A Method to Calculate the Support Length of Beams Resting on Masonry Walls

Rehabilitation, strengthening, and retrofitting of existing masonry buildings represent an important challenge for the construction engineering field. Often, slab strengthening/retrofitting is performed by replacing existing timber and steel beams or by adding new beams to improve the slab load-carrying capacity. The computation of the stresses at the beam–masonry interface (i.e., the contact pressure) is crucial to properly design the beam support length, preventing local failure of masonry and beam. This paper presents a simple analytical procedure to compute the contact pressure at the beam–masonry interface. The analytical procedure is validated by comparison between analytical and corresponding numerical results obtained by finite element modeling. Different types of beam (solid and laminated timber beams and steel beams) were considered, as well as different support conditions (simply resting on the wall considering different support lengths or fully embedded). The results obtained show that the method proposed is simple and reliable, which makes it suitable for professional practice.

Study on the effect of the fastener support structure on rail corrugation in metros based on the friction-induce vibration

Rail corrugation is very serious in Cologne egg fastener track; effective control measures are still lacking. The cause of the corrugation wear on a curved metro track is analyzed based on the friction-induced vibration theory. A finite element model is established to study the frequency domain and time domain features of the friction-induced oscillation of this system. The influences of the fastener spacing and the fastener support length on the corrugation wear are investigated to develop countermeasures. The simulation results show that the friction-induced vibration of the wheel-track system is the wavelength-fixed mechanism of the corrugation wear of rail of the curved Cologne egg fastener track. There are two reasons why the low rail corrugation wear is more serious. The contact resultant force between the low rail and the wheel is obviously bigger than that between the wheel and the high rail, resulting in a higher wear rate of the low rail. The contact force fluctuation of the low rail caused by the friction-induced vibration is more severe, resulting in a higher corrugation wear evolution speed on the low rail. The friction-induced oscillation cannot be eliminated only by adjusting the fastener support length and spacing. However, the long-wavelength corrugation wear instead of the more harmful short-wavelength corrugation wear can be produced by adjusting the fastener support length and the fastener spacing to alleviate the influence of corrugation wear on the vehicle-track system.

Study on the additional support length requirements of single-span bridges due to skew using a simplified method

Skew bridges with seat-type abutments are frequently unseated in earthquakes due to large transverse displacements at their acute corners. It is believed these large displacements are due to in-plane rotation of the superstructure. Lack of detailed guidelines for modeling of skew bridges, many current design codes give empirical expressions rather than theoretical solutions for the additional support length required in skew bridges to prevent unseating. In this paper, a parametric study has been carried out to study the influence of skew angle, aspect ratio and fundamental periods of bridges on the additional support length requirements of single-span bridges due to skew using a shake table experiment validated Simplified Method, which is capable of simulating gap closure based on response spectrum analysis. This method is developed based on the premise that the obtuse corner of the superstructure engages the adjacent back wall during lateral loading and rotates about this corner until the loading reverses direction. A design response spectrum specified in AASHTO LRFD Specifications was employed to represent the design-level earthquakes. The results show the additional length required to prevent unseating due to skew increases with the skew angle in an approximately linear manner when the angle is less than a critical value and decreases for angles above this value. This critical skew angle increases with the aspect ratio approximately in a linear manner and shows negligible dependence on the fundamental periods of the bridges, and combination of span length and width. In addition, the critical skew angle varies between 58° and 66°, when the aspect ratio is varied from 3.0 to 5.0. The results also show that the empirical formulas for minimum support length requirements of skew bridges in current codes and specifications can not accurately reflect the influence of skew.

Effect of skew on the minimum support length requirements of single-span bridges with seat-type abutments

Skew bridges are known to be susceptible to girder unseating during earthquakes, and empirical equations for minimum support length are used in their design. To determine the degree of conservatism or un-conservatism in these equations, a rigorous model of a skewed bridge was developed in OpenSees and validated against a comprehensive dataset from shake table experiments. The validated model was then used to perform a parameter study on a series of single-span, simply supported, prototype bridges with seat-type abutments. Nonlinear response history analyses were performed that included impact and friction effects at the abutments and were repeated for both far-field and near-field motions. It was found that the additional support length required to prevent unseating is a linear function of skew angle over the range 0°–60° for both types of motions. This is contrary to common practice, which uses a quadratic function (American Association of State Highway and Transportation Officials, AASHTO) or the inverse of cosine of angle of skew (Federal Highway Administration (FHWA)). Consequently, common practice appears to be underestimating support length requirements by up to 50% at midrange skew angles of 30°–40°.

The possibility of DIC system application in numerical models updating

The paper presents the results of updating of numerical models of the rectangular steel plate members in a plane state of stress, the updated parameter was a support length. Three different members loaded in a static or dynamic way were analyzed. The article shows examples of purely numeric updating. The data used to the update of numerical models was obtained from numerical simulations and it corresponds to the data, which can be measured by using the Digital Image Correlation (DIC) system. The main aim of the paper is to check the possibilities of the DIC system application in updating of numerical models.