CALCULATION OF ELEMENTS IN CENTRAL COMPRESSION OF DEFORMABLE STRUCTURES

ABSTRACT

In this article, the determination of the stresses and the calculation of their strengths under the influence of the compressive force of the compressible elements with different cross-sectional surfaces are considered using examples.

АННОТАЦИЯ

В данной статье на примерах рассмотрено определение напряжений и расчет их прочности под действием сжимающей силы сжимаемых элементов с различными поверхностями поперечного сечения.

Keywords: Construction, cross-sectional area, stress, strength, compressive element, compressive strength, priority.

Ключевые слова: Конструкция, площадь поперечного сечения, напряжение, прочность, сжимающий элемент, прочность на сжатие, приоритет.

All constructions, machines, mechanisms and details used in our daily life must satisfy the conditions of durability, integrity and priority in order to work flawlessly without causing any danger in the working processes. Structural elements must resist various deformations in working conditions. In this process, the correct selection of the material and cross-sectional surfaces of structural elements is the basis for their undamaged operation. In this article, we consider the assessment of the strength of structural elements under the influence of compressive forces.

The compressive elements of constructions include columns, beams, columns and beams of trusses, and some elements. Under the influence of the compressive force N, compressive stress sappears on the cross-sectional surfaces. Wood materials perform well in compression versus elongation. Because, in this case, eyes, cracks and other defects have very little effect on strength. Therefore, for the preparation of compressible elements, materials of type II, i.e., with a calculated resistance R _s =13 MPa, are used. Brushes with a cut surface size greater than 13 cm work relatively well, because in this case the percentage of cut fibers is less than that of boards. Therefore, the calculated resistance is also high, that is, R _c =15 MPa. In particular, this value is much higher R _c =16 MPa in wood with a circular cross-section surface, because in this case the fibers are not cut at all.

The strength and stability of the compressed elements depends on the cross-sectional area (A), their length ( l ) and the connection of the ends. This relationship jis taken into account by the longitudinal bending coefficient ( ). Compressive wooden elements are calculated according to strength and stability as follows.

; 

The first formula is calculated for strength for elements up to 7 times the thickness of the length of the element, and the second is for priority for elements greater than the above value. If the cross-sectional area is equal to the full surface of the element, or the weakening area does not exceed 1/4 of the total area, then A _h = A _br . If the above indicator is more than 25%, or if the ratio exceeds 1/4, A _h = 2/3 ×A _nt is equal. If the weakened surfaces extend to the outer edges, or if there is a non-symmetrical weakening, then A _h = A _nt . Longitudinal bending coefficient is jrelated to the calculated length of the element ( l ₀ ), the radius of inertia of the cross-section surface (r) and the elasticity of the rod ( l)

depends. l= l ₀ /r. Then, j= 3000 / l2 if l> 70; j= 1 – 0.8

( l/100)2 will be if l£70 . The calculated length depends on the connection of the ends of the compression rods (Fig. 1).

Figure 1. Calculation scheme of central compressible struts

The radius of inertia of the cross-section surface (r) depends on the cross-sectional area (A) and the moment of inertia of the cross-section surface (J).

The radius of inertia is 0.289h for cones and 0.25d for circular materials. The elasticity of the compressive elements lis also limited ( ), and this value is as follows.

a) up to 120 for columns and belts of trusses;

b) up to 150 for other elements;

c) for compressible connectors it is up to 200;

If the elasticity of the cross-sectional surface land jthe corresponding calculated resistance R _s are known, the load-carrying capacity of the compressible element is determined as follows

N = j×A ×Rc

The deformation scheme of the compressed element is presented in Fig. 2.b.

Figure 2. a) standard sample; b) longitudinal stress and deformation connection diagram

If lthe value of ductility ( ) is given, then the longitudinal bending coefficient ( j) can be determined from the Euler curve. jis always less than 1.

Figure 3. Longitudinal bending coefficient and ductility diagram

Thus, the value of the longitudinal bending coefficient is determined, and the strength of the compressible elements is checked by the formulas given above.

It can be seen that the structural elements not only resist compressive deformation, but also resist longitudinal bending when under compressive force. In short, when calculating construction elements, the material from which they are made and the surface of the cross section should be taken into account, and their strength should be checked.

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