OVERVIEW OVERVIEW

• 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 Proportional Limit.• Point B represents Elastic Limit beyond which the

material will not return to its original shape when unloaded 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 load.

• Point D is ultimate stress or Ultimate Strength of material.

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

Why do we perform Pipe Stress Analysis ?• In order to keep stresses in the pipe and fitting with code

allowable levels

• In order to keep nozzle loadings on attached equipment with allowable of manufacturers 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.

Design Data required for in order to do Pipe Stress Analysis• Pipe size and wall thickness/ schedule.• Intermediate Components i.e. valves, reducers, elbows• Pipe Material• Operating Parameters such as temperature, Pressure,

Fluid Contents• Insulation details i.e. material and wt.• Corrosion allowance.• External equipment movement• Wind and earthquake criteria

WHAT IS STRESS ANALYSIS?

• Piping Stress analysis is a term applied to calculations the effect of

(A) Static Loading. (B) Dynamic Loading.• Resulting from the Effects Of 1.Gravity 2.Temperature Changes 3.Internal Pressure 4.Fluid Transients (Changes in Fluid flow rate) 5.Wind Pressure 6.Seismic Activity

CLASSCIFICATION OF LOADS ? 1.Primary loads:These are loads due to forces on piping. • 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.. Pressure, Weight, Spring hanger pre load, Applied forces.

- 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 due to displacements of piping. 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 = 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

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

Stresses Due to Sustained Loads

As per B31.3

The longitudinal stresses in pipe due to weight and pressure should not exceed Sh i.e.

S sus = [ ( ii Mi)2 + ( io Mo)2]1/2/ Z + P Do/ 4t <= Sh

ii , io = inplane, outplane intensification factors

Mi , Mo = inplane , outplane bending moment due to sustained loads.

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 = equivqlent 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

Wind loadingg= 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.

Earthquake 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.

SOL+SL<=1.33 Sh

Where,

SOL- 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 E = Expansion Stress range (psi)

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

= (Mx2+ My

2+ Mz2)1/2

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

EXCEPTION• All 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 No 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, iny-Resultant total displacement StrainL-developed length of pipe between Anchor,ftU-anchor distance i.e straight line between Anchor,ftK1-0.03

PIPE EXPANSION

FLEXIBILITY

How Pipes Flex When Absorbing Thermal Expansion

Calculating Free Thermal Expansion

Review of Expansion

Force and Stresses

Tensile and Compressive Stress

Strain (Stretching)

Young’s Modules

PROBLEMS

Question :-

THANKS