History of WRC 107. Using WRC 107 and NozzlePRO FEA. Presented by: Ray Delaforce

Transcription

1 History of WRC 107 Using WRC 107 and NozzlePRO FEA Presented by: Ray Delaforce 1

2 History of WRC 107 Pressure Example of vessel membrane analysis stress was handled in a cylinder by the subject codes, to such internal as: pressure ASME Section VIII, Division 1 ASME Section VIII, Division 2 PD 5500 (British Code) EN (European Code) AD 2000 (Merkblatter) (German Code) CODAP (French Code) They mainly concentrated on primary membrane stresses (more later) These stresses had to be below the yield stress of the metal The strain is not to exceed about 0,2% Yield σ Within this region 2 0,2% ε

3 History of WRC 107 Example Stress analysis of membrane is really stress required in a cylinder subject to internal pressure The code allowable stress is about here, below yield In the case of nozzles subject to external loads, the stresses can be here That is beyond the scope of the codes Strains go beyond 0,2% Yield σ Within this region 3 0,2% ε

4 History of WRC 107 Stress analysis is really required WRC107 was published for this purpose WRC107 offered a graphical method of doing the stress analysis Here is a typical graph: Many of the graphs are difficult to read more of that later WRC107 first published in

5 Let History us look of WRC at some 107 principles of stress analysis Stress analysis is really required WRC107 was published for this purpose WRC107 offered a graphical method of doing the stress analysis Here is a typical graph: Many of the graphs are difficult to read more of that later WRC107 first published in 1965 Revised 1968 Revised 1970 Revised 1972 Revised 1979 Based upon the theoretical work of Prof. Biljaard of Cornell University Attachments (nozzles) on cylinders and spheres only can be analysed There are also geometric limitations Using WRC 107 is very tedious and time consuming PV Elite and CodeCalc make this analysis simple and fast 5

6 Let us look at some principles of stress analysis Consider Suppose the a bar force subject were to delivered a tensile by force this arrangement Once the stress passes yield, it continues to stretch until collapse occurs So, we could re-label the strain axis as time to collapse This shows we must under normal conditions stay below yield σ Fracture! Yield 6 0,2% TIME ε

7 Let us look at some principles of stress analysis σ Suppose = force the / area force thus were stress delivered is directly by this related arrangement to the load (force) If the weight were heavy enough fracture would occur The stress is directly proportional to the load σ = force / area thus stress is directly related to the load (force) σ Fracture! Yield 7 0,2% TIME ε

8 Let us look at some principles of stress analysis σ Suppose = force now / area we thus have stress table under is directly the weight related to restrict the load its (force) movement By definition this is a Primary Stress The Internal stress is directly related to the external load Fracture will occur as the stress increases beyond yield The stress also exist Everywhere in the bar membrane stress Everywhere designates the stress as a General Stress Therefore we have a General Primary Membrane stress σ Fracture! Yield 8 0,2% TIME ε

9 Let us look at some principles of stress analysis Suppose The weight now is we NOT have related table to under the stress. the weight Only to the restrict movement its movement The weight can only descend so far The stress is now controlled by movement Stress does not reach fracture, because movement is limited The weight is NOT related to the stress. Only to the movement Yield σ 9 0,2% TIME ε

10 Let us look at some principles of stress analysis Now The weight consider is NOT a related Cantilever to the subject stress. to Only un-restricted to the movement force This is known as Secondary Stress Controlled by movement of another element Internal stress not related to the force in the other component Also called strain related Yield σ 10 0,2% TIME ε

11 Let us look at some principles of stress analysis We Now again we consider restrict the a Cantilever motion of subject the weight to un-restricted force There is an internal bending stress in the beam This bending stress can exist everywhere at this location This stress has the following characteristics The internal stress is directly related to the load - Primary It exists Everywhere General This is a General Primary Bending stress 11

12 Let us look at some principles of stress analysis We Now again look restrict at this arrangement the motion of the weight The bending stress is NOT directly related to the load (weight) The bending strain is restricted, and does not proceed to fracture It is strain controlled, and not load controlled We have a Secondary bending stress Yield σ 12 0,2% TIME ε

13 Let us look at some principles of stress analysis Now Sum up look what this we arrangement have learned so far: The rod is heated, so it expands Again the stress is controlled by the strain This is also a Secondary stress also called an Expansion stress Yield σ 13 0,2% TIME ε

14 Let us look at some principles of stress analysis Sum Consider up what a nozzle we have in a shell learned subject so far: to an external moment Primary stress Directly related to the imposed load: eg σ= F/A If the load is great, failure can occur Secondary stress Relate to the strain induced in the component strain controlled The strain is restricted so failure does not occur Often from expansion of another component example, thermal expansion There is one more stress category we have deal with 14

15 Let us look at some principles of stress analysis Consider a nozzle in a shell subject to an external moment The shell deforms to accommodate the moment like this Notice how it pulls the shell to the left, giving rise to a membrane stress This stress fades away rapidly from the nozzle to shell junction The bending stress is ignored for the moment 15

16 Let us look at some principles of stress analysis Consider Summing a what nozzle we in have shell learned subject so to far: an external moment The shell deforms to accommodate the moment like this Notice how it pulls the shell to the left, giving rise to a membrane stress This stress fades away rapidly from the nozzle to shell junction That stress does not exist everywhere, therefore it is LOCAL This is a Local Primary Membrane stress Over this distance The bending stress is treated as Secondary stress 16

17 Let us look at some principles of stress analysis Summing what we have learned so far: ASME Section VIII, Division 2 gives them symbols These stresses can exist in combination Stress type Symbol Allowable stress General Primary Membrane Local Primary Membrane Primary Bending P m P L P b S 1,5S 1,5S Secondary: Local Membrane Local Bending Q 3S or 2S y 17

18 Let us look at some principles of stress analysis Summing This is the what Hopper we have diagram learned from so ASME far: Section VIII, Division 2 ASME Section VIII, Division 2 gives them symbols These stresses can exist in combination Stress type Symbol Allowable stress Primary Primary + Local Primary + Local Primary + Local + Secondary P m P m + P L P m + P L + P B P m + P L + P B + Q S 1,5S 1,5S 3S of 2S y 18

19 Let WRC us 107 look Force at some and principles Moment Convention of stress analysis This is the Hopper diagram from ASME Section VIII, Division 2 19

20 WRC Type of 107 Loading Force and per Moment normal stress Convention analysis Nozzle removed here is the hole Labeling convention P M T DU AU BU CU AL BL CL U = upper surface (outside) L = lower surface (inside) V L A C M L V C Radial force P Longitudinal force Circumferential force Longitudinal moment M C V L V C M L Circumferential moment M C Torsional moment B M T 20

21 Type WRC of 107 Loading Demonstration per normal (First) stress analysis Sustained load Loads that are there for long periods Pressure Weight (on an attachments) Occasional Loads that are momentary (lasting a short time) Wind loading Seismic loading Because they are short lived add 20% to allowable stress Expansion Strain controlled From thermal expansion of piping Always Secondary Stresses Operating loads These are commonly Sustained + Thermal (eg: CAESAR II) 21

22 WRC 107 Demonstration Does not discuss (First) Pressure Thrust on the nozzle Here are the regions around the nozzle Here are the final stress final stress Categories 22 S 1,2S 1,5S 1,8S 1,8=1,2 x 1,5 3S

23 WRC There 107 is a Does stress not concentration discuss Pressure at the Thrust Nozzle on to the Shell nozzle junction d O Thrust F = Pπd O2 /4, this can be added in PV Elite (Demo) P Before After 23

24 Adding There is the a stress scf (Pressure concentration Indices) at the - Nozzle (Demo) to Shell junction The stress increases at the junction like this: S C S A S A is the average stress, S C is the increases stress S C /S A is known as the stress concentration factor (scf) It is usually about 3 ASME VIII, Division 2 calls the scf by the name of Pressure Index 24

25 We Adding now the have scf two (Pressure analyses Indices) - (Demo) S C S A It now FAILS, we can fix the problem be adding a re-pad (Demo) 25

26 WRC107 We now have deficiencies two analyses Nozzle junction Edge of the pad 26

27 WRC107 Introduction deficiencies to NozzlePRO FEA analysis It only considers 4 points around the nozzle The method is only an approximation We need better tools to get a better answer The answer if FEA! 27

28 Introduction Setting the nozzle-vessel to NozzlePROin FEA Global analysis Units Now we set the same nozzle up in CodeCalc (Demo) 28

29 What is a direction cosine? Setting the nozzle-vessel in Global Units +x B A C +y Radial force Longitudinal force Circumferential force Longitudinal moment P V L V C M L Circumferential moment M C Torsional moment M T Radial force P is in the +X direction Longitudinal force VL is in the -Y direction from B to A Circumferential force VC is in the +Z direction from D to C We need to know the Orientation of the Nozzle and the Vessel +x and +y are known as Direction Cosines We need to understand Direction Cosines 29

30 What is a direction cosine? These Let us angles construct define a 3 dimensional the direction world, cosines or system The axes can be thought of as the corners of a box y r x z Label the 3 directions by the letters x, y and z A vector can be represented by an arrow from the origin The vector can be represented by r, defines magnitude & direction The magnitude (length) is defined as r, or simply r 30

31 What is a direction cosine? Let These the angles direction define cosines the direction be represented cosinesby Vx, Vy and Vz y a y φ y r a z φ z φx a x x z Now, put in the distances along the axes of the vector The direction cosine of y is defined as cos( ) = a y φ y r a x Similarly cos( a z φ ) = r, and cos( ) = x φ z r 31

32 What is a direction cosine? Let the direction cosines be represented by Vx, Vy and Vz Then Vx = cos( φ x ), Vy = cos( φ y ) and Vz = cos( φ z ) y a y φ y r a z φ z φx a x x z Now, if Vy = 1, it follows that φ = 0 O because cos(0 O y ) = 1 But, if Vx = 0, and Vz = 0, then φ = 90 O and = 90 O x φ z The vector would then point in the direction of +y 32

33 What is a direction cosine? Let the direction cosines be represented by Vx, Vy and Vz Then Vx = cos( φ x ), Vy = cos( φ y ) and Vz = cos( φ z ) y a y φ z =90 O a z φ x =90 O a x x z Now, If Vz = if 0, Vy Vx = 1, = 1 it and follows Vy = that 0, the vector = 0 O because would point cos(0along O ) = 1x axis φ y But, if Vx = 0, and Vz = 0, then φ = 90 O and = 90 O x φ z The vector would then point in the direction of +y 33

34 What is a direction cosine? Let the direction cosines be represented by Vx, Vy and Vz Then Vx = cos( φ x ), Vy = cos( φ y ) and Vz = cos( φ z ) y a y φ x φ z =90 O y =90 O a z φ z =90 O a x x z If Vz Vx = 0, Vx Vy = 10 and Vy Vz = 0, 1, the vector would point along xz axis 34

35 What is a direction cosine? We Let the just direction set the direction cosines be cosine represented to 1 for the by Vx, particular Vy and direction Vz Then Vx = cos( φ x ), Vy = cos( φ y ) and Vz = cos( φ z ) y a y φ x y =90 O a z φ z =90 O φ x =90 O a x x z If Vx = 0, Vy = 0 and Vz = 1, the vector would point along z axis 35

36 What is a direction cosine? We just set the direction cosine to 1 for the particular direction +x B C A Thank you for watching are there +y any questions 36