ACKNOWLEDGEMENT

The success of the 22nd Annual Meeting of the International Institute of Ammonia Refrigeration is due to the quality of the technical papers in this volume and the labor of their authors. lIAR expresses its deep appreciation to the authors, reviewers, and editors for their contributions to the ammonia refrigeration industry.

Board of Directors, International Institute of Ammonia Refrigeration

ABOUT THIS VOLUME

lIAR Technical Papers are subjected to rigorous technical peer review.

The views expressed in the papers in this volume are those of the authors, not the International Institute of Ammonia Refrigeration. They are not official positions of the Institute and are not officially endorsed.

EDITORS Christopher P. Combs, Project Coordmator

M. Kent Anderson, President

International Institute of Ammonia Refrigeration 11 10 North Glebe Road

Suite 250 Arlington, VA 22201

+1-703-3 12-4200 (voice)

www .iiar.org +1-703-312-0065 (fax)

2000 ILAR Ammonia Refrigeration Conference Nashville, TN

Technical Paper #6

Pipe Stress or Flexibility Analysis in Refrigeration Piping

Thomas Riley Fisher Refrigeration

South Bend, IN

2000 IIAR Ammonia Refrigeration Conference Nashville, TN

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Introduction

Refrigeration piping design is a function of 1) the refrigerant material properties; 2) the fluid

flow characteristics within the piping, as defined using Bernoulli’s theorem for the total

energy balance; 3) the mechanical characteristics of the pipe, as defined using mechanics of

materials; and, 4) the installed system costs. The third area is discussed in this paper. Within

mechanics of materials, flexibility analysis is used to predict the piping system behavior

under specified loading conditions.

ASME B3 1.5, Pressure Piping Code for Refrigeration Piping (“The Code”) is the governing

standard for the mechanical design of refrigeration piping systems. It states within ASME

B3 1.5 in paragraph 5 19.4.2 through 5 19.4.4 that flexibility analysis shall be performed on all

refrigeration piping. This includes formal calculations where reasonable doubt exists as to

the adequate flexibility of a system. The degree of accuracy in the analysis and calculations

used need only be sufficient to give a conservative answer. Further, in calculating the

flexibility of a piping system, all points between anchor points shall be treated as a whole.

Allowable Stress Design is the method of analysis utilized. It is a method of proportioning

members, such that the elastically-computed stresses produced in the members by nominal

loads do not exceed specified allowable stresses. This analysis shall include any support

friction and linear and angular movements of the anchors. Finally, accompanying any

flexibility calculation, “there shall be an adequate statement of the method and any

simplifying assumptions used” (paragraph 5 19.4.3).

As stated in ASME B31.5, adequate flexibility may generally assumed to be available,

allowing for calculation omissions, in systems that:

1. Are duplicates of successfully operating installations or replacements of systems with a satisfactory service record.

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2. Can be readily judged adequate by comparison with previously analyzed systems.

3. Are of uniform size, have no more than two points of fixation (anchors) and no intermediate restraints, are designed for essentially non-cyclic service, and satisfy the following approximate criterion:

30 * S A ( L - U)’ Y <

D * E ,

where:

Y = resultant of movements absorbed by the pipe, in.

SA = allowable stress range, (see stress below).

L = length of pipe between anchors, ft.

U = length of a straight line joining the anchors, ft.

D = nominal pipe size, in.

E, = modulus of elasticity of the piping material in the cold (“out of service”)

Condition, psi.

Using Figure 4A as an example:

L = 20 feet + 14 feet + 18 feet + 8 feet = 60 feet

U = J ( 2 0 - 8 ) 2 t 1 4 2 + 1 8 2 = 25.8 feet

This strong set of statements implies that a significant amount of work must be implemented

on a continuing basis. The key is exception “2”. I pose that there is a tool in the designer’s

kit to mitigate the dilemma: it is the “design book”. The piping designer is reminded in

ASh4E B3 1.5 that the Code is not a design handbook and that the Code does not do away

with the need for the designer or competent engineering judgment. The Code is a guide used

to aid in the creation of a piping design handbook. It is my experience that design books that

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are written with the help of the Code are not as helpful as they should be. In general, the

information found in a contractor’s design book is better than the Code, in that this

information is a result of a contractor having learned from his mistakes. Other elements of a

design book come from industry piping practices and specifications. Of course, the whole

purpose of the design book is to engineer-out the mistakes and to minimize the time to

complete a design. This paper is not for the purpose of giving you a design book. In fact,

there is no such thing as a single design book. A design book is a function of the location of

the system, the temperature, the service and the environment of the application, as well as the

life and cost of the system.

Stress

Stress is broken down into normal stress (Sigma), compressive and tensile and tangential

stress (Tau), and shear. Within a pipe for cylindncal coordinates there are three stress axes

plus shear or torsional stress. The three axis stresses are lateral or .axial stress, radial stress

and circumferential, or Hoop, stress. With each stress there are two associated shears, one

with each other cardinal axis. ASME B31.5 utilizes the maximum principal planes of stress

theory for failure of the piping components. The coordinate axis is rotated to obtain the

maximum stress (Sigma) value and the minimum shear (Tau) value. The theory states that

yielding occurs when the magnitude of any of the three mutually perpendicular principal

stresses exceeds the yield strength of the material, reduced by a suitable safety factor. The

Code breaks stresses into three general categories: Primary, Secondary, and Peak.

Primary Stress

Primary Stress is defined as the plastic deformation and bursting that results from mechanical

loadings. The primary stress is not self-limiting. It shall result in failure when the yield

strength is exceeded across the entire cross-section unless the load is reduced or removed.

The primary stresses are further broken down into general primary membrane stress, local

primary membrane stress and primary bending stress. Failure under general primary

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membrane stress occurs when the stress equals the yield stress of the material. In bending,

the entire cross-section does not see equal amounts of stress; a shape factor is applied to the

yielding moment to establish when failure shall occur. Failure under moment loading occurs

when the moment equals the yield moment multiplied by the shape factor. The combination

of the general primary membrane stress and the bending loading results in reduced allowable

yield points for both stress and bending. The allowable stress value is established in the

Code at the lower value of stress obtained from using 25% of the specified tensile strength,

or 62.5% of the specified yield strength for 0.2% offset (minimum value for temperatures of

lO0T (37.8"C), and less or average value for temperatures above 100°F (37.8"C) but below

400°F (204.4OC). A portion of Table 502.3.1 from the 1992 ASME B3 1.5 is shown in Table

1. In shear, the allowed stress is 0.8 that allowed in stress. For the purposes of this paper,

only ammonia system piping is considered. Ammonia refrigerant is a group B2 (formerly

group 2) refrigerant. Only refrigerants in groups 3 and 4 require radiographic testing or

reductions in allowable stress values for less than 100% radiographic testing.

As an example, for seamless carbon steel pipe ASTM A 53, Grade B:

Allowable Stress 15 ksi

Allowable Stress 2 1.9 ksi

- Min. Tensile Strength * 0.25 -

Mm. Yield Strength * 0.625 -

- 60 ksi * 0.25 - Or

- - 35 ksi * 0.625 -

The former is smaller; thus, the allowable stress used is 15ksi.

Further, for Electric Resistance Weld (ERW) steel pipe ASTM A 53, Grade B:

Allowable stress seamless pipe (*) Longitudinal Joint Factor (E) = allowable stress

12.8 ksi - 15 ksi * 0.85 -

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The sum of the longitudinal stresses (axial) or the hoop stress (circumferential) may not

exceed the operating temperature allowable stress. The excess of the allowable operating

stress above the actual stress may be added to the allowed bending stress. The bending stress

is based upon “self-springing” and utilizes a stress range for its allowable stress.

Self-springing is the reduction in stress over time caused by local yielding or creep. The

allowable bending stress range, “SA” is:

SA = f(1.25 * S, + 0.25 * S,>

where:

S , = “minimum (cold) normal temperature”, the normal non-operating

condition - (i.e., ambient idle conditions)

“maximum (hot) normal conditions”, the normal operating conditions

(i.e.¶ for suction lines it is the cold temperature value and for high stage

discharge and hot gas lines, it is the hot temperature value)

the stress range reduction factor for cyclic conditions (See Figure 1)

reproducing Figure 502.3.2 Stress Range Reduction Factors, from the

Code. The “f” factor does not apply to the longitudinal or hoop stresses

because they operate within the elastic range without fatigue.

Sh =

f =

The local primary stresses can exceed the yield strength in a portion of the cross section

without failing. Under this state, they will behave as secondary stresses and redistribute

themselves as the local pipe wall distortion occurs.

Secondary Stress

Secondary Stress is defined as the localized plastic deformation developed by forced

displacements. The piping system must conform to imposed strains rather than applied

forces to satisfy system distortion. The secondary stress tends to be self-limiting. The Code

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sets the allowed stress level in terms of a stress range. The allowable bending stress is the

same as the Primary Stress bending stress.

Peak Stress

Peak Stress allows no deformations resulting in high stress levels. It is the highest stress in a

local area. Examples of this are thermal gradients, pipe fittings, and welds. Stress levels

above the elastic region result in pipe-systedlow-cycle fatigue failure. Failure generally

occurs in less than 100,000 cycles. The allowable stress is one half the peak stress. By

choosing a value of cycles, with "N" larger than that expected, a conservative, stress-range

reduction factor is obtained.

The Code covers temperatures down to -20°F. Below this temperature brittle fracture is

considered to occur in some materials. Between -20°F and -150°F impact testing of ferrous

materials is not needed if the allowable stress is reduced to 40% of the 100°F allowable

stress, or if austenitic stainless steels Type 304,304L, or 3 16 are used. Impact tested ferrous

materials such as A333 Grade 6 (to -5O"F);Grade 7 (to -100°F) or Grade 3 (to -150°F) could

be used per ASME B31.5 (see Chapter JII, m523.2.2 ( f ) (4)).

Loads

The refrigeration piping system is affected by thermal expansion and contraction, seismic

activity, and wind and fatigue, as well as by dead and live loads. Loads are divided into

sustained loads, occasional loads and expansion loads.

Sustained Loads are internal pressure, external pressure and weight (dead & live):

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Internal Pressure

The most severe condition of coincident pressure and temperature shall be used. In addition,

the pipe thickness in this calculation is reduced by the corrosion and erosion allowance and,

if applicable, by the thread depth. Longitudinal seams are combined into the allowable stress

(Hoop Stress).

2*s, * t P = Do - (0.8 * t )

ASME B31.5,¶504.1.2 Eq. (3)

where:

P = Internal pressure, psig.

SA = Allowable stress including longitudinal seam factor and corrected for

temperature, psi.

t = Manufacturer’s minimum wall thickness of pipe less mechanical thread,

corrosion and erosion allowances, inches. The manufacturer’s minimum wall

thickness is 0.875 of the nominal wall thickness.

Do = Manufacturer’s maximum outside diameter of pipe, in. For pipes larger than

11/2 inch OD, nominal OD is increased by 1.0%. Below 2 inch OD, 1/64 inch is

added.

0.8 = 2 * y. Where “y” is 0.4 and DJt > 6.0.

The force T“ is exerted across the entire thickness “t”.

out-of-round allowance is used to reduce the allowable stress.

For internal pressure, no

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Table 2 has zero corrosion and erosion allowance and the Schedule 80 pipe through 12 inch

is threaded. Table 3 has 4 mils per year corrosion allowance over a twenty-year life and no

erosion allowance. Threaded pipe is the same as Table 2. Table 4 uses schedule 80 pipe

similar to Table 3 except that the pipe is without threads. ASME B3 1.5 (¶505.1.1) only goes

up to 6-inch nominal pipe size. It appears that the Schedule 80 pipe is assumed to be

threaded. Tables 2 & 3 show that in some small and larger pipe sizes a material change,

fabrication method, or a thicker walled pipe needs to be selected (the shaded values).

External Pressure

Internal pressure is assumed to be zero psia. The external pressure is atmospheric, or 14.7

psia. Compressive collapse is graphically evaluated using computed values:

L/D,andD,/ t

Having found factor “B”, the allowable sustainable exterior pressure is computed:

where:

L = Do =

t =

Pa =

B =

length of pipe segment, in.

The manufacturer’s maximum outside diameter of pipe, in. For pipes

larger than 1.5 in. OD, nominal OD is increased by 1.0%. Below 2 in.

OD, 1/64 inch is added.

Manufacturer’s minimum wall thickness of pipe, less mechanical thread,

corrosion and erosion allowances, in. The manufacturer’s minimum wall

thickness is 0.875 of the nominal wall thickness.

Allowable external working pressure, psi.

Factor derived from ASME B31.5. (FIG. 504.1.1-A or FIG.504.1.1-B.)

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No form allowance for out-of-round piping has been included.

Table 5 shows tabulated pressures for similar pipes to those shown in Tables 2 & 3. The

effect of low temperature is unknown and not covered in the Code. Only M-inch schedule

80, %-inch schedule 80, and 30-inch standard weight pipe A106 seems to be getting into a

problem area for temperatures above -20°F. This Table would cover vacuum drying of the

piping system at ambient temperature. It may not cover the noma1 operation of a deep

vacuum, low temperature suction line.

Weight

Weight is divided into dead loads and live loads. Further there are other classes of weight

that are occasional and are treated under that heading. The weight loads described here are

those found in the normal operation of the system. Dead loads include the pipe and fittings

themselves, insulation, valves, weight of refrigerant in liquid and recirculation suction lines,

and snow or ice loads within the refrigerated space. This last item needs to be designed into

the piping system, if the facility has not designed out ice buildup within the refrigerated

space through air management and defrost control. All of these exert downward forces and

they are also used to evaluate seismic forces. Table 6 gives some comparisons of the

magnitudes of these weights.

Occasional and Expansion Loads

Occasional loads are weight (dead and live loads), wind, seismic, relief valve discharge and

hydraulic shock.

Weight

A dead load is the snow or ice load on exterior pipe. This can be found in ASCE 7-95,

Minimum Design Loads for Buildings and Other Structures (formerly ANSI A58.1). We are

directed to the building codes and we must consider the horizontal projection of our pipe

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(including the pipe insulation), which is treated as a structure with a curved roof. As an

example, the Minnesota Building Code, Chapter 1365, requires a 30 to 40 lb/ft2 base snow

load, depending on where you are. This is reduced 20% for pitches between 1:8 and 3:8, and

reduced 40% for pitches greater than 3:8. The minimum snow load is 20 lb/ft2. Table 6

includes snow load weights for a 301b/ft2 base snow load area. This example reduces down

into the following equation:

+ (20 * D0i * 0.649) WS = [ 30 lb/ft2 * (Doi - * ( 0.124 + ( 0.8 * 0.2271 ) ) ) 1 - 12 inchedfoot

= 1.844 * D0i lbs/linear ft

where:

D,i is diameter of the outside of the insulation in inches.

A second dead load in the Minnesota Building Code is an ice load, as described in

1300.5700, Radial Ice on Open Frame Towers. The ice and snow loads do not need to be

considered at the same time, and only the larger need be determined.

A live load is liquid refrigerant (e.g., flooding of’vapor lines) in piping other than the liquid

lines.

Wind

The effect of wind loading needs to be taken into account for exposed pipe. ASCE 7-95,

Mnimum Design Loads for Buildings and Other Structures, 6 covers this area. Again, we

have a load in which the calculation procedure is determined from the building codes. The

Minnesota Building Code chapter 1305.14, eliminates exposure “D” in the UBC, and chapter

1305.16 defines the minimum basic wind speed as 80 mph. The requirements in the 1997

UBC are used below as an example:

P =C, * Cq* qs * IW * Doi / 12 in/ft

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where:

P = C, =

c, =

qs =

I w =

Design wind pressure, lbs/ft.

Combined height, exposure and gust factor coefficient. For 40 feet above

ground level and open flat terrain, C, = 1.3 1.

Pressure coefficient, cylindrical members within tower accessories. For 2

inches (Doi) and less C, = 1.0. For over 2 inches diameter (Do,),

C, = 0.8.

Wind stagnation pressure, lbs/ft2. It is a function of the Basic wind speed

shown in map Figure 2. The basic wind speed varies from 70 to 110 mph.

At 80 mph qs = 16.4 lbs/ft2.

Occupancy category. Occupancy can be categorized as either “Special” or

“Hazardous” with Iw equal to 1.0 or 1.15 respectively. Without delving

further into the building code to determine how “toxic” is defined, and

desiring not to incur wind load failure, I arbitrarily choose Iw = 1.15.

P = 1.31 * 0.8 x 16.4lbs/ft2 * 1.15 * Doj / 12in/ft = 1.65 * Doi lbs/ linear foot

where:

DOi = diameter of the outside of the insulation in inches.

Table 6 includes wind load values for different pipe sizes, with and without 4” of insulation.

The wind force is exerted perpendlcular to weight.

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Seismic

The effect of earthquakes in regions where they are a factor shall be designed for a horizontal

force in conformity with good engineering practice. This can be found in ASCE 7-95,

Minimum Design Loads for Buildings and Other Structures. Again we are directed to the

Building Codes. As an example, the UBC, Chapter 1630 gives:

E = (p* Eh) + Ev

where:

E =

p = ReliabilityRedundancy factor, given as 1 .O.

Eh = Earthquake load due to design lateral force, “Fp”.

Ev = The load effect resulting from the vertical component of the earthquake

Entire earthquake load on an element of the system.

ground motion and taken as zero for Allowed Stress Design.

UBC, Chapter 1632, gives

Eh =Fp =4.0* C a * Ip* Wp

where:

Fp = The lateral force on nonstructural components

Ca = Seismic coefficient as a function of seismic zone, soil profile, and a near

source factor. There are five seismic zones, six if you count zero ranging

from zero to four. Figure 3 shows the seismic zone map of the United

States. Soil profiles range from hard rock to soft soil. When no soil

profile is available, a stiff soil (Sd) is assumed. The near source factor

ranges from low to high intensity and zero to 10 km in distance from the

source. For a moderate earthquake 5 km from the source, a factor of 1 .O is

obtained.

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Ip = Importance factor is 1.0 for Special, and 1.5 for Hazardous, as found

earlier. Arbitrarily, I choose Ip = 1.5.

Wp = Weight of an element or component.

Fp,zl = 4.0 * 0.12 * 1.5 * Wp = 0.72 * Wp

Fp,z4 = 4.0 * 0.44 * 1.0 * 1.5 * Wp = 2.64 * Wp

Table 6 includes seismic load values for different pipe sizes for zone 1 and zone 4. The seismic force is exerted perpendicular to weight.

Relief Valve Discharge

The discharge force from a relief valve is a function of the mass flow rate, the velocity, the

static gauge pressure at discharge and the discharge flow area. These resolve down to an

applied force and moment, as well as the mass of the valve assembly.

Hydraulic Shock

The result of transient accelerations of liquid slugs in the piping system.

Load Combinations Using Allowable Stress Design

ASCE 7-95, Minimum Design Loads for Buildings and Other Structures, 2.4 lists the

following combinations of loads (cases) that shall be considered:

1. Dead 2. Dead + Live + Thermalexpansion + Snow 3. Dead + (Wind or Seismic ) 4. Dead +Live + Snow + (Wind or Seismic) 5. Dead +Live + Thermal expansion + Snow + ( Wind or Seismic )

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Case 1 is the constructed refrigeration system out of service. Case 3 is the out of service

system experiencing an upset (wind or seismic). Case 2 is the refrigeration system under

normal operation and Cases 4 and 5, the operating system under an upset. The load types

have been discussed earlier. ASCE 7-95 further allows a 25% reduction of all loads, other

than dead loads, when there are three or more loads combined and the allowable stress has

not been increased to account for these combinations. ASME B31.5 approaches the problem

from a different direction. For operation of the system in Cases 2, 3, and 4, the sum of the

longitudinal stresses can be as high as 1.33 times the allowable stress. Peak stress periods

allow an increase of 15% above allowable stress for periods of up to 10% of the operating

time. An increase of 20% above allowable stress is allowed for periods up to 1% of the

operating period.

Calculation of Pipe Stress

Radial stresses are the result of thick wall pipe and rigidly connecting different schedule pipe

together without beveling and tapering the ends. Remember, the Code prohibition on the use

of pipe with an outside diameter to thickness ratio equal to or less than 4? This is why!

Because of this, radial stresses are usually small and need not be considered in the

computations.

Circumferential, or Hoop, stress is due to the internal pressure

(Do - (0.8 * t ) ) 2* t

Se = P

where:

Se = Hoop stress, psi.

P = Internal design operating pressure, psig (e.g., for ammonia: 150,250 or

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Do =

t =

Outside diameter of the pipe, in.

wall thickness of the pipe, less allowances for threading, corrosion and

erosion, in.

The calculated hoop stress needs to be equal to or less than the allowed stress for the

temperature of operation. When the calculated hoop stress meets the conditions during

operation, it shall meet them for all the cases.

Longitudinal stress is the pure bending stress of the element plus the axial pressure. The

longitudinal component of the axial pressure is one half of the value of the hoop stress. At

this point the coordinate system is changed from polar to Cartesian (rectangular) to proceed

with the macroanalysis of the system. The principal planes of stress can be solved with six

equations. They are:

CMx = 0 C M y = O CMz = 0

where:

M = the moment along a ordinal axis and:

CFx = 0 CFy = 0 CFz = 0

where:

F = the force along a cardinal axis.

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Use of the beams of uniform cross-section tables gives for a fixed end beam:

Se = a = w * L~ * 12in/ft Sm 12 * Sm

The Crane Company found that the deflection of a pipe 2” and more in diameter deflected

less than for the fixed end beam model. For pipes of 2” and less diameter, test deflections

were more than the fixed-end beam but less than for the hinged beam model. The hinged

beam model results in the following:

Se = 1~ = w * L~ * 12in/ft Sm 8 * Sm

In both cases the reaction forces are:

F = w * L 2

where:

Se = Longitudinal Bending Stress, psi.

M = Maximum Moment, lb/in.

Sm = Section modulus of the pipe, in3.

w = Weight of the pipe, lb/ft.

L = Length between supports, feet.

F = Reaction force of support, lb.

An actual piping system is never as simple as described above. A normal piping system is

realized by first solving for all of the reaction forces (supports) in the system. Segment

weights or distributed forces can be replaced with point forces acting through the center of

gravity of the respective segments. Then, the overall system can be solved by a method

called weight balancing, in which a larger piping system is broken down into statically

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solvable segments. In straight runs, each two supports are handled as an equilibrium free

body. In horizontal bends, each three supports are handled as an equilibrium-free body.

After having worked your way through the entire piping system, moments and torque at any

point can be determined. The shears at those points are found by:

Sb = M St = - T Sm 2 * Sm

where:

Sb = Bending Stress, psi.

St =

M = Moment, lb/in.

T = Torsion, lb/in.

Sm = Section modulus of the pipe, in3.

Shear or Torsional Stress, psi.

Then, the shears are combined to form the total expansion stress from pure bending and

torsion.

The total expansion stress must be less than the allowable stress (SA) discussed earlier.

Wind and seismic activity are handled similarly. The piping system is rotated onto its side

and solved like the weight case. In the wind and seismic cases, two solutions need to be

found when it is unknown from which horizontal ordinal axis the forces are being applied.

Expansion stress due to thermal expansion and contraction is handled differently because the

static solution is indeterminate. The engineering solution is to assume that the system is

totally unrestrained and determine the change of one end anchor point relative to the others.

This change in length is restrained by the members perpendicular to it. The book, ZTT

Grinnell Industrial Piping, Inc, Piping Design and Engineering, provides a good 3-D - 133 -

example with two anchor points. See Figure 4A & 4B. The solution entails computing the

centroids in each axis plane, the two moments of inertia in each axis and the products of

inertia, the resultant forces (done simultaneously utilizing matrix algebra), and the cardinal

moments and torques. The final total expansion stress at each point is then computed as

shown above. When supports are provided or additional anchor points are present, a

different approach is needed. One such approach is the model of the guided cantilever

uniform beam. One end is fixed while the other end deflects to absorb the adjacent

expansion and confraction. The amount of absorbed stress is inversely proportional to the

stiffness of the deflecting member relative to the combined stiffness of all the members

resisting the load. The beam formulas are:

F = 12 * E * I * d 1728 * L3

M = 1 2 * F * L = 6 * E * I * d 2 144 * L2

where:

F = Developed force, psi.

E = Modulus of elasticity at installation temperature, psi.

I = Moment of inertia of the system component, in3.

d = Deflection or change of length, in.

L = Length of member, ft.

Weight balancing is again used to work through the entire pipe system to determine the

reaction forces, moments and torques. As an alternate, Z T T Grinnell Zndustrial Piping, Znc.

Piping Design and Engineering has compiled tables of precalculated shapes to allow quick

determination of forces and moments over a broad range of pipe configurations used to

mitigate therrnal expansion and contraction. After all the forces and moments are evaluated,

the stresses are computed the same as had done above.

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Controlling Stresses

So far, the hand calculation of the methods above can be seen to require substantial time.

There are several software programs on the market of varying complexity that can be used to

do repetitive calculations. For either the manual or the computer-aided method, meticulous

work is required.

Not addressed above is pipe supports. This is where we re-enter the realm of the design

book. Who remembers seeing any of the following?

1. Place pipe supports 10 feet apart.

2. Place a pipe support 2 feet from a horizontal change in direction.

3. Place a pie support next to a valve.

4. . Follow MSS SP-69 suggested maximum span between supports of pipe.

5. Follow IIAR-2 recommended pipe support spacing.

6. Table of minimum distance to first rigid support.

All of these relate to pipe stress and mechanical integrity of the piping. These statements are

not all compatible. They are dependent on the type of pipe and the conditions of operation.

The maximum span for straight pipe can be either a maximum deflection of the pipe to allow

drainage or a maximum allowed stress to not exceed the stress limits. The pure bend flexure

formula rewritten to solve for span is:

12 * Sm * Se 12 in./ft. * w Ls=F 12 in./ft. * w

where:

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L1 = Length of large pipe between supports, ft.

Ls = Length of small pipe between supports, ft.

Sm = Section modulus of the pipe, in3.

Se = Longitudinal Bending Stress, psi.

w = Weight of the pipe, lbs/foot.

The minimum length to the first rigid support equation is:

d*D, "10' 1.6*Se

where:

L = Length of pipe to first support, ft.

d = Deflection to be absorbed, in.

Do = Outside diameter of the pipe, in.

Se = Longitudinal Bending Stress, psi.

By using these equations, suitable spans can be determined to select pipe support locations.

Likewise the thermal expansion and contraction is computed in reverse to find the maximum

deflection a system can have before the expansion and contraction must have compensation.

Having established a set of design book criteria, systems can be designed. The first few

systems for each set of rules should have stress analysis to evaluate the success of the criteria

at holding the system within the allowable stress levels. It would be expected that an

additional set of safety factors would need to be applied to remain out of an overstressed

condition. Having once validated the procedure, future systems designed within the design

book parameters can then be expected to be'within allowable stress levels.

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Conclusions

We need to go back to our offices and evaluate our design books for incomplete design book

statements. Specifications should be tightened to help the designer and contractor cover

what stress analysis combinations are to be evaluated, and what wind, earthquake and snow

loads are to be included in the design. Operations and site-specific data also need to be

included to arrive at proper designs. The Code gives our industry a wide range of materials

and procedures to choose from in establishing a good economical design. Use them to find

the competitive product. Computers can chum out numbers endlessly. It is our job to work

smartly.

- 137 -

TABLE 5023.1 ALLOWABLE STRESSES, ksi Multiply by lo00 t o obtain psi

Grade, Min. Min. Type, Tensile Yield Longitudinal or

Spec. or Strength, Strength, Spiral Joint Material No. Class ksi ksi Notes Factor

Seamless Carbon Steel Pipe and Tube

Steel pipe ASTM A 53 A Steel pipe ASTM A 53 B

Steel pipe ASTM A 106 A Steel pipe ASTM A 106 B Steel pipe ASTM A 106 C Steel tube ASTM A 179 C Steel tube ASTM A 192 . . .

48.0 60.0

30.0 35.0

. . .

. . . . . . ...

48.0 60.0 70.0 47.0 47.0

30.0 35.0 40.0 26.0 26.0

. . .

. . . . . . . . . . . . ... ... ...

Steel tube ASTM A 210 A-1 60.0 37.0 . . . . . (a) Steel pipe ASTM A 333 1

Steel pipe ASTM A 333 6 Steel tube ASTM A 334 1 Steel tube ASTM A 334 6

55.0 60.0 55.0 60.0

30.0 35.0 30.0 35.0

. . .

. . .

. . .

. . .

...

. . .

. . .

. . .

Steel pipe API 5L Steel pipe API 5L

A B

48.0 60.0

30.0 35.0

. ..

... . . . . . .

Carbon Steel Pipe and Tube Electric Resistance Welded Pipe and Tube

(a1 Steel pipe ASTM A 53 A Steel pipe ASTM A 53 B

(a) Steel pipe ASTM A 135 A Steel pipe ASTM A 135 B Steel tube ASTM A 178 A Steel tube ASTM A 178 C

0.85 0.85

48.0 60.0

30.0 . . . 35.0 . . .

48.0 60.0 47.0 60.0

30.0 . . . 35.0 ... 26.0 ... 37.0 ...

0.85 0.85 0.85 0.85

Steel tube ASTM A 214 . . . Steel tube ASTM A 226 . . .

0.85 0.85

47.0 47.0

26.0 ... 26.0 ...

Table 1: Allowable Stresses, ksi (ASME B31.5-1992 Edition- Table 502.3.1) Reprinted from ASME B31.5-1992 Edition by permission of the American Society of Mechanical Engineers.

A l l rights reserved.

- 138 -

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!SY

Nominal Diameter

( in) 1 /2 3/4 1 1 114 1 1/2 1 112 2 2

I

w

w I

P

Schedule

80 80

80 40 80 40 80

ao

ASTM 106 gr A T > -20 F T.r -20 F T > -20 F Tc -20 F T > -20 F Tc -20 F T > -20 F Tc -20 F

ASTM 106 gr B ASTM 53 gr A ERW ASTM 53 gr B ERW

ksi 12 4.8 15 6 10.2 4.08 12.8 5.12 1440 576 1801 720 1224 490 1536 61 5 1292 517 1615 646 1098 439 1378 55 1 1456 582 I a20 728 1238 495 1553 62 1 1300 520 1625 650 1105 442 I 387 555 60 1 240 75 1 300 51 1 204 64 1 256

1239 496 1549 620 1053 42 1 1322 529 561 224 70 1 280 476 191 598 239

1153 46 1 1442 577 980 392 1230 492

Note: 1) Sch 80 pipe is butt welded. 2) Shaded areas show pressure less than 250 psi for f> -20 F and less than 150 psi for T< -20 F.

Table 4: Allowed Internal Pressure (PSI) Corrosion Allowance 4 mils/year for 20 years Sch 80 pipe is butt welded.

Corrosion allowance 0 milslyear for 20 years Corrosion allowance 4 milslyear for 20 years

I

;; h, I

Nomina I Diameter

( in ) 1 12 314 1 1 114 1 112 I 112 2 2 2 112 3 4 5 6 8

10 12 12 1 4 . 14 16 16 18 18 20 20 24 24 30 30

Schedule

80 80 80 80 40 80 40 80 40 40 40 40 40 40 40 Std. 40 20 Std. 20 Std. 20 Std. Std. 30 Std. 30 Std. 30

ASTM 106 gr A

1363 1156 1017 877 895 823 732

1091 828 695 583 503 439 388 332 255 31 2 116 197 76

132 53 94 65

184 41

122 22 99

ASTM 106 gr B

1704 1467 1299 1117 1140 1049 957

1393 1042 855 683 583 513 42 1 353 255 331 116 209 76

132 56 99 70

173 41

132 21 99

Note: 1) Sch 80 pipe is threaded. 2) No allowance is made for out of round pipe. 3) Shaded values have less than full vacuum capability. 4) Effect of temperatures ( T < -20 F ) unknown.

ASTM 106 gr A ASTM 106 gr B

49 77

233 121 183 602 405 370 307 260 247 197 187 106 149 40 88 26 49 20 45 31 89 16 75

54

Table 5: Allowed External Pressure T> -20 O F (PSI) Corrosion allowance 0 mils/year for 20 years / Corrosion allowance 4 mildyear for 20 years.

45 86

245 115 183 694 439 385 335 30 1 247 186 181 116 149 41 88 26 57 21 38 31 89 16 76

57 ~~~,~~~~~~

Nominal Schedule Pipe Insulation Diameter

( i n ) 112 314 1 1 114 1 1/2 1 112 2 2 2 112 3 4 5 6 8

P 10 I 12

12 14 14 16 16 18 18 20 20 24 24 30 30

I

w

w

80 80 80 80 40 80 40 80 40 40 40 40 40 40 40 Std. 40 20 Std. 20 Std. 20 Std. Std. 30 Std. 30 Std . 30

Notes:

(Lbs. )/ft 1.09 1.47 2.17 3.00 2.72 3.63 3.65 5.02 5.79 7.58

10.79 14.62 18.97 28.55 40.48 49.56 53.52 45.61 54.57 52.27 62.58 58.94 70.59 78.60

104.13 94.62

125.49 1 18.65 196.08

1 inch (Lbs. )/ft

0.07 0.08 0.09 0.10 0.1 1 0.1 1 0.13 0.13 0.1 5 0.18 0.22 0.26 0.30 0.38 0.46 0.54 0.54 0.59 0.59 0.67 0.67 0.75 0.75 0.82 0.82 0.98 0.98 1.22 1.22

4 inch (Lbs. )/ft

0.76 0.79 0.83 0.89 0.93 0.93 1 .oo 1 .oo 1.08 1.18 1.34 1.50 I .67 1.98 2.32 2.63 2.63 2.83 2.83 3.14 3.14 3.46 3.46 3.77 3.77 4.40 4.40 5.34 5.34

Ammonia Refrigerant Snow (Minn.) Wind Seismic w/o Liquid Seismic w/ liquid 95 F

(Lbs. )/ft 0.07 0.12 0.20 0.35 0.54 0.48 0.89 0.79 1 .27 I .95 3.34 5.22 7.53

13.00 20.45 29.25 28.99 36.20 35.61 47.77 47.09 60.93 60.16 74.84 73.15

108.99

O F (Lbs. )/ft

0.08 0.14 0.23 0.48 0.61 0.54 1 .oo 0.90 1.43 2.20 3.76 5.89 8.49

14.65 23.06 32.98 32.69 40.81 40.15 53.85 53.09 68.69 67.83 84.37 82.46

122.87

1 inch ins. (Lbs. )lft

5 6 6 7 7 7 8 8 9

10 12 14 16 20 24 27 27 30 30 33 33 37 37 41 41 48

4 inch ins. (Lbs. )/ft

16 17 17 18 18 18 19 19 20 21 23 25 27 31 35 38 38 41 41 44 44 48 48 52 52 59

0 inch ins. 4 inch ins. (Lbs. )/ft (Lbs. )/ft

1 15 2 15 2 15 3 16 3 16 3 16 4 17 4 17 5 18 6 19 7 21 9 22

11 24 14 27 18 31 21 34 21 34 23 36 23 36 26 40 26 40 30 43 30 43 33 46 33 46 40 53

Zone # 1 (Lbs. )/ft

1 2 2 3 3 3 3 4 5 6 9

12 15 22 31 38 40 35 41 40 47 45 53 59 78 71

Zone # 4 (Lbs. )/ft

5 6 8

10 10 12 12 16 18 23 32 43 54 81

113 138 148 128 152 146 174 1 65 195 21 7 285 26 1

Zone # 1 (Lbs. )/ft

1 2 2 3 3 4 4 5 6 8

11 16 21 33 47 61 64 64 70 79 86 94

102 120 I37 160

Zone # 4 (Lbs. )/ft

5 6 9

11 11 13 15 18 22 29 42 58

. 77 119 174 225 235 236 258 288 314 346 375 440 503 586

105.95 .119.44 48 59 40 53 94 343 180 658 172.22 194.15 59 70 50 63 89 327 229 840 167.11 188.40 59 70 50 63 145 532 281 1029

1 ) Insulation used has a density of 1.8 Ibslft3. 2) Seismic includes pipe and 4 inches of insulation with and without 0 F ammonia liquid

Table 6: Loads (lbdft)

502.4.1-504.1.1 ASME D31.5-1992 Edition

Cycles per day for 20 yr life [Note ( I ) ]

8 10

I

c.r P P I

. . 2 3 4

1 4

I

6 8 IO5

20 30 40

0

2 3

50

Total number N of cycles during anticipated life

NOTE: I1 1 Assuming 365 day per year operation.

Figure 1: Stress Range Reduction Factors (ASME B31.5-1992, Fig. 502.3.2) Reprinted from ASME B31.5-1992 Edition by permission of the American Society of Meclianical Engineers. All rights reserved.

'I 4

I

I

VI I

Figure 2: Basic Wind Speed (A58.1-1982 Fig. 1) Reprinted from ASCE 7-95 “Tviinimum design loads for buildings and other structures,” copyright 0 1995, by permission of the American Society of Civil Engineers.

I

c P m

I

For areas outside of the United States, see Appendix Chapter 16.

Figure 3: Seismic Zone Map of the United States (1997 Uniform Building Code Fig. 16-2) Reproduced from the 1997 edition of the Uniform Building Code, copyright 0 1997, with permission of the publisher, the International Conference of Building Oflicials.

\

b

h t

\a

Figure 4A and 4B: Grinnell - Piping Design and Engineering Multiple Plane System Reprinted from Piping Design and Engineering fifth edition (Revised 1976), by permission of

ITT Grinell Industrial Piping, Inc.

- 147 -

- 148 -