Etymology 1From buckle.
- present participle of buckle
- A young male domestic goat of between one and two years.
- 1994, Carla Emery, The Encyclopedia of Country Living, Ninth
Edition, Sasquatch Books, ISBN 1-57061-377-X, page 715,
- If you do have extra milk, then by all means raise your extra bucklings and cull doelings for meat.
- 1994, Mary C. Smith and David M. Sherman, Goat
Blackwell Publishing, ISBN 0-8121-1478-7, page 429,
- The newborn doe kids destined to become habitual aborters (and the buckling that carries the trait) are above average in weight and have a very fine haircoat.
- 1997, Ruth Schubarth, “Born Backwards”, in Linda M.
Hasselstrom, Gaydell M. Collier, and Nancy Curtis (eds.), Leaning
Into the Wind: Women Write from the Heart of the West, Houghton
Mifflin Books, ISBN 0395901316, page 161,
- I milk the goats and put wethers (the castrated bucklings) in the freezer with ducks, chickens, rabbits, and lambs.
- 1994, Carla Emery, The Encyclopedia of Country Living, Ninth Edition, Sasquatch Books, ISBN 1-57061-377-X, page 715,
- sense young male goat Not all sources agree on the exact age range for which this term applies; for example, one source applies it to kids as young as six months.
- Dutch: bokking (cognate)
In engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high compressive stresses, where the actual compressive stresses at failure are greater than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as failure due to elastic instability. Mathematical analysis of buckling makes use of an axial load eccentricity that introduces a moment, which does not form part of the primary forces to which the member is subjected.
Buckling in columns
The strength of a column may therefore be increased by distributing the material so as to increase the moment of inertia. This can be done without increasing the weight of the column by distributing the material as far from the principal axes of the cross section as possible, while keeping the material thick enough to prevent local buckling. This bears out the well-known fact that a tubular section is much more efficient than a solid section for column service.
Another bit of information that may be gleaned from this equation is the effect of length on critical load. For a given size column, doubling the unsupported length quarters the allowable load. The restraint offered by the end connections of a column also affects the critical load. If the connections are perfectly rigid, the critical load will be four times that for a similar column where there is no resistance to rotation (hinged at the ends).
Since the moment of inertia of a surface is its area multiplied by the square of a length called the radius of gyration, the above formula may be rearranged as follows. Using the Euler formula for hinged ends, and substituting A·r2 for I, the following formula results.
- \sigma = \frac = \frac
where F/A is the allowable stress of the column, and l/r is the slenderness ratio.
Since structural columns are commonly of intermediate length, and it is impossible to obtain an ideal column, the Euler formula on its own has little practical application for ordinary design. Issues that cause deviation from the pure Euler strut behaviour include imperfections in geometry in combination with plasticty/non-linear stress strain behaviour of the column's material. Consequently, a number of empirical column formulae have been developed to agree with test data, all of which embody the slenderness ratio. For design, appropriate safety factors are introduced into these formulae.
Self-buckling of columns
A free-standing, vertical column of circular cross-section, with density \rho, Young's modulus E, and radius r, will buckle under its own weight if its height exceeds a certain critical height:
- h_ = \left(\frac\right)^.
Buckling of surface materialsBuckling is also a failure mode in pavement materials, primarily with concrete, since asphalt is more flexible. Radiant heat from the sun is absorbed in the road surface, causing it to expand, forcing adjacent pieces to push against each other. If the stress is great enough, the pavement can lift up and crack without warning. Going over a buckled section can be very jarring to automobile drivers, described as running over a speed hump at highway speeds.
Similarly, railroad tracks also expand when heated, and can fail by buckling. It is more common for rails to move laterally, often pulling the underlain railroad ties (sleepers) along with them.
Energy methodOften it is very difficult to determine the exact buckling load in complex structures using the Euler formula, due to the difficulty in deciding the constant K. Therefore, maximum buckling load often is approximated using energy conservation. This way of deciding maximum buckling load is often referred to as the energy method in structural analysis.
The first step in this method is to suggest a displacement function. This function must satisfy the most important boundary conditions, such as displacement and rotation. The more accurate the displacement function, the more accurate the result.
In this method, there are two equations used to calculate the inner energy and outer energy.
- A_ = \frac \int (w_(x))^2dx
- A_ = \frac \int (w_(x))^2dx
where w(x) is the displacement function and the subscripts "x" and "xx" refer to the first and second derivatives of the displacement. Energy conservation yields:
Lateral-torsional bucklingWhen a beam is loaded in flexure, the compression side is in compression, and the tension side is in tension. If the beam is not supported in the lateral direction (i.e., perpendicular to the plane of bending), and the flexural load increases to a critical limit, the beam will fail due to lateral buckling of the compression flange. In wide-flange sections, if the compression flange buckles laterally, the cross section will also twist in torsion, resulting in a failure mode known as lateral-torsional buckling.
Plastic bucklingBuckling will generally occur slightly before the theoretical buckling strength of a structure, due to plasticity of the material. When the compressive load is near buckling, the structure will bow significantly and approach yield. The stress-strain behaviour of materials is not strictly linear even below yield, and the modulus of elasticity decreases as stress increases, with more rapid change near yield. This lower rigidity reduces the buckling strength of the structure and causes premature buckling. This is the opposite effect of the plastic bending in beams, which causes late failure relative to the Euler-Bernoulli beam equation.
Dynamic bucklingIf the load on the column is applied suddenly and then released, the column can sustain a load much higher than its static (slowly applied) buckling load. This can happen in a long, unsupported column (rod) used as a drop hammer. The duration of compression at the impact end is the time required for a stress wave to travel up the rod to the other (free) end and back down as a relief wave. Maximum buckling occurs near the impact end at a wavelength much shorter than the length of the rod, at a stress many times the buckling stress if the rod were a statically-loaded column. The critical condition for buckling amplitude to remain less than about 25 times the effective rod straightness imperfection at the buckle wavelength is
- \sigma L = \rho c^2 h
where \sigma is the impact stress, L is the length of the rod, c is the elastic wave speed, and h is the smaller lateral dimension of a rectangular rod. Because the buckle wavelength depends only on \sigma and h, this same formula holds for thin cylindrical shells of thickness h.
Source: Lindberg, H. E., and Florence, A. L., Dynamic Pulse Buckling, Martinus Nijhoff Publishers, 1987, pp. 11-56, 297-298.
- Timoshenko, S. P., and Gere, J. M., Theory of Elastic Stability, 2 ed., McGraw-Hill, 1961.
- Nenezich, M., Thermoplastic Continuum Mechanics, Journal of Aerospace Structures, Vol. 4, 2004.
buckling in Bulgarian: Загуба на устойчивост
buckling in German: Knicken
buckling in Spanish: Pandeo
buckling in French: Flambage
buckling in Italian: Instabilità a carico di punta
buckling in Hebrew: קריסה
buckling in Dutch: Knik (constructieleer)
buckling in Japanese: 座屈
buckling in Polish: Wyboczenie
buckling in Sicilian: Abbruscamentu