How to check the Stability of ANY Truss?

  • Thread starter Thread starter Vigardo
  • Start date Start date
  • Tags Tags
    Stability Truss
AI Thread Summary
To determine the stability of 2D and 3D trusses without complex calculations, the conditions M + R >= 2J for 2D and M + R >= 3J for 3D must be satisfied, where M is the number of members, R is the number of support reactions, and J is the number of joints. However, meeting these conditions alone does not guarantee stability, as trusses can still be unstable due to improper constraints, such as parallel or collinear reactive forces. The discussion highlights the need for a systematic approach or "recipe" for assessing stability through simple geometric checks. Participants are encouraged to share references or methods that can provide sufficient conditions for stability in both 2D and 3D trusses. The quest for a reliable and straightforward method to evaluate truss stability continues.
Vigardo
Messages
87
Reaction score
7
TL;DR Summary
I´m need a method to determine 2D or 3D truss stability without solving complex matrix equations. It should be easily implemented in a computer program. Thanks!
Dear experts,

I´m searching for some method to determine whether any 2D or 3D truss is stable without solving complex matrix equations. I want to implement such method in a simple computer program to discard any a priori non-stable trusses for further analysis.

Do you know any book or reference where this may be well explained? Can you help me?

So far, I´ve found that the condition of stability can be expressed mathematically as M + R >= 2J for a 2D planar truss of M members, R support reactions, and J joints. Similarly, the condition becomes M + R >= 3J for a 3D space truss [1]. In case such conditions were not fulfilled, the truss should be Instable due to Partial Constraints.

However, fulfilling such conditions does not guarantee stability, it just seems to be something "necessary" but not "sufficient" to asses truss stability.

In [2], it is said that for planar trusses, the structure may yet be Unstable due to Improper Constraints when:
A) All of the reactive forces are parallel for the entire truss or any component part of the truss;
B) All of the reactive forces are collinear (intersect at one point) for the entire truss or any component part of the truss.

For example, the following structures fulfill such condition (M=4, R=6 and J=5, and thus M+R>=2J), but evidently they are not stable.
1699295981514.png
1699296169100.png

Please, don´t hesitate to correct me if I´m wrong at any point. Thanks!
 
Engineering news on Phys.org
In 3D happens something similar, M=6, R=12 and J=6, and thus M+R>=3J (18 = 18). It is evident that this 3D truss it is not stable because the vertical member will rotate easily due to the lack of restraints.
1699379188409.png


I need a "recipe" or sequence of simple geometrical checks or rules that work in all situations.

Is there any "sufficient" condition(s) for 2/3D truss stability?
 
How did you find PF?: Via Google search Hi, I have a vessel I 3D printed to investigate single bubble rise. The vessel has a 4 mm gap separated by acrylic panels. This is essentially my viewing chamber where I can record the bubble motion. The vessel is open to atmosphere. The bubble generation mechanism is composed of a syringe pump and glass capillary tube (Internal Diameter of 0.45 mm). I connect a 1/4” air line hose from the syringe to the capillary The bubble is formed at the tip...
Thread 'Physics of Stretch: What pressure does a band apply on a cylinder?'
Scenario 1 (figure 1) A continuous loop of elastic material is stretched around two metal bars. The top bar is attached to a load cell that reads force. The lower bar can be moved downwards to stretch the elastic material. The lower bar is moved downwards until the two bars are 1190mm apart, stretching the elastic material. The bars are 5mm thick, so the total internal loop length is 1200mm (1190mm + 5mm + 5mm). At this level of stretch, the load cell reads 45N tensile force. Key numbers...
I'd like to create a thread with links to 3-D Printer resources, including printers and software package suggestions. My motivations are selfish, as I have a 3-D printed project that I'm working on, and I'd like to buy a simple printer and use low cost software to make the first prototype. There are some previous threads about 3-D printing like this: https://www.physicsforums.com/threads/are-3d-printers-easy-to-use-yet.917489/ but none that address the overall topic (unless I've missed...
Back
Top