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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
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.
One of the variables in the above equation that reflects the geometry of the specimen is the slenderness ratio, which is the column's length divided by the radius of gyration. [ 4 ] The slenderness ratio is an indicator of the specimen's resistance to bending and buckling, due to its length and cross section.
Different deformation modes may occur under different conditions, as can be depicted using a deformation mechanism map. Permanent deformation is irreversible; the deformation stays even after removal of the applied forces, while the temporary deformation is recoverable as it disappears after the removal of applied forces.
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 ...
For two-dimensional, plane strain problems the strain-displacement relations are = ; = [+] ; = Repeated differentiation of these relations, in order to remove the displacements and , gives us the two-dimensional compatibility condition for strains