In Fig 10, we again see the stress state for an element along the length of the pipeline and here, show the magnitude of the stresses. As we progressively pressurize the balloon ie, blow it up , we go through states 2, 3, 4, 5 and then 6. At this point, I want to introduce another Ôengineering diagramÕ called the MohrÕs Circle. These stresses and strains can be calculated using the Lamé equations, a set of equations developed by French mathematician. Spherical vessels are theoretically 2 times stronger than cylindrical ones but due to the manufacturing difficulties, cylindrical ones are generally preferred in the industry.
In simple Tension equals It can be seen from the figure that the Hoop falls off appreciably as the material near the outside of the tube is not being stressed to the limit. Some of our calculators and applications let you save application data to your local computer. Now here shows one, tiny-tiny cube of steel that makes up the ÔwallÕ of our pipeline; and also shown are the normal stresses that act on it. Please read for more information. This is where the weld would be, joining two sections of pipe.
Many things can alter the position of the failure envelope. Each element of pipe are subjected to the below mentioned stresses which act in the direction as shown in the fig. The hoop stress in the steel membrane of the cylinder would then be 17,000 psi, a very reasonable stress for carbon-steel to handle. Both are a function of the pressure, pipe radius and wall thickness, just as was the case with the spherical balloon. These Stresses may be expected to vary over any cross-section and equations will be found which give their variation with the radius. Here is an online Thick Walled Tube Hoop Stress Calculator which helps to calculate hoop stress for Thick wall cylinder, pipe or pressure vessel.
Remember, this is just conjecture and in no way represents an analysis of the catastrophic events of September 9, 2010. Now let us define these stresses and determine the expressions for them. When a thick-walled tube or cylinder is subjected to internal and external pressure a hoop and longitudinal stress are produced in the wall. Please note the following: the two ends of this one-section of pipe look distinctly different. Before we leave this comparison, let me offer one more photo from the Internet labeled Fig. One is the Hoop Stress and the other, the Longitudinal Stress. Longitudinal stress: Stress acts in longitudinal direction.
The radial stress for a thick walled pipe is given by where ri is the inner radius, ro is the outer radius, pi is the inner absolute pressure and po is the outer absolute pressure. The majority of numerical problems can be solved by the application of equations and. The maximum, tensile normal stress is shown on the x-axis ie, the normal stress axis to the right; and you will note there is a small, negative or compressive normal stress to the left. Shear stress is 0 at the orientation where principal stresses occur. Units for t, and d are inches in. Of course, we all realize that this is not possible. The circumferential stress and longitudinal stresses are usually much larger for pressure vessels, and so for thin-walled instances, radial stress is usually neglected.
It's the 2 nd principal stress. Again, compare this photo with the fracture surfaces seen in the second photo on this web page, the one showing the critical pipeline section from San Bruno. The steel material sees many, many cycles of this type of pumping motion. The resulting stress state on vessel is plane stress situation since all stresses are tangent to surface of vessel. At some time, it may even be reduced enough to intercept the ÔallowableÕ or ÔsafeÕ normal stress limit; and what was safely contained at say 400 psi can no longer bear the load. In the media, it has been reported that there are both longitudinal and circumferential welds in the failed pipeline. If the membrane were thinner, the stresses would go up for the same degree of pressurization.
In practical engineering applications for cylinders pipes and tubes , hoop stress is often re-arranged for pressure, and is called. This formula is expressed mathematically as? To understand shear stress, place an imaginary, but heavy, cardboard box on the floor and try and slide it across the floor. In , a cylinder stress is a distribution with ; that is, which remains unchanged if the stressed object is rotated about some fixed axis. Where does the compressive stress come from? So, one must inspect the pipeline with some regular frequency to assure that conditions are knownÉ not that they havenÕt changed, but that the new pipeline condition will not adversely impact the integrity of the pipeline. This is one type of repeat cycle. These are very important when consider ÔwhyÕ something failed. You should concentrate on what is happening right on the two, perpendicular axes! We can introduce the concept of a Ôfailure envelopeÕ in this diagram, Fig.
The formula is expressed as? The rubber membrane thickness is a small fraction of the radius of the balloon. As you will soon see, for a given pressurization level, the stress trying to blow the ends off is only one-half of the stress trying to split the cylinder along its length! Provided that the tubes are made of the same material, the two tubes may be treated as one. It is possible for the pipeline to fail at a moderately low pressurization. The center section is missing and is the section in the street some 160 feet from the crater. The Stresses due to the application of internal pressure are calculated in the usual way. Before the hoop stress can do much of anything, the longitudinal component of stress will overcome the glue and the two halves will go flying! It is usually useful to any force applied to an object with into components parallel to the cylindrical coordinates r, z, and θ. Now many of these issues are in question, as regards the utility and contractors that maintained the service.