Find out what forces are competing on the flue expansion joint first
You just got the task of selecting a flue expansion joint. What is the biggest headache? It must be the thrust. If the thrust is miscalculated, the bracket will deform at the least, or the pipe will fly out at the worst. That will be a big problem. Don't panic, let's first pull out those "competing" forces on the expansion joint one by one.
The first one isBlind plate force, also often called internal pressure thrust. Why is it called blind board force? Because the bellows is like a blind plate, internal pressure acts on both ends, which will create an outward thrust. This force takes the majority, so it's all useless later.
The second isSpring stiffness force。 If you think about it, the bellows itself is an elastomer. If you compress it or stretch it, it will resist. The force of resistance is stiffness multiplied by displacement. Our websiteCorrugated expansion joint for power station industryIn the data, each model will give the stiffness value, which you can get by looking up the table.
And the third isfrictional force。 There are often dust and corrosive substances in the flue, plus the friction of the guide tube and the baffle door. Although this part of the force is not big, it can't be ignored. Especially the collocationFlue gas baffle doorOrDesulfurization flue gas baffle doorThe sealing surface friction will increase the thrust additionally.
Don't just focus on one force. All three forces have to be added to make the total thrust that the flue expansion joint ultimately acts on the fixed bracket.
Take out the formula: How to calculate internal pressure thrust? How to calculate spring force? How to add total thrust?
The formula couldn't be simpler.
- Internal pressure thrust (blind plate force)= Operating pressure × effective area of bellows
- spring force= Bellows stiffness × actual displacement
- frictional force= (This is generally taken empirically, or estimated by friction coefficient × positive pressure)
- Total thrust= internal pressure thrust + spring force + friction force
Attention! The effective area is not the cross-sectional area of the pipe, but the area calculated from the average diameter of the peaks and valleys of the bellows. Many newbies confuse this. You can get a message from usCorrugated expansion joint for power station industryFind the parameter "effective area" directly in the product information, so you don't have to calculate it yourself.
Do you just add the total thrust directly? Not necessarily. If the expansion joint is of axial type and the three force directions are consistent, add it directly. If it is transverse or angular, the force direction is different, so vector synthesis is necessary. However, what we are talking about today is a typical flue scene, most of which are axial displacements, so there is no fault in adding them directly.
Find out the parameters you need from our product information
Okay, now let's take a real case. Suppose you want to select the flue for a coal-fired power plant, working pressure 0.1MPa, temperature 400℃, and pipe diameter DN1200. You flipped through our websiteHigh temperature axial expansion jointProduct page, find the parameter sheet for this specification.
Lo and behold, it says: effective area A =1.13 m², axial stiffness K =200 N/mm, can compensate for axial displacement Δ L =50mm. These figures are measured and calibrated by the manufacturer, and are used directly.
High temperature axial expansion jointBecause of high temperature resistance, the wall thickness and number of layers of bellows are different from those of ordinary models, and the parameters of stiffness and effective area are different. Don't use the general model to set high temperature conditions, that will cause deviation. Each product of our website has an independent parameter page, just check it as needed.
Hands-on calculation: the calculation process of the real thrust of a high temperature axial expansion joint in the flue
Come on, let's do the math.
First step, internal pressure thrust : 0.1 MPa ×1.13 m² =0.113 MN. It is more convenient to convert to kilograms of force, 1 MN ≈ 102 tons of force, so about 11.5 tons.
Second step, spring force: 200 N/mm ×50 mm =10,000 N, that is, 10 kN, about 1 ton.
Step 3, friction: there is much dust in the flue, and there may be slight contact between the guide tube and the bellows. Assuming that the friction coefficient is 0.1, the positive pressure is estimated by the self-weight of the pipeline. However, in practice, many projects are directly estimated by 5% ~10% of internal pressure thrust. Here we take 8% of the internal pressure thrust, about 0.9 tons.
Total thrust ≈ 11.5+1+0.9=13.4 tons。
And guess what? That 13.4 tons is the force acting on the fixed brackets at both ends. If you are using a sliding bracket instead of a fixed bracket, then you have to consider sliding friction, but that's another topic.
Don't forget the deflectors and baffle doors! Do they affect thrust? How to fix it?
Many articles end here, but there is still a pit in the actual project- -guide tubeAndbaffle door。
The role of the guide tube is to divert the medium and protect the bellows from high-speed airflow. However, the inner diameter of the guide tube is smaller than the inner diameter of the bellows, which will form a throttling effect and generate additional differential pressure thrust. Especially when you're in the flue at the same timeFlue gas baffle doorOrDesulfurization flue gas baffle doorWhen the baffle door is closed, the airflow is blocked, the differential pressure will increase, and the thrust on the guide tube will also increase.
How to fix it? A local method: multiply the total thrust by the safety factor of 1.1~1.2, or calculate according to the additional thrust formula of the guide tube provided by the manufacturer. Our websiteSpecific Function of Expansion Joint Guide TubeIt is mentioned in the question and answer that the guide tube will increase the local stress of the bellows, but the thrust correction value is usually given by the manufacturer in the design. When you select a model, ask the sales directly for a "thrust calculation book with deflector", and they all have ready-made data.
In addition, if the back of the flue is connectedDesulfurization flue gas baffle door, also consider the impact load of the baffle door when opening and closing. That thing can double the thrust in an instant, and the fixed bracket must be checked for the most unfavorable working conditions.
What are you gonna do after the math? Do not let the pipe fly by comparing the bearing capacity of the bracket and the fixed point
After calculating the thrust is not the end, but the start. You now have 13.4 tons of thrust in your hand (or with a modified 15 tons added), what do you do next?
Find out the design bearing capacity of the flue brackets and fixed points. Usually the maximum horizontal thrust the support can withstand is marked on the civil engineering drawings. If the support bearing capacity is less than your calculated thrust, it is necessary to thicken the support, increase the number of fixing points, or switch toStraight pipe pressure balanced expansion jointTo offset some of the thrust.
Many accidents of pipeline flying are not due to the poor quality of expansion joints, but because the thrust is too small or the support bearing capacity is not enough. Especially in the renovation project of the old factory, the original bracket design did not consider the large-diameter expansion joint replaced later, and there were problems as soon as it was put into production. Therefore, it is recommended that you check the thrust calculation results with the structural engineer before construction and sign for confirmation.
Don't just look at the numbers, look at the direction. Thrust forces perpendicular to the axial direction of the pipe are equally dangerous, such as lateral wind loads and seismic loads, which are not included in the expansion joint thrust formula, but must be considered separately. Don't wait until the pipe is twisted to regret it.