Gross sectional area. Centrally tensioned and centrally compressed members

4.5. The estimated length of the elements should be determined by multiplying their free length by a factor

according to paragraphs 4.21 and 6.25.

4.6. Composite elements on pliable joints, supported by the entire cross section, should be calculated for strength and stability according to formulas (5) and (6), while also being determined as the total areas of all branches. The flexibility of the constituent elements should be determined taking into account the compliance of the joints according to the formula

(11)

flexibility of the entire element relative to the axis (Fig. 2), calculated from the effective length without compliance;

flexibility of a separate branch relative to the axis I - I (see Fig. 2), calculated from the estimated length of the branch; with less than seven thicknesses () branches take =0;

coefficient of reduction of flexibility, determined by the formula

(12)

width and height of the cross section of the element, cm;

the estimated number of seams in the element, determined by the number of seams over which the mutual shift of the elements is summed up (in Fig. 2, a - 4 seams, in Fig. 2, b - 5 seams);

estimated length of the element, m;

the estimated number of cuts of bonds in one seam per 1 m of the element (for several seams with a different number of cuts, the average number of cuts for all seams should be taken);

the coefficient of compliance of the joints, which should be determined by the formulas of Table 12.

When determining the diameter of nails, no more than 0.1 of the thickness of the connected elements should be taken. If the size of the pinched ends of the nails is less than 4, then the cuts in the seams adjacent to them are not taken into account in the calculation. The value of joints on steel cylindrical dowels should be determined by the thickness of the thinner of the connected elements.

Rice. 2. Components

a - with gaskets; b - without gaskets

Table 12

Connection type

Coefficient at

central compression

bending compression

2. Steel cylindrical pins:

a) the diameter of the thickness of the connected elements

b) diameter > thickness of connected elements

3. Oak cylindrical dowels

4. Oak lamellar dowels

Note: The diameters of nails and dowels, the thickness of the elements, the width and thickness of the lamellar dowels should be taken in cm.

When determining the diameter of oak cylindrical dowels, no more than 0.25 of the thickness of the thinner of the connected elements should be taken.

Ties in the seams should be spaced evenly along the length of the element. In hinged-supported rectilinear elements, it is allowed to put connections in the middle quarters of the length in half the amount, introducing into the calculation according to formula (12) the value taken for the extreme quarters of the length of the element.

The flexibility of a composite element calculated by formula (11) should be taken no more than the flexibility of individual branches, determined by the formula

(13)

the sum of the gross moments of inertia of the cross sections of individual branches relative to their own axes parallel to the axis (see Fig. 2);

gross sectional area of ​​the element;

Estimated element length.

The flexibility of a composite element relative to the axis passing through the centers of gravity of the sections of all branches (the axis in Fig. 2) should be determined as for a solid element, i.e. without taking into account the compliance of the bonds, if the branches are loaded evenly. In the case of unevenly loaded branches, paragraph 4.7 should be followed.

If the branches of a composite element have a different cross section, then the calculated flexibility of the branch in formula (11) should be taken equal to:

(14)

the definition is given in Fig.2.

4.7. Composite elements on pliable joints, some of the branches of which are not supported at the ends, can be calculated for strength and stability according to formulas (5), (6) subject to the following conditions:

a) the cross-sectional area of ​​\u200b\u200bthe element and should be determined by the cross section of the supported branches;

b) the flexibility of the element relative to the axis (see Fig. 2) is determined by the formula (11); in this case, the moment of inertia is taken taking into account all branches, and the area - only supported ones;

c) when determining the flexibility relative to the axis (see Fig. 2), the moment of inertia should be determined by the formula

moments of inertia of the cross sections of supported and unsupported branches, respectively.

4.8. The calculation for the stability of centrally compressed elements of a section with a variable height should be performed according to the formula

gross cross-sectional area with maximum dimensions;

coefficient taking into account the variability of the section height, determined according to Table 1, Appendix 4 (for elements of a constant section);

buckling coefficient determined according to item 4.3 for flexibility corresponding to the section with maximum dimensions.

Bending elements

4.9. Calculation of bending elements, secured against buckling of the flat form of deformation (see clauses 4.14 and 4.15), for strength under normal stresses should be carried out according to the formula

calculated bending moment;

design resistance to bending;

design modulus of the element's cross section. For solid members for bending components on yielding joints, the calculated modulus of modulus should be taken equal to the net modulus multiplied by the factor ; values ​​for elements composed of identical layers are given in Table 13. When determining the weakening of the sections, located on the section of the element with a length of up to 200 mm, they are taken combined in one section.

Table 13

Coefficient notation

Number of layers per element

The value of the coefficients for the calculation of bending components during spans, m

Note. For intermediate values ​​of the span and the number of layers, the coefficients are determined by interpolation.

4.10. Calculation of bending elements for shearing strength should be performed according to the formula

design shear force;

static gross moment of the shifted part of the cross section of the element relative to the neutral axis;

gross moment of inertia of the cross section of the element relative to the neutral axis;

calculated width of the section of the element;

design resistance to shearing in bending.

4.11. The number of cuts , evenly spaced in each seam of a composite element in a section with an unambiguous diagram of transverse forces, must satisfy the condition

(19)

the calculated bearing capacity of the connection in this seam;

bending moments in the initial and final sections of the section under consideration.

Note. If there are bonds of different bearing capacity in the seam, but

identical in nature of work (for example, dowels and nails), bearing

their abilities should be summed up.

4.12. The calculation of elements of a solid section for strength in oblique bending should be carried out according to the formula

(20)

components of the calculated bending moment for the main axes of the section and

section modulus netto about the main axes of the section and

4.13. Glued curvilinear elements that are bent by a moment that reduces their curvature should be checked for radial tensile stresses according to the formula

(21)

normal stress in the extreme fiber of the stretched zone;

normal stress in the intermediate fiber of the section for which the radial tensile stresses are determined;

the distance between the extreme and considered fibers;

the radius of curvature of the line passing through the center of gravity of the diagram of normal tensile stresses, enclosed between the extreme and considered fibers;

calculated wood tensile strength across the fibers, taken according to clause 7 of Table 3.

4.14. Calculation for the stability of the flat form of deformation of bent elements of rectangular section should be carried out according to the formula

maximum bending moment in the section under consideration

maximum gross modulus in the area under consideration

The coefficient for bending elements of rectangular cross section, hinged against displacement from the bending plane and fixed against rotation around the longitudinal axis in the reference sections, should be determined by the formula

the distance between the support sections of the element, and when fixing the compressed edge of the element at intermediate points from displacement from the bending plane - the distance between these points;

cross section width;

the maximum height of the cross section on the site;

coefficient depending on the shape of the curve of bending moments in the section, determined according to tables 2, 3, appendix 4 of these standards.

When calculating bending moments with a height linearly changing along the length and a constant width of the cross section, which do not have fastenings from the plane along the edge stretched from the moment, or with the coefficient according to the formula (23) should be multiplied by an additional coefficient. The values ​​are given in Table 2, Appendix 4. At =1.

When reinforcing from the bending plane at intermediate points of the stretched edge of the element in the section, the coefficient determined by formula (23) should be multiplied by the coefficient:

:= (24)

the central angle in radians that defines the section of the element of circular shape (for rectilinear elements);

the number of intermediate reinforced (with the same step) points of the stretched edge on the section (for the value should be taken equal to 1).

4.15. Checking the stability of the flat form of deformation of bending elements of an I-beam or box-shaped cross-section should be carried out in cases where

width of the compressed belt of the cross section.

The calculation should be made according to the formula

coefficient of longitudinal bending from the plane of bending of the compressed chord of the element, determined according to clause 4.3;

design compressive strength;

gross modulus of the cross section; in the case of plywood walls, the reduced modulus of resistance in the bending plane of the element.

Elements subjected to axial force with bending

4.16. Calculation of eccentric-tensioned and tension-bent elements should be made according to the formula

(27)

4.17. Calculation for the strength of eccentrically compressed and compressed-bent elements should be made according to the formula

(28)

Notes: 1. For hinged elements with symmetrical diagrams

bending moments sinusoidal, parabolic, polygonal

and close to them outlines, as well as for console elements should

determine by formula

coefficient varying from 1 to 0, taking into account the additional moment from the longitudinal force due to the deflection of the element, determined by the formula

bending moment in the design section without taking into account the additional moment from the longitudinal force;

coefficient determined by formula (8) p.4.3.

2. In cases where bending moment diagrams in hinged elements have a triangular or rectangular shape, the coefficient according to formula (30) should be multiplied by the correction factor:

(31)

3. With an asymmetric loading of hinged elements, the magnitude of the bending moment should be determined by the formula

(32)

bending moments in the calculated section of the element from the symmetrical and skew-symmetric components of the load;

coefficients determined by formula (30) at slenderness values ​​corresponding to symmetrical and oblique buckling forms.

4. For elements of a section variable in height, the area in formula (30) should be taken for the maximum section in height, and the coefficient should be multiplied by the coefficient taken from Table 1, Appendix 4.

5. When the ratio of stresses from bending to stresses from compression is less than 0.1, the compressively-bent elements should also be checked for stability according to formula (6) without taking into account the bending moment.

4.18. The calculation for the stability of the flat form of deformation of the compressed-bent elements should be carried out according to the formula

(33)

gross area with the maximum dimensions of the section of the element on the site ;

for elements without fixing the stretched zone from the deformation plane and for elements having such fixings;

buckling coefficient determined by formula (8) for the flexibility of the section of the element with the estimated length from the plane of deformation;

coefficient determined by formula (23).

If there are fastenings in the element in the area of ​​the deformation plane from the side of the edge stretched from the moment, the coefficient should be multiplied by the coefficient determined by the formula (24), and the coefficient - by the coefficient by the formula

(34)

When calculating elements of a section with a variable height that do not have fastenings from the plane along an edge stretched from the moment or at , the coefficients and determined by formulas (8) and (23) should be additionally multiplied, respectively, by the coefficients and given in Tables 1 and 2 appendix .4. At

4.19. In composite compressed-bent elements, the stability of the most stressed branch should be checked, if its estimated length exceeds seven branch thicknesses, according to the formula

(35)

The stability of a compressively-bent composite element from the bending plane should be checked using formula (6) without taking into account the bending moment.

4.20. The number of bond cuts , evenly spaced in each seam of a compressed-bent composite element in a section with an unambiguous diagram of transverse forces when a compressive force is applied over the entire section, must satisfy the condition

where the coefficient is taken from Table 1, Appendix 4.

gross static moment of the shifted part of the cross section relative to the neutral axis;

with hinged ends, as well as with hinged fastening at intermediate points of the element - 1;

with one hinged and the other pinched end - 0.8;

with one pinched and other free loaded end - 2.2;

with both pinched ends - 0.65.

In the case of a longitudinal load distributed evenly along the length of the element, the coefficient should be taken equal to:

with both hinged ends - 0.73;

with one pinched and the other free end - 1.2.

The estimated length of intersecting elements connected to each other at the intersection should be taken equal to:

when checking stability in the plane of structures - the distance from the center of the node to the point of intersection of the elements;

when checking stability from the plane of the structure:

a) in case of intersection of two compressed elements - the full length of the element;

Name of structural elements

Ultimate Flexibility

1. Compressed chords, support braces and truss support posts, columns

2. Other compressed elements of trusses and other through structures

3. Compressed link elements

4. Stretched truss belts in the vertical plane

5. Other tension elements of trusses and other through structures

For overhead power lines

The value should be taken at least 0.5;

c) in the case of intersection of a compressed element with a stretched element of equal magnitude - the greatest length of the compressed element, measured from the center of the node to the point of intersection of the elements.

If the intersecting elements have a composite section, then the corresponding slenderness values ​​determined by formula (11) should be substituted into formula (37).

4.22. The flexibility of the elements and their individual branches in wooden structures should not exceed the values ​​\u200b\u200bspecified in Table 14.

Features of the calculation of glued elements

plywood with wood

4.23. The calculation of glued elements made of plywood with wood should be carried out according to the reduced cross-section method.

4.24. The strength of the stretched plywood sheathing of slabs (Fig. 3) and panels should be checked according to the formula

moment of section modulus reduced to plywood, which should be determined in accordance with the instructions of clause 4.25.

4.25. The reduced modulus of the cross section of glued plywood boards with wood should be determined by the formula

distance from the center of gravity of the reduced section to the outer edge of the skin;

Fig.3. Cross section of glued plywood and wood boards

static moment of the shifted part of the reduced section relative to the neutral axis;

design chipping resistance of wood along the fibers or plywood along the fibers of the outer layers;

the calculated section width, which should be taken equal to the total width of the frame ribs.

Calculation of elements of wooden structuresby limit states of the first group

Centrally stretched and centrally compressed elements

6.1 The calculation of centrally tensioned elements should be made according to the formula

where is the calculated longitudinal force;

Estimated wood tensile strength along the fibers;

The same for unidirectional veneer wood (5.7);

The cross-sectional area of ​​the net element.

When determining attenuation, located in a section up to 200 mm long, should be taken combined in one section.

6.2 The calculation of centrally compressed elements of a constant solid section should be made according to the formulas:

a) strength

b) stability

where is the calculated resistance of wood to compression along the fibers;

The same for unidirectional veneer wood;

Buckling coefficient determined according to 6.3;

Net cross-sectional area of ​​the element;

The calculated cross-sectional area of ​​the element, taken equal to:

in the absence of weakening or weakening in dangerous sections that do not extend to the edges (Figure 1, a), if the weakening area does not exceed 25%, where is the gross sectional area; for weakenings that do not extend to the edges, if the weakening area exceeds 25%; with symmetrical weakening that goes to the edges (Figure 1, b),.

a- not facing the edge; b- facing the edge

Picture 1- Loosening compressed elements

6.3 The buckling coefficient should be determined by the formulas:

with element flexibility 70

with element flexibility 70

where the coefficient is 0.8 for wood and 1.0 for plywood;

factor 3000 for wood and 2500 for plywood and unidirectional veneer wood.

6.4 The flexibility of solid section elements is determined by the formula

where is the estimated length of the element;

The radius of gyration of the section of the element with the maximum gross dimensions relative to the axis.

6.5 The estimated length of the element should be determined by multiplying its free length by the coefficient

according to 6.21.

6.6 Composite elements on pliable joints, supported by the entire cross section, should be calculated for strength and stability according to formulas (8) and (9), while they should be determined as the total areas of all branches. The flexibility of the constituent elements should be determined taking into account the compliance of the joints according to the formula

where is the flexibility of the entire element relative to the axis (Figure 2), calculated from the estimated length of the element without taking into account compliance;

* - flexibility of a separate branch relative to the I-I axis (see Figure 2), calculated from the estimated length of the branch; at less than seven thicknesses () of the branch are taken c0*;

The coefficient of reduction of flexibility, determined by the formula

* The formula and its explication correspond to the original. - Database manufacturer's note.

where u is the width and height of the cross section of the element, cm;

Estimated number of seams in an element, determined by the number of seams over which the mutual shift of elements is summed up (in Figure 2, a- 4 seams, in figure 2, b- 5 stitches);

Estimated element length, m;

Estimated number of cuts of bonds in one seam per 1 m of the element (for several seams with a different number of cuts, the average number of cuts for all seams should be taken);

Compliance coefficient of joints, which should be determined using the formulas in Table 15.

a- with gaskets b- without pads

Figure 2- Components

Table 15

Relationship type

Coefficient at

central compression

bending compression

1 Nails, screws

2 Steel cylindrical dowels

a) the diameter of the thickness of the connected elements

b) the diameter of the thickness of the connected elements

3 Glued-in rebars A240-A500

4 Oak cylindrical dowels

5 Oak lamellar dowels

Note - The diameters of nails, screws, dowels and glued rods, the thickness of the elements, the width and thickness of the lamellar dowels should be taken in cm.

When determining the diameter of nails, no more than 0.1 of the thickness of the connected elements should be taken. If the size of the pinched ends of the nails is less, then the cuts in the seams adjacent to them are not taken into account in the calculation. The value of connections on steel cylindrical pins should be determined by the thickness of the thinnest of the connected elements.

When determining the diameter of oak cylindrical dowels, no more than 0.25 of the thickness of the thinner of the connected elements should be taken.

Ties in the seams should be spaced evenly along the length of the element. In hinged-supported rectilinear elements, it is allowed to put connections in the middle quarters of the length in half the amount, introducing into the calculation according to formula (12) the value taken for the extreme quarters of the length of the element.

The flexibility of a composite element, calculated by formula (11), should be taken no more than the flexibility of individual branches, determined by the formula:

where is the sum of the gross moments of inertia of the cross sections of individual branches relative to their own axes parallel to the axis (see Figure 2);

Gross section area of ​​the element;

Estimated element length.

The flexibility of a composite element relative to the axis passing through the centers of gravity of the sections of all branches (the axis in Figure 2) should be determined as for a solid element, i.e. without taking into account the compliance of the bonds, if the branches are loaded evenly. In the case of unevenly loaded branches, one should be guided by 6.7.

If the branches of a composite element have a different cross section, then the calculated flexibility of the branch in formula (11) should be taken equal to

the definition is shown in figure 2.

6.7 Composite elements on pliable joints, some of the branches of which are not supported at the ends, can be calculated for strength and stability according to formulas (5), (6) subject to the following conditions:

a) the cross-sectional area of ​​the element should be determined by the cross section of the supported branches;

b) the flexibility of the element relative to the axis (see Figure 2) is determined by the formula (11); in this case, the moment of inertia is taken taking into account all branches, and the area - only supported ones;

c) when determining the flexibility relative to the axis (see Figure 2), the moment of inertia should be determined by the formula

where u are the moments of inertia of the cross sections of the supported and unsupported branches, respectively.

6.8 The calculation for the stability of centrally compressed elements of a section with a variable height should be performed according to the formula

where is the gross cross-sectional area with maximum dimensions;

Coefficient taking into account the variability of the section height, determined according to Table E.1 of Appendix E (for elements of a constant section1);

The buckling factor determined in accordance with 6.3 for the slenderness corresponding to the section with the maximum dimensions.

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