Pounding of a modular building unit during road transportation
Introduction
Modular Building Units (MBU) are box-like structures that are assembled to form a multistorey stacked building. MBUs are transported on trailers (with trucks) to the site where wooden planks or steel jigs are used as mounting layers between the MBU and the trailer-bed. If the truck is driven over a road undulation, or a speed - bump, the excessive vertical bounce created due to its suspension could result in the module to become lifted from the trailer-bed followed by pounding. It is during this pounding scenario that the module would experience shocks in the vertical direction. The phenomenon of shocks and vibrations has been studied in Refs. [1,2]. The module rests directly on wooden planks that are placed on the trailer bed (as an intermediate layer). It is necessary to analyze the pounding hazard on the MBU due to the transmission and amplification of shocks as it could impose a significant amount of dynamic forces on the attached components.
An MBU is made up of structural elements such as beams, columns, braces, structural walls, floor and ceiling slab panels as well as non-structural components such as mechanical-electrical-plumbing (MEP), heating-ventilation-air conditioning (HVAC), interior lighting, gypsum boards and light furniture. A completely (100%) furnished MBU in a factory environment would maximize construction efficiency given that on-site work is minimized [3]. This trend would increase the risks of damage to the MBU and its internal attachments during transportation. Vibrations imparted on the MBU due to road unevenness have been experimentally quantified in Ref. [4]. Vibration hazards on internal attachments to the MBU during road transportation were initially investigated by numerical simulations in Ref. [5]. These simulations in the form of a parametric study (undertaken by the authors) have resulted in the development of acceleration response spectra that can be translated into dynamic forces that are experienced by secondary MEP, HVAC and architectural fittings attached to the inside of the MBU. No uplifting, nor pounding, was considered in these previous investigations. In a follow-up investigation (on MBUs that have not been secured rigidly on the bed of the trailer) the velocities of pounding MBU have been probabilistically estimated [6].
This study quantifies the level of shocks that are generated during the impact between an MBU and a trailer-bed. Standard simulation techniques may then determine the transmission of the acceleration pulse from the point of contact (on pounding) to components attached to the MBU. Results have been presented in the form of floor response spectrum of displacement (RSD) and floor response spectrum of acceleration (RSA) that correspond to deflection and forces sustained by the components respectively [7,8]. Information so derived from the study would serve to guide the design of interior fittings for countering dynamic actions incurred during transportations. The use of floor spectra for estimating dynamic forces on components (including MEP services) produced by pounding is essentially the same methodology used for predicting seismic actions on non-structural components as prescribed in standards such as AS 1170.4 [9]. The components could be experience dynamic forces that are by far higher than design forces that are prescribed by any standard provisions related to seismic actions.
This study is concerned with impact action in the vertical plane in a lifting-pounding scenario, as depicted in Fig. 1. A moving truck-trailer carrying an MBU could become excited by road undulation resulting in a lifting action (Fig. 1 – b) [6]. MBUs that are not fixed to the trailer chassis (like shipping containers) are normally secured with tie-down straps or chains. The vertical restraints are designed to provide a downward force of 20% of the weight of the cargo (MBU) according to the stipulations in load restraint guides. The chains used to secure the load have been known to develop a slack due to truck vibration once the vehicle is in motion. Building code AS 3850.2 cautions the drivers to check the load restraining mechanism in regular intervals during travel. Straps can also experience loss of contact. Replacing chains with straps would further increase the possibility of a loss of contact between an MBU and a trailer-bed during excessive vertical vibration owing to the strap flexibility. Predictions presented in the paper represent the worst scenario of a MBU becoming unrestrained to serve as reference. Considering that a minuscule vertical jump of 12 mm is sufficient to incite impacting velocities of 0.5 m/s, the pounding has been proposed to create a significant hazard to MBU and internal components.
The development and experimental validation of the proposed modelling methodology involved the following task components:
- 1.
An MBU was first scaled down (by a ratio of 1:8) as per the law of dynamic similitude. A numerical model was then developed in LS DYNA and then validated by comparison of the simulated results with results recorded from laboratory experimentation of the MBU test specimen (refer Section 2). The validated scaled-down model was then used to infer impact actions on the prototype.
- 2.
Impact experiments of miniature scale have also been conducted, and this involved dropping a spherical impactor specimen onto a wooden specimen (for emulating the wooden planks which the MBU was mounted upon when placed on the bed of the trailer). Comparative analyses were then undertaken to demonstrate that results derived from the miniature scale experimentation fulfil the same purpose as that of the 1:8 scaled-down model (refer Section 3).
- 3.
The Hunt and Crossley (H & C) mathematical expression has also been used for modelling the forcing function that was generated by the pounding of the spherical impactor on the wooden plank at a miniature scale. Parameters in the H & C model had been determined in priori from results of static compression tests applied to specimens of the wooden planks. Values of parameters in the H & C model to characterize the behaviour of a wide range of wooden planks as cushioning materials were then obtained. This methodology is inexpensive to conduct as only static testing is involved and is potentially of strong appeal to the industry (refer section 4).
- 4.
Analytical modelling of the forcing function sustained by the wooden plank based on assimilating outcomes from step (3) was then undertaken (refer section 5).
- 5.
Numerical simulations of the transmission of the acceleration pulse from the point of contact during pounding to the rest of the MBU were then undertaken. The simulation model treated the MBU as a continuous flexible beam. Results are presented in the form of displacement time-histories and “floor spectra” in the acceleration and displacement (RSA and RSD) formats. The dynamic accelerations that were imposed on a component attached to the MBU were then be calculated using the floor spectra (refer section 6).
Section snippets
Experimental setup of a 1:8 MBU model for drop testing
A 1:8 scaled-down model of an MBU was built in the laboratory in accordance with the dynamic theory of similitude and was based on the ratio of elastic forces to gravitational forces with the prototype. The modelling principles are based on Cauchy's requirements [10] as represented by Eq (1).
Parameters characterizing the 1:8 scaled-down test specimen of a steel module (Fig. 2) with dimensions: metres are listed in Table 1
Simplified spherical impactor model
In day-to-day engineering practices, it may not be viable for the engineer to fabricate a physical model of an MBU for drop testing every time a new type of materials is proposed to be used for cushioning the pounding action on the trailer bed. A key objective of this study was to develop and validate a miniature model comprising a steel sphere and a timber specimen (as shown in Fig. 5 a – d) to waive away the need of fabricating and testing a scaled-down specimen of the MBU. Numerical
Analytical hunts – crossley modelling and quasi-static testing
The motivation behind calling up the Hunt & Crossley model is to expedite simulations of the acceleration pulse that is generated by pounding. A classical approach may then be employed thereby waiving away the need to undertake any impact experiments, nor any time consuming numerical simulations using costly software such as LS-DYNA.
Predicting the forcing function of impact
The drop testing of a scaled-down MBU model has been simplified further into the drop testing of a spherical impactor onto a wooden specimen at a miniature scale. The testing methodology can be simplified further by replacing drop testing of the cushion specimen by quasi-static testing which has been shown to be able to obtain accurate estimates of the compression properties of the wooden plank as cushioning material. A step by step illustration of a new procedure for determining the forcing
MBU response to impact pulse excitation
An MBU is a volumetric box structural unit forming an integral part of the building structural system. Since the impact accelerations under consideration are in the vertical plane, vertical vibrational characteristics of an MBU are stressed in this part. Elastic response behaviour within the box may be assumed given its rigidity. An MBU can be modelled as a one – dimensional system (i.e. as a beam element) which has its cross-section characterized by the equivalent flexural rigidity (as a
Conclusion
The paper was aimed at predicting the dynamic forces sustained by components that are attached to the Modular Building Unit (MBU) during truck transportation. The lifting and pounding of the MBU on the trailer bed were considered to be hazardous to the components. An MBU could be excited into vertical vibrations as the shock waves are transmitted to the rest of the MBU upon pounding. A multitude of experimental, numerical, and analytical methodologies for modelling the acceleration pulse
CRediT authorship contribution statement
Siddhesh Godbole: Concenptualization, Methodology, Software and validation, Writing - original draft - Review. Nelson Lam: Supervision, Conceptualization, manuscript review, resource allocation. M.M.M. Mafas: Experimentation, fabrication, data validation. Emad Gad: Supervision.
Declaration of competing interest
Authors declare that there was no conflict of interest during the course of this project.
Acknowledgement
The authors would like to acknowledge CRC – Low Carbon Living (CRC-LCL) [Grant number RP1031] for providing funding for this research (RP1031) as well as University of Melbourne and Swinburne University of Technology for providing funding and collegial support.
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