Validation of Analytical Multiparameter Homogenization Models for Out-of-Plane Loaded Masonry Walls by Means of the Finite Element Method

The linear elastic analysis of in-plane and out-of-plane loaded masonry walls is still significant under service loads and is required by codes of practice, therefore the knowledge of the homogenized mechanical properties of masonry is of relevant interest. The aim of this paper is to discuss the problem of the out-of-plane loaded masonry walls in detail and to assess the accuracy and reliability of different homogenization approaches presented in the technical literature, with particular interest in recent explicit formulas obtained through an asymptotic model (as reported by Cecchi and Sab in 2002). Several meaningful comparisons are presented for different types of new and historical masonry structures currently employed in Italy. The validation of the analytical models is carried out by means of a three-dimensional (3D) finite-element (FE) out-of-plane homogenization. A final structural comparison among analytical models, FE out-of-plane homogenization, and a computationally expensive heterogeneous 3D FE model is discussed for a simply supported square panel laterally loaded.     

Wrinkling and Edge Buckling in Orthotropic Sandwich Beams

A sandwich beam buckling problem is studied here using two-dimensional elasticity to model the beam constituents. The global and local instability of such a beam with orthotropic constituents under various boundary conditions are investigated. The face sheet and the core are assumed to be linear elastic orthotropic continua. General buckling deformation modes of the sandwich beam subjected to uniaxial compressive loading are considered. The appropriate incremental stress and conjugate incremental finite-strain measure for the instability problem of the sandwich beam, and the corresponding constitutive model are addressed. It is shown that a sandwich beam having a core with a negligible stiffness compared to the face sheets is prone to fail by edge buckling. The present analysis is compared with several previous analytical studies and corresponding experimental results. Finite-element analyses are carried out for comparison against the theoretical predictions. The formulation used in the finite-element code is discussed in relation to the formulation adopted in the theoretical derivation.     

Analysis of Thick Circular Plates Undergoing Large Deflections

This investigation considers the effect of transverse shear deformation on bending of the axisymmetrically loaded isotropic and orthotropic circular and annular plates undergoing large deflection. The analysis treats the nonlinear terms of lateral displacement as fictitious loads acting on the plate. The solution of a von Kármán‐type plate is, therefore, reduced to a plane problem in elasticity and a linear plate‐bending problem. Results are presented for simply supported and clamped plates and are in good agreement with the available solutions. For plates considered in this study, the influence of shear deformation on lateral displacement becomes more significant as the orthotropic parameter increases. The linear and nonlinear solutions for orthotropic plates deviate at a low value of the maximum deflection‐to‐thickness ratio (w/h). Consequently, the extent of w/h within which the small‐deflection theory is applicable to orthotropic plates is much lower than the value of about 0.4 typically used for isotropic plates, and it depends, in general, on the degree of orthotropy. The technique employed in this study is well suited for the analysis of nonlinear plate problems.     

Axisymmetric Vibrations of Reinforced Orthotropic Shallow Spherical Caps

Axisymmetric vibrations of reinforced shallow. spherical caps manufactured from orthotropic materials are considered. The closed form solution is obtained for the natural frequency of the cap with a clamped and immovable circular edge by assuming that the motion component parallel to the cap boundary plane (in plane) is negligible. Parametric studies are performed to assess the effect of various geometric and structural parameters on the natural frequency of the cap and, most importantly, to identify the most influencing parameters of the problem. From the generated data, it is concluded that the national frequency increases with increasing extensional stiffness and eccentricity of reinforcements and to a lesser extent with increasing bending stiffness of reinforcements. Other important parameters include the base circle radius and the initial rise of the cap.     

Finite-Difference Solution of a Both-End-Fixed Orthotropic Composite Beam under Uniformly Distributed Loading Using Displacement Potential Function Formulation

The elastic solution of an orthotropic composite beam under the influence of uniformly distributed loading is obtained numerically. Two ends of the beam are rigidly fixed, and the fibers are oriented along and perpendicular to the direction of the length of the beam. An efficient finite-difference computational scheme based on displacement potential formulation is used to analyze the present mixed-boundary-value elastic problem. The effect of several important parameters such as beam aspect ratio and fiber orientation on the elastic field are investigated. Solutions are presented mainly in the form of graphs and deformed shapes. Finally, the reliability as well as superiority of the present computational scheme is discussed by comparing the present solution with the corresponding finite-element solutions.     

Fatigue Evaluation of Rib-to-Deck Welded Joints of Orthotropic Steel Bridge Deck

This study reported fatigue test results of 300-mm-wide specimens with three details: 80% partial joint penetration (80%PJP), weld melt-through (WMT), and both. The specimens were cut out from full-scale orthotropic deck specimens of 16-mm-thick deck plate. In the fatigue test, the deck plate was subjected to cyclic bending loading and the rib was free from loading. The fatigue fracture surfaces showed that the presence of WMT may affect the initiation of fatigue cracks. A propensity to root cracking rather than toe cracking was observed. Plotting fatigue test results in an S-N diagram showed that the specimens with WMT seemed to have slightly lower fatigue strengths than the 80%PJP specimens, but the difference is more likely to be within a usual scatter of test data, which means that both details have comparable fatigue strength. The present test results satisfied the S-N curves of JSSC-E (80?MPa at 2×106 cycles) or AASHTO-C (89?MPa at 2×106 cycles).     

Full-Scale Fatigue Tests of Steel Orthotropic Decks for the Williamsburg Bridge

Final design of the replacement orthotropic deck panels for the rehabilitation of the Williamsburg Bridge in New York City was based on laboratory fatigue tests of a full-scale prototype and an as-built orthotropic deck panel carried out at Lehigh University in the latter 1990s. The tests focused on determining and comparing the fatigue resistance of two different welded rib-to-diaphragm connection details that were recommended in the 1994 AASHTO LRFD Bridge Design Specifications and an alternative proposed by Steinman. The test on the prototype panel demonstrated that the fatigue resistance of the alternative detail was superior and influenced additional design changes that were incorporated into the replacement panels installed on the southern inner and outer roadways. Subsequent tests on the as-built panel further confirmed that the fatigue resistance of the alternative detail was superior and demonstrated that the additional design changes were also beneficial. Static and dynamic tests revealed the complex behavior of the orthotropic deck panels and demonstrated the effectiveness of retrofit and repair options at cracked connections. An assessment of fatigue resistance based on fracture mechanics models provided theoretical correlation. This research has led to the revision of design specifications for steel orthotropic decks first provided in the 2000 Interim AASHTO LRFD Specifications.     

Spline Semidiscretization Analysis for Orthotropic Plates and Shells

This paper presents a numerical analysis procedure, called spline semidiscretization procedure, for the unified analysis of orthotropic and/or isotropic thin plates and shallow shells of rectangular projection with the two opposite edges in the y direction simply supported. The sine and cosine functions may thus be employed as the displacement trial functions in the y direction. By semidiscretization through dividing plate and shell into N equal subintervals, the B3 spline function, consisting of the (N+3) local B3 spline functions (the first and last three local B3 spline functions have been modified for accommodating to any type of boundary conditions) with respect to the (N+1) points and two extended additional points in the x direction, can then be used as the displacement trial function in the x direction. Governing equations of an orthothopic shallow shell subjected to the distributed, linearly distributed, concentrated loads or their combinations are derived based on its potential energy functional. Unified formulas for the determination of displacements and internal forces of the orthotropic and/or isotropic thin plates and shallow shells are obtained. In comparison to the conventional finite element method, with the displacement trial functions having the good properties with piecewise polynomial as well as orthogonality and decoupling, the present procedure has remarkably fewer unknowns to be solved (more precisely, a term by term analysis involving only much smaller matrices can be conducted), and thus it is computatively more efficient. Likewise, the computational program, with minimal preparation of input data, can be very easily developed through the present formulation. Numerical results indicate that the present method can render a very high accuracy. The fast convergence shown in numerical examples demonstrates the reliability of the results.     

LRFD Orthotropic Plate Model for Live Load Moment in Filled Grid Decks

Due to the orthogonal elastic properties and significant two-way bending action, orthotropic plate theory may best be used to describe the behavior of concrete filled grid bridge decks. The current AASHTO LRFD specification employs an orthotropic plate model with a single patch load to predict live load moment in concrete filled grid bridge decks, which may not be conservative. This paper presents alternative equations to predict maximum moments, based on classical orthotropic plate theory, which include multiple patch loads, both the LRFD design truck and tandem load cases, and the two most common deck orientations. The predicted moments are verified through finite-element analyses.     

Analytical Solutions to General Orthotropic Plates under Patch Loading

Orthotropic plates are widely used in bridge deck systems. However, these are not commonly treated as such within design specifications, and semianalytical solutions are not presently available for all deck types. This paper develops deflection equations for infinitely wide and simply supported thin plates considering each of the three cases of orthotropy: (1)?relatively torsionally stiff, flexurally soft; (2)?uniformly thick plate; and (3)?torsionally soft, flexurally stiff; subjected to arbitrary patch loading. These are common boundary and loading conditions encountered for bridge deck applications. The reported analytical solutions enable rapid evaluation of multiple moving patch loads to determine maximum design load effects and permit validation of numerical and finite-element methods. Application of the solutions will produce guidelines that can prescribe design demands and establish practical design simplifications for treatment of different bridge deck and slab systems in a uniform and consistent manner.