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The deformation elements and (above) can be used to find the direction of the dilatation axis, the line along which the material elements stretch (also known as the stretching direction). Several flow patterns are characteristic of large deformation: confluence, diffluence, and shear flow.
A longitudinal deformation (in the direction of the axis) is called elongation. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load.
The design of tension members requires careful analysis of potential failure modes, specifically yielding (excessive deformation) and fracture, which are referred to as limit states. The governing limit state is the one that results in the lowest design strength, as it dictates the member's capacity and prevents structural failure.
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 capac
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 ...
For thick plates, we have to consider the effect of through-the-thickness shears on the orientation of the normal to the mid-surface after deformation. Raymond D. Mindlin's theory provides one approach for find the deformation and stresses in such plates. Solutions to Mindlin's theory can be derived from the equivalent Kirchhoff-Love solutions ...
Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.
This is not true since the actual area will decrease while deforming due to elastic and plastic deformation. The curve based on the original cross-section and gauge length is called the engineering stress–strain curve , while the curve based on the instantaneous cross-section area and length is called the true stress–strain curve .