Stress Analysys

CONCEPTS OF PIPE STRESS ANALYSIS• STRESS:- Stress of a material is the internal resistance per unit area to the deformation caused by applied load.

• STRAIN:- Strain is unit deformation under applied load.

From Figure:-

• O– A represents the stress is directly proportional to strain, and point A is known

• Point B represents Elastic Limit

but will retain a permanent deformation called permanent set.

• Point C is called Yield Point and is the point at which there is an appreciable elongation or yielding of the

material without any corresponding increases of lo

• Point D is ultimate stress or Ultimate Strength

• Point E is the stress at failure known as

RELATIONSHIP BETWEEN STRESS AND STRAIN

Hooke’s Law: By direct experiment with the extension of prismatical bars it has been esta

that within certain limits the elongation of the bar is proportional to the Tensile force.

From this:

€ = ᵟ / E

Where,

€ � Strain

ᵟ � Stress

E � Modulus of Elasticity

It can be derived for a member of length ‘L’

∂ l = PL/AE

Where,

∂ l � Elongation

P � Applied force

L � Length of pipe

A� Area of cross section of pipe.

E � Modulus of Elasticity

WHAT IS STRESS ANALYSIS?

Piping Stress analysis is a term applied to calculations carried out to check the effect of the fol

system:

(A) Static Loading.

(B) Dynamic Loading.

The above loading conditions are primarily result of the following:

1.Gravity

2.Temperature Changes

3.Internal Pressure

4.Fluid Transients (Changes in Fluid flow rate)

5.Wind Pressure

6.Seismic Activity

ONCEPTS OF PIPE STRESS ANALYSIS Stress of a material is the internal resistance per unit area to the deformation caused by applied load.

Strain is unit deformation under applied load.

A represents the stress is directly proportional to strain, and point A is known

Elastic Limit beyond which the material will not return to its original shape when unloaded

but will retain a permanent deformation called permanent set.

and is the point at which there is an appreciable elongation or yielding of the

material without any corresponding increases of load.

Ultimate Strength of material.

Point E is the stress at failure known as Rupture Strength.

RELATIONSHIP BETWEEN STRESS AND STRAIN

Hooke’s Law: By direct experiment with the extension of prismatical bars it has been esta

that within certain limits the elongation of the bar is proportional to the Tensile force.

It can be derived for a member of length ‘L’

Piping Stress analysis is a term applied to calculations carried out to check the effect of the fol

The above loading conditions are primarily result of the following:

4.Fluid Transients (Changes in Fluid flow rate)

Stress of a material is the internal resistance per unit area to the deformation caused by applied load.

A represents the stress is directly proportional to strain, and point A is known Proportionality Limit.

its original shape when unloaded

and is the point at which there is an appreciable elongation or yielding of the

Hooke’s Law: By direct experiment with the extension of prismatical bars it has been established for different materials

Piping Stress analysis is a term applied to calculations carried out to check the effect of the following on a Piping

Why do we perform Pipe Stress Analysis ?

• In order to check and keep stresses in the piping system within code allowable levels

• In order to keep nozzle loadings on equipment connected to the piping system within allowable limits of the

manufacturer or recognized standards (API 610, API 617, NEMA SM 23 etc.) in the pipe and fitting with code

allowable levels.

• In order to calculate the design loads for sizing supports and restraints.

• In order to keep Piping deflections within the limits.

• In order to determine piping displacement for interference checks .

• In order to solve the dynamics problem due to mechanical vibration, fluid hammers, relief valve discharge etc.

CRITICAL LINE SELECTION CRITERIA

Critical lines whose analysis are to be carried out have to be identified properly in the initial phase itself. The lines

identified are further identified as S1, S2, S3, S4 and a brief description of this categories are defined below.

Category S1:

Lines falling in this category shall be brought specifically to the attention of the Stress Analysis group. The level of

investigation and analysis shall be established on an individual case basis. This review shall be carried out at the

beginning of the project and prior to any formal analysis for the following conditions:

Category S2:

Lines in this category require mandatory computer analysis by stress engineer which shall be carried out during the

detail engineering phase of the project:

Category S3:

Lines in this category require mandatory investigation; the analysis can be done by any recognized approximate

method such as guided cantilever method. Proper documentation of the same for future reference of the same is

required. The systems covered are:

Category S4:

All lines designated as Category S4 due to temperature in Attachment 1. Lines in this category can be analyzed by visual

inspection or approximation methods using engineering judgment in accordance with ASME B31.3.

A well tabulated diagram of this classification is shown below as Attachment 1

ATTACHMENT1

Design Data required for in order to do Pipe Stress Analysis

• Pipe size and wall thickness/schedule.

• Details of Intermediate Components i.e. valves, control valves, orifice, relief valves.

• Pipe Material.

• Operating & Design Parameters such as Temperature, Pressure, Fluid Contents.

• Insulation details i.e. material and wt.

• Corrosion allowance.

• Displacement of equipment nozzles.

• Wind and Seismic Data.

LOADS ON PIPING SYSTEMS

1.Primary loads:

These are typically steady or sustained types of loads such as internal pressure of fluid, external pressure, weight of

pipe and fluids and occasional forces such as those from relief valve operation, water hammer, wind and seismic

activities..

These can be divided into two categories based on the duration of loading.

- Sustained loads

• These loads are expected to be present through out the plant operation. e.g.. Internal Pressure, External

Pressure and Weight.

- Occasional loads.

• These loads are present at infrequent intervals during plant operation. e.g.. Earthquake, Wind, etc.

2.Secondary loads (Expansion loads):

These are loads caused by displacement of some kind. This can be caused by thermal expansion of the pipe, Tank

settlement, expansion/contraction of the vessel to which the piping is connected.

e.g. .Thermal Expansion and equipment settlement.

INTERNAL PRESSURE :-

Pipe Thickness Calculation:-(Under Internal Pressure)

• Codes and standard specify the formula to arrive at the required thickness for the pipe to be withstand internal

pressure.

• Corrosion allowance depending upon the services to which the system is subjected and material of construction

used.

• Nominal thickness (t) is to be calculated from Minimum thickness (tm) considering Fabrication Tolerance

12.5%. (i.e 0.125)

• ASME B 31.3 gives Design Equation for piping design.

(Nominal thickness) t = (tm + C )(1+f)

tm = PDO/2(SE+PY)

C= C1+C2

C1-Corrosion allowance

C2-Depth of Thread (Used only upto1 1/2”NB)

f = Fabrication Tolerance of 12.5% (i.e. 0.125)

Where,

tm- Minimum thickness excluding corrosion allowance and fabrication Allowance, in

P-Internal design Pressure, psi

DO-Outside diameter of Pipe, in

E-Joint quality factor.

Y-Temperature coefficient from 304.1.1

S-Maximum allowable stress in Material, psi

(A) Primary Loads:-

1.Stresses Due to Sustained Loads

As per ASME B 31.1

S sus = 0.75i MA / Z + P Do/ 4t <= Sh

Where;

S sus = Sustained Stress (psi)

i = Stress intensification factor

MA = Resultant Moment due to sustained loads (in-lb)

= (Mx2+ My

2+ Mz2)1/2

Sh = Basic allowable material stress at operating Temerature

Z = Section Modulus; in3

Note :- The thickness of the pipe used in calculating SL shall be the Nominal thickness minus Mechanical, Corrosion,

and Erosion allowance.

WIND LOADING

Wind loading is caused by loss of momentum of the wind striking the projected area of the piping system. The static

linear force per foot generated by steady state, constant speed wind load can be calculated as:

f = Peq* S*D sin(a)

f = wind force per unit length ( Ib/ft.)

Peq = equivalent wind pressure (psi)

=V2/ 2g * density of the Air (0.0748 Ib/ft3 at 29.92 in Hg and 70 F temp.)

V = design velocity of wind ( usually the 100 year maximum wind speed), ft./sec

g= gravitational constant , 32.2 ft/sec2

S = Shape factor (drag coefficient), based on Reynolds no. of the wind and shape of structure; this typically

varies between 0.5 to 0.7.

D= Pipe outside Diameter ( including insulation), ft

a= angle of rotation between pipe and wind; 00 represent the pipe axis parallel to wind direction

Since this represent the force associated with steady state air flow of air, the calculated value is often increased

by gusting factor in the range of 1.0 to 1.3 to account for dynamic effect.

SEISMIC LOADING

Stresses Due to Occasional loads

As per ASME B 31.1

S occ = 0.75i MA/ Z + 0.75i MB/ Z + P Do/ 4t <= K Sh

Where

S occ = Occasional Stress (psi)

MB = Resultant Moment due to occasional loads (in-lb)

= (Mx2+ My

2+ Mz2)1/2

K = Occasional load Factor

= 1.15 for occasional load acting no more than 8hrs. at one time and no more than 800 hrs. /year

= 1.2 for occasional load acting no more than 1 hr. at one time and no more than 80 hrs. /year

Stresses Due to Occasional loads

As per B31.3

• The sum of the longitudinal stresses due to pressure, weight and other sustained loads and of stresses

produced By Occasional loads such as Earthquake or Wind shall not exceed 1.33Sh

Socc+SL<=1.33 Sh

Where,

Socc- Occasional load stresses.

SL- Sustained stress.

Sh-Basic allowable stress at maximum Metal temp.

Secondary Loads (Expansion Loads):-

The displacement stress range SE shall not exceed SA (Allowable Displacement stress Range)

SE < SA = f(1.25 Sc +1.25 Sh - SL)

As per B31.1

SE = i Mc/ Z

S A = Expansion Stress range (psi)

MC = Resultant Moment due to expansion loads (in-lb)

= (Mx2+ My

2+ Mz2)1/2

Z = Section Modulus

As per B 31.3

SE = (Sb2 + 4St2) ½

Sb = Resultant Bending Stress,psi

= [(IiMi)2 + (IoMo)2]1/2 / Z

Where;

Mi = in-plane bending moment, in.lb

Mo = out-plane bending moment, in.lb

Ii = in- plane stress intensification factor obtained from appendix of B31.3

Io = out- plane stress intensification factor obtained from appendix of B31.3

St = Torsional stress ,psi

= Mt / (2Z)

Mt = Torsional moment, in.lb

EXCEPTIONS

• All critical piping system require a stress analysis with the Exception of Following

1.Those are duplicates of successfully operating installations.

2.Those are judged adequately by comparison with previously analyzed system.

3.System of uniform size that have not more than two anchor points, No intermediate restrains and fall within the

limitation of the Equation

Dy/(L-U)2 ≤ K1

Where,

D-Outside diameter of pipe, in

y-Resultant total displacement Strain

L-developed length of pipe between Anchor,ft

U-anchor distance i.e straight line between Anchor,ft

K1-0.03

PIPE EXPANSION

STRESS ANALYSIS AND PIPE SUPPORTS

A pipe support is a designed element that transfer the load from the pipe to the supporting structural members. The

type of support to be used is selected based on stress analysis. The main functions of a pipe support are to anchor,

guide, absorb shock and support a specified load.

Pipe Supports are an integral part of any piping system in any industry. The selection and design of the same is of great

importance as it has direct impact on the stability and life span of the piping system.

TYPES OF PIPE SUPPORTS

Pipe supports can be broadly classified into the following types:

• Rigid supports

• Spring supports

• Snubber /Shock absorber

Rigid Supports:

1. Pipe Shoe: It is generally welded to the pipe and is used to rest it on a secondary structural member. Arrangements

on the secondary member can be made so as to provide directional guide or stop to the pipe. It is usually cut from an

ISMB section. The size of the shoe section and its height depends upon the pipe size and also on the insulation

thickness.

2. Rod Hanger: It is a rigid vertical type support provided from top and is designed to absorb tensile load only. It

consists of clamp, eye nut, tie rod and beam attachment. Selection of rod hanger depends on pipe size, load &

temperature.

3. Pipe Saddles: These are used for pipes of sizes greater than 6” dia. They serve the same purpose of the shoes.

However these are suitable to carry higher loads as they are designed for higher size pipes. . These are made fabricated

from plates with gussets or stiffening plates used to strengthen. They can also be made from cut channels stiffened

with plates in between.

Spring Supports:

Spring supports or flexible supports use helical coil compression springs to accommodate loads and associated pipe

movements due to thermal expansions. These are broadly classified into:

• Variable Effort support

• Constant Effort support

• Variable Effort Support:

Variable effort supports or variable spring hangers as they are usually called are used to support pipes subjected to

moderate vertical thermal movement (approximately 50mm). These are used to support the weight of the pipe works

while allowing certain quantum of movement to the pipe with respect to the structural member supporting it. A

Variable spring hanger is simple in assembly with the pipe virtually suspended directly from a helical coil spring

mounted in a spring box. It can also be used to support the pipe from bottom wherein the pipe rests on the assembly

on top of the spring box. This type is called a Can type VSH. The main components are the top plate, rod assembly with

turn buckle, locking rods, spring assembled in a spring box. The data that are to be furnished for purchasing the spring

are as follows:

1. Hot load

2. Thermal Movement

3. Maximum load variation in percentage. The maximum load variation is usually 25%.

4. Type of support whether hanging or foot mounted.

Hot load is the working load of the support in the hot condition when the pipe has travelled from the cold condition to

the hot working condition.

The salient features of this type of support are:

• Allows movement in vertical direction

• Load varies with the movement.

Used where,

• Displacement , 50mm

• Load Variability 25%

Load Variation = [(Hot Load –Cold Load)*100]/Hot load

or, Load Variation = [(Travel * Spring rate)*100]/Hot load

• Constant Effort Supports

When the piping system is subject to large vertical movements there is no choice but to select a constant effort support

(CES). When the Load variation percentage exceeds 25% or the specified max LV% in a variable hanger, it is choice less

but to go for a CES. For pipes which are critical to the performance of the system or so called critical piping where no

residual stresses are to be transferred to the pipe it is a common practice to use CES. In a constant effort support the

load remains constant when the pipe moves from its cold position to the hot position. Thus irrespective of travel the

load remains constant over the complete range of movement. Therefore its called a constant load hanger. Compared to

a variable load hanger where with movement the load varies & the hot load & cold load are two different values

governed by the travel & spring constant. A CES unit does not have any spring rate.

Most prevalent work principle for CSH is Bell Crank Mechanism. The Bell crank lever rotates around the Fulcrum point.

One end of the Bell crank lever is connected to the pipe ‘P’, the other end is connected to the spring by the tie rod.

Thus when the pipe moves down from cold to hot condition, the point P moves down, and as it moves down the Bell

crank lever will rotate in the anti clock wise direction & tie rod connected to the spring will be pulled in, by which the

spring gets further compressed. When the pipe moves up the bell crank lever will rotate (in the clock wise direction) &

the tie rod connected to spring will be pushed out thus allowing the spring to expand or relax.

• Shock Absorber

A shock absorber absorbs energy of sudden impulses or dissipate energy from the pipeline.

SOME COMMON SUPPORTS

How Pipes Flex When Absorbing Thermal Expansion?

Calculating Free Thermal Expansion

METHODS TO REDUCE STRESS AND LOADS ON PIPING SYSTEM

• Introduction of 2D / 3D loops in the system with suitable loop isolating anchors.

• Introduction of bends if possible in the system which would absorb the expansions and maintain flexibility in

the system.

• Introduction of proper supports to optimize the stress, loads and displacements.

• If provision of loops cannot be provided the Expansion Joints can be introduced in the system to absorb the

expansion and in turn reduce the stress.

• Provision of spring hangers in the system to accommodate loads and associated thermal movements.

• In pipe branching's reinforcement pads can be used to reduced the local stresses at the branch.

SIZING OF LOOPS