# What is Buckling: Definition and 100 Discussions

In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress in slender columns.

Buckling may occur even though the stresses that develop in the structure are well below those needed to cause failure in the material of which the structure is composed. Further loading may cause significant and somewhat unpredictable deformations, possibly leading to complete loss of the member's load-carrying capacity. However, if the deformations that occur after buckling do not cause the complete collapse of that member, the member will continue to support the load that caused it to buckle. If the buckled member is part of a larger assemblage of components such as a building, any load applied to the buckled part of the structure beyond that which caused the member to buckle will be redistributed within the structure. Some aircraft are designed for thin skin panels to continue carrying load even in the buckled state.

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1. ### How to Calculate how much a column buckles?

I’m am looking for how to calculate the new horizontal and vertical “size” of a column based on the material and how much force is applied from the top/ends. I have 3D printed TPU pillars that are made to compress and mold to a shape, but I am trying to figure out how much they will compress...
2. ### Engineering Compression buckling of column

Hi, all. The top beam is subjected to uniformly distributed load. FYI, the column is 5m in length. As you can see, the major axis of column is connected to the beam with moment connection on top. However, in the minor axis of column, there's nothing to connecting them.For the major axis, the...
3. ### Capped pressure vessel - strength and stability

Hi, in mechanics of materials books one may easily find fomulas for stress and strain in thin- and thick-walled cylindrical pressure vessels subjected to internal pressure. However, it is assumed that they are open. So what are the formulas for stress and strain in capped vessels (with flat or...
4. ### Engineering How to Find the First Buckling Load from the Deflection Equation?

Hi, I was working through a problem about calculating buckling loads. The problem had the following geometry (I apologise for the poor drawing skills): and the total length is ## L ##. The boundary conditions are therefore: 1. ## y(0) = 0 ## 2. ## y(L) = 0 ## My approach: After taking a cut...
5. ### Can thermal expansion cause buckling in a compressed plate?

Hi, in the Timoshenko’s book "Theory of elastic stability" one can find a case of simply supported rectangular plate uniformly compressed in one direction (compressive load is applied to shorter edges). The formula for critical load is: N_{cr}=\frac{\pi^{2} D}{b^{2}} \left( \frac{b}{a} +...
6. ### I How could Euler have gone about creating his buckling formula?

Admittedly Euler was a genius and I am a noob, but I sometimes feel that there must have been a method or process that he followed to go about such problems and came up with these elegant solutions. It couldn't have been just a sudden flash of genius. For example, I wonder how he could have come...
7. ### Buckling and modal FEA of a submarine structure

Dear FEA experts, I'm trying to model the mechanical behavior (static, modal, and buckling analyses) of an underwater floating structure (e.g. submarine capsule or buoy) under hydrostatic pressure by Finite Element Analysis. To obtain feasible results, the structure should be modeled as freely...
8. ### Understanding Bending Moments and Moment Equilibrium in Structural Analysis

I have a quesrion about forming the eqaution of moment equilibrium. As shown in the picture at cut 1 there are 2 vertical forces and a bending moment. I expect V=A. If I apply moment equilibrium about the point where the bending moment is, we get that Ay*x = M(1). But how about if I take moment...
9. ### Weird (or not) issues in thin-walled cylindrical shell buckling modes

Dear FEA experts, I’m trying to analyse* some finite elements model of a thin walled cylinder with variable cross-section, but I’m observing four weird issues in the buckling modes. The structure is vertically (along z-axis) and horizontally (along y-axis) loaded on top. Would you help me to...
10. ### Subsea Pressure Housing Design – Wall Thickness for Stress & Buckling

I’m designing a subsea sensor that will go to a max depth of 600 m (6 MPa/60 bar). In a simple model, it will be made of a pressure housing cylinder and two end caps, all grade 5 titanium. Some geometry is attached. I’m looking for advice on how to calculate the thickness of the...
11. ### Question 3B Part II: Buckling or Crushing? Joe Seeks an Explanation

Hi all, the question has been posed many times, unfortunetly, there does not seem to be any explanation for finding the mode of buckling in Question 3B part ii, hence we i am posting. 1. Homework Statement Below in image Homework Equations Also elow in image The Attempt at a Solution The...

Hi all, I have recently been asked to calculate the Buckling load on a beam (channel) carrying pipes, (Eulers critical load) this was no problem. Then i was asked to allow for wind loading.. I can not for the life of me figure out how to do this? Any tips for me? Thanks in advance
13. ### APDL Programming buckling FEA C Section Cold Formed Steel

Hi, I am facing issues with my program. Listed below. This is form my masters project. Also in what way can I connect the filleted surfaces shown in fig by a weld or just load or stress transfer connection. fini /clear /title,C160T2B70-1L /prep7 et,1,shell181 r,1,2 mp,ex,1,1.85e5...
14. ### Column buckling in a pin jointed structure

<< Mentor Note -- thread moved from the schoolwork forums to the ME forum because it's more of a general question >> Hi, in these column bucking notes (photo attached below) it says that bar BC will buckle first out of all the other bars in compression, but it does not explain why. I know it...
15. ### How Do You Calculate Geometric Buckling for Cylinders and Spheres?

Mentor note: Thread moved from a different forum section, so missing the homework template. I'm very confused about the attached questions on geometric buckling of a cylinder and a sphere. For this question I'm not given a value for the extrapolated distances (for R' and H') so I simply put the...
16. ### MHB Engineering - Stress and Buckling Load problems

Hello, I am in an engineering summer camp, but since this is a condensed course and it seems the professors assumed the class already had some background in the subject, I am slowly getting lost. They gave us practice tests from previous years, and I was wondering if someone could show me how to...
17. ### How Do You Calculate Buckling Load and Failure Mode in Columns?

Homework Statement i am completely lost with this question. i need to work out: a. what minimum length the column will buckle. b. what load the failure would occur. c. if column was half length what would be mode of failure and the load it would fail at. i would appreciate any help as i am...
18. ### 40 foot shipping containers, yield strength / buckling

Hi, I am currently needing to place (and weld to the ground) a shipping container on a low bridge that is perpendicular to the shore. I was wondering if anyone knows how much force the sides of the container can withstand before buckling and/or bending. In essence, we have to account for very...
19. ### Buckling Simulation: Questions & Answers

Hi everyone, My objective is to create a quantitatively accurate simulation of a column buckling. Ideally, I would like to apply a compressive axial force at or just above the critical load to an initially straight column (perhaps with a small perturbation) and see it transition from the...
20. ### Self Buckling Initial conditions

Hi For a book I'm writing, i try to write a very very very detail proof of self-buckling. I did it almost by taking inspiration of: https://en.wikipedia.org/wiki/Self-buckling But i really really don't get how we arrive to, that when, x=0 as we obviously must have: \dfrac{\mathrm{d}^2...
21. ### A Verifying Buckling Solution with NDSolve/DSolve

Hi I am trying to verify my manual solution for this problem by any way, so I tried NDSolve, and DSolve, in mathematica with no success. I don't need it in mathematica I just need any way poosible, even matlab, or any other numeric way/soltuion. Can some one help, or even give me the final...

Homework Statement I'm reading a paper and I'm trying to understand how does the author arrived from equation (1) to the following buckling load equation (2). I know that the author substitutes equation (1) with the dimensions of the geometry but I still could not understand how he comes to...
23. ### Yielding vs buckling comparison

Homework Statement http://www.continuummechanics.org/eccentriccolumnbuckling.ht In here , i was told that for the eccentrically loaded column , the column will fail due to before it buckles . How is that possible ? Homework EquationsThe Attempt at a Solution The column will start to buckle...
24. ### Secant Equation for Buckling and Yielding in Eccentrically Loaded Structures

Homework Statement In the following example , the secant equation circle part) is used to find the max stress when the whole thing is subjected to force P before buckling , am i right ? Why the author wrote it as the yielding equation ? And why the author use 2 equation for yy axis ? Homework...
25. ### Sign of moment in buckling of column

Homework Statement Can someone explain why the M is assigned to be anticlockwise here ? Homework EquationsThe Attempt at a Solution When i assign it as clockwise , i will get -P(δ -v) , which is different from the author ... Can i do so ? Why ?
26. ### Column under a concentric axial load (Buckling)

Hi everyone, I have a cylindrical column under a concentric axial load. The load which is applied in the column is less than the critical buckling force (according to Euler´s formula). Due to this load, the column suffers a displacement (buckling effect), and I would like to determine which is...
27. ### Buckling of beam in different direction

Homework Statement For the y-y axis buckling , the beam will bend towards either positive or negative y-axis , right ? I don't understand that why for y-y axis buckling , moment of inertia (Iy) about y-axis is used ? Homework EquationsThe Attempt at a Solution IMO , it's wrong ... When the...
28. ### Buckling of column connected to beam

Homework Statement In this question, we are interested inthe buckling of column, so we should calculate the moment of inertia (Ixx) or (Iyy) at the column,right? Homework EquationsThe Attempt at a Solution Why the author calculate (Ixx) and (Iyy) using the cross sectional area of beam? is it...
29. ### Understanding Effective Length in Buckling Equations for Columns

1. The problem http://www.efunda.com/formulae/solid_mechanics/columns/columns.cfm what is the meaning of effective length here? Homework EquationsThe Attempt at a Solution When the ends is fixed or unfixed , or supported , the length remain L , am i right ? what's the difference between actual...
30. ### Post Buckling Analysis in ANSYS

Hello everyone, I am trying to use ANSYS to calculate the reaction force in the edge of a buckled thin plate. (One edge is constrained and the other edge is displaced). According to what I read in the Help Documentation, the study should be done in Static Structural, and a stabilization...
31. ### Negative Buckling: What Are the Conditions?

Under what conditions would negative buckling (B^2) be possible?
32. ### Column buckling under axial+transverse combined load

Dear experts, Do you know the buckling load of a column (one end clamped one end free) under axial compressive and transverse lateral forces (applied combined at top free end)? Does the lateral load reduce the critical load or just reduces the stiffness of the column? Would you help me? -Thanks!
33. ### Critical Buckling loads-how to plot?

Homework Statement Hi all, I am an architect so engineering is not my strong point. for these equations I am unsure how to correctly determine the mode of failure and plot a graph. Any help would be greatly appreciated. Also the attached files have the formulas written and question written...
34. ### Method to decide if calculating buckling failure is compulsory or not?

Is there any method to define weather I have to calculate for determine buckling of column lead to fail or not. Is there is any rule of thumb or formula that show it is required to check for buckling or not (like very short column)
35. ### How to transfer analysis result to second analysis in Abaqus

Hi, I have to check the buckling of a beam in fire. To do this I am following the below stages: 1. Conduct a heat transfer analysis ( transient ) for 30 minutes in fire , to find out the temperature history of the beam. Please not the temperature of the beam is not uniform 2. perform 6 runs...
36. ### Plate Buckling Deflection Function for Rayleigh Ritz Method

G'Day Everybody, I am computing buckling of a rectangular(edges: a*b) specially orthotropic composite plate. The boundary conditions are clamped-clamped at the opposing loaded edges and the other two edges are free (also known as CFCF). After having the boundary conditions and the governing...
37. ### SR & EWR Buckling Analysis Homework

Homework Statement The question is what's the relationship between SR and EWR and if the column will fail by buckling or crushing. I know my last statement in the link below is miles out. https://www.physicsforums.com/threads/column-buckling-answer-confirmation.564927/page-3#post-5244310...
38. ### What is the req.thickness of sheet metal to prevent buckling

My project involves making a 5 ft*3 ft*4 ft (l*b*h) aluminium/stainless steel sheet metal box at the back of a slow moving pedal vehicle. There is no load on the sheet metal, except from small vibrations from road travel. My question is: 1. What gauge of sheet metal thickness would be enough...
39. ### [Material Science] Metal foam sandwich to prevent buckling?

Let's assume for a minute that money was of no concern. If one has a 10 MPa external environment and needs to have vacuumed-out spheres (or 1 atmosphere, close enough to call vacuum) inside of that environment. In particular, I was thinking of a sandwiched lattice of maraging steel, with it's...
40. ### Buckling and column effective length question

Homework Statement If I have a column, fixed at both ends, i am aiming to work out the minimum length where buckling is likely to occur. I know this is a similar question to that asked before, however please bear with me. Column outer diameter 100mm, inner diameter 60mm Youngs modulus...
41. ### How to figure out Mcr (elastic critical moment) beams (abaqus)

I would like to figure out Mcr(elastic critical moment) and Mpl (Maximum plastic moment) in a beam due to buckling in abaqus. How to model material non linearity. How to model geometric imperfection (slightly crooked beams) Is there any way to import I section (rolled) profiles instead of...
42. ### Bucklig: deflection at Euler load

Hello I was trying to calculate the horizontal deflection of the free end of vertical clamped beam. The beam would be loaded at the free end with a horizontal force H and a vertical force P. My idea was to calculate an initial deflection due to the force H. Then calculate the additional...
43. ### Experimental Critical Buckling Load

Hi guys, I was wondering could I get some help with determining the experimental critical buckling load of a pinned ended strut. I am hoping to compare predicted values from Euler buckling and Perry Robertson to experimental values. I have carried out a experiment where by I applied a axial...
44. ### Structural Stability & buckling stress

Q: A structure is made from identical, axially compressible robs connected to a rigid foundation. The rods cannot buckle. In the unloaded configuration the angle between the rods and the horizontal is (alpha); then angle becomes (1-Beta)*alpha when p =/= 0. Find the relationship P(Beta)...
45. ### Mastering Physics Assignments: Tips for Non-Physics Students

I am a BSc product design student. This is one of my assignments and I have never done physics in my life. Can anyone help? I do not understand at all!

Dear experts, I´m trying to model in ANSYS Mechanical (v14.5) the linear buckling behavior of a cylinder made of BEAM4 elements under combined loading (axial compression and bending moment) applied at the ends. How should I set up the boundary conditions of a cylinder to keep rigid the ends...
47. ### Allowable compressive stress in discretely laterally supported lateral buckling

The maximum allowable compressive stress corresponding to lateral buckling in a discretely laterally supported symmetrical I beam does not depend upon : the modulus of elasticity can anyone please tell me the reason ?
48. ### Carbon Fiber Strip Buckling Force Problem

Hey, So Ive been trying to wrap my mind on how to solve this problem. Im trying to use a CFRP Sheet as sort of a spring actuator by using its buckling phenomena to deliver a force to the body its attached to. Kind of vague so here is a video: This video does it electrically, but I...
49. ### Why is the natural frequency of a column at the buckling load?

So apparently the natural frequency is zero for uniform column with axial load when P is equal to the critical buckling load. Could anyone please explain theoretically why this is the case.
50. ### A not-so-standard buckling problem

Hey guys, this came up in one of my past papers, and I'm not quite sure where to go with it. The diagram shows an idealized structure consisting of an L-shaped rigid bar structure supported b linearly elastic springs at A and C. Rotational Stiffness is denoted Î²R and translational stiffness...