PFN1 gene encoding the PFN1 protein are associated with human amyotrophic lateral sclerosis (ALS). We and others recently showed that two of these mutations  cause ALS in rodents. In vitro studies suggested that Met114Thr and Thr109Met cause the protein to behave abnormally and cause neurotoxicity. The mechanism by which a single amino acid change in human PFN1 causes the degeneration of motor neurons is not known. In this study, we investigated the structural perturbations of PFN1 caused by each ALS-associated mutation. We used molecular dynamics simulations to assess how these mutations alter the secondary and tertiary structures of human PFN1. Herein, we present our in silico data and analysis on the effect of G118V and T109M mutations on PFN1 and its interactions with actin and PLP. The substitution of valine for glycine reduces the conformational flexibility of the loop region between the α-helix and β-strand and enhances the hydrophobicity of the region. Our in silico analysis of T109M indicates that this mutation alters the shape of the PLP-binding site and reduces the flexibility of this site. Simulation studies of PFN1 in its wild type (WT) and mutant forms (both G118V and T109M mutants) revealed differential fluctuation patterns and the formation of salt bridges and hydrogen bonds between critical residues that may shed light on differences between WT and mutant PFN1. In particular, we hypothesize that the flexibility of the actin- and PLP-binding sites in WT PFN1 may allow the protein to adopt slightly different conformations in its free and bound forms. These findings provide new insights into how each of these mutations in PFN1 might increase its propensity for misfolding and aggregation, leading to its dysfunction.Profilin-1 (PFN1) is a 140-amino-acid protein with two distinct binding sites―one for actin and one for poly-L-proline (PLP). The best-described function of PFN1 is to catalyze actin elongation and polymerization. Thus far, eight DNA mutations in the  SOD1, TARDP-43, and FUS) have significantly expanded our understanding of ALS over the last 20 years. Multiple cellular pathologies  lead to the progressive loss of motor neurons, resulting in the paralysis and death of voluntary muscles. Available preclinical and clinical models have not led to any interventions that block motor-neuron death or slow the progression of ALS. Further studies are needed to identify the mechanism by which these mutations cause disease and to expedite the development of effective treatments for people with ALS.Amyotrophic lateral sclerosis (ALS) is a progressive and fatal degenerative disorder of motor neurons. Studies of mouse models carrying ALS mutations  9. Mutations in PFN1 represent a novel mechanism underlying ALS, evidenced by the linkage of common polymorphisms in PFN1, tubulin A4A, dynactin, peripherin, and neurofilament genes to ALS14. Importantly, the discovery of PFN1 mutations in ALS3 has led to the development of PFN1 mouse models of the disease5. These models prove that mutations in PFN1 associated with ALS are causal for the disease and provide an extraordinary opportunity to study how PFN1 mutations confer neurotoxicity.The new mutant PFN1 mouse models for ALS that we have created based on familial ALS (fALS) linked PFN1 is an indispensable tool for studying the gene-specific and ALS disease-specific mechanisms of motor neuron degenerationPFN1 mutations associated with ALS (T109M and G118V), and our study sheds light on how these mutations cause ALS and whether there are two different mechanisms at play. The crystal structure of bovine PFN1 in complex with actin and poly-L-proline (PLP), shows that the G118V mutation is located within the actin-binding site, and the T109M mutation near the PLP-binding site. We postulate that the mutation in the actin-binding motif affects the interaction between profilin-1 and actin and dysregulates the dynamics of actin polymerization. On the other hand, we predict that mutations in the PLP-binding motif affect the interaction between PFN1 and PLP and many other ligands binding at this site17.Here, we examined in detail two of the eight 17. Although PFN1 was discovered 30 years ago and has been studied extensively, its potential role in motor neuron disease generated renewed interest in its biology. We hypothesize that the ALS-linked mutations in PFN1 disrupt de novo structural dynamics for PFN1 tertiary and quaternary assembly. This would disrupt actin polymerization and other de novo functions of PFN1, which may have catastrophic effects on the central nervous system or peripheral neurons and glia.PFN1 is a key enzyme in actin polymerization and its dynamics are critically important for all basic cellular activities. We are interested in understanding the structural changes in PFN1 that are caused by ALS-associated mutations. In neurons, proper PFN1 function is essential during development and is implicated in the formation and maintenance of the neuronal cytoskeleton, growth-cone formation, synaptogenesis, synaptic activities, shape and morphological dynamics, and the growth of dendrites and axons. Additionally, the actin-binding and PLP-binding motifs are critical for the multiple functions of PFN1, including actin elongation, polymerization, and dynamics, as well as for interactions with diverse ligands and binding partners (over 50 of which have been described)PFN1 gene, we have analyzed the structure of profilin-1 mutants in silico. We have investigated the biophysical properties of the two mutants, G118V and T109M, using in silico techniques, as these mutants are implicated in causing ALS based on clinical and pathologic evidence and experiments employing cellular and mouse models of ALS20. We postulate that these mutations may cause neurotoxicity via two distinct pathways, changes in actin dynamics (G- to F-actin polymerization) and cellular signaling pathways , via PLP-binding and interactions that require further study. We and others have recently provided evidence in vivo and in vitro that the G118V mutation disrupts actin binding and reduces the F-actin to G-actin ratio, suggesting that impairment of actin polymerization and of other de novo functions of PFN1 is the basis for neuronal death5. Additionally, more recent reports from in vitro studies provide evidence that the T109M mutation disrupts PLP binding20.To explore this hypothesis and to understand the structural, folding, and binding perturbations that may account for PFN1 neurotoxicity, as well as to pinpoint the biophysical changes caused by mutations in the www.rcsb.org/structure/2pav 21. PFN1 binding to actin and PLP plays an important role in its activity. Profilin–actin complex formation is essential for maintaining sufficient levels of actin monomer for polymerization. Recruitment of the profilin–actin complex for polymerization is accomplished through the binding of the last poly-Pro segment of vasodilator-stimulated phosphoprotein (VASP) to the profilin–actin complex23. Thus, impairment of either of these interactions would disrupt the polymerization and growth of the actin filament.In this study, we have generated and analyzed new data on the alteration and perturbation of the 3-D structure of PFN1 protein caused by G118V and T109M mutations to unravel how a single amino acid substitution affects the tertiary structure and properties of PFN1. The G118V mutation reduces the flexibility and increases the hydrophobicity of the polypeptide chain. We reason that these changes are responsible for the misfolding and aggregation of mutant PFN1 and the basis for ultimately blunting actin polymerization. The T109M mutation appears to distort the PLP-binding site, making it sterically unfavorable for PLP binding. For these studies, we utilized the crystal structure of the ternary complex of PFN1 in complex with actin and PLP (PDB code: 2PAV) PFN1 to gain insights into how the altered properties of PFN1 protein might compromise neuronal function and/or survival. A single amino-acid substitution, arising from a missense mutation, can alter the local environment and affect intra-molecular interactions of the residues resulting in conformational changes that are usually local, but that can also be allosteric (affecting remote areas of the molecule). A missense mutation can perturb the molecular structure rather subtly, yet disrupt binding to an associated protein or other ligand. The goal of this study was to simulate and analyze the mutation-induced structural changes and their consequences for diverse interactions.We simulated and analyzed the structural changes caused by ALS-associated missense mutations in 21  on the structure and function of PFN1 in complex with actin or PLP and in its isolated form.We began with the previously determined crystal structure of PFN1 complexed with an actin fragment and a PLP (PDB code: 2PAV)In vivo studies and computer modeling suggest that this mutation likely decreases the solubility and aggregation of PFN119. Glycine is the smallest nonpolar, hydrophobic amino acid, with only hydrogen as its R group. Gly118 is located in a loop that connects a β-strand to the fifth and last α-helix of the protein 2. We sought to test this hypothesis while also assessing other possible impacts on structure that might cause misfolding and lead to further anomalies downstream.26 with that of for amino acids with side chains shows that the presence of side chains severely restricted conformational flexibility. Therefore Gly to Val change could induce conformational changes in the peptide chain and these changes might hinder the binding of PFN1 to actin. Interestingly, the backbone peptide directly interacts via two hydrogen bonds to the side chain of Gln354 in actin . The resulting coordinates showed that the Gln354 side chain of actin moved away from the His120 side chain of PFN1, eliminating the hydrogen bonding and packing interactions . When we superimposed the structural models of PFN1 and the T109M mutant, the overall conformation of the mutant was almost identical to the wild type .The study of tertiary and quaternary structure of PFN1 protein (wild type and mutant) in complex with actin and/or PLP requires an extensive set of molecular dynamics simulations. The simulations on PFN1 protein (wild type and mutant) in association with actin and/or PLP is considerably more complex than in the uncomplexed state. Additionally, these simulations are associated with thermal fluctuations that may not be easily distinguished from functionally relevant behaviors of a protein in different conditions (different mutations or binding states). To avoid such issues, we set out to extensively examine the behavior of isolated WT and mutant PFN1. We performed three sets of independent molecular dynamics simulations for each system including PFN1WT simulations , the PFN1 variants behaved similarly. WT-3 simulations indicate some additional flexibility for the 35–50 region  and root-mean-square fluctuation (RMSF) analyses were performed to systematically compare the overall and residue-based fluctuations of the protein in different conditions  and other physical characterizations of the G118V mutation support this notion, as described below.et al., 2018, manuscript under review). This observation suggests that the mutation of Gly118 is pivotal for proper folding to generate the proper geometry for interactions with actin. In addition, the changes caused by the substitution of glycine with valine may lead to the misfolding and aggregation of the protein. The T109M mutation, on the other hand, appears to distort the PLP-binding site so as to make it sterically unsuitable for PLP binding. Our simulation studies showed that the mutant is unable to maintain the hydrogen-bonding interactions with PLP. We observed that during simulation, wild type PNF1 maintains its hydrogen bonds with PLP, while the hydrogen-bonding interactions decrease sharply for the T109M mutant.In a concurrent study of PFN1 structural characteristics, an analysis of PFN1 with CD showed a spectral shift, indicating a conformational change by extension of the alpha-helix . Mutant structures and the native form of PFN1 were energy-minimized in a solvent box with counter-ions and 0.14 M NaCl for 5000 steps using the “steepest decent” method in GROMACS molecular dynamics simulation software; we used the Assisted Model Building and the Energy Refinement (AMBER99SB-ILDN) force field that refers to both sets of molecular mechanical force fields to simulate biomolecules and uses a package of molecular simulation programs. For more details, refer to http://www.gromacs.org.A crystallographic structure of native PFN1 was retrieved from PDB databank (2PAV). This structure was used to create G118V and T109M mutations using the mutagenesis plugin within Pymol  was added to crudely mimic physiological conditions. The AMBER99SB-ILDN force field was used for all simulations. The system was further energy-minimized for 5000 steps using the steepest descent method. The system was then equilibrated at constant temperature (300 K), in the NVT ensemble  for 300 ps. Next, the system was equilibrated at constant pressure (1 bar) in the NPT ensemble . The final simulation (production) was carried out for each system for 200 ns and was repeated 3 times (three independent simulations for each system). The leap-frog integrator was used for the time evolution of trajectories.To understand the impact of single amino acid (missense) mutations on PFN1 structure, molecular dynamics simulations were performed in explicit solvent for PFN1α). Hydrogen-bonding was analyzed with the Hydrogen Bonds plugin in VMD. Detailed information was generated for all hydrogen bonds in each system using a donor-acceptor cutoff distance of 3 A° and an angle cutoff of 20°. Salt bridges were analyzed with the Salt Bridges plugin in VMD. For each system, a donor-acceptor cutoff distance of 4 A° was used to generate data for individual salt bridges (distances over time). Each salt bridge was plotted to assess the strength of the interaction.The resulting trajectories were analyzed with trajectory analysis modules from the GROMACS simulation package and from Visual Molecular Dynamics (VMD) software. Multiple VMD analyses were performed on the trajectories from nine 200-ns PFN1 simulations, including RMSD (Root-Mean-Square Deviation - backbone) and RMSF (Root-Mean-Square Fluctuation – CDr. Kiaei and UAMS have a financial interest in the technology discussed in this publication. These financial interests have been reviewed and approved in accordance with the UAMS conflict of interest policies.


Methomyl is the most common cause of suicidal death but heroin is the most common cause of accidental death. The problem is to determine the exact cause and manner of death between methomyl or heroin toxicity. The evidence from autopsy includes crime scene investigation, toxicological analysis by liquid chromatography with mass spectrometry, and knowledge of methomyl and heroin intoxication.A 35-year-old Thai man and a 30-year-old Thai woman were found showing evidence of cyanosis, with a fine froth around the nose and mouth. Postmortem interval time was 24 hours. According to the police’s and hotel owner’s records, the couple stayed together for 1 day before being found dead in bed, naked, with a foul and a fine froth around the nose and mouth. A methomyl insecticide sachet and a plastic box containing white powder form of heroin were found at the scene. Laboratory tests of the male corpse identified the presence of methomyl in the blood of the stomach and morphine, codeine, methadone, and tramadol in the systemic blood. Blood cholinesterase enzyme activity and morphine concentration was 3416 U/L or 53%  and 0.058 μg/ml respectively. Laboratory test of the female corpse identified the presence of methomyl in the stomach and blood, and cholinesterase enzyme activity was 1965 U/L or 30.7%.Cause of death of the male corpse was deemed to be due to heroin intoxication as the blood concentration of morphine was more than the lethal concentration with a morphine/codeine ratio of more than 1:1. Methomyl intoxication of the male corpse was unlikely to be the cause of death because methomyl systemic blood concentration was found to be very low, < 2.5 μg/ml, and cholinesterase enzyme levels did not indicate lethal activity . The main problem regarding an insurance claim is that the policy will not pay out in the case of heroin-associated deaths, as it is an addictive drug. The policy would pay out on death by suicide with methomyl insecticide, which was not prohibited by the insurance company after 1 year of insurance. So, it is not clear whether or not the family will receive money from the insurance company. Insecticides are widely used in agriculture in Thailand. The common insecticides are organophosphorus (OP) compounds and carbamates (CM), which act as contact poison to insects without being phytotoxic to the plant. These poisons are toxic to humans and every year more than 200,000 people die due to these poisons globally . Methomyl is classified as a Restricted Use Pesticide (RUP) by the US Environmental Protection Agency , 2. MethHeroin intoxication and death is the most common cause of accidental death in Thailand. The histopathology associated with death by heroin and other opioids is cyanosis and pulmonary edema, which is due to suppression of the respiratory center in the brainstem and respiratory failure . Its hisIn the insurance company policies of Thailand, if a patient dies within a year of taking out a policy, then money cannot be claimed from the insurance company. However, if a person dies by committing suicide as a result of methomyl poisoning more than a year after taking out a policy, then the insurance company will have to pay out. However, if a person dies as a result of heroin intoxication, then money cannot be claimed from the insurance company.We report a case in which a 35-year-old Thai man suspected of suicidal CM poisoning was a victim of heroin overdose.A 35-year-old Thai man and his mistress, a 30-year-old Thai woman, were found dead in a hotel room in Chiang Mai, Thailand. The postmortem time of death was approximately 24 hours. The crime scene had a plastic box which contained some white powder and a container with a label that read Lannate® 40%SP also in the form of white powder which was methomyl insecticide. Both bodies were subjected to postmortem examination. During an autopsy at the Department of Forensic Medicine in Chiang Mai University, a copious amount of fine froth came out of their mouths and nostrils. There was bluish discoloration of their faces which was suggestive of cyanosis. No external injuries were noted. On opening the stomachs, a peculiar smell came from the greenish-brown gastric contents of both corpses. The mucosa of the stomach walls showed general submucosal hemorrhagic gastritis. The brains were edematous. The respiratory passages and the lungs were filled with fine froth. The liver and kidneys of both corpses showed features of congestion. The body fluids and the white powder recovered from the crime scene were subjected to chemical analysis. The viscera were sent for histopathological examination.Analysis by liquid chromatography with tandem mass spectrometry (LC-MS-MS) was done: femoral arterial blood, 100 ml; urine, 100 ml; gastric contents, 100 ml. The laboratory reports of the Thai man and woman are presented in Table This study involves a male corpse who died with his mistress at a hotel in Chiang Mai, Thailand. Methomyl intoxication was initially suspected. The autopsy was performed out at the Department of Forensic Medicine, Faculty of Medicine, Chiang Mai University, Chiang Mai, Thailand. The study was approved by the Department for the Civil Law of Thailand. The methomyl, trade name Lannate® 40%SP, was purchased from the retailer DuPont Co., Ltd., Thailand.A complete autopsy was performed at Department of Forensic Medicine, Chiang Mai University, Thailand. Sample specimens including blood and stomach contents, and witness materials were collected at the scene. At the mortuary, the lungs, liver, heart, and kidneys were removed and histological analysis completed. Paraffin-embedded sections stained with hematoxylin and eosin were examined using light microscope.Blood, urine, and gastric contents were analyzed using liquid LC-MS-MS to assess the presence of the substances: methomyl insecticide, heroin, 6-MAM, morphine, and others.The system used was an Acquisition Method Report with Agilent Technologies 6460 Triple Quad LC/MS with Column of Eclipse Plus C18 1.8 mm 2.1 × 100 mm. The specimens  were collected from the corpses and analyzed immediately by LC-MS-MS.http://massbank.jp/SearchMethod Path was The autopsy on a 35-year-old Thai male corpse and a 30-year-old Thai female corpse, estimated time after death was 24 hours, reported no evidence of external injury. The autopsy was carried out using the following:At the scene of investigation two corpses were present in the rented room. They both had large amounts of fine froth in the nose and mouth and cyanosis was evident  but blood concentration of the female corpse was 6.8 μg/ml. In addition, the cholinesterase enzyme activity of male corpse did not decrease by more than 90% which would be the case in death by methomyl, but in this case was only 53%. Methomyl may be a concomitant cause of death in this case but was not the major cause. It is the policy of insurance companies of Thailand that if a patient dies within a year of taking out a policy, then the legal situation as to whether the patient committed suicide using methomyl or by intoxication with heroin, or any opioids that are narcotic drugs, is irrelevant. The money cannot be claimed from the insurance company under this condition. However, if a patient committed suicide as a result of methomyl poisoning more than a year after taking out the policy, then it is relevant and the insurance company will have to pay out, but if the patient died as a result of heroin intoxication the money cannot be claimed from the insurance company. In this case we concluded that heroin intoxication was the cause of death, not methomyl insecticide. However, if thorough laboratory techniques had not been used in this case, the cause of death would have been methomyl insecticide intoxication because of the evidence found at scene of death. In addition, he died with his mistress which is common in Thailand. This is one of the principal problems faced by forensic medicine teams in Thailand because there are limitations to death investigation techniques in many areas. Forensic pathologists may be judged by the justice system if they give an incorrect diagnosis or opinion in distinguishing between deaths as a result of methomyl or heroin intoxication. The conclusion of the case of the Thai man was a suicide and the possibility of heroin intoxication was based on the scientific data of the laboratory. Insurance cannot pay out the money because it is against the policy and agreement before acceptation.


During tests, the step-by-step loading procedure was applied on different steel fiber content specimens, and the electromechanical impedance values were measured. The Normalized root-mean-square deviation Index (NI) was developed to analyze the EMI information and evaluate the test results. The results show that the normalized root-mean-square deviation index increases with the increase of the axial load, which clearly demonstrates the influence of axial load on the EMI values for steel fiber concrete and this influence should be considered during a monitoring or damage detection procedure if the axial load changes. In addition, testing results clearly reveal that the steel fiber content, often at low mass and volume percentage, has no obvious influence on the PZT’s EMI values. Furthermore, experiments to test the repeatability of the proposed method were conducted. The repeating test results show that the EMI-based indices are repeatable and there is a great linearity between the NI and the applied loading.With the advantages of high tensile, bending, and shear strength, steel fiber concrete structures have been widely used in civil engineering. The health monitoring of concrete structures, including steel fiber concrete structures, receives increasing attention, and the Electromechanical Impedance (EMI)-based method is commonly used. Structures are often subject to changing axial load and ignoring the effect of axial forces may introduce error to Structural Health Monitoring (SHM), including the EMI-based method. However, many of the concrete structure monitoring algorithms do not consider the effects of axial loading. To investigate the influence of axial load on the EMI of a steel fiber concrete structure, concrete specimens with different steel fiber content  (kg/m Distributed short steel fibers in concrete hinder the expansion of microcracks and the formation of macroscopic cracks , enhanciPiezoelectric materials have been used in the health monitoring of concrete structures for many years ,3,4. TheThe sensing technology is a critical part of structural health monitoring ,22. EMI Until now, there have been many methods to evaluate the service performance and health condition of concrete structures ,35. The The influence of axial force on piezoceramic-transducer-based monitoring is crucial for evaluation the health status of structures. The pitch–catch method was employed by Liu et al.  to measu3) were casted. For each fiber content, three specimens were fabricated. The strength of the concrete specimens is 50 Mpa. The EM impedance signals were recorded at the axial force values of 0, 20, 40, 60, 80, and 100 kN, which ensured the specimens deformed within the elastic range of strains. The elastic loading range prevents damage to the steel fiber concrete specimens and narrows the influencing factor to only the axial load for a test period when the load is increased from 0 to 100 kN. A smart aggregate with a 15 mm × 15 mm × 1 mm PZT patch as its sensing core was embedded in each specimen for the EMI measurement. During each test period, the PZT EMI measurements were acquired through an impedance analyzer. Testing results clearly demonstrated that the axial load greatly influences the EMI value and the effect of axial load should be considered for EMI-based structural health monitoring of concrete structures. Experimental results also clearly revealed that the fiber content, normally at a small mass and volume percentage, has no obvious effect on the EMI values.In this paper, the authors proposed to experimentally study the influence of the axial load on EMI-based damage or SHM of steel fiber structures. In addition, the influence of steel fiber content on the EMI values will also be experimentally studied. Standard concrete cube specimens (150 mm × 150 mm × 150 mm) with five different steel fiber contents  , which is the impedance of the piezo-transducer coupled to the host structure, is given byi is the imaginary unit; Aw, Ah, and lA are the width, thickness, and length of the PZT patch, respectively; d32 is the piezoelectric constant; and AZ and SZ represent the electromechanical impedance of PZT and the structure, respectively. Assuming that the mechanical properties of the PZT patch do not vary during the measurement procedure, Equation (1) shows that the electrical impedance of the PZT patch is directly related to the structure’s impedance [RRMSD) is used in this paper, as indicated byith measurement of the EMI real part signal at a certain frequency range, and The electromechanical impedance (EMI) and the electric admittance are reciprocal to each other. In the PZT-transducer-driven, single-degree-of-freedom mass–stiffness–damping system, the mpedance . Axial f3). The stress wave propagation velocity in the 50 MPa strength concrete structure is about 4000 m/s. The concrete mix proportion is shown in The cube specimens were composed of 50 MPa strength concrete with different steel fiber content  , as shown in The step-by-step loading schedule was applied to steel fiber concrete specimens within the elastic range. We purposely chose step-by-step loading so that we could measure the impedance value at a steady state to minimize the dynamic effect. For each loading value, the impedance information of the smart aggregate was directly acquired by the impedance analyzer. The real parts of the impedance for Specimens 1-1, 2-1, 3-1, 4-1, and 5-1 over the frequency range of 10 kHz to 500 kHz were recorded and plotted in i denotes the ith loading condition in the experiment; ith loading condition. The normalized results are shown in The real parts of the recorded impedance values of experiments were analyzed with the RMSD index. Due to the deviation of the RMSD values under different loading conditions, the RMSD results of each specimen were normalized based on the following equation:In all cases in In addition, as shown in It should be noticed that in Experimental results clearly demonstrated that the axial load greatly influences the EMI value and the effect of axial load should be considered for EMI-based structural health monitoring of concrete structures. Experimental results also clearly revealed that the fiber content, normally at a small mass and volume percentage, has no obvious effect on the EMI values.3). Therefore, it is more reasonable to use electrical impedance to study the influence of axial force on the voltage amplitude. In this research, the loading is along the axial direction and the loading level is relatively small to ensure the elastic response of the specimen. In reality, the loading may be complex and loading levels may be large and sometimes damage the steel fiber structures. For the next step, we will investigate the feasibility of electromechanical impedance (EMI)-based damage monitoring of steel fiber concrete structures. In addition, we will study the effectiveness of SA-enabled EMI in a complex state of stresses.To investigate the influence of axial load on concrete, Liu et al.  proposed3 steel fiber content was casted, as shown in In order to demonstrate the repeatability and reliability of the proposed technique, additional experiments were conducted. A new specimen with 90 kg/mThe test procedure was the same as that detailed in As shown in In order to demonstrate the reliability of the proposed method, data fitting was conducted for the nine repeated experimental results as shown in x) = 0.009854x + 0.04817 can be obtained. The R-squared value is 0.9919, which means that there is a good linearity between the normalized RMSD index and loading value. These results can be good evidence for the good reliability of the proposed method.The linear fitting formula f(It should be noted that the distribution of steel fibers in steel fiber concrete is uneven . The une3) were fabricated and tested under the axial loads of 0, 20, 40, 60, 80, and 100 kN, which ensured the specimens deformed within the elastic range of strains. The elastic loading range prevents damage to the steel fiber concrete specimens and narrows the influencing factor to only the axial load for a test period when the load is increased from 0 kN to 100 kN. Each specimen was equipped with an embedded smart aggregate with a 15 mm × 15 mm × 1 mm PZT patch as its core. During each test period, the PZT EMI measurements were acquired through an impedance analyzer. Experimental results clearly demonstrated that the axial load greatly influences the EMI value and the effect of axial load should be considered for EMI-based structural health monitoring of concrete structures. Experimental results also clearly revealed that the fiber content, normally at a small mass and volume percentage, has no obvious effect on the EMI values. Experiments to test the repeatability of the proposed method were conducted. The repeating test results show that the EMI-based indices are repeatable and there is a great linearity between the NI and the applied loading. As an important finding of this research, if an impedance-based index is used for structural health monitoring, the index should be corrected by subtracting the increase caused by the applied load. To address the issue of discrepancy in practice, we will calculate the mean value of the specimens with the same fiber content, and this mean value will be used for the correction. Future work will be the study of the discrepancy among specimens with the same fiber content. For the next step, we will investigate the feasibility of electromechanical impedance (EMI)-based steel fiber concrete structure damage monitoring. It will be an interesting topic for future work to study the effect of loading rate or unloading rate on the impedance response. In addition, we will study the effectiveness of SA-enabled EMI in a complex state of stresses.This paper addressed two important issues related to PZT-enabled electromechanical impedance (EMI)-based structural health monitoring of steel fiber concrete structures. The first is how the axial load affects the EMI values and the second is how the steel fiber content impacts the EMI values. To address these two issues, 50 MPa strength concrete cube specimens (150 mm × 150 mm × 150 mm) with different steel fiber content  (kg/m


ABR) is accelerated by antibiotic consumption and that it represents a serious public health emergency, it is imperative to drastically reduce antibiotic consumption, particularly in high‐income countries. I present the problem of ABR as an instance of the collective action problem known as ‘tragedy of the commons’. I propose that there is a strong ethical justification for taxing certain uses of antibiotics, namely when antibiotics are required to treat minor and self‐limiting infections, such as respiratory tract infections, in otherwise healthy individuals. Taxation would allow a reduction in consumption  and/or ensure that individuals internalize or compensate for their contribution to the erosion of the common good of antibiotic effectiveness. I suggest that revenue from the tax could be used to fund conservation and innovation strategies. Taxation might be a coercive policy, especially for certain individuals, but the ethical case for coercive policies is very strong when the good to be preserved is important enough and when they force individuals to do something they have a moral obligation to do anyway. I argue that, in the case of mild and self‐limiting infections, individuals have a moral duty of easy rescue and a moral duty of fairness to make their contribution to the preservation of the common good of antibiotic effectiveness by foregoing antibiotics. I also suggest that taxing antibiotics in such cases is an all things considered ethically justified policy even if it would introduce inequalities in access to healthcare.To the extent that antibiotic resistance ( For instance, drug‐resistant tuberculosis is on the rise and is currently causing at least 200,000 deaths every year,2The Review on Antimicrobial Resistance (p. 10). Retrieved from http://amr-Review.org/sites/default/files/160518_Final%20paper_with%20cover.pdf, Accessed 16 Aug, 2016.O'Neill, J. (2016). Tackling drug resistant infections globally: Final report and recommendations.  but more generally the total annual number of deaths due to drug‐resistant infections is estimated at around 700,000.3Ibid.Antibiotic resistance (ABR)  in general)4https://www.cdc.gov/drugresistance/about.html. Accessed 17 Aug, 2016.CDC (Center for Disease Control and Prevention). About antimicrobial resistance, updated 2015, Retrieved from  Because of antibiotic consumption, any individual can become a carrier of resistant bacteria that expose her to greater risks in future infections5British Medical Journal, 337, 726–728.Cars, O., Murray, M., Nordberg, O., Sivaraman, S., Lundborg, C. S., So, A. D., & Tomson, G. (2008). Meeting the challenge of antibiotic resistance.  and can pass resistant bacteria on to other people. The fact that ABR is a natural reaction of bacteria to the exposure to antibiotics means that antibiotic effectiveness is, by its very nature, a relatively short‐lived phenomenon. New, effective antibiotics are constantly required to replace those that become ineffective. Unfortunately, today the pipeline of new antibiotics is running dry. There is often a lack of commercial incentives for private companies to pursue Research and Development (R&D) on new antibiotics, mainly because of the cost of research, because new antibiotics would initially have to compete with the old ones for as long as these remain effective, and because the necessary implementation of antibiotic stewardship programs would limit consumption and therefore sales.6Op. cit. note 2, p. 52. Thus, urgent measures are required not only to reduce antibiotic consumption for conservation purposes, but also to fund innovation through R&D.Antibiotic consumption contributes to the development of ABR because, by killing the non‐resistant bacteria, antibiotics confer a selective advantage to the resistant ones, which can more easily proliferate. As put by the Center for Disease Control and Prevention in the U.S., ‘the use of antibiotics is the single most important factor leading to antibiotic resistance around the world: simply using antibiotics creates resistance’.7Journal of Agricultural and Environmental Ethics, 30(2), 179–198.Giubilini, A., Birkl, P., Douglas, T., Savulescu, J., & Maslen, H. (2017). Taxing meat: Taking responsibility for one's contribution to antibiotic resistance.  Here, I will focus on the problem caused by human consumption. Abuse of antibiotics is a significant problem: often doctors prescribe antibiotics that are not necessary, such as in cases of viral infection;8Antibiotics, 2, 316–327.Van der Velden, A., Duerden, M., Bell, J. Oxford, J., Altiner, A., Kozlov, R., … Essack, S. Y. (2013). Prescriber and patient responsibilities in treatment of acute respiratory tract infection – Essential for conservation of antibiotics.  for example, in the U.S. about 40 million people are given antibiotics for respiratory issues annually, but the antibiotics are therapeutically useful only in 27 million such cases.9Op. cit. note 2, pp. 35–36. The solution to the problem of antibiotic abuse does not raise particular ethical issues though: To put it simply doctors should not prescribe unnecessary antibiotics and should be prohibited from prescribing unnecessary antibiotics, because unnecessary antibiotics contribute to a collective cost without producing any individual benefit. More challenging, from an ethical perspective, is the problem of ABR driven by therapeutically justified antibiotic consumption, where individual interest in treating infections conflicts with the collective interest in preserving antibiotic effectiveness.We need to distinguish between two main drivers of ABR: the use and abuse of antibiotics in humans and in animals in the context intensive animal farming.10Op. cit. note 2. Unfortunately, the current global trend of antibiotic consumption is going in the exact opposite direction. Of particular concern is the increase in the consumption of last‐resort antibiotics such as carbapenem and colistin. According to a recent study, the total global increase in antibiotic consumption between 2000 and 2015 was 65%. If effective policies are not implemented, global consumption is projected to increase by 200% between 2015 and 2030.11Proceedings of the National Academy of Sciences of the United States of America, 115(15), E3463–E3470.Klein, E., van Boeckel, T., Martinez, E., & Pant, S. (2018). Global increase and geographic convergence in antibiotic consumption between 2000 and 2015. Using antibiotics more responsibly could slow down the development of resistance.12Ibid. Thus, the increase in antibiotic consumption in LMICs might be seen as an overall positive datum, as it indicates that many more people in those countries have access to healthcare than was the case 15 or 20 years ago. However, such an increase needs to be closely monitored in order to ensure that the health benefits in terms of treatment of infections are not outweighed by the harms of ABR. At the same time, the still too‐high rates – despite the slight decrease – of antibiotic consumption in HICs do unquestionably constitute an urgent problem that needs to be addressed. Based on their data, Klein and colleagues conclude that13Ibid.[r]educing antibiotic consumption rates in HICs and slowing the growth rate of consumption in LMICs is urgently needed to contain the problem of resistance, particularly given the long timescales and resources necessary for development of new antibiotics. However, there is a need to balance access to essential medications, particularly in LMICs where the burden of infectious diseases likely still outweighs the burden of resistant infections and where in many countries there is a significant unmet need for antibiotics (p. E3467).It is interesting to dissect the data just provided. On the one hand, in low‐ and middle‐income countries (LMICs) the increase in consumption rate was 77%, while the consumption rate in high‐income countries (HICs) fell by 4%. On the other hand, the consumption rate in most LMICs remains lower than the consumption rate in HICs, and indeed is too low in many countries where access to antibiotics is still difficult, and as a consequence infectious diseases proliferate.14Journal of Natural Science, Biology, and Medicine, 4(2), 286–291; WHO India (2018). Combating antimicrobial resistance in India. Retrieved from http://www.searo.who.int/india/topics/antimicrobial_resistance/Combating_Antimicrobial_Resistance_in_India/en/. Accessed 19 Nov, 2018.Kumar, S. G., Adithan, C., Harish, B. N., Sujatha, S., Roy, G., & Malini, A. (2013). Antimicrobial resistance in India: A review.  and is severely burdened by ABR.15British Medical Journal, 358, 25–30.Kakkar, M. et al. (2017). Antibiotic resistance and its containment in India.  Thus, a country like India might need measures to reduce antibiotic consumption in the same way as, if not more than, HICs do. One way to reduce consumption is through investing resources in conservation strategies that reduce the need for antibiotic prescription in the first place, especially in LMICs, such as improved sanitation, better hospital infection control, and wider use of vaccines.The last observation by Klein does not apply to all LMICs; for instance, India is a major contributor to ABR because of its too‐high consumption of antibiotics,16Op. cit., note 2. Reaching a good balance between conservation and innovation is difficult because investing in innovation might discourage efforts to promote conservation, and vice versa.17Science, 345(6202), 1299–1301.Laxminarayan, R. (2014). Antibiotic effectiveness: Balancing conservation and innovation. However, as noted above, reducing consumption is not the only measure needed. Innovation strategies through R&D of new antibiotics are equally important. For instance, the O'Neill Review on Antimicrobial Resistance commissioned by the U.K. Government advocated for an international ‘Global Innovation Fund’ for early‐stage and non‐commercial R&D for which private companies do not have sufficient commercial incentives.in certain cases antibiotic consumption where disincentives are more urgently needed, given high consumption rates, and where there is more potential for generating revenue to fight ABR. This is certainly the case in many HICs. I want to leave open the question whether and how the same kind of policy here proposed could be adopted in some LMICs, such as India. In most such countries, a tax on antibiotics might have very undesirable outcomes, if people were forced by economic considerations to leave infections untreated in a context where public health is already poor and the burden of infectious disease already too high, and indeed much higher than the burden of resistance. It is actually more plausible to suppose that such countries should be at the receiving end of policies aimed at improving conservation. So I wish my taxation model to be taken as a suggestion for a policy to be implemented certainly in HICs, and perhaps worth considering for some LMICs within a more general cost–benefit assessment. In Section 5, I will suggest that the ethical justification for the form of taxation I am proposing is very strong when foregoing antibiotics comes at small cost to individuals, that is, in the case of mild and self‐limiting infections in individuals who, from a medical perspective, could endure such infections without incurring significant risks. In such situations, individuals have a basic ethical duty not to consume antibiotics, which significantly strengthens the ethical justification for a taxation policy, especially if such a policy is supplemented with the provision of some nonfinancial benefit to those who have to forego antibiotics because of the tax. Finally, in Section 6, I will suggest that policies that disincentivize antibiotic use in such circumstances are all things considered ethically justified, even if they entail some inequalities in access to healthcare.In this paper, I will argue that ABR can be counteracted by disincentivizing antibiotic use and by requiring certain consumers of antibiotics to internalize the costs of ABR or to compensate for the cost they are contributing to. In this way, conservation and innovation strategies can be pursued simultaneously by requiring consumers, in certain cases, to contribute to the funding of conservation and innovation strategies. More precisely, as I suggest in Section 4, both conservation and innovation strategies could be funded through revenue generated by taxing Before taking these steps, it is worth saying something more about the tragedy of the commons that antibiotic consumption gives rise to (Section 2) and about the type of solutions that the tragedy of the commons typically calls for (Section 3).2Antibiotic effectiveness is a common good, or a common pool resource. These types of goods are defined, among other things, by the fact that each individual who enjoys them contributes to their erosion.18Science, 162, 1243–1248.Hardin, G. (1968). The tragedy of the commons.  Hardin asked us to imagine that every single herdsman, acting merely out of self‐interest, has their cattle overgraze the commons, so that the resource's availability is progressively eroded by many individual actions. The tragedy arises because individuals do not have any incentive to abstain from contributing to the depletion of the common pool resource: for any herdsman who uses the pasture, the individual benefit is large and the harm produced is insignificant. Therefore, from a self‐interested perspective, there do not seem to be enough reasons for any individual to abstain from grazing the commons. However, if all or many herdsmen act out of self‐interest, the cumulative harm is very large and the herdsmen themselves will be harmed in the long run.Common goods typically give rise to the collective action problem known as ‘tragedy of the commons’. To introduce the problem, Garrett Hardin famously used the efficacious metaphor of a pasture that is available to many herdsmen.19Journal of Medical Ethics, 39, 752–756.Anomaly, J. (2013). Collective action and individual choice: Rethinking how we regulate narcotics and antibiotics. Antibiotic consumption, including therapeutically necessary consumption, presents the same conflict between short‐term individual interests on the one side, and collective and individual long‐term interests on the other. In the case of therapeutically justified antibiotic use, as Jonny Anomaly put it, ‘the benefits of [antibiotic] use are borne by the individual, the costs are socialised, and the consequent harm is the product of many independent actions‘ (p. 754).20British Medical Journal, 340, 1–11.Costelloe, C. et al. (2010). Effect of antibiotic prescribing in primary care on antibiotic resistance in individual patients: Systematic review and meta‐analysis,  It is safe to say that each individual contribution is at least probabilistic.There are, however, two important differences between the tragedy of the commons as described by Hardin and the tragedy of the commons that arises in the case of antibiotic consumption. The first difference is that, unlike the case of cattle overgrazing the commons, in the case of ABR individuals can bear at least part of the costs of their individual actions, because they can become carriers of resistant bacteria that might render subsequent antibiotic use ineffective. The second difference is that, for the same reason, any individual contribution to ABR through antibiotic use is not necessarily and not always negligible : there is a chance that every individual exposed to antibiotics becomes a vector of resistant bacteria that infect others.It might be suggested that, in light of these two differences, it is not appropriate to talk of ‘tragedy of the commons’ in the case of antibiotic consumption. However, I will stick with the label ‘tragedy of the commons’ to refer to antibiotic consumption because the collective action problem generated by ABR calls for types of solutions that are the same as those typically called for by tragedies of the commons in general, namely the reduction of consumption, the internalization of the costs, or the compensation for the costs imposed or to which one contributes.321Op. cit. note 18, p. 1247. The notion of ‘coercion’ is problematic from a philosophical perspective, as it is difficult to explain precisely what coercion involves or what practices can be considered coercive.22The moral limits of the criminal law. New York; Oxford: Oxford University Press; Frankfurt, H. (1988 [1973]). Coercion and moral responsibility. In T. Honderich (Ed.), The importance of what we care about, in essays on freedom of action (pp. 65–86). London: Routledge & Kegan Paul; Held, V. (1972). Coercion and coercive offers. In P. J. Roland and J. W. Chapman (Eds.), Nomos XIV: Coercion (pp. 49–62). Chicago, IL: Aldine‐Atherton, Inc.; Nozick, R. (1969). Coercion. In S. Morgenbesser, P. Suppes, & M. White (Eds.), Philosophy, science, and method: Essays in honor of Ernest Nagel (pp. 440–472). New York, NY: St. Martin's Press; Wertheimer, A. (1989 [1987]). Coercion. Princeton, NJ: Princeton University Press.Feinberg, J. (1989).  For the purposes of the present discussion, ‘coercion’ can be taken to mean the imposition of penalties or disincentives that are large enough to give an individual strong enough reasons to make a certain choice – for example, forego antibiotics – that she would otherwise not have made.According to Hardin, the solution to the tragedy of the commons needs to be ethical in nature: it is necessary that individuals prioritize the long‐term collective interest over their short‐term individual interest. An important part of what ethics is about is the prioritization of other values over one's egoistic interests. Unfortunately, in many cases, prioritizing the collective over the individual good is an ethical choice individuals are unlikely to be willing to make without some form of coercion. As Hardin put it, solving the tragedy of the commons requires some form of ‘mutually agreed upon coercion’.Now, a relevant question for the justification of coercive measures is the following: does a certain individual behaviour constitute an ethical requirement on individuals, independently of the existence of policies that coerce individuals into adopting that behaviour? The question is relevant because the ethical justification for a public policy that coerces individuals into doing something they have an independent ethical obligation to do anyway is stronger than the justification for a policy that coerces individuals into doing something above and beyond their call of  duty.23Developing World Bioethics, 18(2), 182–189.Giubilini, A. et al. (2018). Quarantine, isolation, and the duty of easy rescue in public health.  Because individual moral obligations strengthen the ethical case for coercive policies, it is important to ask two distinct types of questions regarding antibiotic consumption: first, the question as to what type of coercive policies can ensure that the common good of antibiotic effectiveness is preserved as much as possible, compatibly with provision of sufficiently good health care; second, in order to assess whether these policies are ethically justified, the question as to what ethical obligations individuals have with regard to antibiotic consumption. I will address the first question in the next section (4), and the second question in Section 5.Arguably, when implementing a coercive policy, an authority ought to be able to offer the strongest justification possible for it.4In many cases, it is considered acceptable, if not ethically mandatory, to require those who, because of their behaviour, are responsible for a certain collective cost to compensate society for the cost they create or to do something that can prevent their behaviour from resulting in a net cost for society, that is, to internalize the cost. After all, bearing (at least part of) the costs entailed by one's behaviour is a significant part of what taking responsibility for one's behaviour entails.24Journal of Agricultural and Environmental Ethics, 22, 423–435.Anomaly, J. (2009). Harm to others: The social cost of antibiotics in agriculture.  Compensation implies instead that the cost cannot be offset because the benefit produced is not commensurable with the cost, but the individual responsible nonetheless makes up for it in some other way. Thus, someone might think that funding R&D and alternative conservation strategies would not count as internalization because they would not neutralize the cost that the individual is imposing with their current consumption of antibiotics. However, for the purpose of the present discussion, compensation and internalization can be seen as equivalent strategies, to the extent that they are both ways of contributing to conservation and innovation by those who have the responsibility to do so.Strictly speaking, internalization and compensation are different: internalization occurs when the benefit produced is commensurable with and equal to the cost. As put by Jonny Anomaly, internalizing a social cost requires ‘taxing negative externalities (…) at a rate that would offset the social cost of the activities that generate the externalities, and then  using the revenues from the tax to fund socially useful projects‘ (p. 433).25The Annual Review of Resource Economics, 2(4), 1–14; Littmann, J., & Viens, A. M. (2015). The ethical significance of antimicrobial resistance. Public Health Ethics, 8(3), 209–224, p. 214; Op. cit. note 2.Herrmann, M., & Ramanan L. (2010). Antibiotic effectiveness: New challenges in natural resource management.  because it would disincentivize consumption and could generate revenue that could be invested in conservation and innovation strategies.So, a first ethical solution to the tragedy of the commons represented by antibiotic consumption is that people who are responsible for the erosion of antibiotic effectiveness internalize the costs they are imposing on society, or anyway compensate society for the costs to which they are contributing. Taxation – in the form of a so‐called ‘Pigouvian tax’ – is well suited to addressing or preventing tragedy of the commons scenarios in general, and the tragedy of the commons of antibiotic consumption in particular,26The Economic Journal, 91(364), 1011–1014.Masuda, E., & Newman, P. (1981). Gray and Giffen goods.  Another exception is the case of Veblen goods, that is, luxury goods such as diamonds, for which some people are willing to pay more because the higher the price, the higher the perceived benefits, for example in terms of social status . Because consumption rate has sometimes been shown to be less sensitive to price when it comes to certain health goods,27Palgrave Communications, 4, 70.Vuong, Q. H. et al. (2018). Healthcare consumers’ sensitivity to costs: A reflection on behavioural economics from an emerging market.  one might hypothesize that health goods such as antibiotics are also exceptions to the law of demand, perhaps a type of Giffen good. However, even conceding that this hypothesis is at least plausible, it would not be enough to undermine the effectiveness of the tax. As I said before, reducing consumption is only one way of promoting conservation: other conservation strategies, such as improving access to certain vaccines and developing new ones as well as improving hospital infection control,28Op. cit. note 17. would require investments of resources, especially in LMICs. For instance, ‘the introduction of the pneumococcal conjugate vaccine has reduced the burden of pneumococcal disease, avoided many prescriptions for antibiotics, and lowered rates of invasive disease caused by strains not susceptible to penicillin’.29Ibid, p. 1300. Promoting these alternative strategies requires investing resources, and taxing antibiotics in HICs would generate the necessary revenue. Furthermore, revenue from the tax could be used to fund innovation through R&D as well. Thus, even assuming that the antibiotic tax would not disincentivize consumption, it would contribute to internalizing or at least compensating for the costs of antibiotic consumption by contributing towards conservation and preservation strategies. Actually, the less effective the tax is at reducing consumption, the more revenue it would generate for alternative conservations strategies and for R&D, and vice versa.The idea that a tax would be effective at reducing consumption is based on the standard assumption about behavioural economics that level of consumption is sensitive to price, which is one aspect of the more general ‘law of demand’ (Stigler 1947). The law of demand has some rare exceptions though. Some goods are not consumed less or are even consumed more as their price increases. In particular, people are prepared to spend money on certain ‘inferior’ goods – called ‘Giffen goods’ – when they are scarce, if necessary by foregoing other goods; for instance, they would often invest more on an ‘inferior good’ such as bread if its price increased, especially when the price of alternative goods (e.g. meat) increases as well.A milder variant of an antibiotic tax could be a policy that sets a cap, say an annual upper limit, on the amount of tax‐free antibiotics that any doctor can prescribe to her patients. Above that limit, antibiotics could be heavily taxed. In this case, each doctor would probably be inclined to preserve their quota of tax‐free antibiotics for patients who need them the most, and therefore to prescribe antibiotics less often.Yet another alternative taxation policy would be to tax only newer‐generation antibiotics, in order to preserve their effectiveness for as long as possible, in case the tax was effective at discouraging consumption.Three aspects of the tax on antibiotics need to be specified. First, although I have said that my argument remains valid regardless of whether level of consumption will be sensitive to price, it is important to stress that there is scope for promoting such sensitivity: there will always be an amount of money that an individual would not be prepared to pay to access antibiotics, especially if the infection is mild and self‐limiting. So if the only aim was to reduce consumption, then it would just be a matter of finding the right amount that would sufficiently reduce consumption. Second, it is important to point out that a tax is applicable even in collectively subsidized healthcare systems where the cost of drugs is borne, at least in part, by the state. The cost of the drug is distinct from the tax: the former is what pharmaceutical companies are paid for selling the drug; the latter is what the state collects to fund conservation and innovation strategies. Thus the state can pay for the cost of the drug while levying a tax on consumers. Third, on any of the three variants of the taxation policies I have proposed, the tax should be on the patient, not on the doctor: as is the case with many other medical treatments, it is the patient's choice which treatment to receive, unless more restrictive policies than taxation – such as a ban on certain antibiotic use – are necessary . To the extent that the patient is responsible for the decision and the imposition of the cost, it is the patient who should be taxed when their best interest collides with the collective interest.It is tempting to draw an analogy between a tax on antibiotic consumption and a tax on consumption of alcohol and tobacco, which also generates negative externalities, for instance in terms of expenditure to address the health consequences of their consumption. However, we need to be cautious in drawing such analogies. Obviously, a person can decide not to smoke or not to consume alcohol without significant costs to herself . In contrast, foregoing antibiotics can entail significant costs to individuals in terms of deterioration of health due to infections, depending on the type of infection involved and on their general health status. Unlike the case of foregoing alcohol and tobacco, foregoing antibiotics can in some cases be considered supererogatory.For the same reason, the justification for imposing a tax on antibiotics that are necessary to treat major and severe infections is weaker than it would be if foregoing antibiotics, i.e., avoiding paying the tax, were a costless option producing only minimal harms for the individuals . Thus, while a tax on antibiotics needed to treat major infections, or infections in patients with compromised health status, would be very difficult to justify ethically, an ethical case could more easily be made for a tax on antibiotics used to treat minor or mild infections in otherwise healthy patients. In the next section, I will make my contribution to building such ethical case by arguing that foregoing antibiotics in certain cases is a moral obligation, and therefore a policy that restricts access to antibiotics in such cases has a strong ethical justification.30PlosMedicine, 3(2), 177–180.Foster, K., & Hajo, G. (2006). Do we need to put society first? The potential for tragedy in antimicrobial resistance.   Second, and related to this last point, such policies would probably result in inequalities in healthcare provision by leaving certain people, but not others, without effective antibiotic treatments: only those who are willing or can afford to pay the tax will have access to effective antibiotics.Granted, this type of policy would have two ethical costs: first, assuming that consumption rate is sensitive to price, some minor or mild self‐limiting infections might be left untreated, which, as some have argued, might be necessary in order to effectively contain ABR.The question is whether such costs are worth paying, and therefore whether the types of policies here suggested are ethically justified, all things considered. In the next two sections, I will suggest that they are.5As I have said above, the justification for taxing antibiotics is stronger when individuals have an independent moral obligation to forego antibiotics for the sake of the common good or when they have an independent moral obligation to internalize or compensate for the costs they are contributing to. The two moral obligations are related in the sense that the moral obligation to internalize or compensate for the cost of antibiotic consumption is the strongest when individuals are morally responsible for such costs, that is, when they fail to fulfil a moral obligation not to impose such costs or not to contribute  to such costs in the first place. Of course, there might be other sources of the moral obligation to contribute to a common good in ways that are similar or equivalent to internalization or compensation; thus, also those who are not directly responsible for the erosion of antibiotic effectiveness might be ethically required to do something to address the problem . Here, I will focus on the moral obligations of those who are directly causally and morally responsible for ABR.31Utilitas, 19(1), 1–20.Savulescu, J. (2007). Future people, involuntary medical treatment in pregnancy, and the duty of easy rescue.  i.e., when the cost to them of foregoing antibiotics is sufficiently small. A duty of easy rescue is an intuitive and fundamental moral duty that all reasonable people can agree upon, regardless of the ethical theory or ethical viewpoint they adopt. For example, within Tim Scanlon's contractualist perspective, ‘[if] you can prevent something very bad from happening (…) by making only a slight (or even moderate) sacrifice, then it would be wrong not to do so’ (p. 224),32What we owe to each other. Cambridge, MA: Harvard University Press.Scanlon, T. (1998).  and as Peter Singer famously put it, ‘if it is in our power to prevent something bad from happening, without thereby sacrificing anything of comparable moral importance, we ought, morally, to do it’.33Philosophy and Public Affairs, 1(3), 229–243, p. 230.Singer, P. (1972). Famine, affluence, and morality. Now, individuals have a moral obligation to forego antibiotics when foregoing antibiotics would be, so to speak, a form of ‘easy rescue’,Note that Singer's formulation of the duty of easy rescue is more demanding than Scanlon's formulation: Singer leaves the possibility open that individuals ought to make great sacrifices when the harm prevented is comparatively great enough. In the case of antibiotic consumption, this type of moral duty might include, for example, the moral duty to leave serious infections untreated in order to preserve the common good of antibiotic effectiveness. However, as I suggested above, this kind of claim, and policies that would have such implications, are much more difficult to justify ethically. For this reason, I am not endorsing here the Singerian more demanding version of the duty of easy rescue . Rather, I will stick with Scanlon's version. The question I want to ask here is the following. What are the implications of this duty of easy rescue for the collective and individual moral obligation to reduce antibiotic consumption, and therefore for the justification of coercive policies that disincentivize, through taxation, the use of antibiotics?34Op. cit. note 30, p. 178. such as for example respiratory tract infections in otherwise healthy patients, foregoing antibiotics for the sake of preserving the common good of antibiotic effectiveness does seem to be a form of easy rescue: the cost to individuals is sufficiently small, because we are talking of mild and self‐limiting infections, which would anyway be resolved without antibiotics in a slightly longer time; at the same time, the benefit to society in terms of preservation of antibiotic effectiveness is potentially very large, especially if a large enough population foregoes antibiotics for mild and self‐limiting infections.Now, in certain circumstances, and specifically in the case of ‘milder and mostly self‐limiting bacterial infections’,35Medicine Health Care and Philosophy, 21(4),547–560.Giubilini, A., Douglas, T., & Savulescu, J. (2018). The moral obligation to be vaccinated: Utilitarianism, contractualism, and collective easy rescue. This last consideration is worth examining as it requires us to clarify the concept of ‘rescue’ I have used so far. It is true that the moral responsibility to reduce the amount of antibiotics consumed  is primarily a matter of collective, rather than individual, moral responsibility, in two senses. First, it is necessary that a sufficiently large portion of the population contributes to such enterprises in order for ABR to be significantly slowed down. Second, any individual's actual contribution to the collective cost might be negligible and in any case is only probabilistic; after all, any individual consuming antibiotics might not make a significant difference to the erosion of the common good because they might not pass their resistant bacteria on to other people. However, the fact that the obligation in question is primarily collective does not mean that individuals do not have a moral obligation to make their fair individual contribution, regardless of whether or not they do make a difference. The concept of ‘rescue’ here adopted should not be taken literally: the individual duty in question might not be a duty to directly benefit or prevent harm to another individual, as the literal meaning of ‘rescue’ suggests. The same duty justified by the small cost to the individual might arise from other ethical requirements, different from the requirement to benefit or to not harm others directly. As is the case with many other instances of collective obligations – think, for example, of the collective obligation to realize herd immunity through vaccinating a large enough portion of a given population – considerations of fairness in the distribution of certain burdens demand that each individual takes on herself her fair share of the burdens entailed by the collective obligation, at least as long as the burden is sufficiently small.Thus, the justification for the tax and for the moral obligation to forego antibiotics in certain cases lies not only in the potential harm that any individual consumer of antibiotics poses on others, but also on the consideration that it is fair to contribute to the preservation of the common good, when it is sufficiently easy to do so. Thus, because there is a moral obligation to forego antibiotics in certain cases, the ethical justification for a policy that coerces individuals into foregoing antibiotics in such cases is very strong. Granted, the duty of fairness might well extend to cases in which making one's contribution is more burdensome; however, as I said, I will set aside these more controversial cases.It is important to note that there are two distinct but complementary demands of fairness at stake here. If there is a collective obligation to reduce antibiotic consumption, each individual ought to do her fair share to reduce antibiotic consumption by forgoing some antibiotic use when doing so comes at a small individual cost. And if there is a collective obligation to internalize or compensate for the costs of antibiotic consumption, it is fair that those who are morally responsible for such costs – that is, those who have a moral obligation to forego antibiotics in certain cases, but fail to fulfil this moral obligation – primarily bear such costs, and therefore contribute to the internalization or compensation through taxation.36British Journal of General Practice, 61(590), e579–e589.Peters, S. et al. (2011). Managing self‐limiting respiratory tract infections: A qualitative study of the usefulness of the delayed prescribing strategy.  A taxed‐based policy that disincentivizes such uses of antibiotics might be effective in achieving the goals that this U.K. program failed to achieve, given certain behavioural economic assumptions. If it does not, it will nonetheless force those who are morally responsible for the erosion of the common good to internalize or compensate for the cost by funding conservation and innovation strategies.Indeed, foregoing or at least delaying antibiotics in the case of self‐limiting infections, such as respiratory tract infections in otherwise healthy patients, has already been proposed as a type of antibiotic stewardship program. Unfortunately, however, it is not a widely accepted practice: a study in 2011 found that the practice of ‘delayed prescribing’ in case of some respiratory tract infections – where foregoing antibiotics would be an ‘easy rescue’ – introduced in the U.K. by the National Institute for Health and Clinical Excellence was generally not adopted by healthcare practitioners.Importantly, restrictive policies like the one I am defending might require adequate measures to ensure that the impact on those who decide to forego antibiotics because of the financial disincentive is minimized, and therefore that their sacrifice is actually a form of ‘easy’ rescue. Making the sacrifice as easy as possible is simply part of a state's obligation to ensure that the justification for its restrictive policies is the strongest possible from an ethical point of view. Such measures certainly include adequate medical follow‐up on the state of an individual's infection, but might also include some form of non‐financial compensation, for example prioritization on waiting lists for other types of health interventions, should the patient need them.6all things considered? Or would inequality in access to antibiotics represent a strong enough objection against the tax? Here, I am going to argue that it does not, given the constraints on the tax I have mentioned above.Such a taxation policy might imply that some people will be coerced  into foregoing antibiotics while other people will not, at least on certain behavioural economic assumptions. This raises ethical concerns about equality in access to healthcare. Simply put, the rich would be able to pay the tax and therefore to afford antibiotics for any infection, while the poor might have to leave certain mild and self‐limiting infections untreated for economic reasons. So far I have argued that the ethical case for a tax on certain uses of antibiotics is very strong; but is it strong enough to ethically justify such a policy, 37The Journal of Law, Medicine & Ethics: A Journal of the American Society of Law, Medicine & Ethics, 30(2), 170–178, p. 173; Gostin, L. O. (2008). Public health law: Power, duty, restraint. (Revised and expanded 2nd ed.). London: University of California Press, p. 142.Childress, J. F., Faden, R. R., Gaare, R. D., Gostin, L. O., Kahn, J., Bonnie, R. J., … Nieburg, P. (2002). Public health ethics: Mapping the terrain.  suggests that a policy A that is less restrictive than and at least as effective as a policy B ought to be preferred to policy B, other things being equal. Taxation, if effective at tackling ABR, is ethically preferable to a ban because it is less restrictive, that is, because it constrains individual liberties to a lesser degree and therefore allows at least some individuals to make a free choice whether or not to use antibiotics. One might reply here that, so to speak, things are not equal, because taxation has an equality cost that an outright ban does not have. But I have two responses to this reply.Let me start by pointing out that the equality objection could be circumvented by simply banning the use of antibiotics for everyone in the circumstances I have described. This solution might at some point be necessary, if the taxation model does not prove effective. However, a ban is a measure of last resort and therefore it is not preferable to a milder policy such as taxation, which leaves at least some people the opportunity to treat their mild and self‐limiting infections. A principle of ‘least restrictive alternative’, widely appealed to in public health ethics,First, a ban is preferable to a tax on grounds of equality only as a form of ‘levelling down’: we are making people worse off without making anyone better off than they would otherwise be, just for the sake of equality. But the idea that we would need to ‘level down’ in order to avoid inequalities is normally taken to be an objection to prioritizing equality, rather than a solution to the problem of equality. So it is not clear that a ban would be preferable to a tax just because it would fare better with regard to equality. Simply, the value of equality does not seem to outweigh the value of individual liberty or of expected utility when it requires to level down.38Just health. Cambridge: Cambridge University Press.Daniels, N. (2008).  In other words, those who receive worse (or less) healthcare might be further penalized with respect to very valuable things, apart from suboptimal health; examples offered have included unequal risks of stigmatization and of unemployment and unequal chances to enjoy a certain amount of pension years.39Public Health Ethics, 11(3), 311–324. https://doi.org/10.1093/phe/phy020.Haverkamp, B. et al. (2018). Why socio‐economic inequalities in health threaten relational justice. A proposal for an instrumental evaluation.  However, while it is true that the social determinants of health often reflect social inequalities that need to be addressed – an issue that is beyond the scope of this paper – it does not seem that foregoing antibiotics in the circumstances I have described would have such dramatic consequences both for health as valuable in itself  and for health as instrumentally valuable for equality purposes, given that the infections in question are short‐lived in otherwise healthy patients. In other words, to use the terminology of the capability approach that grounds one of the most authoritative accounts of (a certain form of) egalitarianism,40Ethics, 109, 287–337.Anderson, E. (1999). What's the point of equality?  foregoing antibiotics in the circumstances I have described would not deprive individuals ‘of the capabilities needed to function as equals’ (p. 313),41Op. cit. note 39. at least not for a significantly long time. Thus, it does not seem that leaving mild and self‐limiting infections untreated in otherwise healthy patients would significantly compromise fair equality of opportunities. Inequality might be a serious ethical concern (among others) only if antibiotics were taxed in the case of more severe infections.Second, and more importantly, how great a problem is inequality in the case here under scrutiny? There are two reasons for the view that unequal access to healthcare, and consequently an unequal distribution of health, is ethically problematic: first, with regard to the causes, unequal access to healthcare expresses an underlying injustice when we focus on its social determinants; second, with regard to the consequences, unequal access to healthcare might compromise something valuable, not only health itself and the related wellbeing, which are not positional goods, but also – as has been suggested – fair equality of opportunities.some inequalities in levels of wellbeing experienced, for sure, and I am not denying that this is an ethical cost. However, given how vital it is to contain ABR urgently, it is an ethical cost worth paying, because those who would be worse off as a result of the unequal access to antibiotics would still be well off enough – given that they would still have tax‐free access to antibiotics used to treat more serious infections and that they might be compensated. They would still be well off enough both in absolute terms and with regard to those aspects that make unequal access to healthcare ethically unacceptable. In other words, the policy I am proposing would sacrifice a strictly egalitarian ideal but would preserve a sufficientarian conception of distributive justice, which seems an acceptable compromise between the values of expected utility (in terms of containment of ABR) and equality. Equality is an important value, but in certain circumstances it cannot be the most important value.With the kind of taxation policy I am proposing, there would still be 42The patient as victim and vector: Ethics and infectious disease. Oxford: Oxford University Press.Battin, M. et al. (2009).  would be preferable to a tax because the surcharge would not be calculated on the basis of the actual cost of antibiotic consumption and therefore could be kept sufficiently low so as not to price poor people out of the market.43Op. cit. note 19. However, if I am right that inequality in access to healthcare is not a very strong objection in the case of a tax like the one I am proposing, then such a tax is preferable to a fixed‐amount small surcharge because a small surcharge without an equality cost would certainly not be effective at disincentivizing consumption  and might not be sufficient to adequately fund conservation and innovation strategies. A tax could be effective for either or both purposes, once the appropriate amount to be levied was found.Some have suggested that a fixed‐amount modest surcharge on antibiotics7I have argued that, because individuals have a moral obligation to forego antibiotics in the case of mild and self‐limiting infections , there is a very strong ethical case for a tax on antibiotics that disincentivizes individuals from accessing antibiotics to treat minor and self‐limiting infections or that forces individuals to take responsibility for failing to do so by internalizing or compensating for the cost. Such a policy would simply force individuals to fulfil a moral obligation that they anyway have, and the ethical cost in terms of unequal access to healthcare would be small enough to make such a policy ethically permissible all things considered. What exact form such a taxation policy should take requires a separate discussion. Whether some taxation policy would sufficiently slow down ABR and generate enough revenue to allow funding of conservation and innovation strategies is an empirical issue that would need to be tested. Here, my aim was only to provide an ethical analysis and an ethical justification for this type of policy. More coercive policies or policies that demand greater individual sacrifices might be necessary, but they would require a stronger ethical justification.Work on this article was funded by the Oxford Martin School (Program: Collective Responsibility for Infectious Disease) and by the Wellcome Centre for Ethics and Humanities, University of Oxford, which is supported by a Wellcome Centre Grant (203132/Z/16/Z). The article is made Open Access thanks to the Wellcome Trust.The author declares no conflict of interest.


Accelerated construction in the form of steel–concrete composite beams is among the most efficient methods to construct highway bridges. One of the main problems with this type of composite structures, which has not yet been fully clarified in the case of continuous beam, is the crack zone initiation that gradually expands through the beam width. In the current study, a semi-empirical model was proposed to predict the size of cracks in terms of small box girder deflection and intensity of load applied on the structure. To this end, a set of steel–concrete composite small box girders were constructed by the use of steel fibrous concrete and experimentally tested under different caseloads. The results were then used to create a dataset of the box girder response in terms of beam deflection and crack width. The obtained dataset was then utilized to develop a simplified formula providing the maximum width of cracks. The results showed that the cracks initiated in the hogging moment region when the load exceeded 80 kN. Additionally, it was observed that the maximum cracked zone occurred in the center of the beam due to the maximum negative moment. Moreover, the crack width of the box girder at different loading cases was compared with the test results obtained from the literature. A good agreement has been found between the proposed model and experiment results. Advancement in new construction techniques has received much attention in the last decades. The conventional bridge constructions and rehabilitation are usually accompanied by several operational difficulties. In order to overcome the traditional bridge construction problems, quite a few construction techniques were established such as accelerated, rapid, modular, mechanized, or precast constructions. Among them, the accelerated construction is an effective technique to reduce the impact of the bridge construction period on the surrounding traffic flow . MoreoveAccelerated construction of steel fibrous high-performance continuous composite box girder bridge (ACHPCBG-bridge) is classified into two types—steel–concrete composite box girder bridge with single or double cell and small box girder bridge with multiple cells . If the The ultimate loading capacity of the ACHPCBG-bridge is usually determined by either flexural or shear bearing capacity and is governed by the compressive strength of the concrete or tensile strength of the steel girder. Moreover, in some areas with a continuous composite beam subjected to hogging moment, high strength is required to resist the negative bending. In the support region where the negative bending moment acts, a relatively high tensile stress is generated in a concrete slab and compressive stresses are induced in the lower steel region. As such, the mechanical behavior of these girders is strongly nonlinear even for low-level stress at that region, resulting in crack initiation in the slab, which is generally considered as a shortcoming for the durability and service life of a structure. ,21,22,23In any construction, the characteristics of concrete play an essential role. Concrete is brittle and has limited ductile behavior. Therefore, a form of reinforcement is required to enhance structural stability. Steel bars are used as reinforcement in concrete structures; however, there is still a possibility of crack formation internally or externally, which may lead to a major problem in overall stability of structure ,25.The cracks developed in reinforced concrete members extend freely until encountering a reinforcing bar. We need to arrest the cracks to lengthen the lifespan of structures. Hence, a multi-directional and closely spaced reinforcement is required to be used in concrete. The fibers are, thus, an excellent choice to overcome this type of problem in practice. Fiber reinforced concrete (FRC) is composed of short discrete fibers that are uniformly distributed and randomly oriented within the concrete matrix. The fibers are mainly classified into four types—steel, glass, natural, and synthetic—and each of the different fibers have different properties ,28,29,30Fibers in a concrete element increase the structural integrity, provide high tensile strength to plain concrete, reduce the permeability of concrete, and increase the resistance to impact load. Fibers can reduce the number of rebars without loss of strength. They can also eliminate cracks propagation by bridging action. The flexural behavior, bond strength, and especially toughness of SFRC increase as the fiber content increases. Carbon or steel fibers can be added to a cement matrix at a high volume fraction (0.5–3%) to increase the conductivity of the composite. The properties of fiber concrete depend upon the volume of fibers used ,34,35,36Various types of problems occur in composite materials, mostly due to cracks and delamination. The crack in a composite structure may reduce the structural stiffness and strength and redistribute the load, which may either delay the structural failure or accelerate the structural collapse. The crack is not the main cause of structural failure, but rather is the part of the failure process that may lead to the loss of structural integrity. Therefore, it plays an important role in the failure mechanism of steel–concrete composite structures ,41,42,43The composite beam usually consists of a steel section jointly acting with one (or two) flange(s) made of reinforced concrete that is mainly subjected to bending . These tThe current study mainly aimed at investigating the static behavior of the ACHPCBG-bridge under vertical loading and proposing a simplified methodology to estimate the width of cracks. For this purpose, an ACHPCBG-bridge was experimentally tested under several caseloads to get deflection response. Additionally, the cracking process at hogging moment region was measured at each load step. The details of experimental models are discussed in the following sections.Accelerated construction steel–concrete composite small box girder is a construction technique consisting of an open steel box girder, diaphragm, welding stud, and concrete slab. It is difficult to make corresponding scale models, especially of the concrete bridge deck and the thickness of the steel plate. Therefore, based on the 25 m span prototype bridge, a stereotype model of the steel–concrete composite small box girder was prepared with the members-to-actual length ratio of 1:4. The basic parameters of box girder are shown in In the accelerated construction of steel–concrete composite small box girder, concrete material, stud group arrangement, and stud group spacing are three main parameters. At present, ordinary concrete by a grade size below C50 is mainly used in steel–concrete composite structures. However, because of the high strength and low weight, high-performance concrete not only reduces the weight of superstructure and decrease the costs, but also provides higher durability to the main structure. Hence, it is gradually getting more applications in bridge engineering. As to the knowledge of the authors, there is no specific literature or standard available to give unified understanding of the arrangement and spacing of studs in group. From the design point of view, in order to ensure the mechanical performance of the bridge structure, the degree of shear connection should not be too small; however, from the viewpoint of construction process, it is desirable to increase the stud spacing as much as possible to adapt the accelerated construction. The current code for design of steel–concrete composite structures in China  requiresThe structure and main dimension of the composite test beam are shown in Deflection was measured by means of digital displacement transducer deformation gauges at key sections as shown in The digital concrete crack gauges were used to measure the crack width at a key section  of the concrete slab. This crack gauge was used for quantitative detection of the crack width on the concrete surface, known as the common concrete non-destructive testing equipment. The gauge could automatically interpret the measurement and directly display the crack width value on the screen. It had a measuring range of 0.01 to 3 mm, the magnification of 60×, and the estimated accuracy of 0.005. At different loading cases, crack length and crack width were measured. The observed maximum crack width was considered for formulation and verification. In the experimental test of specimen 1, crack number 3 had the maximum crack width of 0.456 mm at the 900 kN load; for specimen 2, however, crack number 2 had the maximum crack width of 0.349 mm. The detail of crack width, crack length, and loading cases of specimens 1 and 2 are presented in The experiment was performed in the structural lab of the Quzhou University. A set of two actuators with total 900 kN loading capacity equipment was used in the experiment to apply the load at the mid-span of the steel–concrete composite beam. The test specimen was supported by a roller system at both ends and hinge support at the center of the two-span continuous beam. The change in behavior of composite girders was carefully observed through the static test. The test girder was loaded up to 100 kN in 20 kN intervals, followed by 50 kN intervals up to 900 kN. The maximum capacity of the instrument was 900 kN. A loading plate (110 cm × 30 cm × 20 cm) and a supporting plate (70 cm × 15 cm × 8 mm) have been used in the experiment. The test setup for the steel–concrete composite beam is illustrated in Figure 5The specimen had two spans of 3 m and the total length of the girder was 6.3 m. A 3D numerical model of the steel–concrete composite girder beam with a clear span of 3 m was simulated in ABAQUS version 6.14 . A detaiABAQUS/standard solver with a linear geometric order was used in the study. Eight-node brick elements with reduced integration (C3D8R) were used to model the concrete and stud. The first-order interpolation, three-dimensional beam element (B31), and four-node shell element with reduced integration (S4R) were used to model reinforcement bars and steel, respectively. The final mesh included 55,496 elements and 67,327 nodes. Steel reinforcement bars were modeled using embedded rebar element. Surface-to-surface contact was used for stud-to-concrete and steel-to-concrete interactions. The material nonlinearities of concrete and steel were modeled using the concrete damage plasticity model and the elastic-plastic bilinear model, respectively. The accuracy of the results basically depends on the size of the mesh, the constitutive model, and boundary conditions . TherefoIn order to simulate the mechanical behavior of concrete, a damage plastic model of concrete was utilized in the current study. The constitutive relationship of concrete is adopted from the uniaxial tension and compressive stress–strain curve of concrete given in the “code for the design of concrete structure” GB 50010-2010 . On the The stress–strain relationship of concrete under uniaxial tension is expressed as follows:Compression stress–strain relationships are assumed as follows:The stress–strain relationship and damage model of C60 concrete are shown in The steel and stiffener were modeled considering the nonlinear behavior of the materials. The elastic-plastic material model was employed based on the nominal stress–strain behavior of steel. In the stud connection, an elastic-plastic bilinear model was utilized. However, the material of steel plates, studs, and steel bars was defined by the ideal elastoplastic model. That is, when the steel yields, the bearing capacity does not increase, but the deformation continues to increase. The stress–strain relationships of steel plates, studs, and bars are shown in The bonding between the materials was done by the use of interaction in Abaqus. The stud and concrete was modeled by the penalty method considering a friction coefficient of 0.4 in the tangential direction and hard contact in the normal direction to avoid penetration between the two contact surfaces . On accoThe validation of experimental results was performed using the numerical analysis data as described earlier in The first crack observed when the load exceeded 80 kN; then, by increasing the load intensity, further crack formations were observed in the specimen. The cracks formed on the box girder were marked by a set of numbers demonstrating the occurrence order. Crack number 3 had the maximum crack width and was considered in the formulation process. The major cracks observed in the specimen are presented in There are many situations where an individual wants to use a simplified model and finds a formula that best fits a given set of data. Simplifying the model is the best solution and is the process of constructing a mathematical function with the best fit to a series of data points, giving a mathematical ideal solution. L (kN) is the intensity of the load excreted on the beam.As the first step, with experimental results a simplified formula was developed between the deflection and the load applied on the beam. It was done by fitting a first-order polynomial function to the data presented in C (mm) is the maximum width of crack observed before failure. Substituting Equation (12) in Equation (13) gives a new expression, as follows:Next, using the data obtained from the experimental tests, a third-order polynomial regression model was developed between the load and crack width. It was done by fitting a third-order polynomial function to the data presented in To adopt the proposed model for the prediction of crack size in steel–concrete composite small box girder, one can simply calculate the maximum deflection under the static load case. The equivalent intensity of the load can then be calculated using Equation (12). Next, Equation (13) can be utilized to approximate the maximum width of the crack generated in box girder beam. However, the limitation of the proposed model regarding the dimension and construction size should also be considered while utilizing the proposed model. Having Equation (14), the crack width is available at any desired beam deflection. The behavior of central deflection and crack width at negative bending moment region is shown in It is noteworthy that the provided relationship is limited to the upper yield points of the elastic stage. In order to validate the results and evaluate the accuracy of the proposed formula, a laboratory model was created. The experimental model was performed under different loads, and the maximum deflection was calculated in each case. Additionally, the crack width was measured from the experimental test. The results are reported in As observed, the crack widths obtained from the simplified model are appropriately close to the results of the experiments. To better observe the accuracy, the results of the proposed and experimental models are depicted in To further evaluate the model, a few studies were selected from the literature to compare with the proposed formula. Su et al.  experimeThe current study aimed at investigating the behavior of ACHPCBG-bridge utilizing experimental models. Therefore, a vertical loading was gradually applied to the beam, and the maximum deflection along the beam was observed at certain points. Additionally, the cracking mechanism was investigated by the experimental model and the maximum width of the cracks were measured by a digital crack gauge on the beam surfaces. Finally, a simplified formula was developed approximating the crack width as a function of deflection▪A semi-empirical formula was developed based on experimental studies to approximate the width of crack in ACHPCBG-bridge. ▪It was observed that the crack zone initiated when the load exceeded 80 kN with a crack width of 0.045 mm. The appeared crack propagated in full width, i.e., 0.7 m of the beam, when the load reached 150 kN. In this condition, the crack width was recorded as 0.08 mm.▪By the use of steel fiber in a concrete, the integrity and load resistance capacity are consequently increased. In this case, the maximum width of the crack was limited to 0.456 mm at 900 kN load.▪If construction can be done properly in a systematic manner, crack propagation would be effectively limited due to the bridging action of fibers. The main conclusions drawn from the current study are as follows:Since the proposed formula is presented as an explicit function, it can be practically used to predict crack width. The proposed formula can also be used as a limit state function in reliability analysis to calculate the probability of failure for ACHPCBG-bridge. As the experiment models were designed by a 1:4 ratio based on 25 m prototype model, the application of the proposed method is limited to the models within a similar range of parameters. This issue can be investigated by the authors in future research.