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تحلیل دقیق تنش‌های میان‌رویه در تیر بتن مسلح تقویت شده با ورق پیشانی

  • M. EdalatiAffiliated withFaculty of Engineering, Ilam University Email author 
  • , F. IraniAffiliated withDept. of Civil Engineering, Ferdowsi University of Mashhad



This paper introduces an exact method to calculate interfacial shear and normal stresses in strengthened reinforced concrete (RC) beams by fiber reinforced polymer (FRP) sheets or steel plates (e.g. a soffit plate). As the combination of maximum interfacial shear and normal stresses is localized at the end of the soffit plate, the debonding phenomena initiates at that position and may produce a sudden failure of the structure. The effects of shear deformations are perfectly considered in the RC beam, adhesive layer and soffit plate. Thus, the composite RC beam is assumed as a Timoshenko beam. Application of shear deformations in the Timoshenko beam ends in a pair of simultaneous fourth-order and second-order ordinary differential equations. These equations in engineering literature are called coupled differential equations. These coupled equations are solved in an analytical form, without omitting any part of them. In a strengthened Timoshenko RC beam, the shear curvature should be added to the bending curvature. The Timoshenko beam assumption makes it possible to use this solution for both ordinary beams and short-span beams (while considering the shear deformations). In order to reduce the shear rigidity, especially in short-span beams, the equivalent flexural rigidity should be used instead of the actual flexural rigidity. Disregarding this reduction coefficient leads to incorrect results in short-span beams with a span-to-depth ratio less than five, and to an inaccurate solution in ordinary beams. In beams with a sandwich-like construction, the increase in deflection due to the shear deformation effect may be as great as 50 percent. An increase in the deformation before debonding causes a significant rise in the interfacial shear and the normal stresses, particularly between sandwich layers. The present paper helps to realize the effects of interfacial stresses on the behavior of strengthening RC structures by FRP sheets or steel plates. Finally, the concordance of the obtained and existing results proves that the accuracy of the proposed approach towards predicting interfacial shear and normal stresses is quite acceptable.

Key Words

interfacial shear and normal stresses soffit plates (FRP sheet or steel plate) RC beam, coupled differential equations