated by Stress Engineer will be required.

It is the stress analyst’s function to

a) Decide on which set amount of of conditions govern the that must be provided in flexibility layout, and

b) To establish, by one method or another, that the required flexibility has been provided in layout.

Under the heading (a), there are number of criteria defining the minimum acceptable flexibility and these fall into two main categories:

i) Maximum allowable stress range in the pipe

ii) The limiting values of forces amd moments which piping is permitted to impose on connected equipment.

The flexibility required in those cases where the piping reaction on connected equipment governs, invariably overrides that required to satisfy the maximum stress range condition.

Under the heading (b), the stress analyst, having decided which criteria applies, has the choice of:

i) Accepting a layout based on past experience,

ii) Analysing a layout by an approximate method, and

iii) Performing comprehensive stress analysis.

Code and Regulation

The stress engineer's first charge is to ensure the compliance with all applicable code regulations, both national and local, apart from satisfying other conditions required. For a particular, contract, the piping specification/design specification will state. which code is to be used for the purpose of design and in case of anomaly, which document is to take precedence. Code sets forth engineering requirements deemed necessary for safe design and construction of pressure piping. While safety is the basic consideration, this factor alone will not necessarily govern the final specification for any piping system. Code is not a design hand book. It does not do away with the need of designer or for competent engineering judgement.

The code requirements for design are stated in terms of basic design principles and formulas. These are supplemented as necessary with specific requirements to assure uniform application of principles and to guide selection and application of piping elements. The code prohibits design and pratices known to be unsafe and contains warnings where caution, but not prohibition, is warranted.

Some codes and standards in present use are:

American National Code for Pressure Piping ANSI B 31.

On global basis this is tne most widely used code and compliance with its requirements will almost certainly be accepted as dem Qnstrating the structural integrity of a piping system. It has its origins in a document issued in 1935 as “An American Tentative Standard Code for Pressure Piping”. In order to keep the code abreast of current developments in the various fields of Engineering and Technology, several revisions and supplements and new editions were published since the first “Americal Standard Code for Pressure piping” ASA - B31.1appeared in 1942. -In order to deal with specia1ised requirements with different categories of-piping, following Codes are presently used.

B 3.1 - Power piping

B 31.3 - Petroleum refinery piping

B 31.4 - Oil transportation piping

B 31.5 - Refigeration piping

B 31.8 - Gas transmission and distribution piping

B 31.9 - Building services piping

B 31.11 - Shirry transportation piping systems

Code Requirements

(A) Design Pressure:

The design pressure of each component in a piping system shall not be less than the pressure at the most severe condition of coincident internal or external pressure and temperature (minimum or maximum), expected during service. The most severe condition is that which results in the greatest required component thickness and the highest component rating.

(B) Design Temperature

The design pressure of each component in a piping system is the temperature at which, under coincident pressure, the greatest thickness or highest component rating is required.

(i) Uninsulated Metallic Components:

- For fluid temperatures below 100F (38 C), the component temperature shall be taken as the fluid temperature.

- For fluid temperature 100 F (38 C) and above, unless a lower average wall temperature is indicated by test or heat transfer calculations, the temperature for uninsulated component shall be no less than following.

(a) Valves, pipe, lapped end welding fittings and other components having wall thickness comparable to that of pipe: 95 % of fluid temperature

(b) Flanges~ (except lap joint) including those on fittings and valves: 90% of fluid temperature

(c) Lap joint flanges :85% of fluid temperature (d)B~lting:80t of fluid temperature.

(ii) Externalli Insulated Piping:

The component design temperature shall be fluid temperature unless calculations, tests or services experience based on measurement supports use of another temperature. When the piping system is heated or cooled by tracing or jacketing, this effect shall be considered in establishing component design temperature.

(iii) Internally Insulated Piping:

The component design temperature shall be based on heat transfer calculations.

Scope of Code Rules

Let us consider various aspects of design of piping system which must be dealt with by any code worthy of such a description and which are of importance to stress engineer in exercise of his duties. Every such piping code will contain recommendations, or mandatory requirements on the following design topics.

(a) The thickness of pipe -to withstand internal pressure

(b) The thickness of pipe to withstand external pressure

(c) Reinforcement requirement of branch connection

(d) Minimum flexibility requirements for external expansion

(e) Allowable stresses for various piping materials

It is the matter of stress analysist demonstrating compliance with the requirement coming under heading of (c), (6) and (e). We shall now consider the above three topics in turn to see how these affect the piping system.

(c) Reinforcement requirement of branch connection

When a pipe which is subjected to an internal pressure has a hole cutin it for branch connecti6ns, a disc of material which would normally be carrying tensile stresses in the _hoop direction is removed and some alternative path must be - provided for loads which were originally carried via: the disc. Most of the code for design of piping system adopts the area replacement or compensation approach whereby with~n a specified distance from the edge of the hole, an additional area of material is provided equal to the area of
material removed.

The replaced material may take a form of a doubler pad or of one of the proprietar y forged fittings (e.g. weldolet etc.) depending on service requirements. The notion is illustrated in the sketches of fig. 1 for the case of simple pipe replacement.

Occasionally, reinforcement has to branch intersections which is to cater for which arise from thermal expansion effects. the stress engineer shall specify the same if by piping specification for pressure purpose.

In various codes, the sketches of fig. 1 appear as single drawing at section AA, showing the cross section of the material to be replaced and boundary within which the replacement material must be located. Where the wall of the pipe is thicker than the minimum required for internal pressure, credit may be taken for excess material when calculating replacement material but always within boundary sets in fig. 2. The fig. 2 is essentially fig. 304.3.3. of

Th, Tb -> Nominal thickness of ‘header and branch

th, tb -> Thickness of pipe required for pressure design

L4 -> Height of reinforcing zone outside of run pipe = 2.5(Th - C)

Or 2.5(Tb - c) + Tr whichever is less

T -> Minimum thickness of reinforcement ring or saddle

Th’ To -> Minimum thickness of header and branch

(Nominal thickness - mill tolerance)

d2 =d1, or (Tb - C)+(Th - C)+ d1,/2 whichever is greater

The required reinforcement area

The reinforcement area A required for a branch connection under internal pressure is

A1 = t d (2 - sin β)

For branch connection under external pressure, area Aa is one and half of the area required for internal pressure.

Available area

The area available for reinforcement

A2 + A3 + A4-≥ A1

All the above area are within reinforcing zone.

In the above expression,

A2 is the area resulting from excess thickness of header pipe

A2 = (2d2 - d1) (Tb - th - c)

A3 is the area resulting from excess thickness of branch pipe.

A3 = 2L4(Tb - tb - c)

Example
A 10" nom. dia. pipe has design condition of 65~F and 400 psig., It is made from seamless material to specification. A53GRB Sch20. The corrosion allowance is 0.03. inch. It has a 4" nom. branch, sch40 of same material. What are suitable dimension of reinforcement to be made from material of equal quality to that of pipe material.

The minimum thickness required for both 10" and 4" header from the basic equation:

The minimum thickness required for both 10" and 4" header from the basic
equation:

The nominal thickness: Th, = 0.219 Tb = 0.207

The thickness in excess = 0.219 - 0.1418 - 0.03

(For header) = 0.0472 inch

The thickness in excess = 0.207 - 0.0593 - 0.03

(For branch) = 0.1177 inch

d1 = 4.5 - 2 (0.207 - 0.03 - 0.0593) = 4.2646 inches

d2 = d1 = 4.2646 inches

L4 is min.of 2.5(Th - c) or 2.5(Tb - c) + tr

i.e. 2.5 ( 0.22) or 2.5 x 0.207 + 0.2 5 (say)

Hence L = 0.55 inch

The required area for replacement = th x d1

A1 = 0.1418 x 4.2646

A1 = 0.6047 inch2

The compensation “area available in header

A2 = (2 d2 - d1) x excess thickness

= 4.2646 x 0.0472

= 0.2012 inch

The compensation area available in branch

A3 = 2 L4 x excess thickness

= 2 x 0.55 x 0.1177 inch

= 0.1294 inch

Total area for compensation area available

A2 + A3 = 0.2012 + 0.1294 inch

= 0.3306 inch

Hench cross section area of pad

A = A1 - (A2 + A3)

= 0.6047 - 0.3306

= 0.2740 inch

Hence the width of ring section of 1/4" thick

Here the cross section of fillet weld is neglected. For more conservative calculation, this area also may be considered.

Minimum Flexibility Requirements

‘A pipe’ is erected at ambient temperature, say between 4ff F - 800 F, in different climates . (700F (210 C), - is normally used~ The same pipe when in operation in a modern petrochemical plant could well be at a temperature in excess’ of 10000 F if it were reactor piping system or it could be down near -200~F if it were associated with an Ethylene refrigeration system.

If pipe is made of carbon steel or low alloy steel, it will expand with a rate of 3/4"-1" for each l000 F temperature rise. This means the pipe running between two equipment 100 ft. apart may well expand by 3 to 4 or more inches as it heats up,- but as ends are not free to-move, this increase in length can only be accommodated by straining the pipe.

This straining produces a stress in pipe. However, when the pipe is next taken out of service, it cools down to ambient temperature, the expansion returns to zero and hence the stress. Every time that the pipe is put into or taken out of service, the same cycle of event occurs. The pipe starts from stress free condition when dold and has stresses imposed which reach a maximum at operating condition and reduce to zero when the pipe is taken out of service.

The type of straining described, if repeated often enough will cause the pipe to crack. The cracking will start at a point or points where the stresses is maximum. This is what is called “fatigue failure”.

The various codes and standards covering the design of piping system puts a limit to maximum stresses which the system can be subjected when put to use. This limit is called the “allowable stress range for expansion” and generally denoted by SA.

1. Internal Pressure/External Pressure Stress:

As you have already learnt, the stresses due to internal pressure is considered safe when the thickness including reinforcement are adequate (using the value SH’ the allowable stress at the operating temperature).

2. Longitudinal Stresses (SL):

The sum of longitudinal stresses due to pressure, weight and other sustained loading shall not exceed the basic allowable stress (SH). Pipe thickness for calculation of SL must be reduced by allowance such as corrosion, erosions, manufacturing tolerance and grove depth. (1.33 times in case of occasional loads such as wind/earth quake)

3. Allowable displacement stress is-given by

SA = f (1. 25 Sc + O. 25 Sf-{)

Sc - Basic allowable stress at min. temp. SH - Basic allowable stress at max. temp.

f - stress range reduction factor for cyclic condition for total number of full temperature cycles over expected life

Stress range reduction factor

When SW-is greater than the calculated value of SL’ the difference between them may be added to the term 0.25 SH in the above equation. In that case, the revised formula becomes;

S = f [ 1.25 (SC + SM) - SL ]

Analysis of Metallic Piping

No formal analysis of adequate flexibility is required for a piping system if;

(a) it duplicates or replaces without significant change, a system with a successful service record,

(b) it can be readly judged adequate by comparison with previously analyzed system,

(c) it is of uniform size, has no more than two point of fixation, no intermediate restrains and falls within limitation set by the equation;

D - outside diameter of pipe in rnm.

Y - resultant total displacement strains in mm to be absorbed by the system

L - developed length of piping system in metre

U - anchor distance, straight line between anchors, metre

The above equation is always conservative but care shall be taken for abnormal condition such as unequal leg, U bends, to large diameter thin wall pipe (where the stress intensification factor is 5 or more) or to condition where the extraneous motions other than the direction connected to anchor point constitutes a large proportion of expansion duty.

User must be aware of the other fact that above equation does not ensure that the terminal reaction will be satisfactory. The weight effect is also not considered in the equation.

In Plane and Out Plane Bending Moment

As per code ANSI B3l.3, code defines ir.-?lane and out-plane bending moments which are shown in figure 2.3.

                               Figure 2.3

After application of the in-plane bending moments Ml, the bend or branch remains in the original plane. But when out-plane bending moment Mo is applied, the bend or branch connection goes out of original plane. The torsional moment about axis of pipe is denoted by Mt.

Flexibility (Guided Cantilever Method)

Suppose we have 2 vessels T-l and T-2, say 50 ft. apart and that we have to run pipe between 2 Nozzles at same elevation. Obviously the most economical way of doing is as shown in figure 2.4.

                       Figure 2.4

Now further suppose that every thing is carbon steel and the vessel T-l has its temperature raised to 350 F. when the valve is opened, there will be an expansion between centres of T-l and T-2 and that will be;

To absorb the above expansion, one of the following tow things may happen.

(1) Pipe will dent the vessel at two nozzles as shown in figure 2.5

(2) The pipe may buckle as shown in figure 2.6

It is possible to calculate the stresses in pi?e and vessel and even if these stresses are within allowable limits, still this will not be cor.sic~red as good engineering practice.

Hence, for the similar connection, the plot has to be laid differently and provided in two sections perpendicular to each other as shown.

With the above configuration for the piping, as point B moves by δ out to B1, it is able to bend the leg BC into new position BIC. The onger leg is easier to bend use to the expansion of BC.

We will calculate the minimum length 1 required forBC to absorb the expansiond. As per the elastic theory (Guided cantiliver method);

Now if the stress range is 16000 psi and considering Youngs modulus of elasticity at ambient temperature value of carbon steel,

So when locating the equipment T-2, be minimum of 16.5 ft. The above method can be applied for the location of guides in L shape configuration.

Continued to Flexibility Analysis of Piping (Part-2)

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