Counterexamples to the Maximum Force Conjecture

Dimensional analysis shows that the speed of light and Newton’s constant of gravitation can be combined to define a quantity F*=c4/GN with the dimensions of force (equivalently, tension). Then in any physical situation we must have Fphysical=fF*, where the quantity f is some dimensionless function of dimensionless parameters. In many physical situations explicit calculation yields f=O(1), and quite often f≤1/4. This has led multiple authors to suggest a (weak or strong) maximum force/maximum tension conjecture. Working within the framework of standard general relativity, we will instead focus on idealized counter-examples to this conjecture, paying particular attention to the extent to which the counter-examples are physically reasonable. The various idealized counter-examples we shall explore strongly suggest that one should not put too much credence into any truly universal maximum force/maximum tension conjecture. Specifically, idealized fluid spheres on the verge of gravitational collapse will generically violate the weak (and strong) maximum force conjectures. If one wishes to retain any truly general notion of “maximum force” then one will have to very carefully specify precisely which forces are to be allowed within the domain of discourse.

Optimization and Form-finding of the Heavy Cable Suspending a Deck

The heavy spanning cable supporting a uniform deck is important in the design of suspension bridges. The analytic design method is presented in this paper. The problem depends on three non-dimensional parameters: the ratio of cable length to the horizontal spanning distance, the ratio of vertical to horizontal distance, and the ratio of deck density to cable density. Given these parameters, useful tables of maximum tension and sag are determined. There exists an optimum cable length for which the maximum tension is minimized. In addition, it is shown that continuous loads and discrete loads are equivalent if the number of evenly-spaced discrete loads are more than 10.

Development and evaluation of a biodegradable packaging from the aryl of the fruit of Hymenaea stigonocarpa Mart. ex Hayne

The fruits of Hymenaea stigonocarpa have a sweet, starchy fibrous structure used as food among wild animals and man in the field. The study aimed to develop and evaluate a biodegradable packaging from the starchy aryl solution of the jatobá fruit (H. stigonocarpa). The amylaceous solution was obtained from the arils of H. stigonocarpa, the biodegradable film was prepared according to the casting technique. The physical-chemical characteristics for thickness (mm), humidity (%), water solubility (%), biodegradability time and transmittance (T%) were evaluated. Morphology by optical micrographic and scanning electron, mathematical modeling in 3D, and for the mechanical parameters of tensile strength, maximum tension, elongation and elasticity module. The results obtained for the biodegradable film were brown yellow color, aroma and homogeneity, thickness 0.27 mm, humidity 12.45%, solubility in water 57.48%, biodegradability of 100%, maximum and minimum transmittance 82.25 and 1.32 (T%), in the optical micrograph small imperfections were observed and in the scanning electron micrograph small cracks. The mathematical modeling in 3D presented a surprising result, which is an important device in the aid of imaging. The mechanical characteristics for maximum tension 3.17 N, rupture stress 1.34 MPa, elongation 2.99% and elasticity with 90.07 MPa presented satisfactory results comparable to other biodegradable films of native starch. Biodegradable packaging from Hymenaea stigonocarpa aryl has great potential for use as a food packaging.

Effect of Heat Aging on Properties and Structure of SBS Modified Bitumen Waterproof Membrane

The properties of SBS modified bitumen waterproof membrane (SMBM) will deteriorate under the action of heat. In this paper, SBS modified bitumen (SMB) and SMBM were aged at 80 °C for different times (0,10,20,30,40 days). The low temperature flexibility, softening point, viscosity and mass changes ratio of SMB and mechanical properties of SMBM before and after aging were tested, the microstructure and chemical structure of SMB were investigated by fluorescence microscope (FM) and Fourier transform infrared spectroscopy (FTIR). The results show that the low temperature flexibility, softening point and viscosity of SMB decrease significantly at the initial stage of heat aging (10 days), especially the influence of heat aging on the low temperature flexibility and viscosity of SMB is more obvious, and their properties degradation rate slowdown in the later stage of aging. The mass changes ratio of SMB first decreases and then increases with aging time. FM shows that the network crosslinking structure of SMB is destroyed gradually with the extension of aging time. The network crosslinking structure disappears after 40 days of heat aging. FTIR shows that carbonyl and sulfoxide compounds are increasing after aging, more carbonyl compounds than sulfoxide compounds are formed after aging for 10 days, and the degradation rate of SBS decreases. The maximum tension of SMBM first increases and then decreases, the elongation at maximum tension decreases with aging time.

The importance of Böhler’s angle in calcaneus geometry: A finite element model study

Objectives: Calcaneal fractures are the most common tarsal fractures following a foot-ankle trauma. The Böhler’s angle is an important measurable angle before, during, and after surgery. In this study, we aimed to investigate correlation between Böhler’s angle, calcaneal strength, and subtalar joint stress using a finite element analysis (FEA). Patients and methods: Between January 2016 and December 2016, computed tomography (CT) scans were used with MIMICS® software for FEA. The ankle and foot of a 23-year-old male person with a height of 180 cm and weighing 80 kg was modeled as reference. Raw coronal CT images were obtained in Digital Imaging and Communications in Medicine format with the resolution of 512X512 pixels and 0.3-mm slice intervals in 135 kV. The structures including tibia, fibula and 26 other bones (talus, calcaneus, cuboid, navicular, three cuneiforms, five metatarsals, and 14 components of phalanges), cartilage and ligamentous tissues were modeled to form ankle joint. After determining Böhler’s angle as 35 degrees for the reference model, a fracture line was created on calcaneus. Calcaneus was remodeled with the Böhler’s angle of 45, 40, 30, 25, 20, 10, and 0 degrees respectively. All models were transferred to ANSYS software for FEA and the loads on the lower extremities with normal posture were applied on models. Results: Analysis of all models based in the reference model revealed that maximum tension values on calcaneus increased, while the Böhler’s angle decreased, indicating a statistically significant difference. The decreased Böhler’s angle indicated statistically significantly higher maximum tension values (p=0.04). Action force in subtalar joint was evaluated by comparing with the forces in reference model. The increased Böhler’s angle was found to be associated with statistically significantly decreased amount of load on subtalar joint. The decreased Böhler’s angle was related to the statistically significantly increased amount of load on subtalar joint. Conclusion: Our study results suggest that decreased Böhler’s angle increases the possibility of subtalar arthrosis, although overcorrection of the Böhler’s angle seems not to increase the risk of subtalar arthrosis.

DIFFERENTIAL EQUATIONS FOR TRAIN STARTING WITH ELASTIC CONNECTIONS

The starting mode for the train is the most difficult. An effective method of pulling is the selection of coupling clearances. In this case, the cars are set in motion sequentially and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method has two significant drawbacks - a small fixed value of the gaps in the couplings and the shock nature of the impulse transfer. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the train start-off mode is essentially due to the replacement of the simultaneous start-off of the sections with alternate ones. To exclude longitudinal vibrations of the composition, after reaching the maximum tension of the coupling, the possibility of its harmonic compression should be mechanically blocked.

Maximum Bridging Suture Tension Provides Better Clinical Outcomes in Transosseous-Equivalent Rotator Cuff Repair: A Clinical, Prospective Randomized Comparative Study

Background: Some studies reporting clinical outcomes after transosseous-equivalent (TOE) repair have attributed type II rotator cuff failure to excessive bridging suture tension, as it can cause overloading on the medial row. In a previous biomechanical cadaveric study, increasing bridging suture tension over 90 N did not improve the contact area and ultimate failure load of the TOE construct, despite increasing the contact force and contact pressure. Purpose: To compare the clinical outcomes of different bridging suture tensions after TOE rotator cuff repair based on the results of a previous biomechanical study. Study Design: Randomized controlled trial; Level of evidence, 2. Methods: A total of 78 patients who underwent arthroscopic rotator cuff repair for medium- to large-sized tears were prospectively enrolled and randomly divided into 2 groups according to the applied bridging suture tension: optimum tension group (96.3 ± 4.9 N) and maximum tension group (199.0 ± 20.3 N). Bridging suture tension was measured with a customized tensiometer, as used in the previous biomechanical study. The functional outcome was measured at the final follow-up (27.4 ± 5.9 months [range, 24-45 months]) using the visual analog scale for pain, American Shoulder and Elbow Surgeons score, Simple Shoulder Test, and Constant score, and the anatomic outcome was evaluated using magnetic resonance imaging or ultrasonography at least 12 months after surgery. Results: Overall, 64 patients (32 in each group) were analyzed. The functional outcomes improved significantly compared with preoperative values (all P < .05) but did not show significant differences between the 2 groups (all P > .05). Regarding the anatomic outcomes, the maximum tension group (n = 1; 3.1%) had a significantly lower healing failure rate than the optimum tension group (n = 9; 28.1%) ( P = .013). One patient in the maximum tension group had a type II failure. Conclusion: Maximum bridging suture tension in TOE repair for medium- to large-sized rotator cuff tears provided better anatomic healing with less risk of medial rotator cuff failure, which differs from the results of a previous time-zero biomechanical study.

Analysis of A Cable Loaded Uniformly Along the Horizontal Using MATLAB

Cables can be defined as a flexible structure which can only support tensile load and offers no resistance when compressed or bent in a curved shape. They have several applications in engineering structures for supporting and transmitting load form one point to another such as bridges, trolley wheels, supports suspension roofs and main load carrying cables in any structure. Hence it becomes necessary for extensive design and analysis study on cables. Therefore in the present paper work, cable of length 600m is uniformly loaded along the horizontal is been considered for the analysis with the mass of 18kg/m of its length and supports its own weight. The aim of the work is to determines mid length tension, maximum tension and total cable length for h= 10, 20, 30, 40, 50, 60, 70 and 80 meters using MATLAB. The result shows that as h increases, the tension in mid length and maximum tension is decreasing, whereas total length of the cable is found increasing.