Structural Analysis of a Pultruded Composite Beam: Shear Stiffness Determination and Strength and Fatigue Life Predictions

This dissertation is focused on understanding the performance of a particular fiberreinforced polymeric composite structural beam, a 91.4 cm (36 inch) deep pultruded double-web beam (DWB) designed for bridge construction. Part 1 focuses on calculating the Timoshenko shear stiffness of the DWB and understanding what factors may introduce error in the experimental measurement of the quantity for this and other sections. Laminated beam theory and finite element analysis (FEA) were used to estimate the shear stiffness. Several references in the literature have hypothesized an increase in the effective measured shear stiffness due to warping. A third order laminated beam theory (TLBT) was derived to explore this concept, and the warping effect was found to be negligible. Furthermore, FEA results actually indicate a decrease in the effective shear stiffness at shorter spans for simple boundary conditions. This effect was attributed to transverse compression at the load points and supports. The higher order sandwich theory of Frostig shows promise for estimating the compression related error in the shear stiffness for thin-walled beams. Part 2 attempts to identify the failure mechanism(s) under quasi-static loading and to develop a strength prediction for the DWB. FEA was utilized to investigate two possible failure modes in the top flange: compression failure of the carbon fiber plies and delamination at the free edges or taper regions. The onset of delamination was predicted using a strength-based approach, and the stress analysis was accomplished using a successive sub-modeling approach in ANSYS. The results of the delamination analyses were inconclusive, but the predicted strengths based on the compression failure mode show excellent agreement with the experimental data. A fatigue life prediction, assuming compression failure, was also developed using the remaining strength and critical element concepts of Reifsnider et al. One DWB fatigued at about 30% of the ultimate capacity showed no signs of damage after 4.9 million cycles, although the predicted number of cycles to failure was 4.4 million. A test on a second beam at about 60% of the ultimate capacity was incomplete at the time of publication. Thus, the success of the fatigue life prediction was not confirmed.

[1]  Jolyn Louise Senne.  Fatigue Life of Hybrid FRP Composite Beams , 2000 .

[2]  Jose P Gomez,et al.  LABORATORY AND FIELD TESTING OF COMPOSITE BRIDGE SUPERSTRUCTURE , 2000 .

[3]  S. White,et al.  Stress analysis of fiber-reinforced composite materials , 1997 .

[4]  M Pecce,et al.  EXPERIMENTAL EVALUATION OF BENDING AND TORSIONAL DEFORMABILITY OF FRP PULTRUDED BEAMS , 1996 .

[5]  A. Rao,et al.  Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates , 1970 .

[6]  B. Omidvar.  Shear Coefficient in Orthotropic Thin-Walled Composite Beams , 1998 .

[7]  E. Smith,et al.  Formulation and evaluation of an analytical model for composite box-beams , 1991 .

[8]  J. N. Reddy,et al.  Relationships between bending solutions of classical and shear deformation beam theories , 1997 .

[9]  F. J. Plantema,et al.  Sandwich Construction: The Bending and Buckling of Sandwich Beams, Plates and Shells , 1966 .

[10]  Sung Nam Jung,et al.  Shear Correction Factors for Thin-Walled Composite Boxbeam Considering Nonclassical Behaviors , 1996 .

[11]  Cornelius O. Horgan,et al.  On Saint-Venant's principle in plane anisotropic elasticity , 1972 .

[12]  D. Roylance.  INTRODUCTION TO COMPOSITE MATERIALS , 2000 .

[13]  H. G. Allen.  Analysis and design of structural sandwich panels , 1969 .

[14]  Mark V. Fulton,et al.  Free-Vibration Analysis of Composite Beams , 1991 .

[15]  Douglas A. Foutch,et al.  A Shear Lag Anomaly , 1982 .

[16]  S. Dharmarajan,et al.  Shear Coefficients for Orthotropic Beams , 1973 .

[17]  L. Bank,et al.  Shear coefficients for multicelled thin-walled composite beams , 1989 .

[18]  N. J. Pagano,et al.  Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension , 1970 .

[19]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[20]  D. B. Goetschel,et al.  Quantification of Saint-Venant's principle for a general prismatic member , 1985 .

[21]  T. Schniepp.  Design Manual Development for a Hybrid, FRP Double-Web Beam and Characterization of Shear Stiffness in FRP Composite Beams , 2002 .

[22]  Hota V. S. GangaRao,et al.  Warping Solution for Shear Lag in Thin-Walled Orthotropic Composite Beams , 1996 .

[23]  Yeoshua Frostig,et al.  High‐Order Theory for Sandwich‐Beam Behavior with Transversely Flexible Core , 1992 .

[24]  Lawrence C. Bank,et al.  Flexural and shear moduli of full-section fiber reinforced plastic (FRP) pultruded beams , 1989 .

[25]  Determination of the Design Parameters for the Route 601 Bridge: A Bridge Containing the Strongwell 36 inch Hybrid Composite Double Web Beam , 2001 .

[26]  Julio F. Davalos,et al.  Static shear correction factor for laminated rectangular beams , 1996 .

[27]  L. Bank.  Shear coefficients for thin-walled composite beams , 1987 .

[28]  Z. Hashin,et al.  The Elastic Moduli of Fiber-Reinforced Materials , 1964 .

[29]  Ole Thybo Thomsen,et al.  Analysis of local bending effects in sandwich plates with orthotropic face layers subjected to localised loads , 1993 .

[30]  G. D. Sims,et al.  Mechanical and structural properties of a GRP pultruded section , 1987 .

[31]  Ioannis G. Raftoyiannis,et al.  ULTIMATE BENDING STRENGTH OF COMPOSITE BEAMS , 1991 .

[32]  M. Baruch,et al.  Localized Load Effects in High-Order Bending of Sandwich Panels with Flexible Core , 1996 .

[33]  Inderjit Chopra,et al.  Experimental and theoretical analysis of composite I-beams with elastic couplings , 1991 .

[34]  Hota V. S. GangaRao,et al.  Static Behavior of Pultruded GFRP Beams , 1997 .

[35]  O. Bauchau.  A Beam Theory for Anisotropic Materials , 1985 .

[36]  Dewey H. Hodges,et al.  Nonclassical Behavior of Thin-Walled Composite Beams with Closed Cross Sections , 1990 .

[37]  E. Barbero.  Introduction to Composite Materials Design , 1998 .

[38]  Donald F. Adams,et al.  Contact finite element modeling of the short beam shear test for composite materials , 1995 .

[39]  J. Whitney.  Elasticity analysis of orthotropic beams under concentrated loads , 1985 .

[40]  J. Jensen.  On the shear coefficient in Timoshenko's beam theory , 1983 .

[41]  C. C. Huang,et al.  Shear deformation coefficient for generally orthotropic beam , 1979 .

[42]  S. Timoshenko,et al.  LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars , 1921 .

[43]  S. Timoshenko,et al.  X. On the transverse vibrations of bars of uniform cross-section , 1922 .

[44]  Warping effects in transverse bending of thin-walled beams , 1987 .

[45]  Stephen R. Swanson,et al.  Response of Orthotropic Sandwich Plates to Concentrated Loading , 2000 .

[46]  Nelson R. Bauld,et al.  A Vlasov theory for fiber-reinforced beams with thin-walled open cross sections , 1984 .

[47]  Y. Frostig,et al.  High-order bending of sandwich beams with a transversely flexible core and unsymmetrical laminated composite skins , 1995 .

[48]  Y. Surrel,et al.  Experimental evidence of the cross-section warping in short composite beams under three point bending , 2001 .

[49]  Julio F. Davalos,et al.  Analysis and design of pultruded FRP shapes under bending , 1996 .

[50]  Stephen R. Swanson.  An examination of a higher order theory for sandwich beams , 1999 .

[51]  Su-Seng Pang,et al.  Bending analysis of laminated composite box beams , 1994 .

[52]  H. Wagner,et al.  Simultaneous Determination of Shear and Young's Moduli in Composites , 1981 .

[53]  Michel Grédiac,et al.  Closed-form solution for the cross-section warping in short beams under three-point bending , 2001 .

[54]  Scott R. White,et al.  Laminated composite thin- and thick-walled beam theory and coupled deformations , 1995 .

[55]  Julio F. Davalos,et al.  On the Mechanics of Thin-Walled Laminated Composite Beams , 1993 .