An analytical method for full-range mechanical behavior of continuous slab-deck in multi-span simply supported concrete bridges

Connecting the ends of girders with a continuous slab-deck to make a multiple-span simply supported girder bridge provides many benefits, but there is no suitable nonlinear analysis model which considers continuous slab-deck cracking under tension and bending. In this article, the rotational spring model is further refined to replace the restraining effects at both ends of the girder by the simplified mechanical model associated with axial stiffness, bending stiffness, and shear stiffness. Then, it is introduced into the analysis of continuous slab-deck. The more accurate rotations and displacements of both ends of continuous slab-deck are obtained to investigate the more precise moment and tension of the continuous slab-deck. Furthermore, this article presents an improved nonlinear analysis model of continuous slab-deck based on a detailed boundary rotational spring model. The displacements of important positions and the strain of key components in continuous slab-deck after cracking are investigated by numerical analysis and full-scale model test to verify the accuracy of the proposed nonlinear analysis model. The result shows that the nonlinear analysis model presented in this article could successfully evaluate the depth of cracks and the stress of rebars in continuous slab-deck, and it is instructional in predicting the cracking state of the continuous slab-deck and the reinforcement design.

Protein degradability of grassland forage under simulated rotational spring grazing

A cutting experiment was conducted to analyze the changes in the crude protein (CP) fraction content and in the estimated ruminal protein degradability of forage, obtained in conditions of simulated rotational spring grazing on permanent grassland. The field trial was conducted on permanent pasture during 2015 and included three cuttings as a simulated rotational spring grazing. For determination of protein degradability of pasture forage, the fractionation of the CP according to Cornell Net Carbohydrate and Protein System (CNCPS v6.5) and the Streptomyces griseus protease assay were used. Relative to CP, no significant differences were found among cuts for ammonia N content (A1 fraction) and for protein fraction C which is completely unavailable to the animals. Values for soluble true protein (A2 fraction) and cell wall-associated protein, which is acid detergent soluble (B2), were significantly increased (p<0.05) while a significant reduction (p<0.05) of the moderately degradable protein (B1) content was determined during the growing season. The lower rumen degradable protein (RDP) content of grassland herbage was obtained in the second cut which was significant (p<0.05) according to the CNCPS procedure. Obtained high solubility and degradability of CP in pasture require adequate content of readily available carbohydrates in rations for grazing ruminants to provide efficient utilization of consumed protein.

Flutter Instability of Cracked Rotating Non-Uniform Beams Subjected to Distributed Follower Force

In this paper, the effect of an open edge crack on the instability of rotating non-uniform beams subjected to uniform distributed tangential compressive load is studied. The local stiffness due to the presence of crack is considered in the global stiffness matrix of the structure using the finite element method. The cracked beam element is modeled as two equal sub-beam elements connected by a massless rotational spring. Based on the fracture mechanics, the strain energy release rate and the stress intensity factors are employed to investigate the stiffness of the rotational spring. Then, the modified shape functions are developed to reflect the crack stiffness in the finite element analysis. To validate the accuracy of the finite element model and results obtained, comparisons have been made between the results obtained and those available in the literature. The effects of several parameters, including the linear and nonlinear thickness variations, angular velocity, crack location and size, on the instability of cracked rotating non-uniform cantilevers are also examined. The results show that the location of crack significantly influences the critical magnitude of the follower force that destabilizes the cantilevers. In addition, geometric non-uniformity reduces the stability of the cracked cantilevers. For the same amount of cantilever mass, different patterns of mass distribution result in different stability diagrams.

Yield and nutritional value of permanent grassland forage under simulated rotational grazing

A cutting experiment was conducted to test the changes in botanical composition, yield and nutritional value of forage, obtained in conditions of simulated rotational spring grazing on permanent grassland. The experiment was carried out on permanent pasture in vicinity of Sabac, Serbia in 2015 included three cuttings as a simulated rotational spring grazing. The highest share of grasses was noted in the first cut and decreased in the second and third cut, with increased forbs participation, and relatively constant percentage of legumes. The highest dry matter (DM) yield was obtained for the first harvest, followed by the second cut, and the lowest forage production was determined for the third harvest, with only 11.04 and 17.42% of the first and second cut yield. There were not found the significant differences between cuts for herbage DM and crude protein content. Markedly lower value for non-protein N concentration (p<0.05) was determined in the third cut. The fiber content increased during the grazing season (p<0.05), with the highest value determined in the herbage obtained in the second cut. The highest energy values (p<0.05) had the herbage produced in the first cut (DM basis), wherein the lowest values were found in the forage from the second harvest. These results indicate that especially herbage yield of analyzed grassland as chemical composition and nutrition value are highly variable during the growing season. The accurately defined optimal period for using is necessary to provide the high-quality forage for grazing animals.

Comparative study of direct and inverse problems of cracked beams

In recent decades, the analysis and evaluation of the cracked structures were hot spots in several engineering fields and has been the subject of great interest with important and comprehensive surveys covering various methodologies and applications, in order to obtain reliable and effective methods to maintain the safety and performance of structures on a proactive basis. The presence of a crack, not only causes a local variation in the structural parameters (e.g., the stiffness of a beam) at its location, but it also has a global effect which affects the overall dynamic behavior of the structure (such as the natural frequencies). For this reason, the dynamic characterization of the cracked structures can be used to detect damage from non-destructive testing. The objective of this paper is to compare the accuracy and ability of two methods to correctly predict the results for both direct problem to find natural frequencies and inverse problem to find crack’s locations and depths of a cracked simply supported beam. Several cases of crack depths and crack locations are investigated. The crack is supposed to remain open. The Euler–Bernoulli beam theory is employed to model the cracked beam and the crack is represented as a rotational spring with a sectional flexibility. In the first method, the transfer matrix method is used; the cracked beam is modeled as two uniform sub-segments connected by a rotational spring located at the cracked section. In the second method which is based on the Rayleigh’s method, the mode shape of the cracked beam is constructed by adding a cubic polynomial function to that of the undamaged beam. By applying the compatibility conditions at crack’s location and the corresponding boundary conditions, the general forms of characteristic equations for this cracked system are obtained. The two methods are then utilized to determine the locations and depths by using any two natural frequencies of a cracked simply supported beam obtained from measurements as inputs. The two approaches are compared with a number of numerical examples for simply supported beams including one crack. The theoretical results show that the accuracy of the Rayleigh’s method to predict natural frequencies decreases for higher modes when crack depth increases. It is also found that for the inverse problem, the transfer matrix method show a good agreement with those obtained from previous works done in this field.

Simplified formulations for the determination of rotational spring constants in rigid spread footings resting on tensionless soil

In spread footings, the rotational spring constants, which represent the soil-structure interaction, play an important role in the structural analysis and design. To assign the behaviour of soil, which is generally represented via Winkler-type tensionless springs, necessitates time consuming iterative computing procedures in practice. In this study, a straightfor­ward approach is proposed for the soil-structure interaction of rigid spread footings especially subjected to excessive eccentric loading. By considering the uplift of footing, the rotational spring constants of those type footings under axial load and biaxial bending are easily attained through the proposed simplified formulations. Since these formulations enable manual calculation, iterative computer efforts are not required. The formulations under consideration can be applicable to sym­metric and non-symmetric rigid spread footings. The numerical results of this study are verified with SAP2000.