01_Stress Analysis - Basics

Kvaerner Powergas

Stress Analysis - BasicsName of presenter : Pankaj ShroffDate : 10/3/03

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Kvaerner Powergas India Pvt.Ltd.

Introduction to Stress - Strain Relationship

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

STRESS - STRAIN CURVE: It is a curve in which unit load or stress is plotted against unit

elongation, technically known as Strain

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STRESS & STRAIN CURVE

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O - A represents the stress is directly proportional to strain, and point “A” is known as Proportional Limit.

Point B represents Elastic Limit - Beyond which the material will not return to its original shape when unloaded

Point C represents yield point - Point at which an appreciable elongation or yielding of the material without any corresponding increase in load

Point D represents ultimate stress or strength Point E represents rupture strength

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What is Stress Analysis?

Stress Analysis is a term used to calculate stresses generated in the elements due to various Internal & External forces

Piping Stress Analysis is a term applied to calculation, which address the static & dynamic loading resulting from the effects of gravity, temperature change, Internal/ External pressure, change in fluid flow rate, wind/ seismic activity.

Codes & standards establish the minimum requirements of stress analysis.

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Purpose of Piping Stress Analysis

Safety of plants Safety of environment Safety of piping & piping components Safety of connected equipment and supporting structure Piping deflections are within the limits Equipment Design Structural design

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Design Codes Used in stress Analysis

ASME B 31.1 - Power piping design ASME B 31.3 - Process Piping ASME B 31.4 - Cross country liquid transportation

pipeline ASME B 31.5 - Refrigerant Piping ASME B 31.8 - Cross country gas transportation

pipeline

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Design Codes w.r.t. Plant life cycle

ASME B 31.3 Plants have plant life of 20 to

30 years Factor of safety 3:1 Lower pipe thickness for the

same condition Relative Low plant cost Chemical plants designed with

this code as if fails only affect few people hence high reliability not required

ASME B 31.1 Plants have plant life of about

40 years Factor of Safety 4:1 Higher pipe thickness for the

same condition Relative high plant cost Power plants require high

reliability hence design as per this code. All steam Piping is designed as per this code even in Chemical plant

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Modes of Failure

FAILURE BY GENERAL YIELDING Failure due to excessive plastic deformation

YIELDING AT SUB ELEVATED TEMPERATURE Body undergoes plastic deformation under slip action of grains

YIELDING AT ELEVATED TEMPERATURE After slippage, material re-crystallises & yielding continues without

increasing loads. This is also known as Creep.

FAILURE BY FRACTURE Body fails without undergoing yielding

BRITTLE FRACTURE Occurs in brittle material

FATIGUE Due to cyclic condition, a small crack grows after each cycle & results in

sudden failure

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Principle axis & stress (Cont…)

Stress is defined as ratio of Force to Area Consider a cube taken out of pipe The origin of principle axis system is at the centre of the cube

Each force acting on the cube can be trigonometrically reduced to force

components represented by vectors, acting on each principle axis. The resultant of the component of each force acting on the cube, divided

by the area of the cube face is called PRINCIPLE STRESS

Longitudinal Axis

Circumferantial

Radial

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Longitudinal Principle Stress Principle stress acting along the centreline of the pipe This stress is caused by longitudinal bending, axial loading or

pressure

Radial Principle Stress Principle stress acting on a line from the centre of the pipe

radially through the pipe wall It is a compressive stress acting on the pipe ID caused by internal

pressure or tensile stress caused by external vacuum

Circumferantial Principle Stress (Hoop Stress) Principle stress acting on a line perpendicular to the Longitudinal

and Radial stress This stress attempts to separate the pipe wall in the

Circumferantial direction Caused by Internal pressure

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When two or more Principle stresses act at a point on a pipe, a SHEAR STRESS will be generated.

Ex. Pipe support - where radial stress caused by supporting member acts in in combination with the Longitudinal bending caused by pipe overhang

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Theories of Failure

MAXIMUM PRINCIPAL STRESS THEORY This theory states that yielding in a piping component occurs

when the magnitude of any of the three mutually perpendicular principle stresses exceeds the yield point strength of material

MAXIMUM SHEAR STRESS THEORY This theory states that failure of a piping component occurs

when the maximum shear stress exceeds the shear stress at the yield point in a tensile test.

In the tensile test, at yield, S1 = Sy (Yield stress), S2 = S3 = 0. So yielding in the components occurs whenMaximum shear stress = S1- S2/2 = Sy/2

The maximum principle stress theory forms the basis for piping systems governed by ASME B 31.3

The maximum or Minimum normal stress is called principle stress

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Stress Catagories

PRIMARY STRESSES Developed by Imposed loading and are necessary to satisfy the

equilibrium between external & internal forces & moments of the piping system.

Primary stresses are not self limiting. As long as the load is applied, the stress will be present and will

not diminish with time or as deformation takes place The failure mode is gross deformation progressing to rupture Ex. Circumferantial stress due to internal pressure &

Longitudinal bending stress due to gravity

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Stress Catagories (Cont…)

SECONDARY STRESSES Developed by the constraint of displacements of a structure.

These displacements are caused by thermal expansion or by outwardly imposed restraints and anchor point movements.

Secondary stresses are self limiting Stress condition will developing a piping system, local yielding

will occur, thus reducing these stresses Failure mode is crack initiation & propagation through the

pressure boundary resulting in a leak

PEAK STRESSES Caused by discontinuities or abrupt changes in a pipe wall,

when a pipe is subjected to primary or secondary stress Stress concentration points which can cause crack initiation

contributing to a Fatigue failure

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Classification of Loads

PRIMARY LOADS Sustained Loads

– Loads expected to be present through out the plant operation– Ex. Pressure, Weight

Occasional Loads– Loads are expected at infrequent intervals during plant operation– Ex. Earthquake, Wind

EXPANSION LOADS Loads are due to displacement of piping Ex. Thermal expansion, Seismic anchor movements, Building

settlement

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REQUIREMENTS OF ASME B 31.3

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Definition & Basis for Allowable Stress

Allowable Stress of Material is based on a function of the yield or Tensile strength at cold to moderate temperatures or based on creep rates or stress for rupture in elevated temperature service

Sc - Allowable stress at COLD condition, which includes cryogenic service or Ambient installed temperature for elevated temperature service

Sh - allowable stress in HOT operating condition, which would be the Design temperature for elevated temperature service or Ambient for cold or cryogenic service

SA - allowable stress range

SE - Displacement Stresses

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Definition & Basis for Allowable Stress (Cont…)

Allowable Stress Values are tabulated in Appendix A, Table A - 1 in B 31.3

The basis of these values, at temperatures below the creep range, is the lowest of the following, 1/3 of specified minimum tensile strength at room temperature 1/3 of tensile strength at temperature 2/3 of specified minimum yield strength at room temperature 2/3 of yield strength at temperature (For Austenitic SS and

Nickel alloys, this value may be as large as 90 % of yield strength at temperature)

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DESIGN PRESSURE Defined as most severe sustained pressure which results in the

greatest component thickness and highest component pressure rating

DESIGN TEMPERATURE Defined as the sustained pipe metal temperature representing

the most severe conditions of coincident pressure and temperature

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ALLOWANCES FOR PRESS. & TEMP. VARIATIONS Nominal pressure stress (Hoop stress) shall not exceed the

yield strength of the material at temperature Sum of the Longitudinal stresses due to pressure, weight and

other sustained loading plus stresses produced by occasional loads, such as wind or earthquake may be as high as 1.33 times hot allowable, Sh

It is permissible to exceed the pressure rating or the allowable stress for pressure design Sh at the temperature of increased condition by not more than:

– 33 % for no more than 10 hours at any one time and no more than 100 hours/ year OR

– 20 % for no more than 50 hours at one time and no more than 500 hours/ year

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VIBRATION In vibrating system, the stress concern is HIGH CYCLE, LOW

STRESS. However guidance presented in code for checking cyclic stress levels is based on LOW CYCLE, HIGH STRESS. Hence can not be used for Vibrating Piping system

A separate method of using SE with Design Fatigue Curves for material shall be used to determine the same

SA is based on the no. of thermal or equivalent cycles the system will experience in the plant life.

Code tabulates Stress range reduction factor “f”. “f” ranges from 1 for 7000 cycles or less to 0.3 for 200,000 cycles

Basis of 7000 cycle is one cycle per day for 20 years

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Governing Equations

Stresses Due to Sustained Loads SL <= Sh

SL = (PD/4t) + Sb

Stresses Due to occasional Loads Sum of longitudinal loads due to pressure, weight and other

sustained loads and stresses produced by occasional loads such as earthquake or wind shall not exceed 1.33 Sh

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Governing Equations

Stress range due to expansion loads SE <= SA

SE = (Sb 2 + 4 St 2) 1/2

where,– Sb = Resultant Bending moment = [(iiMi)2 + (ioMo)2]1/2 / Z– St = Torsional stress = Mt/ 2Z– Mt = Torsional Moment– Z = Section modulas of pipe = (л/32Do)(Do4-Di4)– ii = Inplane stress intensification factor– io = Outplane stress intensification factor– Mi = Inplane bending moment– Mo = Outplane bending moment

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Governing Equations

Sb = resultant bending stress St = Torsional stress

Allowable Stress Cold = Sc = (2/3) Syc

Syc = (3/2) Sc

Allowable Stress range Hot = Sh = (2/3) Syh

Syh = (3/2) Sh

Syc = Allowable stress at cold temperature

Syh = Allowable stress at hot temperature

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Governing Equations

Allowable Stress = Syc +

Syh

= 3/2 ( Sc + Sh)= 1.5 (Sc + Sh)= 1.25 (Sc + Sh) after dividing with FOS

Final Allowable stress = SA = f [ 1.25 (Sc + Sh) - SL] or

SA = f [1.25 Sc + 0.25 Sh] SL = stiffness caused by pressure & weight or Longitudinal

stress Sc = allowable stress at cold condition Sh = allowable stress at hot condition f = Stress range reduction factor based on no. of cycles

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CONSIDERATIONS IN STRESS ANALYSIS

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Initial Steps

Review of BEP and any other client’s requirement/ Local statutory requirements related to stress analysis and piping design

Preparation of Design basis Preparation of stress critical line list

Refer to PIP 209 - KPGI procedure for preparing stress critical lines

Considerations are,– Criticality from temperature point of view– Criticality from size point of view– Criticality from connected equipment point of view– Criticality from Pressure relief/ Vibration point of view– Criticality from Earthquake/ Wind or any other occasional load point of view

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Prerequisite Data

P & I Diagrams Piping Specification Line Designation List Equipment Datasheet Allowable nozzle loads for fabricated equipment and

Proprietary equipment Nozzle displacements for proprietary equipment Stress sketch or layout showing line routing Software - Caesar II or Caepipe or Triflex or any other

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Design Steps

Initial setting of Caesar configuration file for the project and shall not change on a project

Review the stress sketch from following angles, All the components of P & I D are marked on the sketch Piping specification is identified correctly All probable support locations are marked Visual review of line to find some obvious reasons because of which it will not

work and needs re routing

Feed the geometry in the program Apply correct physical parameters such as pressure, temperature, density. Build various cases of analysis based on stress critical line list Result checking,

Check stresses Check Nozzle loads Check support loads and deflection

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Design Steps Cont…)

If all found OK clear line to layout and document the results If not found OK, adjust in supports to make it OK If still not found OK, go back to layout and get revised possible routing &

rerun At the end of the project, final line configuration need to be checked with

the stress model.

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Nozzle Loads - Fabricated Equipment

Fabricated equipment nozzle loads depends upon the diameter of, thickness, material of construction and design code of equipment.

At the start of the project acceptable equipment nozzle load table for the project shall be obtained from fabricated equipment group.

The nozzle loads given are based on nozzle size, rating of the flange, type of equipment.

The nozzle loads are given at the nozzle to shell/ dish end junction and not at flange.

The nozzle loads are considered as local loads at the junction while designing the equipment except in few cases of large nozzles.

The local stresses on nozzle/ shell junction are checked by using WRC 107 or WRC 297 design codes.

Nozzle loads exceeding the table value shall be given for approval to fabricated equipment group

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Nozzle Loads - Proprietary Equipment

Proprietary equipment nozzle loading data is generally available from equipment supplier. However some of the proprietary equipment are designed and constructed as per International codes and are having standard acceptable nozzle loading given in the code. Still before proceeding with design it need to be confirmed from vendor

Some of the acceptable nozzle loading are, Centrifugal Pumps API 610 Steam Turbines NEMA SN 23 Centrifugal Compressor API 617 Reciprocating compressor Vendor to give Reciprocating Pumps Vendor to give Air Fin cooler API 661 Fired Heater Vendor to give Reforming furnace Vendor to give Large storage tanks API 650 Any other proprietary equipment Vendor to give

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What Next?

Read following ASME B 31.1 & ASME B 31.3 - Design section Design of Piping System - M W Kellogg Piping Stress Calculation Simplified - S W Spielvogel PIP 203 - Stress analysis guideline of KPGI PIP 209 - KPGI guideline for deriving stress critical line list Caesar II - Design manual

Manual calculation using charts given in M W Kellogg book for following, L shape - Legs & anchor load calculation Symmetrical expansion loop - Legs & anchor load calculation Guided Cantilever Pipe span v/s stress generated

Feed a sample line and do analysis. Compare it with previously analysed results.

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Thank You

01_Stress Analysis - Basics

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