An approximation of deflection line function at the rod loaded by buckling under self-weight

Rad se bavi aproksimacijom točne funkcije linije otklona za štap opterećen izvijanjem zbog vlastite težine pomoću funkcije, što je najbolje prikazano točnim oblikom ovog štapa. U ovom radu predlažemo metode derivacije kritične duljine izvijanja pomoću točnog rješenja i pomoću metode energije. Za zamjenske funkcije linije otklona su izabrane varijante goniometrijskih funkcija i polinomi. Pojedinačni koeficijenti funkcija su izabrani na temelju postojećih rubnih uvjeta i u slučaju nedovoljnog broja, oni su izabrani kako bi se izrazio točan oblik linije otklona štapa na najprikladniji način, koji je prenesen iz konkretnog primjera rješenja pomoću softvera SolidWorks. Rad prikazuje pogreške kritičnog izračuna duljine izvijanja nasuprot točnom rješenju, kao i maksimalna apsolutna i relativna odstupanja kod bočnog pomicanja za odabranu funkciju. Od pojedinačnih zamjenskih funkcija je naknadno izabrana ona koja ispunjava uvjet za opće korištenje i ima najmanja odstupanja od točnog rješenja.The paper deals with an approximation of the exact deflection line function at a rod loaded by self-weight buckling via the function, which is best-presented by the exact shape of this rod. In this paper, we suggest the methods of derivation of the critical buckling length by the exact solution and by the energy method. For the substitute functions of deflection line, the variants of goniometric functions and polynomials are chosen. Individual coefficients of the functions are chosen on the basis of existing boundary conditions and in the case of their insufficient count, they are chosen in order to express the exact rod deflection line shape in the most suitable way, which was transposed from the concrete example solution by SolidWorks Simulation software. The paper shows the errors of critical buckling length calculation against the exact solution, as well as the maximum absolute and relative deviations in the lateral displacement for the chosen function. From the individual substitute functions, one function that meets the condition for general use and has the lowest deviations from the exact solution, is subsequently chosen

Determination of Critical Load in a Nonuniform Circular Steel Column under the Eccentric Axial Load

The purpose of this paper is to determine a critical load for a nonuniform circular steel tube under eccentrically axial load. The circular tube has variable cross section at flattened ends with existing holes used for connection between members. Three different cases of eccentricities are studied with the drilled holes either on the same side or on the opposite side of column axis. The critical load is calculated from the differential equation of deflection curve which is solved by the power series and Runge-Kutta method. In addition, the loading tests were performed on a total of 180 specimens with different diameters, slenderness, and connection. The calculated results are compared and shown in a good agreement with those obtained from the experimental results. The results also show that the critical load decreases rapidly even at a small value of eccentricity and thus may have a significant effect on the load-carrying capacity

Numerical Study of Heated Tube Arrays in the Laminar Free Convection Heat Transfer

Laminar free convection heat transfer from a heated cylinder and tube arrays is studied numerically to obtain the local and average Nusselt numbers. To verify the numerical simulations, the Nusselt numbers for a single cylinder were compared to other authors for the Rayleigh numbers of 103 and 104. Furthermore, the vertically arranged heated tube arrays 4 × 1 and 4 × 2 with the tube ratio spacing SV/D = 2 were considered, and obtained average Nusselt numbers were compared to the existing correlating equations. A good agreement of the average Nusselt numbers for the single cylinder and the bottom tube of the 4 × 1 tube array is proved. On the other hand, the bottom tubes of the 4 × 2 tube array affect each other, and the Nusselt numbers have a different course compared to the single cylinder. The temperature fields for the tube array 4 × 4 in basic, concave, and convex configurations are studied, and new correlating equations were determined. The simulations were done for the Rayleigh numbers in the range of 1.3 × 104 to 3.7 × 104 with a tube ratio spacing S/D of 2, 2.5, and 3. On the basis of the results, the average Nusselt numbers increase with the Rayleigh numbers and tube spacing increasing. The average Nusselt number and total heat flux density for the convex configuration increase compared to the base one; on the other hand, the average Nusselt number decreases for the concave one. The results are applicable to the tube heaters constructional design in order to heat the ambient air effectively

Determination of the Reference Temperature for a Convective Heat Transfer Coefficient in a Heated Tube Bank

The paper presents a theoretical analysis of heat transfer in a heated tube bank, based on the Nusselt number computation as one of the basic dimensionless criteria. To compute the Nusselt number based on the heat transfer coefficient, the reference temperature must be determined. Despite the value significance, the quantity has several different formulations, which leads to discrepancies in results. This paper investigates the heat transfer of the inline and staggered tube banks, made up of 20 rows, at a constant tube diameter and longitudinal and transverse pitch. Both laminar and turbulent flows up to Re = 10,000 are considered, and the effect of gravity is included as well. Several locations for the reference temperature are taken into consideration on the basis of the heretofore published research, and the results in terms of the overall Nusselt number are compared with those obtained by the experimental correlations. This paper provides the most suitable variant for a unique reference temperature, in terms of a constant value for all tube angles, and the Reynolds number ranges of 100–1000 and 1000–10,000 which are in good agreement with the most frequently used correlating equations

Strength and Deformation Analyses of Selected Filaments for Large-Format Additive Manufacturing Applicable to the Production of Firefighting Water Tanks

Large-format additive manufacturing is a candidate for tremendous savings in terms of time and cost while simultaneously enabling higher flexibility, quality, and variability. Most of the design constraints of small-scale polymer 3D printers still apply to large-format additive manufacturing. The paper details both the strengths and deformation-related design considerations for additive manufacturing to gain a better understanding of the material capabilities and limitations, mechanical characteristics, and how to use them for large-format additive manufacturing (LFAM). The results show that the tested materials for additive manufacturing meet the requirements from the stress and deformation points of view. Compared to the steel and composite material, the strength limits are lower, but high enough for the given load. The materials HI TEMP, HI TEMP CF, PA12CF, PA6/66, and PLA seem to be the most promising for LFAM to create a firefighting water tank. The results may be considered as an introduction to further research that should lead to real solutions for the production of atypical tanks

Influence of Boundary Conditions on the Solution to a Mathematical Model for a Given Wooden Plate

The article examines deformation of wood veneer and internal forces resulting from bending. Wood is modelled as an orthotropic material. A thin circular wooden plate hemispherically supported at its free edge is bent by axial hubbing of the punch with a hemispherical end. The analysis of the models is carried out by the ANSYS software. Geometric boundary conditions are calculated and set by a macro formed by the APDL (ANSYS Parametric Design Language) scenario language. For the reason of comparison the models were solved for a given plate with simplified boundary conditions

Influence of Boundary Conditions on the Solution to a Mathematical Model for a Given Wooden Plate

The article examines deformation of wood veneer and internal forces resulting from bending. Wood is modelled as an orthotropic material. A thin circular wooden plate hemispherically supported at its free edge is bent by axial hubbing of the punch with a hemispherical end. The analysis of the models is carried out by the ANSYS software. Geometric boundary conditions are calculated and set by a macro formed by the APDL (ANSYS Parametric Design Language) scenario language. For the reason of comparison the models were solved for a given plate with simplified boundary conditions

Accuracy in the geometrical characteristics reduction method of step shaft at deflection computing

Ovaj rad se bavi računalnom metodom određivanja progiba stupnjevane osovine koristeći metodu redukcije promjera.Ova metoda je proučavana analitički na odabranom obliku vratila u različitim varijantama promjera i duljine pojedinih raspona, gdje su vrijednosti progiba uspoređivane s izračunatim vrijednostima bez tog smanjenja. Te vrijednosti su odabrane kao točne i verificirane su numerički proračunom u PTC Creo softveru za simulaciju. Relativni postotci pogreške su interpretirani grafički, a u ovom radu su istraženi i ograničavajući uvjeti za njihovo korištenje. Cilj rada je ukazati na ograničavajuće uvjete korištenja ove metode, koja se ne može uvijek susresti u praksi. Isto tako u radu se ukazuje na moguće propuste koji se mogu učiniti u ovom postupku, i to je prikazano na pogrešnoj dimenziji osovine koja utječe na pouzdanost i sigurnost rada.The paper deals with the computing method of step shaft deflection in an intended place by using the diameter reduction method. This method is analytically studied on the selected shaft shape at different variants of diameters and individual span lengths, where values of deflection are compared with computed values without using this reduction. These values were selected as exact, which was verified by numerical computing in PTC Creo Simulate software. The relative percentage errors are graphically interpreted, and the contribution also deals with the creation of limiting conditions for their use. The aim is to point at limiting conditions of using this method, which may not be always met in practice. It also points to possible failures of this method, which is shown in an incorrect dimension of the shaft, influencing the reliability and safety of operation