Transverse Load Distribution Research Articles

Laboratory Testing of Stress-Laminated Wood Decks on Steel Beams

Four different stress-laminated wood decks were laboratory-tested to measure composite action between deck and steel beams, transverse load distribution, performance of connectors, and deck construction cost. The models were subjected to cyclic loading varying from 9 to 89 kN. Static load tests were conducted after every 100,000 cycles. During static testing, strains and deflections in the beams were measured at 22, 44, 67, and 89 kN. The loss of tension in the connectors was also monitored after every 100,000 cycles. The readings were used to compare the composite action, load distribution, and tension loss in connectors. Load distribution values were verified with theoretical calculations.

Theoretical and Experimental Evaluation of FRP Components and Systems

Two bridge superstructural systems and two other floor systems are constructed and tested under concentric static loads using fiber reinforced plastic (FRP) shapes. Structural performance of individual FRP components is established through three‐ and four‐point bending tests. Structural efficiency of each system is analyzed in terms of joint efficiency, transverse load distribution, composite action between FRP components, and maximum deflections and stresses. Theoretical prediction of system performance is conducted by the orthotropic plate theory, finite‐element method, and a method to predict beam stiffnesses based on simplified classical lamination theory (CLT). The correlation between theoretical and experimental results is good and reveals that the simplified CLT can be effectively used in future designs. The bridge and floor systems tested herein had undergone deflections smaller or at the most equal to the allowable (L/1,000 and L/360, respectively) for loads larger than the corresponding allowabl...

Interlaminar stress mixed finite element analysis of unsymmetrically laminated composite plates

An interlaminar stress mixed finite element method based on the local high-order lamination theory is presented. The nodal unknowns in this C 0 isoparametric element are three displacements, three rotations, and five higher-order functions as the generalized degrees of freedom in the mid-surface of each layer and three interlaminar stress functions as the generalized degrees of freedom at the interface between the layers. The interlaminar stresses at the interface can then be accurately determined. The unsymmetrically laminated composite plates, which are fully simply supported, subjected to a sinusoidal distribution of transverse load are examined in order to validate the present interlaminar stress mixed finite element. The finite element results presented here are compared with the three-dimensional elasticity solutions and other finite element solutions based on global high-order lamination theories.

An interlaminar stress mixed finite element method for the analysis of thick laminated composite plates

An interlaminar stress mixed finite element method, based on local high order lamination theory wherein the local displacement fields are expanded in terms of high order polynomial series through thickness within each ply and the displacement continuity requirements at the interface between layers are regarded as the constraints introduced into the formulation, is developed. In this C 0 isoparametric mixed interlaminar stress element, the nodal unknowns are three displacements, three rotations and five higher-order functions as the generalized degrees of freedom in the mid-surface of each layer and three interlaminar stresses functions as the generalized degrees of freedom at the interface. The interlaminar stresses at interfaces can then be uniquely determined. A generally rectangular thick laminated composite plate, with fully simple supports, subjected to a sinusoidal distribution of transverse load are examined in order to validate the credibility of the present mixed interlaminar stress element. Both the present analytical and finite element results are compared with the 3-D elasticity solutions obtained by Pagano and other finite element solutions based on the global high order lamination theories.

Analysis of sandwich plates using a mixed finite element

The stress and displacement analysis of the thick sandwich plate is presented here by using an interlaminar stress mixed finite element based on local high-order deformable theory. The displacements of a sandwich plate are assumed to be high order polynomial functions layer-by-layer through the plate thickness. Since the interlaminar stresses at the interface between layers in this finite element scheme are regarded as primary variables, they can then be accurately determined. The accuracy of this finite element scheme is checked by comparing the present results with 3-D elasticity solutions of a simply supported sandwich plate. The response of a thick angle-ply, fiber-reinforced plastic (FRP) faced sandwich with fully simple supports, subjected to a sinusoidal distribution of transverse load is evaluated. The present finite element results are compared with results obtained from other finite element schemes.

An exact solution for the bending of point-supported orthotropic rectangular thin plates

A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse load are arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.

Ultimate Load Test of Slab‐on‐Girder Bridge

An ultimate load test on a short‐span simply supported bridge having six rolled‐steel girders and a noncomposite deck slab is described. The main conclusions drawn from the test are as follows: (1) The bearing restraint forces reduced the bending moment at midspan by a minimum of 11%; (2) the transverse load distribution pattern of the bridge improves by a relatively small margin as the ultimate limit state is approached; (3) any composite action between the deck slab and a girder that may exist at service loads, and is due only to bond or friction between steel and concrete, completely breaks down as the load approaches the failure load for the girder; and (4) a girder continues to carry loads long after the formation of first yield.

Variability analysis of timber bridge responses

Large variations in timber moduli of elasticity cause large variations in the loads accepted by various girders (stringers) of a timber bridge. These variations cannot be accounted for by deterministic analyses based on the assumption of constant material properties. In this paper the problem of variation of loads accepted by timber stringer is studied through Monte Carlo simulations. Two separate mathematical models are used for representing timber bridges; one model assumes that transverse load distribution is due only to the transverse shear stiffness of the bridge, and the other that it is due to the transverse bending stiffness. Each model, however, is a special case of the more general and accurate bridge model, known as the semicontinuum model. It has been shown that both models yield similar conclusions regarding the variability of load acceptance by the girders. It is found that the coefficient of variation of loads accepted by those girders which resist appreciable amounts of the applied loads is always less than the coefficient of variation of the timber modulus of elasticity, and that the amount of variation depends upon the transverse position of the loads and the load distribution characteristics of the bridge. A simple expression is given by which the upper bound value of a distribution coefficient, corresponding to a desired confidence limit, can be estimated.

Bridge Evaluation for Multipresence of Vehicles

It is customary in North America to evaluate a short-span bridge on a busy highway exactly the same way as a bridge on a lightly travelled road. This paper proposes that multipresence reduction factors can be used as the means for taking account of the volume of traffic. These factors, strictly speaking, are applicable only to bridges that carry a high volume of traffic; however, in bridge-design codes such as AASHTO and OHBDC, they are used for all bridges irrespective of the volume of traffic. New multipresence-reduction factors, to be used in conjunction with AASHTO, Ontario, and CSA codes, are proposed for different classes of highways. In addition, the paper presents simplified methods of transverse load distribution that incorporate the proposed reduction factors in such a way that the designer or evaluator can see immediately the effect of volume of traffic on live load responses without having to perform extra calculations.

Welded‐Versus Bolted‐Steel I‐Diaphragms in Composite Bridges

In the design of composite bridges, the North American practice either ignores or minimizes the contribution of transverse disphragms to the transverse load distribution; this results, among other disadvantages, in heavier longitudinal steel girders than necessary as well as in the loss of headroom. Recent tests have shown that when transverse steel I‐diaphragms are rigidly joined in a welded connection to the longitudinal steel girders, the wheel loads on the bridge become distributed in an orthotropic manner. The influence of bolted and welded transverse I‐diaphragms (to the longitudinal girders) on the response of composite bridges are investigated. Several composite bridge models were tested; repeated load tests were also conducted to examine the fatigue resistance of the longitudinal steel girders as influenced by the welding attachments. The experimental results are compared to theoretical ones based on the finite element method. It is concluded that the response of welded‐diaphragm composite bridges is superior to that of bolted‐diaphragm bridges and that this construction technique be used to rehabilitate existing composite bridges and/or improve their load rating.

Lateral Distribution of Live Loads on Highway Bridges

AASHTO specifications give a load fraction based on only two major variables that affect load distribution on highway bridges. For more economical design, a refinement of the AASHTO values is needed. In this paper, the processes for beam‐and‐slab and box‐girder bridge systems are shown. It is concluded that to make an economical design of a long bridge of moderate span, the accuracy of the transverse load distribution is a key factor. The finite element modeling methods for finding very accurate load distribution normally cannot be used early enough to help the designer at the beginning of the design process. For a multibox bridge, cross‐sectional transverse influence lines can always be developed with relatively short calculations for load distribution and torque.

Effects of intermediate diaphragms in distributing live loads in beam-and-slab bridges

For small-span to medium-span bridges, the beam-and-slab type of construction is popular, mainly because of its ease of construction, and is preferred in practice even though this form of construction may sometimes exhibit rather poor transverse load distribution qualities. This deficiency is often reduced by the incorporation of one or more diaphragms in the deck construction. Although the use of diaphragms in beam-and-slab bridges is very extensive, their use is almost entirely empirical rather than based upon any logical method of analysis. Thus, the requirements for diaphragms that are found in codes of practice all over the world usually consist of simple and arbitrary statements. It is proposed here to carry out a thorough theoretical study of the structural behaviour of diaphragms in beam-and-slab bridges, with a view to establishing this behaviour on a well-reasoned footing. Key words: beam-and-slab bridge, diaphragm, cross frame, grillage analogy, finite element method, orthotropic plate theory.

Optimal design of tie-beams

The paper concerns the determination of the optimal cross-sectional area distribution of a simply supported tie-beam that minimizes the maximum deflection, subject to: (a) a volume constraint, and (b) the longitudinal elongation of the tie-beam not exceeding a given value. The transverse load distribution considered is symmetrical about the mid-span of the tie-beam. The solution to the problem is obtained directly by two independent approaches.

Longitudinal Load Distribution Factor of Helical Gears

This paper deals with the longitudinal load distribution and the bending moment distribution of a pair of helical gears with a known total alignment error. The load distribution along the contact lines is calculated by the finite element method based on the plate theory including transverse shear deformation. Empirical formulas for both longitudinal load distribution factor and bending moment distribution factor are proposed for practical use. The load distribution factor in AGMA 218.01 is examined, and it is concluded that the load distribution factor is close to the calculated results if the value of unity is taken as the transverse load distribution factor.

Load distribution in continuous composite bridges

The influence of transverse diaphragms on the load distribution in composite bridges has been minimized in current design codes. Tests have shown that when diaphragms having an I-section are rigidly connected to the longitudinal girders, a rigid gridwork is formed; this gridwork in composite action with the concrete deck distributes the wheel loads on the bridge in an orthotropic manner. In this paper, the influences of the number of diaphragms, aspect ratio, skew, and cracking of the concrete deck on the transverse load distribution in continuous composite bridges are examined. The theoretical results are verified and substantiated by tests on two 1/8-scale bridge models. The results indicate that such diaphragms, rigidly connected to longitudinal girders, significantly enhance the transverse load distribution, and thus a reduction in the design load for the girders results; the degree of this enhancement increases with increase in the width as well as the skew angle of the bridge. Furthermore, transverse cracking of the concrete deck at the intermediate support(s) does not appear to influence significantly the transverse distribution of the design parameters.