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A column under a concentric axial load exhibiting the characteristic deformation of buckling The eccentricity of the axial force results in a bending moment acting on the beam element. The ratio of the effective length of a column to the least radius of gyration of its cross section is called the slenderness ratio (sometimes expressed with the ...
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 an axially loaded tension member, the stress is given by: F = P/A where P is the magnitude of the load and A is the cross-sectional area. The stress given by this equation is exact, knowing that the cross section is not adjacent to the point of application of the load nor having holes for bolts or other discontinuities. For ex
In the case of a material line element or fiber axially loaded, its elongation gives rise to an engineering normal strain or engineering extensional strain e, which equals the relative elongation or the change in length ΔL per unit of the original length L of the line element or fibers (in meters per meter). The normal strain is positive if ...
The slenderness ratio is an indicator of the specimen's resistance to bending and buckling, due to its length and cross section. If the slenderness ratio is less than the critical slenderness ratio, the column is considered to be a short column. In these cases, the Johnson parabola is more applicable than the Euler formula. [5]
Consider as a simple example a rigid beam of length L, hinged in one end and free in the other, and having an angular spring attached to the hinged end. The beam is loaded in the free end by a force F acting in the compressive axial direction of the beam, see the figure to the right.
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
By convention, the strain is set to the horizontal axis and stress is set to vertical axis. Note that for engineering purposes we often assume the cross-section area of the material does not change during the whole deformation process. This is not true since the actual area will decrease while deforming due to elastic and plastic deformation.