[Weekly Question] (Issue 6, 2009) — “Theoretical Discussions on Static Analysis””
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This issue’s theme is “Theoretical Discussions on Static Analysis.” The activities for this issue focus on discussion, with CaesarII serving as the analysis tool. 1. Borrowing the question from lijia*: For accidental load conditions, the equation in standard B31.3 is: PD2/(Do2–Di2) + MA/Z + MB/Z < kSh. Here, MA represents the moment term generated by sustained loads, while MB represents the moment term generated by accidental loads. This equation indicates that in accidental load conditions, the stress is the sum of sustained stresses and accidental stresses. Therefore, we cannot rely solely on wind loads to meet the standard requirements. How can “W + P1 + WIND” be considered as a single load condition? The “W + P1 + WIND” condition is only applicable to linear systems; it is insufficient for nonlinear systems. For the same reason, “T1” is not sufficient for expansion load conditions. The best ways to establish accidental load conditions are: (1) W + P1 + T1 (OPE), (2) W + P1 + T1 + WIND (OPE), (3) W + P1 (SUS), (4) L1 – L3 (EXP), (5) L2 – L1 (OPE), (6) L5 + L3 (OCC). Is condition (6) equivalent to MA/Z + MB/Z? 2. In static analysis, what are the basic formulas for stress analysis (Code B31.3)? 3. What are the basic formulas utilized by the software in static analysis (Standard B31.3)? The discussion format can be a textual description or screenshots. I hope everyone will actively participate, discuss together, learn together, and improve together! This post was last edited by fanking on 2009-3-15 17:31]
(1) Primary stress—The stress generated by pressure, gravity, or concentrated forces is called primary stress. It is characterized by an increase as external force increases, and it has no self-limiting nature. When its value exceeds the material’s yield limit, the pipe will undergo plastic deformation until it fails. Criterion: S1 ≤ S1a = Sh ① (2) Secondary stress – the stress generated due to the restraint of the pipe’s deformation. It does not directly reach equilibrium with external forces; it has self-limitation. When the pipe yields locally or experiences slight deformation, the stress decreases. At this point, the redistribution of stress brings the strain in the material to self-equilibrium. Criterion: S2 ≤ S2a = f(1.25Sc + 0.25Sh) ② (3) When Sh > S1, the remainder of S1 can be added to S2a; that is, S2a ≤ f ③ In fact, S1 must be less than Sh, so the criterion for secondary stress is③
I hope forum members can use some classic examples for discussion and analysis!
This post was last edited by ythhw on 2010-3-5 09:09. Primary stress and secondary stress should be understood from fundamental theoretical perspectives; what is the theoretical basis for using such calculation methods to verify pipelines? There are detailed explanations in the information about Tang Yongjin; it is recommended to read it carefully
As for the principles, I recommend you take a look at Tang Yongjin’s book on pressure pipeline analysis. A single stress is non-self-limiting, so it cannot exceed the required stress. That is, 2/3 of the yield limit. Secondary stress is self-limiting, so it is determined based on the stability analysis of the pipeline. And it allows plastic deformation to occur once, but not multiple times. It is also the case that the sum of primary stress and secondary stress is less than twice the yield limit and three times the required stress; by then taking into account the safety factor and the effects of cycling, the aforementioned formula is obtained.
The basic theories are too complex; I can’t understand them. What’s the difference between static analysis and dynamic analysis?