What do the numbers 2 and 3 in the formula B=2/3EA for the calculation of pressure vessels under external pressure respectively mean?

That’s right, Zheng Jinyang, Process Equipment Design, 3rd edition, P118

This post was last edited by FMSD on 2015-7-9 at 11:15. Thank you to the person who posted above. Also, the charts used for calculating external pressures are all in the form of curves; such a representation makes it difficult and less accurate to find intermediate values. Where can I find more accurate material parameters, ones that are more precise than those presented in curve charts? Additionally, the manufacturing geometric errors of cylinders also affect the instability calculations. There are significant size errors in the welding of large-diameter cylinders as well as in their fabrication using rolling machines. Are there any specified limits for such errors in the relevant standards?

But why is B=2EA/3 also used in the calculations for tower stability? Axial compression instability and external pressure instability are not the same thing, right?

This post was last edited by fzujunru on 2016-6-14 at 11:05, with A representing the strain at the moment of instability. B is the corresponding stress. Container instability is divided into circumferential instability and axial instability. Circumferential instability is caused by the circumferential compressive membrane stress in the container; during this instability, the cross-section of the container changes from circular to wavy. Axial instability is caused by the film stress resulting from the axial compression of the container; during instability, the cross-section remains circular, while the axis changes from a straight line to a wavy line. B=2EA/3, which is essentially the relationship between stress and strain. All quantities in this formula are scalars, independent of the stress direction. So both types of instability apply.

This post was last edited by FMSD on 2016-11-25 at 11:34. What I’m asking is what the 2 represents. According to Zheng Jinyang’s Process Equipment Design, 3rd edition, page P118, the maximum stress σ when a cylinder is under pressure should be given by σ=PD/(2t). As for the 2 in the denominator, my understanding is that in the linear elastic stage of mechanics of materials, the stress σ is equal to the elastic modulus E multiplied by the strain ε. The 3 represents a safety factor; thus, σ can be expressed as σ=Eε/3. The formula B=2EA/3 is only applicable when a cylinder is under pressure. Then why do the standards use the same formula B=2EA/3 for axial compression instability and external pressure instability?

The last edit to this post was made by fzujunru on 2016-6-16 at 10:57. In my opinion, there are two possibilities: 1. Design P65 and P67 according to the principles for process equipment; the critical stress for axial instability, σcr, is 0.25Et/R, which is several orders of magnitude lower than the critical stress for circumferential instability, σcr = 1.1E(t/D)^2. Additionally, a value of B = 2AE/3 is used for axial instability – is this done for practical simplicity in engineering? 2. Axial instability: A = 0.094δe/R; circumferential instability: A = 1.1/(D/δe)^2. It is also assumed that B = 2AE/3. The standards for towers must take into account this difference when defining A. It’s just my personal understanding; I’m not sure if it’s correct, but I’ll consider it as a contribution to the discussion: lol. The standard JB4710-2005, in its standard explanations on pages P107–110, discusses the axial stability of cylindrical structures, but I really didn’t quite understand it

2 is the 2 in the denominator of the mean diameter formula; it represents twice the effective thickness calculated using material mechanics! 3 is the stability safety factor!

This post was last edited by FMSD on 2016-11-25 at 11:36. I’m also wondering why both axial stability and external pressure stability have B=2EA/3