Stress analysis of steel beams strengthened with a bonded hygrothermal aged composite plate
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Stress analysis of steel beams strengthened with a bonded hygrothermal aged composite plate M. Ameur Æ A. Tounsi Æ S. Benyoucef Æ M. Bachir Bouiadjra Æ E. A. Adda Bedia
Received: 18 May 2007 / Accepted: 25 November 2008 / Published online: 9 December 2008 Springer Science+Business Media, B.V. 2008
Abstract In this paper, the problem of interfacial stresses in steel beams strengthened with bonded hygrothermal aged composite laminates is analyzed using linear elastic theory. The analysis is based on the deformation compatibility approach developed by Tounsi (Int. J. Solids Struct. 43:4154–4174, 2006) where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adopted model takes into account the adherend shear deformations by assuming a linear shear stress through the depth of the steel beam. This solution is intended for application to beams made of all kinds of materials bonded with a thin composite plate. For steel I-beam section, a geometrical coefficient n is determined to show the effect of the adherend shear deformations. This research is helpful for the understanding on mechanical behaviour of the interface and design of such structures.
M. Ameur Universite´ Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algeria M. Ameur A. Tounsi (&) S. Benyoucef M. Bachir Bouiadjra E. A. Adda Bedia Laboratoire des Mate´riaux & Hydrologie, Universite´ de Sidi Bel Abbes, BP 89 Cite´ Ben M’hidi, 22000 Sidi Bel Abbes, Algeria e-mail: [email protected]
Keywords Steel I-beam section Interfacial stresses Strengthening Hygrothermal aged composite plate Adherend shear deformations Nomenclature A1 The cross-sectional area of the steel beam 0 A Inverse of the extensional matrix A 0 D Inverse of the flexural matrix D E1 The elastic modulus of the steel beam Ea The elastic modulus of adhesive EL Longitudinal Young’s modulus of FRP plate ET Transversal Young’s modulus of FRP plate Em The elastic modulus of matrix Ef The elastic modulus of fibre Gm The transverse shear modulus of matrix Gf The transverse shear modulus of fibre Ga The transverse shear modulus of adhesive G1 The transverse shear modulus of the adherend 1 GLT The transverse shear modulus of FRP plate I The second moment of area KS The shear stiffness of the adhesive Kn Normal stiffness of the adhesive per unit length M(x) The bending moment
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MT(x) Ni (i = 1, 2) UN1 (x, y)
V(x) Vm Vf C T b2 q ti (i = 1,2) ta u1 u2 uN1
wi (i = 1, 2) e1 e2 eM 1 eN2 rxy(1) rn c1 sa rN1 tLT tm tf n
M. Ameur et al.
The total applied moment The longitudinal resultant force for adherend ‘‘i’’ Longitudinal displacements in steel beam induced by the longitudinal forces Shear force Matrix volume fraction Fibre volume fraction Moisture Temperature The width of the soffit plate The uniformly distributed load The thickness of adherend ‘‘i’’ The thickness of adhesive The longitudinal displacement at the base of adherend 1 The longitudinal displacement at the top of adherend 2 The longitudinal displacement induced by the lon
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