Optimal design of long-span steel portal frames using fabricated beams

This paper considers the optimal design of fabricated steel beams for long-span portal frames. The design optimisation takes into account ultimate as well as serviceability limit states, adopting deflection limits recommended by the Steel Construction Institute (SCI). Results for three benchmark frames demonstrate the efficiency of the optimisation methodology. A genetic algorithm (GA) was used to optimise the dimensions of the plates used for the columns, rafters and haunches. Discrete decision variables were adopted for the thickness of the steel plates and continuous variables for the breadth and depth of the plates. Strategies were developed to enhance the performance of the GA including solution space reduction and a hybrid initial population half of which is derived using Latin hypercube sampling. The results show that the proposed GA-based optimisation model generates optimal and near-optimal solutions consistently. A parametric study is then conducted on frames of different spans. A significant variation in weight between fabricated and conventional hot-rolled steel portal frames is shown; for a 50 m span frame, a 14–19% saving in weight was achieved. Furthermore, since Universal Beam sections in the UK come from a discrete section library, the results could also provide overall dimensions of other beams that could be more efficient for portal frames. Eurocode 3 was used for illustrative purposes; any alternative code of practice may be used.

Deciphering the performance hints hidden in J. S. Bach’s quaver beams

Bach often beamed his quavers beyond the beat-unit indicated by the time-signature, as if to indicate the way he perceived, phrased or articulated a musical line. In my previous study in 2011 I demonstrated the significance for both performers and editors of critical editions of quaver beaming against a broader background of Bach’s notational practice. In this article, I go one step further and demonstrate that Bach’s quaver beams reflect how Bach responded to his pieces in composition and performance, which sheds light on how he engaged with and perceived his music from motivic to structural levels. This enquiry has never before been pursued thoroughly and it promises to uncover the ideas that guided his notational practice as well as his spontaneous responses to the challenges he faced while writing out his music on paper

High-energy monoenergetic proton beams from two stage acceleration with a slow laser pulse

We present a new regime to generate high-energy quasimonoenergetic proton beams in a "slow-pulse" regime, where the laser group velocity vg<c is reduced by an extended near-critical density plasma. In this regime, for properly matched laser intensity and group velocity, ions initially accelerated by the light sail (LS) mode can be further trapped and reflected by the snowplough potential generated by the laser in the near-critical density plasma. These two acceleration stages are connected by the onset of Rayleigh-Taylor-like (RT) instability. The usual ion energy spectrum broadening by RT instability is controlled and high quality proton beams can be generated. It is shown by multidimensional particle-in-cell simulation that quasimonoenergetic proton beams with energy up to hundreds of MeV can be generated at laser intensities of 1021W/cm².

Strength model for end cover separation failure in RC beams strengthened with near-surface mounted (NSM) FRP strips

As an alternative to externally bonded FRP reinforcement, near-surface mounted (NSM) FRP reinforcement can be used to effectively improve the flexural performance of RC beams. In such FRP strengthened RC beams, end cover separation failure is one of the common failure modes. This failuremode involves the detachment of the NSM FRP reinforcement together with the concrete cover along the level of the tension steel reinforcement. This paper presents a new strength model for end cover separation failure in RC beams strengthened in flexure with NSM FRP strips (i.e. rectangular FRP bars with asectional height-to-thickness ratio not less than 5), which was formulated on the basis of extensive numerical results from a parametric study undertaken using an efficient finite element approach. The proposed strength model consists of an approximate equation for the debonding strain of the FRP reinforcement at the critical cracked section and a conventional section analysis to relate this debondingstrain to the moment acting on the same section (i.e. the debonding strain). Once the debonding strain is known, the load level at end cover separation of an FRP-strengthened RC beam can be easily determined for a given load distribution. Predictions from the proposed strength model are compared with those of two existing strength models of the same type and available test results, which shows that the proposed strength model is in close agreement with test results and is far more accurate than the existing strength models.

Finite element modeling of debonding failures in FRP-strengthened RC beams: A dynamic approach

This paper is concerned with the finite element simulation of debonding failures in FRP-strengthened concrete beams. A key challenge for such simulations is that common solution techniques such as the Newton-Raphson method and the arc-length method often fail to converge. This paper examines the effectiveness of using a dynamic analysis approach in such FE simulations, in which debonding failure is treated as a dynamic problem and solved using an appropriate time integration method. Numerical results are presented to show that an appropriate dynamic approach effectively overcomes the convergence problem and provides accurate predictions of test results.

Improved model for interfacial stresses accounting for the effect of shear deformation in plated beams

A significant increase in strength and performance of reinforced concrete, timber and metal beams may be achieved by adhesively bonding a fibre reinforced polymer composite, or metallic such as steel plate to the tension face of a beam. One of the major failure modes in these plated beams is the debonding of the plate from the original beam in a brittle manner. This is commonly attributed to the interfacial stresses between the adherends whose quantification has led to the development of many analytical solutions over the last two decades. The adherends are subjected to axial, bending and shear deformations. However, most analytical solutions have neglected the effect of shear deformation in adherends. Few solutions consider this effect approximately but are limited to one or two specific loading conditions. This paper presents a more rigorous solution for interfacial stresses in plated beams under an arbitrary loading with the shear deformation of the adherends duly considered in closed form using Timoshenko’s beam theory. The solution is general to linear elastic analysis of prismatic beams of arbitrary cross section under arbitrary loading with a plate of any thickness bonded either symmetrically or asymmetrically with respect to the span of the beam.

Bond behavior of NSM FRP strips between two adjacent cracks in concrete beams: A numerical study

Strengthening RC structures with near-surface mounted (NSM) fibre reinforced polymer (FRP) composites has a number of advantages compared with that with externally bonded (EB) FRP sheets/plates. As with EB FRP, the performance of the bond between NSM FRP and concrete is one of the key factors affecting the behaviour of the strengthened structure. This paper presents a numerical investigation into the behaviour of NSM FRP loaded at its both ends to simulate the NSM FRP-toconcrete bond between two adjacent cracks in RC members. The main objective of this study is to quantitatively clarify the effect of the bondline damage during slip reversal on the ultimate load (bond strength). The results show that the bondline damage has a significant effect on the load-carrying capacity of the NSM FRP-to-concrete bonded interface and should be considered in FE modeling of the interface.

Mitigation of concrete cover separation in frpstrengthened RC beams using FRP U-jackets

Concrete cover separation is a common failure mode of reinforced concrete (RC) beams strengthened with a fibre-reinforced polymer (FRP) plate bonded to the tension face (FRP-plated RC beams). Plate-end FRP U-jackets have previously been explored as a mitigation measure to delay or suppress concrete cover separation, although its effectiveness needs further clarification. The paper presents the first systemic experimental study on the use of FRP U-jackets of different forms for mitigating the concrete cover separation failure. A total of ten full-scale FRP-plated RC beams were tested. The test results show that both the ultimate load and the ductility of the beams were enhanced by the U-jackets. Among the forms of U-jackets explored, those inclined at 45o are the most effective.

Analytical model for bar-end cover separation failure in RC beams strengthened with near-surface mounted FRP

The flexural performance of RC beams can be improved using the near-surface mounted (NSM) FRP strengthening technique. A likely failure mode of such FRP-strengthened RC beams is bar-end cover separation which involves the detachment of the NSM FRP reinforcement together with the concrete cover along the level of the steel tension reinforcement. This paper presents a new analytical strength model for this failure mode. The proposed strength model and two existing strength models for this failure mode are compared with test results to demonstrate the superior performance of the new analytical model.

Strengthening timber beams with near surface mounted carbon fiber reinforced polymer rods

Many timber structures may require strengthening due to either decay and aging or an increase of load. This paper presents an experimental study in which eleven timber beams were tested, including three unstrengthened reference beams and eight beams strengthened with NSM CFRP bars. The test parameters include the position of NSM (tensile face or the bottom of the sides), the number of CFRP bars (1 or 2), and additional anchorage of NSM CFRP bars (steel wire U anchors or CFRP U strips). The test results show that the ultimate flexural strength of the timber beams were increased by 14%∼85% with an average of 47% due to NSM CFRP bar strengthening. Their deflection corresponding to the peak load was increased by 33% in average.