Partial-interaction flexural stresses in composite steel and concrete bridge beams

doi:10.1016/S0141-0296(00)00121-8

Engineering Structures

Volume 23, Issue 9, September 2001, Pages 1186-1193

https://doi.org/10.1016/S0141-0296(00)00121-8 Get rights and content

Abstract

Even though mechanical shear connectors in composite steel and concrete beams require slip to transmit shear, most composite bridge beams are designed as full-interaction because of the complexities of partial-interaction analysis techniques. However, in the assessment of existing composite bridges this simplification may not be warranted as it is often necessary to extract the greatest capacity and endurance from the structure. This may only be achieved using partial-interaction theory which truly reflects the behaviour of the structure. This paper develops a new concept of the partial-interaction focal point and simplifies partial-interaction theory to derive a simple procedure for deriving the partial-interaction flexural stresses from standard and easily obtained full-interaction parameters. This will allow engineers to develop more accurate procedures for determining the strength and endurance of existing composite bridge beams. Use of the procedure is illustrated by way of an example.

Introduction

Current composite steel and concrete bridge beams are designed using full-interaction theory assuming there is no relative displacement, or slip, between the steel and concrete components along their interface. However, results obtained from full and small-scale T-beam tests performed as early as 1943 have shown that there is slip along the steel–concrete interface [1]. Furthermore, push tests have shown that mechanical shear connectors have slip even under very small loads [2], [3].

Slip occurs because mechanical shear connectors have a finite stiffness. Hence, the connectors must deform before they can begin to carry load and this is known as partial-interaction. Therefore, the total cyclic range of shear load resisted by the shear connectors R_pi must be less than that predicted from a full-interaction analysis R_fi. As the fatigue life of the shear connectors is dependent on R raised to the exponent m, where m is approximately equal to 5, even a small reduction in R_fi results in a large increase in the fatigue life [4], [5]. This implies that current full-interaction design procedures are safe and simple. However, in the fatigue assessment of existing structures, more accurate assessment techniques are required in order to extend the life of the structure as much as possible. A simple tiered assessment approach has been developed [6] based on partial-interaction theory that can be used to predict the remaining strength or endurance of the shear connection. Unfortunately, there is a trade-off and the reduction in the longitudinal shear force due to partial-interaction acting along the steel–concrete interface requires that the adjacent steel and concrete components are subjected to greater flexural stresses than that currently predicted by full-interaction analyses [7].

This paper develops a new concept of a partial-interaction focal point and extends the classic linear–elastic partial-interaction theory, developed by Newmark et al. [1], to derive a simple mathematical model that can be used to predict the partial-interaction change in the steel and concrete stresses from the standard and easily derived full-interaction stresses. In this paper, the model is developed for simply supported steel and concrete composite bridge beams with a uniform distribution of connectors subjected to a single concentrated load. However, as we are dealing with fatigue type loads, it is assumed that the steel and concrete components remain linear–elastic, hence, the principle of superposition may be used to determine the effect of multiple concentrated, or axle loads. All of the relationships presented in this paper have been verified by computer simulations using a finite element program that was developed to model the behaviour of composite steel and concrete beams subjected to fatigue loading [6].

Section snippets

Bounds of strain distributions

The elastic design of composite steel and concrete beams usually assumes full-interaction. The effect of partial-interaction on the flexural stresses is discussed in this section, by investigating the change in the strain distribution at a point along a beam under a given load condition.

It must first be acknowledged that two extremes or bounds exist with regard to the strain distributions at a section. One bound occurs when the connector shear stiffness is infinite, that is full-interaction,

Partial-interaction curvature

In order to develop a relationship for the curvature anywhere along a beam due to partial-interaction, the following relationship was developed [6] from linear–elastic partial-interaction [1] which must be integrated with respect x, the distance from the support to the design point $dφ dx = (ks/p)d_{c} −V^{∗} E_{s} I_{o}$ where k is the connector stiffness, p is the connector spacing, d_c is the distance between the centroid of the steel and the centroid of the concrete, and V^* is the shear force V₁ or V₂, depending

Quantifying the increase in curvature

For a single concentrated load acting on a simply supported span, the maximum moment and, hence, curvature at a design point occurs when the load is situated at the design point. As the maximum full-interaction curvature at a design point is readily calculable using Eq. (1), this section develops a magnification factor MF_φ that can be applied to the full-interaction curvature φ_fi in order to determine the more realistic partial-interaction curvature φ_pi.

The magnification factor is defined as $MF_{φ} =$

Simplified curvature magnification factor

The mathematical model developed in Eq. (15) is too computationally intensive to be accepted and used in everyday design or assessment situations. Therefore, a set of simplified equations is developed that do not significantly reduce the accuracy of the mathematical model.

The simplified model involves estimating MF_φ at the supports, the quarter-span and the mid-span, and joining these points by straight-line segments. As the distribution of MF_φ in Fig. 3 is symmetrical about the mid-span of the

Partial-interaction focal points

The previous section developed a procedure for predicting the partial-interaction curvature from the full-interaction curvature. However, in order to determine the partial-interaction strain distribution, so that the corresponding flexural stresses can be calculated, the position of the strain profile at the known curvature must be determined. This section develops a means of locating the partial-interaction strain distribution by quantifying the location of the focal points mentioned

Partial-interaction strain distribution

As any strain distribution at a section passes through the two focal points regardless of the connection stiffness, it follows then that the points where the full-interaction and no-interaction strain distributions intersect can be used to define the position of the focal points.

Dealing with the focal point in the steel component first, the strain distribution in the steel under full-interaction and no-interaction can be defined using the following equations respectively $(ε_{s})_{fi} = M E_{c} I_{nc} (y_{s} − y ̄_{ns})$ and

Summary of proposed procedure

The following summarises the proposed procedure for determining the partial-interaction strain distribution so that the corresponding flexural stresses can be found using the relationships developed in this paper:

1.
Calculate the full-interaction curvature φ_fi at a design point using Eq. (1),
2.
Determine the magnification factor MF_φ using either the mathematical model of Eq. (15) or the simplified model of , , ,
3.
Find the partial-interaction curvature φ_pi by multiplying φ_fi with MF_φ,
4.
Define the location

Illustrative example

The following example is used to illustrate the detrimental effect of partial-interaction on the flexural stresses using both the increase in the full-interaction curvature as derived from the magnification factors and the focal points.

Suppose that a 50.4 m long simply supported composite beam has been designed using a full-interaction analysis procedure. The cross-sectional geometry of the beam is such that (1/A′)=2.80×10⁶ mm² and d_c=1410 mm. A uniform distribution of connectors was used

Conclusion

A simple procedure has been developed to predict the partial-interaction strain distribution at a design point directly from standard full-interaction analyses. Although partial-interaction can substantially increase the endurance of the shear connectors, it also increases the flexural stresses acting on the cross-section. This can potentially induce tensile stresses in the concrete slab that can lead to premature cracking, and/or reduce the fatigue life of the steel section. It is suggested

Acknowledgements

This project was funded by an Australian Research Council Grant.

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Proc. Soc. Experimental Stress Analysis
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There are more references available in the full text version of this article.

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