Discrete Diaphragm Research Articles

Sustainable approaches to improve the resilience of modular buildings under wind loads

Prefabricated volumetric modular building (PVMB) technology is an emerging technology that can make the construction industry walk towards sustainability by reducing the emission of pollutants leading to various environmental impacts. However, the knowledge of the lateral behaviour of PVMBs is limited. This could lead to significant building failure in future, as the climate continues to change, it is expected that building performance will be affected. Thus, this research aims to study the resilience of PVMBs under changing wind loads and identify the most sustainable approach to improve resilience. A 25-storey case-study building was analysed with modifications added to increase its lateral stiffness. Three methods of increasing the resilience were used: (1) increasing the size of structural elements; (2) increasing the inter-component connection stiffness; and (3) introducing discrete diaphragms. The results showed that using chevron bracings of the same section size as X-bracings can maintain the same resilience against the wind while decreasing total bracing steel volume by 32%. Among the analysis cases, structures with concrete cores (CC) have the highest stiffness to withstand the increased wind loads. The building with CC at the centre can withstand a 100% higher serviceability wind speed (i.e. 74 ms−1) than building without modifications (i.e. 37 ms−1). At the same time, the building with CC on either side can withstand a 45% higher wind speed than building without modifications. Further considering the sustainability aspects, the environmental effects of global warming can be reduced by about 160% when fully modular buildings are constructed with recycled steel.

Novel discrete diaphragm system of concrete high-rise modular buildings

Modular high-rises are attractive for metropolises, but few applications exist, partly due to the lack of knowledge about their lateral behaviors. Existing concrete modular high-rises usually adopt a time-consuming and labor-intensive cast-in-situ concrete layer on modules to satisfy the continuous rigid diaphragm assumption. This study aims to develop an innovative discrete diaphragm system for concrete modular high-rises without a cast-in-situ concrete layer. A private residential building in Hong Kong (HK) was selected as the case building, in which the novel horizontal and vertical connection designs were proposed. A simplified spring model considering in-plane axial and shear behaviors was proposed to simulate the horizontal connections. A three-dimensional finite element model of the case building with discrete diaphragms was established using the spring model. A parametric study was conducted to examine the influence of horizontal connections on the deflection and natural periods of the case building under the HK code-specified wind loads. A comparative study was conducted using five cases with different connection stiffness sets to systematically investigate the influence of horizontal connections on the structural responses of the case building under the wind loads. Results show that the discrete diaphragm system is feasible for concrete modular high-rises in HK. Effects of horizontal connections on the lateral behavior of concrete modular high-rises should be considered in the structural design when the discrete diaphragms are adopted. This study breaks through the continuous rigid diaphragm assumption and proves that appropriate flexible horizontal connections are a feasible option for concrete modular high-rises under wind loads.

Engineering finger-operated peristaltic pumps

Peristaltic pumping has been widely adopted in microfluidic systems over the past decade. Most applications lie, however, in the regime where fluids or biospecimens are continuously pumped through the entire fluidic system, leaving the initial filling stage of fluid into an air-filled channel underexplored. We propose a compact, quasi-1D, lumped element model for describing the initial filling process of liquid into microfluidic channels driven by peristaltic pumps with discrete diaphragm valves. In addition, we experimentally demonstrated that the liquid penetration length into the fluid channel could be decently controlled (~ 0.3 mm/cycle) using human fingers as the source of actuation pressures. Moreover, we show from our experiments the possibility of controlling the profiles liquid penetration lengths to be other than Lucas–Washburn’s $$ l\,\sim\,t^{{\frac{1}{2}}} $$ dependence: Linear liquid penetration length profiles can be achieved via liquid channels with exponentially decaying cross-sectional areas. In the above ways, our model has successfully demonstrated that finger-operated peristaltic pumps can serve as an upgraded alternative for capillary-driven microfluidics, offering extra runtime adjustment capability in understanding and engineering of microfluidics in the initial filling stages.

Torsional behaviour of curved composite beams in construction stage and diaphragm effects

During the concrete-casting process of curved steel–concrete composite beams in construction stage, all loads including the wet concrete weight are carried by the curved open thin-walled steel girder. In order to determine the required diaphragm spacing, firstly the curved girder is simplified to straight one by using the M/r method, and its torsional behaviour is subsequently derived by solving the restrained torsional differential equation with the initial parameter method, where the discrete diaphragms are treated to be equivalent to a continuous elastic thin plate. Taking the maximum stress ratio of the warping normal stress to the bending normal stress as the control index, effects of the number of diaphragms, the span of the curved girder, the span-to-radius ratio, the girder height and the flange width on the stress ratio are studied. The parametric analysis results indicate that with the increase of the number of diaphragms, the stress ratio decreases exponentially; and with the increase of the span-to-radius ratio, the warping stress ratio increases linearly; additionally, longer span leads to reduced stress ratios, but the variation of the girder height and the flange width has little influence on the stress ratio. Calculation formulae for determining the required diaphragm spacing are obtained eventually by regression analyses. Based on the research outcomes herein, given the limit value of the warping stress ratio in the practical design of curved composite beams under construction, the maximum diaphragm spacing of the open thin-walled steel girder can be determined by using the formulae proposed in this paper.

High‐Order Behavior of Sandwich Beams with Flexible Core and Transverse Diaphragms

The bending behavior of a sandwich beam with transversely “soft” core and transverse diaphragms is analytically investigated using variational principles. The beam consists of one or two skins, upper and lower, interconnected at discrete locations through transverse diaphragms, metallic or composite laminated, with a symmetric lay‐up and a fully or partially bonded (delaminated) transverse flexible core made of foam or low‐strength honeycomb type. The diaphragm is rigidly connected to the skins but may be bonded or unbonded with the adjacent core through its entire height. The analysis considers the discrete diaphragm as a concentrated interference that affects the beam's behavior through particular boundary and continuity conditions. The behavior of the beam is determined with the aid of a high‐order theory that uses a two‐dimensional elasticity formulation for the core, in the longitudinal and the transverse directions, combined with a beam theory for the skins and the diaphragms. The core‐diaphragm interaction is determined explicitly for the bonded and the unbonded cases and the equivalent conditions in terms of the solution unknowns are derived. The presence of a discrete diaphragm yields concentrated effects that affect the beam's behavior globally and locally. These localized effects are significantly important for the safety of the structure and are explicitly determined by the analysis for the entire structure as well as in the vicinity of the diaphragm. A study that investigates the effects of the existence of a reinforcing diaphragm and its interaction with the adjacent core in a vertical cut‐off end connection between a sandwich panel and its supporting members is presented, including the level of stress concentration involved.

On stress concentration in the bending of sandwich beams with transversely flexible core

Stress concentrations in sandwich beams with a ‘soft’ core subjected to bending loading are investigated and the level of stresses is analytically determined. The cases discussed include stress concentration effects (i) in the vicinity of concentrated loads and supporting zones; (ii) at the edges of debonding regions-edge and inner delamination types at the interface layer between the skins and the core; and in the vicinity of vertical cut-off connections; and (iii) at the location of diaphragms that are bonded and unbonded with the adjacent core and embedded in it. The results are determined with the aid of a variational rigorous, analytical, systematic elastic high-order theory that uses closed form solutions. This theory is applicable to any type of sandwich construction with and without discrete diaphragms (i) to any type of loading, concentrated or distributed; and (ii) to any type of boundary conditions including cases in which at the same section the conditions at the upper skin are different from those at the lower skin. The stress concentration effects are presented in terms of deflections, internal forces and normal stresses (peeling) in the interface layers between the skin and the core. A parametric study is conducted and investigates the level of stresses as a result of (i) the vertical modulus of elasticity of the core; (ii) the delamination length; (iii) the reinforcing diaphragm in a typical connection; and (iv) the presence of diaphragms, either bonded or unbonded with the adjacent core, at specific locations.

Errors in the Finite Difference Solution of Hyperbolic Partial Differential Equations

Publisher Summary This chapter describes the errors in the finite-difference solution of hyperbolic partial differential equations. When a model of a distributed parameter system is to be produced for a simulation, two approaches are possible: (1) treating the system as a series of linked subsystems, that is, lumped parameters, and producing the model equations using the relevant conservation equation for each lump; or (2) producing the relevant partial differential equations to describe the system by use of the conservation equations. Hayashi and Ransford considered the errors involved in replacing distributed head losses in water hammer calculations by fictitious discrete diaphragms at the end of short lengths of pipe, that is, lumping the friction losses. Their analysis showed the errors between the maximum pressure predicted by simple models with that from a model with an infinite number of diaphragms. If the upper frequency limit of interest is known, then the number of finite difference segments to be used for distortionless propagation can be calculated.