Deformation analysis beam bending

In general, developing appropriate stress and deformation analysis solutions for the design of complex structures made with viscoelastic polymer-based materials can be very difficult and challenging. However, as discussed in this section, the various analytical approaches mentioned earlier can be illustrated using the elementary analysis associated with beams in pure bending. 

Derivations for almost all analytical models for FRP strengthened flexural members are based on the typical schematic FBDs of Fig. 10.14. This particular case represents a differential segment of an FRP strengthened beam under uniformly distributed load, and the bending stiffness of the FRP laminate is assumed to be much smaller than that of the beam to be strengthened. Forces, moments and stresses acting on these basic FBDs reflect the individual assumptions preset for any analysis. The interfacial adhesive shear and normal stress are denoted by t x) and a(x), respectively. Equation [10.19] is the mathematical representation of the basic definition of shear stress t(x) in the adhesive layer, which is directly related to the difference in longitudinal deformation between the FRP laminate at its interface with the adhesive and the beam s soffit. 

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