1

2

The bending moment distribution caused by current, waves, vessel motions and offset, and VIV can only be determined by global riser analysis.

3

A proper analysis must include all loading conditions and take every failure mode into account. Play the video “Storm in the North Sea”.

4

5

Collapse of a pipe is caused by external pressure (section collapse). Buckling of a riser is caused by axial compressive force (loss of top tension). Plastic hinge occurs when an excessive bending moment is applied to the pipe which causes the cross section to pinch.

6

The rupture of a material is typically perpendicular to the 1st principle stress. What direction is the 1st principle stress is an internally pressurized pipe? It’s the hoop direction. Therefore, which direction is perpendicular? The axial direction. Press page down to see a picture of a burst failure.

7

8

Press page down to see a picture of a fatigue failure. There is typically a ductile tearing section that is characterized by beach marks. Each beach mark represents once loading cycle. The initiation site can be found by tracing the beach marks backwards.. Once cross section is reduced to the point where the remaining section cannot sustain the load, sudden brittle fracture occurs. The brittle fracture surface typically looks torn and random.

9

The ductile surface is on top. The beach marks propage downward. The brittle fracture section is at the bottom.

10

Once of the key outputs of the global riser analysis is an operatability window. This chart provide curves which depict the normal, extreme, and survival windows of operation. The normal limit is based on 0.67% of yield strength, extreme 80%*YS, and survival 100%*YS. The chart can graph vessel offset vs top tension so that the maximum tension (pipe yield) and minimum tension (system hanging weight) can be plotted. The minimum tension is the tension below which compression in the riser occurs.

11

This is a different type of operability window. The vessel offset is plotted vs the significant wave height (Hs). Limit curves are plotted for accidental, extreme and normal operations. The limit curves for the maximum stroke and maximum angle of the system are also plotted.

Actual operating window from a riser analysis.

A decision tree is a single page lookup table which provides a vessel operation a definition of operations which are normal (green), extreme (yellow), prepare for EQD (orange), and ESD or EQD (red).

14

Step through the formulation of the hoop stress and longitudinal stress equations for internal pressure. If you cut a pipe laterally, the pressure that acts on the end cap generates a pressure end load and a longitudinal wall stress. If you cut a pipe axially, the pressure on the half section generates a hoop stress. Derive both thin wall equations on the white board.

15

For internal pressure, use internal radius for r. For external pressure, use external radius for r. For both internal and external radius, use differential pressure for P and mid-wall radius for r.

16

If an internally pressurize pipe is not leaking there must be an end cap with pressure end load even if the pipe is very long. The only cases without pressure end load are 1) if the end cap is sealed to the pipe but not physically connected to the pipe (dogbone, production stab, pressure test at pipe mill) 2) a buried pipeline will have the pressure end load be reacted through its interaction with the soil 3) the external end load is perfectly balanced with the internal end load 4) the very long pipeline is pressurized so that it will flow out the open end. See Sparks Fig 4.4.

17

For a flange and groove. See Figure 3-7.

18

The thick wall equations for pressurized pipe were developed by Lame’ to design cannon barrels for war making. Lame’s equations are published in French and were first translated in English by Timoshenko. These equations are republished in Shigley and other modern machine design books.

19

The von Mises formula listed is for principal stresses only. If shear stress is involved, then this equation is not appropriate. The hoop and radial stress vary from the ID to the OD. Hoop stress has the highest magnitude at the ID. The axial stress is constant thru the section. The von Mises stress is always maximum at the ID. See Sparks Section 4.1.

20

21

22

External pressure due to hydrostatic head of the seawater column can cause collapse of the riser pipe. The best collapse calculations are in API 5C3 or ISO 13628-7. Differential pressure is defined as the internal pressure – external pressure. Differential pressure is often used in the stress calculations in place of internal pressure. This is okay for pipe bodies and even complex section, but this may not be okay for seals. Also, components in fatigue service do not get a benefit from external pressure.

23

These are some basic collapse calculations from API 5C3 for reference.

Yes for pressure containing components that do not have seals and are not in fatigue service unless regulations require otherwise. This is true for any shape (simple or complex). For round parts you can prove that the equivalent stress (Von Mises) contains a differential pressure term. You can also show for round parts that first principal stress is does not have a differential pressure term. For non-round parts, FEA can be conducted to prove the same. For seals, you need to check how the seal acts from pressure on both sides.

25

26

External pressure can cause collapse and buckling during deployment. For buckling to occur during deployment, the buoyance force must be greater than the weight of the riser. If the riser is heavier than the buoyancy, then the riser will deploy to any depth without buckling. The axial end cap force caused by external pressure is distributed throughout the body of the riser pipe and isnt confined to just the end of the pipe. Draw a picture of this on the whiteboard to demonstrate. See Sparks Fig 3.4.

External pressure can cause collapse and buckling during deployment. For buckling to occur during deployment, the buoyance force must be greater than the weight of the riser. If the riser is heavier than the buoyancy, then the riser will deploy to any depth without buckling. The axial end cap force caused by external pressure is distributed throughout the body of the riser pipe and isnt confined to just the end of the pipe. Draw a picture of this on the whiteboard to demonstrate. See Sparks Fig 3.4.

The riser carries the weight of the internal fluid inside the riser. Correspondingly, the wellhead carries the weight of the fluid in the wellhead. This is an important concept as the structural stability of the riser is dependent on the top tension keeping the riser in tension (not compression). It is customary and required to include the riser contents in the top tension calculation. In order to understand this concept, its important to know that the weight of the internal fluid acts at every level of the riser and not just and the bottom. The way the internal fluid imparts it weight on the riser is through hydrostatic pressure head. The hydrostatic pressure at any level is equal to the weight of fluid above that level divided by the internal area. This is also true weith the external pressure (equals to the buoyancy force at that level divided by the external pressure). Internal fluid weight and buoyancy acts on every level of the riser. See Sparks Fig 2.4.

29

30

31

See Sparks Fig 4.1.

32

Bending is the primary cause of fatigue damage in a riser. Classic bending caused linear distribution of stress and strain in a plate with a tensile and compressive stide. For a pipe, the same is true except there is no material in the ID. Thus the distribution of stress and strain is relatively small, but there is still a tensile and compressive side. See Sparks Fig 4.5.

33

Draw a cross section of a pipe and show how the stress and strains vary thru pipe.

35

Catenary equations define the shape of a long wire under uniform lateral loading. Catenary equations involve hyperbolic functions

A pressurized fluid cannot generate a bending moment on a submerged object. Therefore an internally pressurized fluid cannot generate a bending moment on the containing vessel. This is counter intuitive because a bent pipe straightens when pressurized. Also a straight pipe is more stiff when pressurized? See Sparks Fig 2.1.

37

Read the bullet points. Discuss the figure. The figure show how the lateral force cause a lateral reaction and the riser to displace. The top tension creates a restoring force to resist the deflection. Stiffness is define as the force to cause a unit deflection. Top tension increases stiffness and reduces deflection and therefore increases radius of curvature and reduces bending stress (reduces fatigue damage). Increasing stiffness also changes the vibration frequencies of the riser. Also, the student should be aware of the differences in total tension and effective tension. The effective tension is the externally applied tension from the tensioner plus the hanging weight of the equipment below the point of interest. The total tension include the effective tension plus the effect of pressure end load and hydrostatic pressure head. The stiffness of the system is dependent on the effective tension (not the total tension). See eqn 2.19.

38

39

All three diameters increase. OD increases faster than the ID so that TD can also increase. If you are in doubt, imagine inflating an inner tube (outside of a tire). The message here is that internal pressure increases the radius curvature of a pipe. Normally we interpret increasing or decreasing curvature with an external bending moment. In this example only pressure is applied (no external bending moment) and we know a fluid cannot generate a bending moment.

40

The answer is that the method of superposition states that multiple loads on a linear system can be calculated separately and their results added together. Therefore, the answer is that the pipe deflects axially 0.182” and laterally 0.463”. This is absolute truth of strength of mechanics, but a quick FEA can easily prove this. The point is that pressure does not affect the stiffness of a riser system. Pressure increases the radius of curvature of the riser, but does not change the lateral displacement of the riser.

Read the bullets on the slides. This is a key point of riser analysis.

A bent pipe straightens because its curvature increases due to the internal pressure. Recall the hollow pressurized torus example. A pipe is not more stiff when it is pressurized when the stiffness is defined by force/lateral deflection. A pressurized pipe is more stiff when the stiffness is defined a force/change in curvature. This is the reason why pressure does not affect the stiffness of a riser pipe, but does affect the force required to spool a pressurized hose.

There are two methods to determine the ultimate limit of the system. Traditionally, we have define the ultimate limit as a percentage of yield stress. This is called the working stress design. A more modern approach is to define the ultimate limit as a percentage of the limit state of the structural relative to the load type. For pipes in an internal pressure, the limit state is burst. For externally pressurized pipe, the limit state is collapse or yield. For pipes undergoing bending, the limit state is plastic hinge (shown in the FEA contour plot). For a tensioned pipe, the limit state is yield. For a compressed pipe, the limit state is buckling or yield depending on what comes first.

44

45

This a simple method to estimate a conservative value of plastic hinge. You can apply this method to any section shape as long as you have it half centroid. This method works well for compact sections only.

47

Axial stress in the equation above is also true stress. If the first term in the axial stress is remove, the remaining equation is effective stress.

48

Typically, working stress is used for normal operations and limit states are used for extreme and accidental operations.

49

The riser stretches due to top tension, pressure, and thermal elongation. This need to be estimated so that the tension is designed to accommodate stretch. If the tension does not have enough stroke, the tensioner may bottom out which causes the riser to go in compression.

50

The required stroke of the tension may be underestimated causing the tensioner to bottom out and the riser to go into compression.

51

In order to conduct a fatigue analysis, the fatigue performance of a component must be understood and mathematically defined. There are standard set of fatigue curves used in industry (DNV C203). In order to use these curves, they must be adjusted to the stress concentration factors of a particular design. A finite element analysis can be conducted to estimate the magnitude of the SCF. A fatigue test could also conducted.

52

SCFs can be calculated using Shigleys Mechanical Engineering Design, Roarks Formulas for Stress and Strain, Petersons stress concentration factors book, or FEA.

53

This is an example of an SCF chart that can be found in a engineering design textbook. It is here for reference.

55

Connectors can have 4 limits states. First, they can be structurally overloaded causing failure. Since the combinations of load which cause structural failure is more complicated than a pipe, a load capacity chart is provided. An example is shown in the slide. Another connector limit state is a sealability limit. Sealability load charts show the combination of loads where gas and liquid seal can be maintained. The third limit state is a hub separation limit. At hub separation, the connector may experience higher fatigue damage due to cyclic loads since the preload of the connector is no longer protecting the connector. Also, if external loads cause hub separation and those loads are removed the connector may have lost some of its preload due to yielding. The last limit state is fatigue. Connector fatigue is normally defined as an stress amplification factor, stress concentration factor, reference cross section, and fatigue curve.

56

This load chart shows the hub separation, sealability as well as structural limits. For reference.

Next slide for the answer

58

The bolt tension remains the same until the external tension is increased above the total preload on the flange. Thereafter the bolt tension increases 1 for 1 with the external tension.

This is a graph of what was depicted in the previous slide. Notice how the bolt tension does change as long as the external load is less than the preload even if load cycling is occurring.

These are two more bolt loading cases. If the external load is greater than the preload, then the bolt tension follows the external load including any load cycling. If the external load cycles about the bolt preload, then the bolt load is partially protected by the preload.

This slide is a result of an FEA on an actual flange. It depicts the same behavior as the previous graph.

62

The problem with stress amplification factors is that they are constant for all load inputs. As shown in the previous slide, the fatigue performance changes with increase load amplitude. Therefore, a better method to define fatigue performance of a connector is a non-linear equation (since SAF assumes a linear relationship between applied load and fatigue stress).

63

Traditionally the stress tension is removed from the wall of a pressurized cylinder as shown on the right (the sides are square to the hoop and radial directions). The leads to the three principal stresses in a pressurized pipe (axial, radial, hoop). The application of pressure generates reactions in all three principal directions. CP Sparks discovered that if the stress tensor was rotated by 45 degrees as shown on the left, then only two stresses are required to understand the stress state (shear and effective stress). It turns out the third stress is just a hydrostatic stress (a stress that is equal on all faces) which does not cause deformation and failure. See Sparks Fig 4.2.

64

Notice how the cylinder axially and diametrically grows with internal pressure. This results in a wall thinning. At the stress tensor level, the element is shearing as shown in the before and after shot.

See Sparks Eqns 4.7, 4.8 and 4.9.

66

The principle stress directions in a pressurized pipe is the hoop (1st), axial (2nd), and radial (3rd). The maximum equivalent stress in an internally pressurized pipe is the ID. It turns out that this is also the location of maximum shear stresses.

67

68

69

70

71

72

This a simple method to estimate a conservative value of plastic hinge. You can apply this method to any section shape as long as you have it half centroid.

74

75

External pressure due to hydrostatic head of the seawater column can cause collapse of the riser pipe. The best collapse calculations are in API 5C3 or ISO 13628-7. Differential pressure is defined as the internal pressure – external pressure. Differential pressure is often used in the stress calculations in place of internal pressure. This is okay for pipe bodies and even complex section, but this may not be okay for seals. Also, components in fatigue service do not get a benefit from external pressure.

76

77

The riser stretches due to top tension, pressure, and thermal elongation. This need to be estimated so that the tension is designed to accommodate stretch. If the tension does not have enough stroke, the tensioner may bottom out which causes the riser to go in compression.

78