Second Moment Of Area Research Articles

Experimental Study on the Lateral Torsional Buckling Behaviour of the Triangular Web Profile Steel Section

A triangular web profile (TriWP) section is a structural steel section that is made of two flanges connected to a web plate of triangular profile. Only certain research works have been carried out to study the characteristic, behaviour and the advantages offered by this section compared to the normal flat web (I-beam). An area that is not given full attention is the capability of this section to resist the lateral torsional buckling moment capacity compared to that of the normal flat web. The objectives of this thesis are to study the lateral torsional buckling behaviour of Triangular Web Profile (TriWP) steel section and compare to that of the flat web by experimental and to find the value of Mb, moment buckling resistance for TriWP. The scope of study covered the experimental work and theoretical investigation of triangular web profile steel section subjected to lateral torsional buckling moment resistance. The effect of the shape of the triangular web profile beam compared to that of the flat web beam was also be studied. For the buckling moment resistance, several factors were taken into account such as buckling parameter, torsional index, warping constant and torsional constant. All these factors are related to the second moment of area with respect to minor axis. The lateral torsional buckling test includes 8 specimens (4 flat webs and 4 TriWP). Each specimen was tested in two different sizes which is 200x100x6x3 and 180x75x5x3. Findings from the lateral torsional buckling tests were compared to the manual calculation using BS 5950: Part 1:2000. The lateral torsional buckling test shows that the moment buckling resistance of the triangular web profile steel beam section is better than that of the flat web in smaller size while in bigger size flat web beam has better moment resistance than that of triangular web profile steel beam. The section properties such as width (B), depth (D), thickness of flange (tf) and thickness of web (tw) affect the buckling moment resistance, Mb of the steel section

Strength properties of extant hominoid hallucal and pollical metapodials

Functional comparisons of cortical bone strength properties between hominoid hallucal and pollical metapodials (Mt1 and Mc1, respectively) are lacking. Determining which of these two elements is stronger, and by how much, could be informative because the hallux and pollex are used differently both within and among extant hominoids during locomotion and manipulation (i.e., functional differentiation between autopod pairs). Here, we compare Mt1 and Mc1 midshaft cortical area, polar section modulus, and polar second moment of area, calculated from high-resolution computed tomography images in humans (n = 21), chimpanzees (n = 47), gorillas (n = 24), orangutans (n = 20), siamangs (n = 8), and gibbons (n = 21). Intraindividual comparisons between bones within species were made using paired t-tests. Log10-transformed Mt1:Mc1 ratios were created to assess relative strength asymmetry between bones, and interspecific comparisons of these proportions were made using analyses of variance. Absolute strength differences between the Mt1 and Mc1 for all variables were significantly larger in the Mt1 for all species (p < 0.05). Significant differences across species in Mt1:Mc1 proportions were also found, thereby demonstrating that strength asymmetry between bones differs among taxa (p < 0.05); asymmetry was lowest in orangutans, intermediate in gorillas, and greatest in humans, chimpanzees, siamangs, and gibbons. These findings support the hypothesis that the Mt1 is better adapted structurally than the Mc1 for bearing mechanical loads during weight support of locomotion in all extant hominoids and that pedal hallucal grasping likely engenders higher loads than manual pollical grasping in nonhuman hominoids. Thus, functional differentiation in autopod use within and among hominoids is reflected in hallucal and pollical metapodial strength properties.

Structural analysis of non-prismatic beams: Critical issues, accurate stress recovery, and analytical definition of the Finite Element (FE) stiffness matrix

Non-prismatic beams are widely employed in strategic structures like bridges and sport arenas, requiring accurate analyses for a reliable and effective design. Unfortunately, features of non-prismatic beams lead their modeling to be a non-trivial task: (i) variations of both cross-section area and second moment of area impede an easy computation of analytical solutions compelling to use approximated methods; (ii) stress distributions in prismatic and non-prismatic beams are substantially different, as proved by analytical results available since the beginning of the past century; and (iii) the peculiar stress distribution in non-prismatic beams entails complicated constitutive relations, as highlighted in recent publications. Usually, commercial software does not properly account for all the features of non-prismatic beams, leading to inconsistent structural analyses, erroneous estimations of the stress distribution, and -consequently- coarse predictions of the structural element strength. The present paper proposes a strategy to effectively overcome the above-mentioned problems. We derive an accurate analytical model for 2D non-prismatic beams, able to handle the non-trivial stress distribution and the complicated constitutive relations. Thereafter, we compute both homogeneous and particular solutions using the symbolic calculus software MAPLE and we analytically define the Finite Element (FE) stiffness matrix for a planar, symmetric, linearly-tapered beam. Finally, we compare the proposed FE and SAP2000 solutions, considering several beams with different geometries, loads, and constraints. Numerical results highlight the reliability of the proposed modeling strategy, since the resulting FE consistently handles all the critical issues of non-prismatic beams with an extremely low computational cost. Conversely, SAP2000 solution remarks the need of ad hoc analysis tools and modeling strategies to be used for the design of non-prismatic structural elements.

Optimal design of steel buckling-restrained braces considering stiffness and strength requirements

This paper is concerned with the optimal (or least weight) design of steel buckling-restrained braces against global buckling. First, the global buckling prevention criterion of steel buckling-restrained braces (BRB) is reconstituted to take on a symmetric expression, i.e., (Pcr/Pu−1)[Mr/(v0Pu) −1] ≥ 1, so as to provide clarity on the equal importance of the stiffness and strength requirements of the restraining member, where Pcr is the elastic buckling load, Mr the yield moment resistance, and v0 the initial imperfection of the restraining member whereas Pu is the ultimate compressive load of the core under cyclic axial loads. It is shown herein that the optimal design of the restraining member satisfies (1) the boundary of the global buckling prevention criterion, and (2) the relationship between the stiffness term Pcr/Pu and the strength term Mr/(v0Pu) in view of the maximum feasible cross-sectional height-to-thickness ratio as specified by the adopted design code recommendation. The satisfaction of these two conditions furnishes a unique optimal design of the restraining member. The optimal design can be expressed as an explicit equation in terms of the second moment of area of the restraining member. A design example is presented to illustrate the material (or weight) efficiency of all-steel BRB designs based on the proposed design equation.

Non-uniform rational B-spline based free vibration analysis of axially functionally graded tapered Timoshenko curved beams

The free vibration of axially functionally graded (FG) tapered Timoshenko curved beams is studied with the numerical approach. By using the non-uniform rational B-spline (NURBS) basis functions, the exact geometry and the generalized displacement field are formulated. Variable geometric parameters and material properties, including the curvature, cross-sectional area, area moment of inertia, mass density, and Young’s modulus, are expanded as functions of the coordinate in a parametric domain. Based on Hamilton’s principle, the weak formulation is derived by applying a refined constitutive relation which considers the thickness effect. Natural frequencies and mode shapes are obtained from the eigenvalue equation. Circular, elliptic, and parabolic curved beams are considered in numerical examples. The obtained results are in good agreement with those in the existing studies and those calculated by the finite element software ANSYS. Moreover, the effects of the material gradient, taper ratio, slenderness ratio, and height-span ratio on vibration behaviors are discussed.

Scaling of petiole anatomies, mechanics and vasculatures with leaf size in the widespread Neotropical pioneer tree species Cecropia obtusa Trécul (Urticaceae).

Although the leaf economic spectrum has deepened our understanding of leaf trait variability, little is known about how leaf traits scale with leaf area. This uncertainty has resulted in the assumption that leaf traits should vary by keeping the same pace of variation with increases in leaf area across the leaf size range. We evaluated the scaling of morphological, tissue-surface and vascular traits with overall leaf area, and the functional significance of such scaling. We examined 1,271 leaves for morphological traits, and 124 leaves for anatomical and hydraulic traits, from 38 trees of Cecropia obtusa Trécul (Urticaceae) in French Guiana. Cecropia is a Neotropical genus of pioneer trees that can exhibit large laminas (0.4m2 for C. obtusa), with leaf size ranging by two orders of magnitude. We measured (i) tissue fractions within petioles and their second moment of area, (ii) theoretical xylem hydraulic efficiency of petioles and (iii) the extent of leaf vessel widening within the hydraulic path. We found that different scaling of morphological trait variability allows for optimisation of lamina display among larger leaves, especially the positive allometric relationship between lamina area and petiole cross-sectional area. Increasing the fraction of pith is a key factor that increases the geometrical effect of supportive tissues on mechanical rigidity and thereby increases carbon-use efficiency. We found that increasing xylem hydraulic efficiency with vessel size results in lower leaf lamina area: xylem ratios, which also results in potential carbon savings for large leaves. We found that the vessel widening is consistent with hydraulic optimisation models. Leaf size variability modifies scaling of leaf traits in this large-leaved species.

A unified procedure for the vibration analysis of elastically restrained Timoshenko beams with variable cross sections

A generalized analytical method is developed for the vibration analysis of Timoshenko beams with elastically restrained ends. For a beam with any variable cross section along the lengthwise direction, the finite element method is the only unified approach to handle those kinds of problems, since the analytical solutions could not be obtained by the governing equations when the cross section area and the second moment of area changing variably lengthwise. In this article, a unified approach is proposed to study the Timoshenko beam with any variable cross sections. The cross section area and second moment of area of the beam are both expanded into cosine series, which are mathematically capable of representing any variable cross section. The translational displacement and rotation of cross section are expressed in the Fourier series by adding some admissible functions which are used to handle the elastic boundary conditions with more accuracy and high convergence rate. By using Hamilton's principle, the eigenvalues and the coefficients of the Fourier series are both obtained. Some examples are presented to illustrate the excellent accuracy of this method. Analytical solutions of the vibration of the beam are achieved for different combinations of boundary conditions including classical and elastically restrained ones. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of Timoshenko beams with any variable cross section.

Functional Morphology and Morphological Diversification of Hind Limb Cross-Sectional Traits in Mustelid Mammals.

SynopsisLocomotor habits in mammals are strongly tied to limb bones’ lengths, diameters, and proportions. By comparison, fewer studies have examined how limb bone cross-sectional traits relate to locomotor habit. Here, we tested whether climbing, digging, and swimming locomotor habits reflect biomechanically meaningful differences in three cross-sectional traits rendered dimensionless— cross-sectional area (CSA), second moments of area (SMA), and section modulus (MOD)—using femora, tibiae, and fibulae of 28 species of mustelid. CSA and SMA represent resistance to axial compression and bending, respectively, whereas MOD represents structural strength. Given the need to counteract buoyancy in aquatic environments and soil’s high density, we predicted that natatorial and fossorial mustelids have higher values of cross-sectional traits. For all three traits, we found that natatorial mustelids have the highest values, followed by fossorial mustelids, with both of these groups significantly differing from scansorial mustelids. However, phylogenetic relatedness strongly influences diversity in cross-sectional morphology, as locomotor habit strongly correlates with phylogeny. Testing whether hind limb bone cross-sectional traits have evolved adaptively, we fit Ornstein–Uhlenbeck (OU) and Brownian motion (BM) models of trait diversification to cross-sectional traits. The cross-sectional traits of the femur, tibia, and fibula appear to have, respectively, diversified under a multi-rate BM model, a single rate BM model, and a multi-optima OU model. In light of recent studies on mustelid body size and elongation, our findings suggest that the mustelid body plan—and perhaps that of other mammals—is likely the sum of a suite of traits evolving under different models of trait diversification.

Walking on chains: the morphology and mechanics behind the fin ray derived limbs of sea-robins.

Fish fin rays (lepidotrichia) are typically composed of paired and segmented flexible structures (hemitrichia) that help support and change the shape of the fins to affect water flow. Yet, marine ray-finned fish that are members of the family Priontinae (sea-robins) have specialized pectoral fin rays that are separated from the fin and used as limbs to walk along the seafloor. While previous kinematic studies have demonstrated the use of these specialized fin rays as walking appendages, there is little information on how the morphology of the 'walking rays' and associated musculature facilitate underwater walking. Here, we examine the musculoskeletal anatomy of the walking and pectoral fin rays in the striped sea-robin Prionotus evolans and compare the mechanical properties of the rays with those of the smaller northern sea-robin Prionotus carolinus We aimed to determine what structural modifications in the walking rays allow them to function as a supportive limb. We found enlarged processes for muscle attachment, bone extensions that brace the hemitrich articulations, and reduced flexibility and increased second moment of area along the rostro-caudal bending axis in the rays used for walking. This novel limb design may have promoted the benthic foraging behavior exhibited by these species by uncoupling locomotion and feeding.

Effects of Span Length and Additional Structure on Flow-Induced Transverse Vibration Characteristic of a Cantilevered Rectangular Prism

We consider the effects of the aspect ratio L/H (where L is the length of a prism, and H is the height of a prism normal to the flow direction) and the size of additional structures (which are a plate and a fin on the surface of a prism) on a vibration characteristic of a cantilevered rectangular prism. The present research is intended to support the analysis of energy harvesting research on the flow-induced vibration in water flow using a magnetostrictive phenomenon. The prisms are constructed from stainless steel and mounted elastically to a plate spring attached to the ceiling wall of the water tunnel. The prisms with aspect ratios of L/H ≥ 5 have reasonably identical vibration characteristics. However, the difference in the vibration characteristic appears distinctly on a rectangular prism with an aspect ratio of L/H = 2.5. The rectangular prism with an aspect ratio of L/H = 10 and a side ratio of D/H = 0.2 has a stable and large response amplitude and oscillates with a lower velocity. The length of the added plate and the size of the added fin influence the velocity of vibration onset. If the length of the added plate and fin size on the rectangular prism with D/H = 0.2 becomes large, the curve of the response amplitude shifts to that of the rectangular prism with D/H= 0.5. The response amplitude of the rectangular prism with/without plate or fin is found to be related to the second moment of area of the prism.

Nanomechanical Characterization of Apolipoprotein A-I Amyloid Fibrils

Amyloid fibrils represent a special type of protein aggregates that are currently receiving enormous attention due to their strong implication in molecular etiology of a wide range of human disorders. Amyloid fibrils represent highly ordered self-assemblies sharing a core cross-β-sheet structure. Such organization of the fibrils is responsible for amyloid insolubility and exceptional mechanical properties. The remarkable rigidity of the protein fibrillar aggregates is due to intra- and interstrand hydrogen bonds which stabilize the β-strand scaffold of amyloid fibrils. Increasing evidence indicates that physical properties of amyloid assemblies, especially their mechanical characteristics, play essential role in determining their cytotoxic action. This highlights the necessity of deciphering the correlation between the elastic properties of amyloid aggregates and their cytotoxicity. In the present paper we utilized the atomic force microscopy (AFM) to visualize and analyze the amyloid fibrils of G26R/W@8 mutant of N-terminal fragment of human apolipoprotein A-I (apoA-I). The examination of AFM images revealed the existence of two polymorphic forms of apoA-I fibrils – twisted ribbon and helical ribbon. The quantitative analysis of apoA-I elastic properties was performed within the framework of worm-like model of polymer chain using the Easyworm software. The Easyworm package analyzes the images of individual polymer chains obtained by the atomic force microscopy and allows calculation of the persistent length of a chain in three regimes depending on the ratio between the contour and persistent lengths of the polymer. The set of evaluated parameters included the Young’s modulus, persistent length, bending rigidity and the second moment of inertia. All parameters calculated for the helical ribbon conformation were higher than those of the twisted ribbon. These findings suggest that helical ribbon represents a more rigid and mechanically stable configuration. The results obtained may prove of importance for a deeper understanding the mechanics-driven pathological activities of amyloid fibrils.

The effects of seeding rate on yield, lodging resistance and culm strength in wheat

ABSTRACT We compared the effects of four seeding rates, 60, 100, 140, and 180 seeds m−2, on yield, lodging resistance and culm strength using two Japanese wheat cultivars Ayahikari and Iwainodaichi. With the decreasing seeding rate, maximum tiller number decreased, percentage of productive culms increased and spike number m−2 decreased, and the spikelet number per spike, percentage of fertile spikelets, grain number per spikelet and grain number per spike increased. Consequently, grain yield was not significantly affected. Lodging was not observed, but the lodging index was significantly affected by the seeding rate and was the highest in the plots sown at 180 seeds m−2. The bending moment at the breaking point and flexural rigidity of the basal internode with leaf sheaths were highest in the plots sown at 60 seeds m−2. In conclusion, the culm strength and stem lodging resistance increased with decreasing seeding rate. Section modulus and bending stress, which constitute the bending moment at the breaking point, and the moment of inertia area and Young’s modulus, which represent the flexural rigidity, were highest in plots sown at 60 seeds m−2. Therefore, the seeding rate was considered to influence the culm morphology and functions of the cell wall components. The effects of the seeding rate on culm characteristics and lodging resistance did not differ between the two cultivars, and ‘Ayahikari’ had consistently stronger culms than ‘Iwainodaichi’. We suggest that low seeding rates method would be suitable for heavily fertilized cultivation for both cultivar with high and low culm strength. Abbreviations AMeDAS: the automated meteorological data acquisition system; HSD: honestly significant difference

Twist-to-bend ratio: an important selective factor for many rod-shaped biological structures

Mechanical optimisation plays a key role in living beings either as an immediate response of individuals or as an evolutionary adaptation of populations to changing environmental conditions. Since biological structures are the result of multifunctional evolutionary constraints, the dimensionless twist-to-bend ratio is particularly meaningful because it provides information about the ratio of flexural rigidity to torsional rigidity determined by both material properties (bending and shear modulus) and morphometric parameters (axial and polar second moment of area). The determination of the mutual contributions of material properties and structural arrangements (geometry) or their ontogenetic alteration to the overall mechanical functionality of biological structures is difficult. Numerical methods in the form of gradient flows of phase field functionals offer a means of addressing this question and of analysing the influence of the cross-sectional shape of the main load-bearing structures on the mechanical functionality. Three phase field simulations were carried out showing good agreement with the cross-sections found in selected plants: (i) U-shaped cross-sections comparable with those of Musa sp. petioles, (ii) star-shaped cross-sections with deep grooves as can be found in the lianoid wood of Condylocarpon guianense stems, and (iii) flat elliptic cross-sections with one deep groove comparable with the cross-sections of the climbing ribbon-shaped stems of Bauhinia guianensis.

Calcaneal elongation and bone strength in leaping galagids.

Small-bodied vertical clinging and leaping primates have elongated calcanei which enhance leap performance by optimizing leap velocity, distance, and acceleration, but at the expense of experiencing relatively large forces during takeoff and landing. This study tests the hypothesis that the elongated calcaneus of leaping galagids is adapted to resist larger and more stereotyped bending loads compared to more quadrupedal galagids. The calcanei of 14 individuals of Otolemur and 14 individuals of Galago (three species of each genus) were μCT scanned. Calcaneal cross-sectional properties (maximum and minimum second moments of area and polar section modulus) were obtained from a slice representing the 50% position of bone segment length and dimensionless ratios were created for each variable using calcaneal cuboid facet area as a proxy for body mass. There were no significant differences in size-adjusted bending strength between Galago and Otolemur. Galago exhibited more elliptically shaped calcaneal cross sections, however, suggesting that its calcanei are more adapted to stereotyped loading regimes than those of Otolemur. The results suggest that the calcaneus of specialized leapers is adapted to more stereotyped loading patterns. The lack of predicted bone strength differences between Galago and Otolemur may be related to body size differences between these taxa, or it may indicate that loads encountered by Galago during naturalistic leaping are not reflected in the available experimental force data.

Relation between cross-sectional bone geometry and double zonal osteon frequency and morphology.

While double-zonal osteons (DZ) are characterized by a hyper-mineralized ring inside their lamellae, recent findings suggest that this ring is also defined by a change in the collagen fibers' orientation. Collagen and minerals are essential components to the maintenance of adequate bone strength and their alteration can modify the mechanical properties of the bone tissue. Consequently, the aim of this study is to explore the effect of past loads, as estimated from cross-sectional geometric properties, on the formation of DZ osteons compared to type I (common) osteons. The sample consists of paired humerus and femur midshaft sections (n = 23) of Eurocanadian settlers from the historical St. Matthew cemetery, Quebec City (1771-1860). Histomorphometric variables included in this study are osteon density for DZ and type I osteons (DZD; OPD), osteon area (DZOn.Ar; On. Ar), Haversian canal area (DZH.Ar; H.Ar), and the area within the hypermineralized ring (HR. Ar). Loading history is estimated from cross-sectional properties including the following variable: cortical and total area (CA, TA), maximum and minimum second moment of area (Imax , Imin ) and polar moment of area (J). When the humerus and femur of the same individuals are compared, the femur has a higher OPD, DZD, and relative DZD (DZD/OPD). DZ osteons have a smaller area and Haversian canal area compared to type I osteons. The area within the hypermineralized ring in DZ is higher than the Haversian canal area of the type I osteons. Correlations between the residual scores of the regression of histomorphometric variables and cross-sectional properties of the humerus on the femur were not significant. Based on the analysis of the entire cross-section, the lack of correlation between variations in cross-sectional properties and remodeling combined with the significant differences between humeri and femura suggests that the creation of DZ or type I osteons in the bone tissue might be due to a bone specific response, possibly related to differences in bone tissue age that needs to be further investigated. Definitive conclusion regarding biomechanical loads still seem to be premature as regional variations associated with mechanical properties remain to be explored.

Effect of uncertain parameters on the deflection of beams

AbstractIn the classical Euler‐Bernoulli cantilever beam theory the deflection w depends on different parameters. On the one hand we have material and geometric parameters, like the Young's Modulus E, the second moment of area I and the length of the beam L. On the other hand there are different loading types like point loads F, distributed loads, or varying loads. All these parameters are usually modeled in a deterministic way. In this contribution we analyze the distribution of the maximum beam deflection of a cantilever beam wmax depending on uncertain parameters. To this end we model the input parameters as random variables (XF, XL, XE) or different random fields (Ei). For the random fields Monte‐Carlo simulations are used to calculate the resulting distribution.

The age-related decrease in material properties of BALB/c mouse long bones involves alterations to the extracellular matrix.

One possibility for the disproportionate increase in fracture risk with aging relative to the decrease in bone mass is an accumulation of changes to the bone matrix which deleteriously affect fracture resistance. In order to effectively develop new targets for osteoporosis, a preclinical model of the age-related loss in fracture resistance needs to be established beyond known age-related decreases in bone mineral density and bone volume fraction. To that end, we examined long bones of male and female BALB/c mice at 6-mo. and 20-mo. of age and assessed whether material and matrix properties of cortical bone significantly differed between the age groups. The second moment of area of the diaphysis (minimum and maximum principals for femur and radius, respectively) as measured by ex vivo micro-computed tomography (μCT) was higher at 20-mo. than at 6-mo. for both males and females, but ultimate moment as measured by three-point bending tests did not decrease with age. Cortical thickness was lower with age for males, but higher for old females. Partially accounting for differences in structure, material estimates of yield, ultimate stress, and toughness (left femur) were 12.6%, 11.1%, and 40.9% lower, respectively, with age for both sexes. The ability of the cortical bone to resist crack growth (right femur) was also 18.1% less for the old than for the young adult mice. These decreases in material properties were not due to changes in intracortical porosity as pore number decreased with age. Rather, age-related alterations in the matrix were observed for both sexes: enzymatic and non-enzymatic crosslinks by high performance liquid chromatography increased (femur), volume fraction of bound water by 1H-nuclear magnetic resonance relaxometry decreased (femur), cortical tissue mineral density by μCT increased (femur and radius), and an Amide I sub-peak ratio I1670/I1640 by Raman spectroscopy increased (tibia). Overall, there are multiple matrix changes to potentially target that could prevent the age-related decrease in fracture resistance observed in BALB/c mouse.

Buckling and Post-Buckling Behavior of Uniform and Variable-Density Lattice Columns Fabricated Using Additive Manufacturing.

Lattice structures are known for their high strength-to-weight ratio, multiple functionalities, lightweight, stiffness, and energy absorption capabilities and potential applications in aerospace, automobile, and biomedical industry. To reveal the buckling (global and local) and post-buckling behavior of different lattice morphologies, both experimental and simulation-based studies were carried out. Additionally, a variable-density lattice structure was designed and analyzed to achieve the optimal value of critical buckling load. Latticed columns were fabricated using polyamide 12 material on multi jet fusion 3D printer. The results exhibited that the buckling in lattice columns depends on the distribution of mass, second moment of inertia I, diameter and position of vertical beams, number of horizontal or inclined beams, and location and angle of the beams that support the vertical beams. The number of horizontal and inclined beams and their thickness has an inverse relation with buckling; however, this trend changes after approaching a critical point. It is revealed that vertical beams are more crucial for buckling case, when compared with horizontal or inclined beams; however, material distribution in inclined or horizontal orientation is also critical because they provide support to vertical beams to behave as a single body to bear the buckling load. The results also revealed that the critical buckling load could be increased by designing variable density cellular columns in which the beams at the outer edges of the column are thicker compared with inner beams. However, post-buckling behavior of variable density structures is brittle and local when compared with uniform density lattice structures.

Cross-Sectional Geometry and Scaling in the Baculum of Cuban Hutias (Rodentia: Capromyidae).

Bacula from 61 individual hutia (Rodentia) from five species were studied. The purpose was to investigate cross-sectional geometry as an indicator of mechanical behavior in order to answer questions around the origin and maintenance of the mammalian baculum. From images of the apical and basal cross sections, the following variables were calculated: perimeter, cross-sectional area, maximum second moment of area, and polar moment. An allometric analysis showed that these variables were related to body size. The orientation of the maximum second moment of area was analyzed by means of circular statistics. This orientation was transverse in both the apical and basal cross sections. Values for the second moment of area and polar moment, obtained from the predicted value of the allometric equations, showed that either the bending moment or the twisting moment of the baculum must be relatively low in hutias, compared with those of the radius in the same species. The results of the second moment of area predict that the main bending stress acting on the baculum is transverse. At the same time, shear stress would not be negligible. Anat Rec, 303:1346-1353, 2020. © 2019 American Association for Anatomy.

Effect of Caponisation on Bone Development in Native Male Chickens

Abstract The aim of the study was to determine the effect of caponisation on the morphometric traits and mechanical parameters of tibial and femoral bones in Greenleg Partridge cocks. The experiment involved 200 cocks. At the age of 8 weeks, 100 birds were subjected to surgical castration. At week 24, the birds were slaughtered and tibial and femoral bones were collected from 10 non-caponised cocks and 10 capons. The caponisation surgery had no effect on the weight and length of any of the long bones but resulted in reduction (P≤0.05) of the ash content in both bones and Ca in the femur. It also influenced the geometric structure of the bones, i.e. there was an increase (P≤0.05) in the second moment of inertia in the tibial bone and the cross-sectional area and mean relative wall thickness in the femoral bone of the capons. The three-point bending test revealed a negative effect of caponisation on the mechanical strength of the bone. Values characterising the highest bone material strength, i.e. yielding load (femur), maximum force moment (tibia) and yielding deformation, bending point resistance, and load-to-deformation (both bones), declined in the capons. The investigations demonstrated a negative effect of caponisation on the quality of long bones. The tibial bone seems to be slightly more sensitive to the caponisation effects than the femoral bone. It can be assumed based on the analysis of biomechanical traits that the bones of capons are more susceptible to deformations or fractures due to their modified geometry and mechanical brittleness.