Baricentro di una sezione composta da profilati metallici

Center of Gravity of a Section Made of Metal Profiles Calculating the XG and YG coordinates of the center of gravity of a section made of metal profiles is a fundamental operation in structural analysis to determine the center of gravity, or center of mass, of the section. This case is particularly interesting because it involves one of the most common construction materials in the world: steel. In this case, we immediately note the absence of axes of symmetry. After carefully defining the section's measurements, we establish a reference system with its origin at the lowest and leftmost corner of the section itself. The formulas used. The section is composed of three metal profiles and two metal sheets. The metal profiles are UNP200, IPE160, and L150x100x14. The first sheet measures 520x800 mm and is 14 mm thick. The second L-shaped sheet is 10 mm thick. The working drawing is included in the video lesson. The metal element being calculated is also described in 3D graphics. We will divide the cross-section into six elements, including three profiles, as described above, and three rectangular sheet metal elements. All useful profile measurements, such as cross-section area, thicknesses, various dimensions, and the position of the center of gravity, are provided in the profile tables, easily found online. To calculate the XG and YG centroid coordinates, we use formulas based on a weighted average of the coordinates of the centers of gravity of the individual parts that make up the cross-section. The formulas are: XG=Sy/Atot and YG=Sx/Atot where: Sy is the static moment of the cross-section about the y-axis Sx is the static moment of the cross-section about the x-axis Atot is the total area of ​​the cross-section The same formulas can be written in terms of integrals: XG=Integral(x.dA)/Integral(dA) and YG=Integral(y.dA)/Integral(dA) Specifically, it is best to use the discretized formulas in terms of summation: XG=Sum(xi.Ai)/Sum(Ai) and YG=Sum(yi.Ai)/Sum(Ai) The summations range from 1 to n depending on the number of components into which the cross-section can be divided. In this case, we will have six figures: three profiles and three sheet metal rectangles. Therefore, the sums will extend from 1 to 6. The specifications of each of the three profiles are as follows: Ai area of ​​the ith profile xi x coordinate of the center of gravity of the ith profile yi y coordinate of the center of gravity of the ith profile The specifications of the three sheet metal rectangles are as follows: bi base of the ith rectangle hi height of the ith rectangle Ai area of ​​the ith rectangle xi x coordinate of the center of gravity of the ith rectangle yi y coordinate of the center of gravity of the ith rectangle The ith area is calculated with the formula Ai=bi.hi The calculation procedure. First, note that the section in question does not have axes of symmetry; consequently, we must calculate the XG coordinate and the YG coordinate. So, to perform the calculations, we adopt this procedure: (1) Subdivide the cross-section into simple elements: profiles with areas A1, A2, A3, and rectangles with areas A4, A5, A6. (2) Identify the centroid coordinates of each element with respect to the origin, xi and yi. (3) Apply the above formulas to obtain XG and YG. In this case, as in many others, we will make extensive use of the spreadsheet, which will greatly facilitate the calculations. You will find the details in the video lesson. Introduction of drillings. The drillings in the cross-section are effectively "voids," and as such, their areas must be deducted from the calculation. In this case, we will have seven rectangular "voids" to insert into the calculation using the same spreadsheet as before. The seven empty areas will be numbered from 7 to 13, -A7, -A8, -A9, -A10, -A11, -A12, -A13. Conclusions. The centroid coordinates of the original section (without holes) will be XG=290.18 mm YG=141.80 mm. The centroid coordinates of the holed section will be XG=288.49 mm YG=138.01 mm. References to previous lessons. Centers of gravity of simple plane figures    • Baricentri di figure piane semplci   Centers of double-T sections    • Baricentri di sezioni a doppio T   Center of gravity of a trapezoid without integrals    • Calcolo delle coordinate baricentriche del...   Center of gravity of a trapezoid with integrals    • Calcolo del Baricentro del Trapezio con gl...   Center of gravity of a parabolic segment    • Baricentro di un segmento parabolico   Center of gravity of a half-parabolic segment    • Baricentro di mezzo segmento parabolico   Center of gravity of a generic parabolic segment    • Baricentro di un segmento parabolico generico   Center of gravity of a bridge section https://www.staticafacile.it/baricent... Center of gravity of a box girder section    • Baricentro di una sezione a cassone