WS 5 Basic Concepts of Stress Analysis Design Bases

New Webinar Series

by Piping Technology & Products, Inc.

Session #5: Basic Concepts of Stress Analysis – Design Bases

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Jerry Godina

If you have any questions, comments or suggestions, please email us at [email protected]

To request a PDH certificate, email [email protected]

Hyder Husain

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Fronek Anchor Darling Ent., Inc. ASME Nuclear Qualified

Pipe Shields, Inc. ISO 9001-2000 Certified

Sweco Fab, Inc. ASME U-Stamp R-Stamp

PIPING TECHNOLOGY & PRODUCTS, INC.

Member of MSS, SPED, APFA,

U.S. Bellows, Inc. Member of EJMA

PT&P Subsidiaries

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Topic Session / Date

Introduction I. Overview of Piping

(completed)

Preliminary

Piping Design

I. Piping System

Components

(completed)

II. The Total System

(completed)

Basic Concepts

of Stress

Analysis

I. Flexibility Analysis

(completed)

II. Design Bases

August 8, 2012

Influences on

Pipe Support

Design

I. Rigid Supports

August 15, 2012

II. Spring Supports

August 22, 2012

III. Restraints

August 29, 2012

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All phases of a project, from inception to operation, be effectively communicated and correctly executed.

• Contract documents • Design documents • Fabrication details • Procedures, and specification

Must be developed to communicate, monitor, and document the design, fabrication, and erection of piping systems precisely.

PROJECT EVOLUTION The typical project evolution can generally be divided into three principal stages.

The first stage comprises inception, assignment of responsibilities, preliminary design, and estimating.

• Contract Specifications • Codes and Standards • Design Criteria • Calculations • System Descriptions • System Flow Diagram • Piping and Instrumentation Diagram • Piping Physical Sketches and Composite Drawings

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The second stage comprises detailed design, procurement, and definitive cost estimating. (Depending on the project schedule, production of hardware, site preparations, and construction may also be initiated at this stage.)

• Design Specifications

• Procurement Specifications

• Erection Specification

• Physical Design Drawings

• Stress Analyses

• Piping Spool Drawing

• Equipment Drawings

• Pipe Support Drawings

The third stage comprises completion of engineering, production of equipment, erection, start-up, and commercial operation of the systems.

• Supplier’s Deviation Disposition Request

• Field Change Request

• Nonconformance Report

• Start-up Field Report 6


The design bases discussed here are generic and should be considered during the course of design of any piping system, regardless of its function.

Design bases are:

1. Physical Attributes

2. Loading and Service Conditions

3. Environmental Factors

4. Materials-related Factors

5. Pressure Integrity over its Design Life

6. Joint Design

7. Pipe Specification

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Size, layout and dimensional limits or proportions of the piping system

Dimensional standardized items have been established for most piping components such as

• fittings • flanges • valves • diameter • wall thickness

Customized Aspects: Certain piping systems require special design practices for configuration control, to ensure constructability, or in-service performance. • Location of clean out should be designed with adequate clearance, and mechanically

joined, to allow for ready disassembly and maintenance. • Adequate drainage of condensate or other liquids that may separate from the gas stream • Weld joints spaced a minimum of one pipe diameter to facilitate radiographic

examination of the joints • High temperature, high-pressure piping systems

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Loading conditions are moments, pressure changes, temperature changes, thermal gradients, or any other parameters that affect the state of stress of the piping system. Typical examples of loading conditions include:

• internal pressure

• piping system deadweight

• steady-state temperatures

• transient temperatures

• wind loads

• snow and ice loads

• seismic

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Environmental factors refers to operating conditions that result in: 1. Progressive physical 2. Chemically induced deterioration of the piping system

This can ultimately lead to a breach of the pressure boundary or a gross structural failure. Failures that are the results of environmental factors are usually slow to progress and frequently involve localized areas of the piping system.

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• specific chemical

• metallurgical

• physical properties Materials-related considerations are the specific chemical, metallurgical, and physical properties of a piping system’s material constituents that can ultimately determine its suitability for a particular service. Proper materials selection can be a crucial design consideration that will determine the adequacy of performance of a piping system where extremes of temperature, chemical attack, or erosion are significant factors in its operation.

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Pressure integrity

• Maintenance of a leak-tight condition in piping systems’ pressure-containing boundaries

• The control of the level of stress or strain within predefined criteria limits

• Maintenance of the pressure integrity of a piping system, within predefined criteria limits, is a major objective of the design process.

Leakage integrity

• Pressure integrity is not synonymous with leakage integrity

• Leakage integrity is only an assurance of a leak-tight condition without regard for the state of stress or structural stability of the pressure boundary.

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Joint design and selection can have a major impact on the long-range operation, maintenance, and performance of the piping system. Factors that must be considered in the joint selection phase of the project design include:

• Degree of leakage integrity

• Periodic maintenance requirements

• Specific performance requirements

• In addition, since codes do impose some limitations on joint applications, joint selection must meet the applicable code requirements

• Various pipe joints include:

─ Butt Welded

─ Socket Welded

─ Brazed / Soldered

─ Screw / Threaded

─ Flanged

─ Compression

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www.pipingtech.com 14 Piping Technology & Products, Inc.

Flange Weld

Compression Weld

Butt Weld

Socket Weld


Piping specification is written for each service such as:

• steam

• air

• oxygen

• caustic

The specification contains information about:

• piping material

• thickness, flanges

• branch connection

• instrument connection

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To determine the distribution of stress in a structure it is necessary to solve a boundary value problem :

• boundary conditions, i.e. displacements and/or forces on the boundary

• Constitutive equations, such as Hooke’s Law for linear elastic materials, are used to describe the stress-strain relationship in this calculations.

• A boundary value problem based on the theory of elasticity as applied to structure expected to deform elastically , i.e. infinitesimal strain, under design loads.

• When the loads applied to the structure induce plastic deformations, the theory of plasticity is implemented.

• Analytical or close-form solutions can be obtained for simple geometries, constitutive relations, and boundary conditions.

• Numerical methods such as the finite element method, the finite difference method and the boundary element method which are implemented in computer programs.

• All real objects occupy a three-dimensional space. The stress analysis can be simplified in cases where the physical dimensions and the loading conditions allows the structure to be assumed as one dimensional or two-dimensional.

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• Straight pipe • Curved pipe • Two nodes N1 & N2 • x,y,z Gobal coordinate • X’, y’,z’ Local coordinate

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Each Node Displacement & Rotation: Dx’, Dy’, Dz’, Rx’, Ry’, Rz’ Forces & Moments: Fx’, Fy’, Fz’, Mx’, My’, Mz’ {F’}= {Fx1’, Fy1’, Fz1’, Mx1’, My1’, Mz1’, Fx2’, Fy2’, Fz2’, Mx2’, My2’, Mz2’} T

{D’} = {Dx1’, Dy1’, Dz1’, Rx1’, Ry1’, Rz1’, Dx2’, Dy2’, Dz2’, Rx2’, Ry2’, Rz2’} T

For each element we have in local coordinate {F’}=[K’]{D’} - - - - - - - - (1) [K’] is a 12x12 stiffness matrix

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CONVERSION TO GLOBAL COORDINATE Before the mathematical assembly can be performed Using rotational matrix consisting of directional parameters, convert local stiffness, forces and displacements into the Global Co-ordinate system For each element we have in local coordinate {F’}=[K’]{D’} - - - - - - - - (1) For each element we have in local coordinate {F’} = [L]{F} and {D’} = [L]{D} - - - - - - - - (2) [L] = 12 x12 transformation matrix consisting of four sets 3x3 rotational matrices placed at the diagonal {F}= force vector in global coordinates {D}= displacement vector in global coordinates Substitute (2) into (1) [L]{F} =[K’] [L]{D} or {F} = [L]-1[K’] [L]{D} The global stiffness matrix, [K], of each element is then created by applying the rotational transformation on the local stiffness matrix [k’] as {F} = [K]{D}, where [K]= [L]-1[K’] [L]= [L]T[K’] [L] - - - - - - (3)

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• In the actual assembling process, the force/displacement relation (3) is partitioned to

• Where 1 and 2 denote node N1 and N2.

• Each F* and D* sub vector represents six components corresponding to six degrees of freedom.

• Restraints and anchors are treated as additional stiffness added to the diagonal of the corresponding node location.

• These N degrees of freedom are all potentially related


• For a system with n-node points, the total number of degrees of freedom is N =6n

• Therefore, the system has (Nx N) overall stiffness matrix relating the forces at all degrees of freedom with the displacements at all degrees of freedom.

• The assembly of the overall stiffness matrix uses the force vector and displacement vector, both representing all degrees of freedom, as the starting template.

• Each element matrix as given by Eq. (4) is placed inside the, overall stiffness matrix at the location representing the proper degree of freedom in the force and displacement template.

• All element stiffness values placed at the same location inside the overall stiffness are simply added together algebraically.


• The assembly is completed when all element matrices are included in the overall matrix.

The final over all equation looks like

F1 K11 K12 . . . . K1N D1 F2 K21 K22 K23 . . . K2N D2 . . . K33 . . . K3N D3 . = . . . . . . . - - - - - - (5) . . . . . . . . . . . . . . . . Fn KN1 KN2 . . . . KNN DN

• After the nodal displacements are solved for each load case, the forces and

moments in global coordinates at each element can be found by using (4).

• These global forces and the moments have to be back to the local coordinate before the stresses can be calculated


Let us consider a simple linear spring

For equilibrium F2 = -F1 Where F1 = kδ1-kδ2 and F2= - kδ1+kδ2

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Excessive piping vibration are a major case of: • Machinery down time • Leaks • Fatigue failure • High noise • Fires and explosions in refineries and petrochemical plants

Excessive vibration levels occur when a mechanical natural frequency of the piping system is excited by some pulsation of mechanical source. The vibration mode shape: lateral (pipe) or radial (shell wall) The natural frequency (cps) is related to the maximum deflection as The aim here is to keep the natural frequency away from the excitation frequency to avoid resonance that amplitude of vibration is too low. Lower frequency has higher energy. One of the reasons for limiting the deflection is to make the pipe stiff enough with high enough natural frequency to avoid large amplitude under any small disturbances.

Piping Technology & Products, Inc. 27

gfn

2

1

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ω/k = a ω = frequency k = wave number a = velocity

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LOW CYCLE FATIGUE • Normal start-up and shut down

cycles • Major load fluctuations • Occasional load cycles • Thermal expansion stress range is the

most common that may produce low- cycle fatigue

SNm=C S= stress range N= number of cycles to failure C= constant: elastic equivalent failure stress for N=1 m= negative slope of the log-log straight line. HIGH CYCLE FATIGUE: Steady state vibration Rapidly fluctuating thermal shock 1 cycle per second = 86400 cycles/ day=3.15 x 10 7 cycles/year: endurance limit A: material with low mean stress, properly stress relieved welds C: material with maximum stress, non-stress-relieved stress

Piping Technology & Products, Inc. 29


Modern software makes it easy to input and display all the data needed to accurately define a piping system analysis model. Input can be accessed or modified on an element by element bases, or data sets can be selected to make global changes. Besides the evaluation of a piping system’s response to thermal, deadweight and pressure loads, software can analyze the effects of wind, support settlement, seismic loads and wave loads. Dynamic analysis capabilities include modal, harmonic, response spectrum and time history analysis.

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• After load conditions are analyzed the designer can then determine the

different scenarios and their subsequent impact on the selection of

adequate support mechanisms.

• These would include:

• Load bearing components

• Guiding elements

• Anchors

• Spring supports

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Next Webinar Session in Series: August 15, 2012 at 10:00 am and 2 pm Central Time

Session 6: Influences on Pipe Support Design – Rigid

Supports

In the 6th webinar in our ongoing series, we will begin our review of different pipe support elements, concentrating primarily on rigid supports. We'll take a look at a variety of support elements ranging from stock catalog items to completely customized parts. Learn which factors of the piping stress analysis have an impact on the overall design and cost. Also, see how adjustability can be incorporated into the design to accommodate for on-site discrepancies.

If you have any questions, comments or suggestions, please email

us at [email protected]

To request a PDH certificate, email [email protected]

WS 5 Basic Concepts of Stress Analysis Design Bases

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Transcript of WS 5 Basic Concepts of Stress Analysis Design Bases