Basic principles of compressive force Vessels subject to External Pressure Before After The result of just air pressure! Presented by: Ray Delaforce
Basic principles of compressive force Consider For a tensile, a simple the force bar subject to promote to a tensile failure force is: F = UTS x A Failure can be predicted with fair precision knowing: The Tensile Strength UTS Cross-sectional area A The tensile force F The force to promote failure is: F = UTS x A That is a simple prediction
Basic principles of compressive force For Now a we tensile, bend the force column to promote (or plate) failure into a is: cylinder F = UTS x A Now, consider a compressive force applied to the same bar It bends like this important - It changes shape! Look at the consequences of changing shape - bending There is both a bending stress and a compressive stress In the case of the bar subjected to tensile there is one stress Here is the change in shape! Does not Stable change shape x F
Basic principles of compressive force Now we bend the column (or plate) into a cylinder Subject it internal pressure P, it becomes a stable circle Now to external pressure P, it becomes less stable P Stable Un-Stable Subject to just Membrane stress x F
Basic principles of compressive force Now Consider we bend the rolling the column process (or to plate) form into cylinder a cylinder from plate Subject it internal pressure P, it becomes a stable circle Now to external pressure P, it becomes less stable P Stable Subject to just Membrane stress Failure is predictable Un-Stable Subject to Membrane and Bending stresses Failure is un-predictable
Basic principles of compressive force Consider Some shapes the rolling subject process to external to form pressure cylinder are from very plate un-round It is passed through roller to form the cylindrical shape Passed back through the rollers until the cylinder is formed This process does not form a perfect cylinder, it is slightly oval D 2 D 1 Codes limit the difference between D 1 and D 2 to about 1-1/4%
Basic principles of compressive force Some Large shapes thin tanks subject are very to external prone to pressure vacuum are collapse very un-round This has to be subject to very special analysis That is why deep sea submersible are spherical it is the most stable shape
Basic principles of compressive force Large A shorter thin cylinder tanks are is also very better prone to withstand vacuum collapse a vacuum condition These tank have a very large D/t ratio, which makes them very weak when subjected to vacuum conditions We learn that the D/t ratio largely determines the ability to withstand even a partial vacuum
Basic principles of compressive force A Theoretical shorter cylinder work has is also been better done to on withstand cylinders a subject vacuum to condition vacuum A long cylinder can be made shorter by adding a vacuum ring Now we have learned two important facts: A large D/t ratio makes a cylinder weaker A large L/D ratio makes a cylinder weaker In every pressure vessel code, these ratios are important For internal pressure, the Pressure it can take can be predicted: P = 2.S.t D That formula does not work for cylinders subject to external pressure: Because there are bending as well as membrane stress present
Basic principles of compressive force Theoretical We look a little work more has closely been done to the on Effective cylinders Length subject of to a vacuum cylinder Cylinder subjected suffer Lobing as the pressure increases Increasing external pressure No Pressure More Pressure More Pressure More Pressure More Pressure No lobes 2 lobes 3 lobes 4 lobes 5 lobes In practice, this is not so predictable To withstand external pressure two metal characteristics are important Young s Modulus E Yield strength S Y These characteristics are not important for internal pressure
Basic principles of compressive force We Consider look a little Conemore instead closely of a to head the Effective Length of a cylinder This is the effective length of the cylinder as it stands alone However, when heads are added, the effective length changes Effective length exists between points of support Now, suppose we add a vacuum stiffening ring There is now another point of support Making the effective length shorter L L
Cone Junction Analysis Basic principles of compressive force Consider a Cone instead of a head This now becomes the Effective Length Why is the point of support not here? It has to do with the Shell to Cone junction We now take a short detour to discuss the cone junction L
Cone Junction Analysis First, we consider the basic principles 13
First, we consider the basic principles Apply internal pressure see what the cone wants to do The cone wants to separate from the cylinder It cannot because it is welded to the cylinder here This is what it does instead Cone Junction Analysis P 14
Cone Junction Analysis First, Consider we consider the free body the basic diagram principles (to see the forces that are acting) Apply internal pressure see what the cone wants to do The cone wants to separate from the cylinder It cannot because it is welded to the cylinder here This is what it does instead Notice the movement P Let us examine the forces that are acting in this region 15
Cone Junction Analysis Let Consider us take the another free body view diagram of the forces (to see acting the forces on the that junction are acting) Treating this point as a hinge: Resolving components The cylinder must have the reaction forces here they are There is a compressive hoop stress here This is the force causing the problems 16
Cone Junction Analysis Let Remember, us take another Stress = view Force of the / Area forces acting on the junction The forces trying to collapse the junction can now be seen By analysing a small piece of the junction we can see the forces There must be a balancing force here it is A compressive hoop stress is trying to collapse the junction F F 17
Cone Junction Analysis Remember, Consider Stress = a cone Force subject / Area to internal pressure We now consider the Area of the junction, and Effective Area Excessive stress can be reduced by Increasing the Area If necessary, we can add a compression ring increases area Full details can be seen in: ASME Appendix 1-5 and 1-8 F F 18
Cone Junction Analysis Consider a cone subject to internal pressure 19
Cone Junction Analysis Consider a cone subject to internal pressure 20
Cone Junction Analysis Consider a cone subject to internal pressure 21
Cone Junction Analysis Let us revisit Consider our illustration a cone subject of the to Cone-Shell internal pressure junction 22
The Cone is treated as Cone a completely Junction Analysis separate element Let us revisit our illustration of the Cone-Shell junction This is the situation if the cone-shell junction is not reinforced If reinforced by self reinforcement or a ring added, this happens Maybe a ring was required to give sufficient reinforcement We also have to consider the small end junction of the cone-shell If the small end is not reinforced, the effective length changes The lengths L are for the cylinders only not the cone itself L L L L 23
The Let us Cone consider is treated this vessel as a completely as an example separate of the element foregoing The cone is turned into a equivalent cylinder With transformed dimensions, only D O is the same Recall, these dimensional ratios are important for cylinders subject to external pressure: A large D/t ratio makes a cylinder weaker A large L/D ratio makes a cylinder weaker L e te D o Let us see how this works in practice 24
Let us consider this vessel as an example of the foregoing 4 516mm When We first both consider end of the design cone are where considered the cone as is reinforced not reinforced (demo) (demo) The large cylinder fails under external pressure 25
Did Let us you consider notice the this cone vessel junction as an example at the large of the end foregoing of the cone failed? 1900mm 4 516mm When both end of the cone are considered as reinforced (demo) 26 The large cylinder withstands the external pressure with a short L
Did There you is notice another the effect cone when junction external at the pressure large end exists of the cone failed? Reinforcing ring required here 27
There is another effect when external pressure exists There moment is a compressive can produce axial a problem stress induced the shell in the shell This does not present a problem, because: The axial stress is half the hoop stress It becomes important when there is a moment present when there is a wind load or, when there is a seismic load 28
Consider There is another what constitutes effect when Load external Cases pressure exists The moment can produce a problem in the shell One side there is an increased compressive stress The combined compressive stress could buckle the shell Let us look at the concept of Load Cases Increased tension Increased compression Compressive stresses added together 29
Consider what constitutes Load Cases The moment can produce a problem in the shell Stress from Pressure: σ P = ± P.D 2.t From weight: σ W = - W π.d.t From the moment: σ M = ± 4.M π.d.t The final equation depends on only: Effects from the pressure Effects from the weight Effects from the applied moment So the final equation is: σ = ± P.D 2.t - W π.d.t ± 4.M π.d.t 30
Consider what constitutes Load Cases The moment can produce a problem in the shell Stress from Pressure: From weight: From the moment: Design pressure Operating weight Seismic moment Hydro pressure Hydro weight Wind moment No pressure No weight Hydro moment Vacuum No moment Thank you for watching Any combination can apply, for example Or perhaps this Any questions? From what we have above, there are 48 load cases in all We can see this in PV Elite (demo) 31