Piping Stress Analysis

PIPING STRESS ANALYSISPIPING STRESS ANALYSIS

M.VIJAY GOPAL & L.HARISH KARTHIK

WHAT IS PIPING STRESS ANALYSIS?WHAT IS PIPING STRESS ANALYSIS?

PIPING STRESS ANALYSIS IS A TERM APPLIED TO CALCULATIONS, WHICH ADDRESS THE STATIC AND DYNAMIC LOADING RESULTING FROM THE EFFECTS OF GRAVITY, TEMP. CHANGES, INTERNAL AND EXTERNAL PRESSURES, CHANGES IN FLUID FLOW RATE AND SEISMIC ACTIVITY.

CODES, STANDARDS AND REGULATIONS ESTABLISH THE MINIMUM REQUIREMENTS OF STRESS ANALYSIS.

PIPING STRESS ANALYSIS IS INTERRELATED WITH PIPING LAYOUT AND SUPPORT DESIGN. (IF NEEDED, LAYOUT SOLUTION SHOULD BE ITERATED UNTIL A SATISFACTORY BALANCE IS OBTAINED BETWEEN STRESSES AND LAYOUT EFFICIENCY. ONCE THE PIPING LAYOUT IS FINALIZED, PIPING SUPPORT SYSTEM MUST BE DETERMINED.)

STRESS-STRAIN RELATIONSHIPSTRESS-STRAIN RELATIONSHIP

PURPOSE OF PIPING STRESS ANALYSISPURPOSE OF PIPING STRESS ANALYSIS

SAFETY OF PIPING AND PIPING COMPONENTS.

SAFETY OF CONNECTED EQUIPMENT AND SUPPORTING STRUCTURE.

PIPING DEFLECTIONS ARE WITHIN LIMITS.

OBJECTIVES OF PIPING STRESS ANALYSISOBJECTIVES OF PIPING STRESS ANALYSIS

CALCULATE STRESSES AND ENSURE THAT CODE ALLOWABLES ARE MET.

CALCULATE MOMENTS AND DEFLECTIONS FOR USE IN DESIGN OF RESTRAINTS AND SUPPORTS.

CALCULATE REACTIONS ON RESTRAINTS AND SUPPORTS.

CALCULATE EQUIPMENT NOZZLE REACTIONS AND ENSURE LIMITS ARE MET.

INPUTS FOR PIPING STRESS ANALYSISINPUTS FOR PIPING STRESS ANALYSIS

WHICH CODE APPLIES TO THE SYSTEM.DESIGN PRESSURE AND TEMPERATURE, INSULATION DETAILS, ETC.MATERIAL SPECIFICATIONFLUID DENSITYPIPE SIZE AND WALL THICKNESS OF EACH OF THE PIPING COMPONENTS. LAYOUT OF THE SYSTEM INCLUDING DIMENSIONS.LIMITATIONS OF END REACTIONS ON TERMINAL POINTS AS ESTABLISHED BY EQUIPMENT MANUFACTURERS.WIND LOADS AND SEISMIC LOADS, IF ANY.CLIENT SPECIFIC REQUIREMENTS SUCH AS SPRING VARIABILITY, UNITS, ETC.

APPLICATIONS OF PIPING STRESS ANALYSISAPPLICATIONS OF PIPING STRESS ANALYSIS

NEW DESIGNS.

MODIFYING EXISTING SYSTEMS.

EXISTING SYSTEMS WITH MAINTENANCE PROBLEMS.

REVIEW PIPING DESIGNS DONE BY OTHERS AND MAKE CALCULATIONS TO DETERMINE IF THEIR DESIGNS MEET ASME B31.1 OR B31.3 CODE RULES, AND TO DETERMINE IF PIPING STRESSES ARE BELOW THEIR RESPECTIVE ALLOWABLE VALUES. THIS REVIEW IS VERY HELPFUL PRIOR TO CONSTRUCTION BECAUSE IT IDENTIFIES PROBLEMS IN DESIGN, DRAWING ERRORS, REFERENCE ERRORS, AND PROVIDES AN OPPURTUNITY TO MAKE CORRECTIONS WHILE THEY ARE THE LEAST EXPENSIVE.

HOW PIPING AND COMPONENTS FAIL?HOW PIPING AND COMPONENTS FAIL?(MODES OF FAILURE)(MODES OF FAILURE)

FAILURE BY GENERAL YIELDING – This failure is by 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-crystallizes and hence yielding continues without increasing load. This phenomenon is known as Creep.

FAILURE BY FRACTURE – Body fails without undergoing yielding.

BRITTLE FRACTURE – Occurs in brittle materials.

FATIGUE – Due to cyclic loading, initially a small crack is developed, which grows after each cycle and results in sudden failure.

WHEN PIPING AND COMPONENTS FAIL? (THEORIES WHEN PIPING AND COMPONENTS FAIL? (THEORIES OF FAILURE)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 principal stresses exceeds the yield point strength of the material. (NOTE: Maximum or minimum normal stress is called Principal Stress).

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. This is also called as Tresca Criterion.

CLASSIFICATION OF LOADSCLASSIFICATION OF LOADS

PRIMARY LOADS – Based on the duration of loading: SUSTAINED LOADS – These loads are expected to be present through out the plant

operation. For example, pressure and weight. OCCASIONAL LOADS – These loads are present at infrequent intervals during plant

operation. For example, earthquake, wind, etc.

EXPANSION LOADS – These are loads due to displacements of piping. For example, thermal expansion, seismic anchor movements, and building settlement.

SUSTAINED AND OCCASIONAL LOADSSUSTAINED AND OCCASIONAL LOADS

SUSTAINED LOADS – 1. Weight effect (live and dead load) 2. Thermal expansion and contraction3. Internal and external pressure loading4. Effects of supports, anchors and terminal movements

OCCASIONAL LOADS –1. Impact forces 2. Wind and seismic loads3. Surge load4. Pressure relief discharge load

TYPES OF STRESSES TYPES OF STRESSES

PRIMARY STRESSES – These are developed by the imposed loading and are necessary to satisfy the equilibrium between external and internal forces and moments of the piping system. Primary stresses are not self-limiting.

SECONDARY STRESSES – These are developed by the constraint of developments of a structure. These displacements can be caused either by thermal expansion or by outwardly imposed restraint and anchor point movements. Secondary stresses are self-limiting.

PEAK STRESSES – Unlike loading condition of secondary stress which cause distortion, peak stresses cause no significant distortion. Peak Stresses are the highest stresses in the region under consideration and are responsible for causing fatigue failure.

STRESS INTENSIFICATION FACTORSTRESS INTENSIFICATION FACTOR

It is defines as the ratio of the max stress intensity to the nominal stress

Used as a safety factor to account for the effect of localized stresses on piping under a repetitive loading

Applied to all components where stress concentration is possible

ALLOWABLE STRESS RANGEALLOWABLE STRESS RANGE

THE ALLOWABLE STRESS RANGE AS PER ANSI B31.1 IS GIVEN AS

Sa = f(1.25Sc+0.25Sh)

HERE, Sa – ALLOWABLE STRESS RANGE AS PER CODE

Sc – ALLOWABLE (TABULAR) COLD STRESS

Sh – ALLOWABLE (TABULAR) HOT STRESS

f - STRESS RANGE REDUCTION FACTOR FOR CYCLIC CONDITIONNo. of cycles factor

7,000 1

7,000 to 14,000 0.9

14,000 to 22,000 0.8

22,000 to 45,000 0.7

45,000 to 1,00,000 0.6

Over 1,00,0000 0.5

ALLOWABLE STRESS RANGE (CONTD.)ALLOWABLE STRESS RANGE (CONTD.)

IT IS CONSIDERED FOR STRESS DUE TO THERMAL EXPANSION, WHICH WILL DIMINISH WITH TIME AS A RESULT OF LOCAL YIELDING OR CREEP.THIS REDUCTION WILL APPEAR IN THE OPPOSITE DIRECTION IN THE COLD CONDITION, WHICH IS CALLED SELF-SPRINGING.THUS, THEORETICALLY THE COLD STRESS WILL INCREASE AND HOT STRESS WILL DECREASE WITH TIME.BUT, THEIR SUM WILL ALWAYS BE A CONSTANT, WHICH IS WHY THE ALLOWABLE STRESS RANGE (Sa) IS OF GREATER CONCERN THAN THE COLD OR HOT STRESSES INDIVIDUALLY.

STRESSES ACTING ON A PIPESTRESSES ACTING ON A PIPE

ST – STRESS DUE TO SHEAR OR TORSION

SL – LONGITUDINAL STRESS

SC – CIRCUMFERENTIAL OR HOOP STRESS

SR – RADIAL STRESS

SB – STRESS DUE TO BENDING OF PIPE

STRESSES ACTING ON A PIPE (CONTD.)STRESSES ACTING ON A PIPE (CONTD.)

TOTAL LONGITUDINAL STRESS : SL = SB+SP

(Significant stresses act in the same direction)

SB= M/SM for straight pipe and SB = M/SM * i for curved pipes

LONGITUDINAL STRESS DUE TO INTERNAL PRESSURE SP = P * AI/AM

CIRCUMFERENTIAL STRESS : SC = P*(D-t)/2t

TORSIONAL STRESS : ST = T/2SM

SM – Section modulus of cross sectionM – bending moment (max)i – stress intensification factorP – design pressureT – torque appliedt – thickness of pipe wall

COLD SPRINGINGCOLD SPRINGING

TO REDUCE ANCHOR FORCES AND MOMENTS.INCORPORATING PRE-STRESS DURING ERECTION OF PIPING STRUCTURE.AMOUNT OF COLD SPRING SHOULD NOT EXCEED MAX EXPANSION (AMOUNT OS COLD SPRING IS EXPRESSED AS A % OF TOTAL EXPANSION).COLD SPRING IS MORE IMPORTANT FOR PIPING WHICH IS TO OPERATE AT TEMPERATURES IN THE CREEP RANGE.PIPING CODES DO NOT PERMIT COLD SPRINGING AS A SOLUTION TO OVERSTRESS.COLD SPRINGING ALLOWS ONLY A THIRD REDUCTION IN FORCES AND BENDING MOMENTS IF THE LINE IS SHORT BY 50% OF ITS TOTAL EXPANSION.

FLEXIBILITY IN PIPING SYSTEMSFLEXIBILITY IN PIPING SYSTEMS

FLEXIBILITY IS A MAJOR CONSIDERATION RIGHT FROM THE PIPING LAYOUT STAGE.STIFF PIPING LAYOUTS CAUSE HIGH STRESS POINTS IN THE PIPING SYSTEM.HIGH STRESSES WITHIN THE SYSTEM LEAD TO CRACKS IN THE PIPE.SPECIAL CONSIDERATION SHOULD BE GIVEN TO HIGH TEMPERATURE LINES, WITH LOOPS, ETC.

COMMON LAYOUTS – A COMPARISON COMMON LAYOUTS – A COMPARISON

GRINNEL STANDARD DESIGNSGRINNEL STANDARD DESIGNS

EXPANSION BENDSEXPANSION BENDS

EXPANSIONS BENDS ARE THE MOST COMMONLY USED TO INCREASE FLEXIBILITY IN PIPING LAYOUTS.EXPANSION LOOPS ARE ALSO USED IN PIPES RUNNING IN STRAIGHT LINES FOR LONG DISTANCES.VARIOUS CONFIGUARTIONS HAVE ALREADY BEEN STUDIED AND THE STANDARD DIMENSIONS ARE FIXED FOR MANY PIPE SIZES.

EXPANSION BENDS - GRINNEL STANDARDSEXPANSION BENDS - GRINNEL STANDARDS

EXPANSION LOOPS vs EXPANSION JOINTSEXPANSION LOOPS vs EXPANSION JOINTS

EXPANSION LOOPS EXPANSION JOINTS

LOW INITIAL COST HIGH INITIAL COST (COMPONENT ITSELF, MAY REQUIRE THRUST

SUPPORTS)

LOW MAINTENANCE HIGH MAINTENANCE

REQUIRES LARGE AMOUNT OF SPACE

REQUIRES VERY LITTLE SPACE (INLINE)

SAME AS THAT OF PARENT PIPE MATERIAL

SUSCEPTABILITY TO STRESS CORROSION OR LEAKAGE (COST

TO REPAIR OR REPLACE)

TIPS FOR FLEXIBLE LAYOUTSTIPS FOR FLEXIBLE LAYOUTS

THE EXPANSION OF EQUIPMENTS TO BE CONSIDERED.LONG RADIUS ELBOWS ARE MORE FLEXIBLE THAN 5D BENDS.PUMPS, TURBINES AND COMPRESSORS MUST HAVE LOW FORCES ON THEM. A LIMITING FORCE OF 5000 psi ON THE EQUIPMENT NOZZLES IS GENERALLY ACCEPTED.DEAD WEIGHT OF PIPING MUST BE CARRIED BY INDEPENDENT SUPPORTS AND NOT BY THE EQUIPMENT NOZZLES.LINES SHOULD BE PLANNED AND GROUPED TOGETHER FOR SUPPORTING. ROUTING SHOULD BE PLANNED TO PROVIDE EASY SUPPORTING POSSIBILITY.COLD SPRING SHOULD NOT BE USED TO MINIMISE OVER STRESSING OF PIPES.STRESSES AT FLANGED CONNECTION TO BE LIMITED TO 10000 psi.

FIG.1 – FLOW IS BETTER FIG.2 – FLEXIBILITY IS BETTER

INDICATIONS OF PIPING PROBLEMSINDICATIONS OF PIPING PROBLEMS

EXCESSIVE PIPE SAG.

BROKEN SUPPORTS OR RESTRAINTS.

BOTTOMED OR TOPPED OUT SPRING SUPPORTS.

UNEXPLAINED ROTATING EQUIPMENT VIBRATIONS.

DAMAGED FOUNDATIONS OF ROTATING EQUIPMENTS AND VESSELS.

FLANGE ALIGNMENT PROBLEMS.

LEAKAGE FLANGES.

SHAKING OR VIBRATING PIPING.

SQUIRMING OR LEAKING EXPANSION JOINTS.

WHEN DO WE REQUIRE STRESS ANALYSIS?WHEN DO WE REQUIRE STRESS ANALYSIS?

THE SYSTEM TEMP. > 400°F (204°C) AND LINE SIZE IS GREATER THAN OR EQUAL TO 3”.PIPING CONNECTED TO LOAD SENSITIVE EQUIPMENTS LIKE FIRE HEATERS, AIR COOLERS, ETC. OR IS CARRYING HAZARDOUS FLUIDS AND DESIGN TEMPERATURE > 250OF.THE PIPING CONNECTED TO ROTATING EQUIPMENTS SUCH AS PUMPS WHERE THE OPERATING TEMPERATURE IS GREATER THAN AMBIENT TEMPERATURETHE SYSTEM CONTAINS EXPANSION JOINTTHE SYSTEM HAS TWO PHASE FLOWLINES 16” AND LARGER WHERE THE OPERATING TEMPERATURE IS HIGHER THAN THE AMBIENTTHE PIPING CONNECTS COMPRESSORS AND TURBINES

WHEN DO WE REQUIRE STRESS ANALYSIS? (CONTD.)WHEN DO WE REQUIRE STRESS ANALYSIS? (CONTD.)

THE PRESSURE EXCEEDS THE PRESSURE FOR AN ANSI CLASS 2500 B 16.5 FITTING.THE PRODUCT OF THE PIPE OUTSIDE DIAMETER (IN INCHES) TIMES THE PRESSURE (IN psi) IS >= 1157.THE SYSTEM PRESSURE IS GREATER THAN 3000 psi.THE SYSTEM USES GLASS REINFORCED EPOXY (GRE) PIPE.UNDERGROUND PROCESS LINES.INTERNALLY LINED PROCESS PIPING & PRESSURE RELIEF SYSTEMS.THIN WALLED PIPE OR DUCT OF 18” DIAMETER AND OVER, HAVING AN OUTSIDE DIAMETER OVER WALL THICKNESS RATIO OF MORE THAN 90.LINES 4” AND LARGER CONNECTED TO AIR COOLER, STEAM GENERATORS OR FIRED HEATER TUBE SECTIONS.

DESIGN & ANALYSIS OF BURIED PIPING DESIGN & ANALYSIS OF BURIED PIPING

ALL LOADS ACTING ON THE SYSTEM.THE FORCES AND THE BENDING MOMENTS IN THE PIPING AND PIPING COMPONENTS RESULTING FROM THE LOADS. LOADING AND STRESS CRITERIA.GENERAL DESIGN PRACTICES.

TERMS ASSOCIATED WITH BURIED PIPING TERMS ASSOCIATED WITH BURIED PIPING

CONFINING PRESSURE – PRESSURE IMPOSED BY THE COMPACTED BACKFILL AND OVERBURDEN ON A BURIED PIPE. CONFINING PRESSURE ACTS ON THE PIPE CIRCUMFERENCE.

FLEXIBLE COUPLING – PERMITS A SMALL AMOUNT OF AXIAL OR ANGULAR MOVEMENT WHILE MAINTAINING THE PRESSURE BOUNDARY.

FRICTION – PASSIVE RESISTANCE OF SOIL TO AXIAL MOVEMENT. FRICTION AT THE PIPE/SOIL INTERFACE IS A FUNCTION OF CONFINING PRESSURE AND THE COEFFICIENT OF FRICTION BETWEEN THE PIPE AND THE BACKFILL MATERIAL. FRICTION FORCES EXIST ONLY WHERE THERE IS ACTUAL OR IMPENDING SLIPPAGE BETWEEN THE PIPE AND SOIL.

INFLUENCE LENGTH – PORTION OF A TRANSVERSE PIPE RUN WHICH IS DEFLECTED OR “INFLUENCED” BY PIPE THERMAL EXPANSION ALONG THE AXIS OF THE LONGITUDINAL RUN.

TERMS ASSOCIATED WITH BURIED PIPING (CONTD.)TERMS ASSOCIATED WITH BURIED PIPING (CONTD.)

PENETRATION – THE POINT AT WHICH A BURIED PIPE ENTERS THE SOIL EITHER AT GRADE OR FROM WALL OR DISCHARGE STRUCTURE.

SETTLEMENT – THE CHANGES IN VOLUME OF SOIL UNDER CONSTANT LOAD WHICH RESULT IN DOWNWARD MOVEMENT, OVER A PERIOD OF TIME, OF A STRUCTURE OR VESSEL RESTING ON THE SOIL.

MODULUS OF SUBGRADE REACTION – THE RATE OF CHANGE OF SOIL BEARING STRESS W.R.T COMPRESSIVE DEFORMATION OF THE SOIL. IT IS USED TO CALCULATE THE PASSIVE SPRING RATE OF THE SOIL.

VIRTUAL ANCHOR – A POINT OR REGION ALONG THE AXIS OF A BURIED PIPE WHERE THERE IS NO RELATIVE MOTION AT THE PIPE/SOIL INTERFACE.

BURIED PIPING LOADSBURIED PIPING LOADS

THERMAL EXPANSION LOADS – INSTALLATIONS WITH CONTINUOUS RUNS. INSTALLATIONS WITH FLEXIBLE COUPLINGS. INSTALLATIONS WITH PENETRATION ANCHORS. INSTALLATIONS WITH FLEXIBLE PENETRATIONS.

PRESSURE LOADS EARTHQUAKE

INPUTS REQUIRED FOR BURIED PIPING STRESS INPUTS REQUIRED FOR BURIED PIPING STRESS ANALYSIS ANALYSIS

PIPE DATA – PIPE OUTSIDE DIAMETER PIPE WALL THICKNESS LENGTH OF PIPE RUNS- TRANSVERSE AND LONGITUDINAL YOUNG’S MODULUS, E PIPE DEPTH BELOW GRADE

SOIL CHARACTERISITICS – SOIL DENSITY (FROM SITE TESTS) PIPE TRENCH WIDTH AT GRADE RANGE OF COEFFICIENT OF FRICTION BETWEEN PIPE AND BACKFILL TYPE OF BACKFILL

OPERATING CONDITIONS – MAXIMUM OPERATING PRESSURE MAXIMUM PIPE TEMPERATURE AMBIENT PIPE TEMPERATURE PIPE COEFFICIENT OF THERMAL EXPANSION