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Southwell Plot constructed from a straight line fitted to experimental data points. The Southwell plot is a graphical method of determining experimentally a structure's critical load, without needing to subject the structure to near-critical loads. [1]
The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally. The critical load puts the column in a state of unstable equilibrium. A load beyond the critical load causes the column to fail by buckling. As the load is increased beyond the ...
In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column. The formula is based on experimental results by J. B. Johnson from around 1900 as an alternative to Euler's critical load formula under low slenderness ratio (the ratio of radius of gyration to ...
These four forms of elastic buckling are the saddle-node bifurcation or limit point; the supercritical or stable-symmetric bifurcation; the subcritical or unstable-symmetric bifurcation; and the transcritical or asymmetric bifurcation. All but the first of these examples is a form of pitchfork bifurcation. Simple models for each of these types ...
Tension tends to pull small sideways deflections back into alignment, while compression tends to amplify such deflection into buckling. Compressive strength is measured on materials, components, [1] and structures. [2] The ultimate compressive strength of a material is the maximum uniaxial compressive stress that it can withstand before ...
Although the material softens it is still generally able to sustain more load before ultimate failure. Therefore, more weight efficient structure can be designed when plastic behavior is considered. For example, a structural analyst may use the tangent modulus to quantify the buckling failure of columns and flat plates.
In mathematical analysis, the maximum and minimum [a] of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum , [ b ] they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function.
Macaulay's method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams.Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading.
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