4.1. Calculation of centrally stretched elements should be made according to the formula
Where N– design longitudinal force;
R p – design tensile strength of wood along the fibers;
F nt – net cross-sectional area of the element.
When determining F nt weakening located in a section up to 200 mm long should be taken combined in one section.
4.2. Calculation of centrally compressed elements of a constant solid cross-section should be made according to the formulas:
a) for strength
b) for stability
Where R c – calculated resistance of wood to compression along the fibers;
j – buckling coefficient, determined according to clause 4.3;
F nt – net cross-sectional area of the element;
F ras – calculated cross-sectional area of the element, taken equal to:
in the absence of weakening or weakening in dangerous sections, not extending to the edges (Fig. 1, A), if the weakening area does not exceed 25% E br, E calc = F br where F br – gross cross-sectional area; for weakening that does not extend to the edges, if the weakening area exceeds 25% F br, F ras = 4/3 F nt; with symmetrical weakening extending to the edges (Fig. 1, b), F race = F nt.
4.3. The buckling coefficient j should be determined using formulas (7) and (8);
with element flexibility l £ 70
; (7)
with element flexibility l > 70
where coefficient a = 0.8 for wood and a = 1 for plywood;
coefficient A = 3000 for wood and A = 2500 for plywood.
4.4. The flexibility of solid cross-section elements is determined by the formula
Where l o – design length of the element;
r– radius of inertia of the element section with maximum dimensions gross respectively relative to the axes X And U.
4.5. Calculated element length l o should be determined by multiplying its free length l by coefficient m 0
l o = l m 0 (10)
according to paragraphs. 4.21 and 6.25.
4.6. Composite elements on compliant joints, supported by the entire cross-section, should be calculated for strength and stability according to formulas (5) and (6), while F nt and F races are determined as the total areas of all branches. The flexibility of the constituent elements l should be determined taking into account the compliance of the compounds according to the formula
, (11)
where l y is the flexibility of the entire element relative to the axis U(Fig. 2), calculated from the estimated length of the element l o without taking into account compliance;
l 1 – flexibility of an individual branch relative to the I–I axis (see Fig. 2), calculated from the estimated length of the branch l 1 ; at l 1 less than seven thicknesses ( h 1) branches are accepted l 1 = 0;
m у – flexibility reduction coefficient, determined by the formula
, (12)
Where b And h– width and height of the cross section of the element, cm:
n w – the estimated number of seams in the element, determined by the number of seams along which the mutual displacement of the elements is summed up (in Fig. 2, A– 4 seams, in fig. 2, b– 5 seams);
l o – design element length, m;
n c – the estimated number of brace cuts in one seam per 1 m element (for several seams with different numbers of cuts, the average number of cuts for all seams should be taken);
k c is the compliance coefficient of compounds, which should be determined using the formulas in Table. 12.
Table 12
Note. Diameters of nails and dowels d, element thickness A, width b pl and thickness d of plate dowels should be taken in cm.
When determining k The diameter of the nails should be no more than 0.1 times the thickness of the elements being connected. If the size of the pinched ends of the nails is less than 4 d, then the cuts in the seams adjacent to them are not taken into account in the calculation. Meaning k connections on steel cylindrical dowels should be determined by thickness A thinner of the elements being connected.
When determining k with oak diameter cylindrical dowels no more than 0.25 thickness of the thinner of the elements being connected should be taken.
The ties in the seams should be spaced evenly along the length of the element. In hinged-supported rectilinear elements, it is allowed to install half the number of connections in the middle quarters of the length, introducing the value into the calculation using formula (12) n c, adopted for the outer quarters of the element’s length.
Flexibility component element, calculated by formula (11), should be taken no more than the flexibility l of individual branches, determined by the formula
, (13)
where å I i br – the sum of the gross moments of inertia of the cross sections of individual branches relative to their own axes parallel to the axis U(see Fig. 2);
F br – gross cross-sectional area of the element;
l o – design length of the element.
Flexibility of a composite element relative to an axis passing through the centers of gravity of the sections of all branches (axis X in Fig. 2), should be determined as for a solid element, i.e., without taking into account the compliance of the connections, if the branches are loaded evenly. In the case of unevenly loaded branches, clause 4.7 should be followed.
If the branches of a composite element have different cross-sections, then the calculated flexibility l 1 of the branch in formula (11) should be taken equal to:
, (14)
definition l 1 is shown in Fig. 2.
4.7. Composite elements on compliant 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 following conditions:
a) cross-sectional area of the element F nt and F races should be determined by the cross-section of the supported branches;
b) flexibility of the element relative to the axis U(see Fig. 2) is determined by 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 flexibility relative to the axis X(see Fig. 2) the moment of inertia should be determined by the formula
I = I o + 0.5 I but, (15)
Where I about and I but are the moments of inertia of the cross sections of the supported and unsupported branches, respectively.
4.8. Calculation of the stability of centrally compressed elements of variable height sections should be performed according to the formula
, (16)
Where F max – gross cross-sectional area with maximum dimensions;
k and N– coefficient taking into account the variability of the section height, determined from the table. 1 adj. 4 (for elements of constant section k and N = 1);
j is the longitudinal bending coefficient, determined according to clause 4.3 for flexibility corresponding to the section with maximum dimensions.
Bendable elements
4.9. Calculation of bending elements, secured against loss of stability in a plane form of deformation (see paragraphs 4.14 and 4.15), for strength under normal stresses should be carried out according to the formula
Where M– design bending moment;
R and – design bending resistance;
W ras – calculated moment of resistance of the cross-section of the element. For solid elements W race = W nt; for bending composite elements on yielding connections, the calculated moment of resistance should be taken equal to the net moment of resistance W nt multiplied by the coefficient k w ; values k w for elements composed of identical layers are given in table. 13. When determining W nt weakening sections located on a section of an element up to 200 mm long are taken combined in one section.
Table 13
| Coefficient designation | Number of layers | The value of the coefficients for calculating bending components during spans, m | |||
| patients | in element | 9 or more | |||
| 0,7 | 0,85 | 0,9 | 0,9 | ||
| k w | 0,6 | 0,8 | 0,85 | 0,9 | |
| 0,4 | 0,7 | 0,8 | 0,85 | ||
| 0,45 | 0,65 | 0,75 | 0,8 | ||
| k and | 0,25 | 0,5 | 0,6 | 0,7 | |
| 0,07 | 0,2 | 0,3 | 0,4 |
Note. For intermediate values of the span and number of layers, the coefficients are determined by interpolation.
4.10. Calculation of bending elements for shear strength should be performed according to the formula
Where Q– design lateral force;
S br – gross static moment of the sheared part of the cross-section of the element relative to the neutral axis;
I br – gross moment of inertia of the cross-section of the element relative to the neutral axis;
b rаs – design cross-sectional width of the element;
R sk – calculated resistance to shearing during bending.
4.11. Number of link cuts n s, evenly spaced in each seam of the composite element in a section with an unambiguous diagram of transverse forces, must satisfy the condition
, (19)
Where T– design bearing capacity of the connection in this seam;
M A, M B – bending moments in the initial A and final B sections of the section under consideration.
Note. If there are connections in the seam of different load-bearing capacity, but the same in nature of work (for example, dowels and nails), load-bearing capacity they should be summed up.
4.12. Calculation of solid cross-section elements for strength during oblique bending should be done according to the formula
, (20)
Where M x and M y – components of the design bending moment for the main axes of the section X And U;
W x and W y – moments of resistance of the net cross section relative to the main axes of the section X And U.
4.13. Glued moment-bending curved elements M, which reduces their curvature, should be checked for radial tensile stresses using the formula
, (21)
where s 0 is the normal stress in the outermost fiber of the stretched zone;
s i– normal stress in the intermediate fiber of the cross-section, for which radial tensile stresses are determined;
h i– distance between the outermost and considered fibers;
r i– radius of curvature of the line passing through the center of gravity of the part of the diagram of normal tensile stresses located between the outermost and considered fibers;
R p.90 – calculated tensile strength of wood across the fibers, taken according to clause 7 of table. 3.
4.14. Calculation of the stability of a flat form of deformation of bendable elements of rectangular constant cross-section should be made according to the formula
Where M– maximum bending moment in the area under consideration l R;
W br – maximum gross moment of resistance in the area under consideration l p.
The coefficient j M for bendable elements of a rectangular constant cross-section, hinged against displacement from the bending plane and secured against rotation around the longitudinal axis in the supporting sections, should be determined by the formula
, (23)
Where l p is the distance between the supporting sections of the element, and when fastening the compressed edge of the element at intermediate points from displacement from the bending plane, the distance between these points;
b– cross-sectional width;
h – maximum height cross section on the site l p;
k f – coefficient depending on the shape of the diagram of bending moments in the area l p, determined according to table. 2 adj. 4 present standards.
When calculating bending elements with a linearly varying height along the length and a constant cross-sectional width, which do not have fastenings from the plane along the stretched from the moment M edge, or m < 4 коэффициент jM according to formula (23) should be multiplied by an additional coefficient k and M. Values k and M are given in table. 2 adj. 4. When m³ 4 k and M = 1.
When reinforced from the bending plane at intermediate points of the stretched edge of the element in the section l p coefficient j M determined by formula (23), should be multiplied by the coefficient k P M :
, (24)
where a p is the central angle in radians, defining the area l p of a circular element (for rectilinear elements a p = 0);
m– the number of reinforced (with the same pitch) points of the stretched edge in the area l p (at m³ 4 the value should be taken equal to 1).
4.15. Checking the stability of the flat form of deformation of bending elements of a constant I-beam or box-shaped cross-section should be carried out in cases where
l p³ 7 b, (25)
Where b– width of the compressed cross-section chord.
The calculation should be made according to the formula
where j is the coefficient of longitudinal bending from the bending plane of the compressed chord of the element, determined according to clause 4.3;
Rс – design compression resistance;
W br – gross moment of resistance of the cross section; in the case of plywood walls - the reduced moment of resistance in the plane of bending of the element.
Initially, metal, as the most durable material, served protective purposes - fences, gates, gratings. Then they began to use cast iron pillars and arches. Advanced Growth industrial production demanded the construction of structures with large spans, which stimulated the emergence of rolled beams and trusses. Eventually metal carcass became key factor development of architectural form, as it allowed the walls to be freed from function load-bearing structure.
Centrally tensioned and centrally compressed steel elements. Calculation of the strength of elements subject to central tension or compression by force N, should be performed according to the formula
where is the calculated resistance of steel to tension, compression, bending at the yield point; is the net cross-sectional area, i.e. area minus section weakening; – operating conditions coefficient adopted according to the tables of SNIP N-23–81* “Steel Structures”.
Example 3.1. A hole with a diameter of d= = 10 cm (Fig. 3.7). I-beam wall thickness – s – 5.2 mm, gross cross-sectional area – cm2.
It is necessary to determine the permissible load that can be applied along the longitudinal axis of the weakened I-beam. The design resistance of steel is taken to be kg/cm2, and .
Solution
We calculate the net cross-sectional area:
where is the gross cross-sectional area, i.e. The total cross-sectional area without taking into account weakening is taken according to GOST 8239–89 “Hot-rolled steel I-beams”.
We determine the permissible load:
Determination of the absolute elongation of a centrally tensioned steel bar
For a rod with a stepwise change in cross-sectional area and normal force, the total elongation is calculated by algebraically summing the elongations of each section:
Where P - number of plots; i– site number (i = 1, 2,..., P).
The elongation due to its own weight of a rod of constant cross-section is determined by the formula
where γ – specific gravity rod material.
Stability calculation
Calculation of stability of solid-wall elements subject to central compression by force N, should be performed according to the formula
where A is the gross cross-sectional area; φ – buckling coefficient, taken depending on the flexibility
Rice. 3.7.
and design resistance of steel according to the table in SNIP N-23–81 * “Steel structures”; μ – length reduction coefficient; – minimal radius of gyration cross section; The flexibility λ of compressed or tensile elements should not exceed the values given in SNIP "Steel Structures".
Calculation of composite elements from angles, channels (Fig. 3.8), etc., connected tightly or through gaskets, should be performed as solid-walled, provided that the largest clear distances in the areas between welded strips or between the centers of the outer bolts do not exceed for compressed elements and for stretched elements.
Rice. 3.8.
Bendable steel elements
Calculation of beams bent in one of the main planes is carried out according to the formula
Where M – maximum bending moment; – moment of resistance of the net section.
The values of tangential stresses τ in the middle of the bending elements must satisfy the condition
Where Q – shear force in section; – static moment of half the section relative to the main axis z;– axial moment of inertia; t– wall thickness; – design shear strength of steel; – yield strength of steel, accepted according to state standards and technical specifications for steel; – reliability coefficient for the material, adopted according to SNIP 11-23–81* “Steel Structures”.
Example 3.2. It is required to select the cross section of a single-span steel beam loaded with a uniformly distributed load q= 16 kN/m, can length l= 4 m, MPa. The cross section of the beam is rectangular with a height ratio h to width b beams equal to 3 ( h/b = 3).
Calculation of wooden structural elementsaccording to limit states of the first group
Centrally stretched and centrally compressed elements
6.1 Calculation of centrally stretched elements should be made according to the formula
where is the calculated longitudinal force;
The calculated tensile strength of wood along the grain;
The same for wood made from unidirectional veneer (5.7);
The net cross-sectional area of the element.
When determining weaknesses located in a section up to 200 mm long, they should be taken combined in one section.
6.2 Calculation of centrally compressed elements of a constant solid section should be made according to the formulas:
a) for strength
b) for stability
where is the calculated resistance of wood to compression along the fibers;
The same for wood made from unidirectional veneer;
Buckling coefficient determined in accordance with 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 cross-sectional area; for weakening that does not extend to the edges, if the weakening area exceeds 25%; with symmetrical weakening extending to the edges (Figure 1, b),.
A- not extending to the edge; b- facing the edge
Picture 1- Loosening of compressed elements
6.3 The buckling coefficient should be determined using the formulas:
with element flexibility 70
with element flexibility 70
where the coefficient is 0.8 for wood and 1.0 for plywood;
coefficient 3000 for wood and 2500 for plywood and unidirectional veneer wood.
6.4 The flexibility of solid cross-section elements is determined by the formula
where is the estimated length of the element;
Radius of inertia of the section of an element with maximum gross dimensions relative to the axis.
6.5 The effective length of an element should be determined by multiplying its free length by the coefficient
according to 6.21.
6.6 Composite elements on compliant joints, supported by the entire cross-section, should be calculated for strength and stability according to formulas (8) and (9), and defined as the total areas of all branches. The flexibility of the constituent elements should be determined taking into account the compliance of the compounds 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 an individual branch relative to the I-I axis (see Figure 2), calculated from the estimated length of the branch; At least seven thicknesses () branches are taken from 0*;
Flexibility reduction coefficient, determined by the formula
* The formula and its explanation correspond to the original. - Database manufacturer's note.
where and is the width and height of the cross-section of the element, cm;
The estimated number of seams in an element, determined by the number of seams along which the mutual displacement of the elements is summed up (in Figure 2, A- 4 seams, in figure 2, b- 5 seams);
Design element length, m;
The estimated number of brace cuts in one seam per 1 m element (for several seams with different numbers of cuts, the average number of cuts for all seams should be taken);
Compliance coefficient of compounds, which should be determined using the formulas in Table 15.
A- with gaskets, b- without gaskets
Figure 2- Components
Table 15
|
Type of connections |
Coefficient at |
|
|
central compression |
compression with bending |
|
|
1 Nails, screws | ||
|
2 Steel cylindrical dowels | ||
|
a) diameter and thickness of the elements to be connected | ||
|
b) the diameter of the thickness of the elements being connected | ||
|
3 Glued rods from reinforcement A240-A500 | ||
|
4 Oak cylindrical dowels | ||
|
5 Oak lamellar dowels | ||
|
Note - The diameters of nails, screws, dowels and glued rods, the thickness of elements, the width and thickness of plate dowels should be taken in cm. |
||
When determining the diameter of the nails, no more than 0.1 of the thickness of the elements being connected should be taken. If the size of the pinched ends of the nails is smaller, then the cuts in the seams adjacent to them are not taken into account in the calculation. The value of connections on steel cylindrical dowels should be determined by the thickness of the thinner of the elements being connected.
When determining the diameter of oak cylindrical dowels, no more than 0.25 of the thickness of the thinner of the elements being connected should be taken.
The ties in the seams should be spaced evenly along the length of the element. In hinged-supported rectilinear elements, it is allowed to install half the number of connections in the middle quarters of the length, introducing into the calculation using formula (12) the value accepted for the outer quarters of the element’s length.
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 cross-sectional area of the element;
Estimated length of the element.
The flexibility of the composite element relative to the axis passing through the centers of gravity of the sections of all branches (axis in Figure 2) should be determined as for a solid element, i.e. without taking into account the compliance of connections if the branches are loaded evenly. In the case of unevenly loaded branches, 6.7 should be followed.
If the branches of a composite element have different cross-sections, then the calculated flexibility of the branch in formula (11) should be taken equal to
the definition is given in Figure 2.
6.7 Composite elements on compliant 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 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 flexibility relative to the axis (see Figure 2), the moment of inertia should be determined by the formula
where and are the moments of inertia of the cross sections of the supported and unsupported branches, respectively.
6.8 Calculation of the stability of centrally compressed elements of variable height sections 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 constant section1);
Buckling coefficient determined according to 6.3 for the flexibility corresponding to the section with maximum dimensions.
A- gross cross-sectional area;
A bn- net cross-sectional area of the bolt;
A d- cross-sectional area of the brace;
Af- cross-sectional area of the shelf (belt);
A n- net cross-sectional area;
Aw- cross-sectional area of the wall;
Awf- cross-sectional area of the fillet weld metal;
A wz- cross-sectional area of the metal fusion boundary;
E- elastic modulus;
F- force;
G- shear modulus;
Jb- moment of inertia of the branch section;
Jm; J d- moments of inertia of the chord and brace sections of the truss;
J s- moment of inertia of the section of the rib, plank;
J sl- moment of inertia of the section of the longitudinal rib;
J t- moment of torsional inertia of a beam, rail;
J x; Jy- moments of inertia of the gross section relative to the axes, respectively x-x And y-y;
J xn; Jyn- the same, net sections;
M- moment, bending moment;
M x; M y- moments about the axes, respectively x-x And y-y;
N- longitudinal force;
Nad- additional effort;
Nbm- longitudinal force from the moment in the column branch;
Q- shear force, shear force;
Qfic- conditional shear force for connecting elements;
Q s- conditional transverse force exerted on a system of planks located in the same plane;
Rba- calculated tensile strength of foundation bolts;
Rbh- calculated tensile strength of high-strength bolts;
Rbp- calculated resistance to crushing of bolted connections;
Rbs- design shear resistance of bolts;
R bt- design tensile strength of bolts;
R bun- standard steel resistance of bolts, taken equal to the temporary resistance σ in according to state standards and technical specifications for bolts;
R bv- design tensile strength of U-bolts;
Rcd- design resistance to diametrical compression of the rollers (with free contact in structures with limited mobility);
Rdh- calculated tensile strength of high-strength wire;
Rlp- calculated resistance to local crushing in cylindrical hinges (trunnions) with a tight contact;
Rp- design resistance of steel to end surface crushing (if there is a fit);
R s- design shear resistance of steel;
R th- calculated tensile strength of steel in the direction of rolled product thickness;
R u- design resistance of steel to tension, compression, bending based on temporary resistance;
R un- temporary tensile strength of steel, taken equal to the minimum value σ in according to state standards and technical specifications for steel;
Rwf- calculated resistance of fillet welds to shear (conditional) along the weld metal;
Rwu- calculated resistance of butt welded joints to compression, tension, bending based on temporary resistance;
R wun- standard resistance of the weld metal in terms of temporary resistance;
Rws- calculated shear resistance of butt welded joints;
Rwy- calculated resistance of butt welded joints to compression, tension and bending at the yield strength;
Rwz- calculated resistance of fillet welds to shear (conditional) along the metal of the fusion boundary;
Ry- design resistance of steel to tension, compression, bending at the yield point;
Ryn- the yield strength of steel, taken equal to the value of the yield strength σ t according to state standards and technical specifications for steel;
S- static moment of the sheared part of the gross section relative to the neutral axis;
W x; W y- moments of resistance of the gross section relative to the axes, respectively x-x And y-y;
W xn; Wyn- moments of resistance of the net section relative to the axes, respectively x-x And y-y;
b- width;
b ef- design width;
bf- width of the shelf (belt);
b h- the width of the protruding part of the rib, overhang;
c; c x; c y- coefficients for calculating strength taking into account the development of plastic deformations during bending relative to the axes, respectively x-x, y-y;
e- eccentricity of force;
h- height;
h ef- design height of the wall;
h w- wall height;
i- radius of gyration of the section;
i min- the smallest radius of gyration of the section;
i x; i y- radii of inertia of the section relative to the axes, respectively x-x And y-y;
k f- fillet weld leg;
l- length, span;
l c- length of rack, column, spacer;
l d- brace length;
lef- estimated, nominal length;
l m- length of the truss or column chord panel;
l s- length of the bar;
l w- length of the weld;
l x; l y- calculated lengths of the element in planes perpendicular to the axes, respectively x-x And y-y;
m- relative eccentricity ( m = eA / W c);
m ef- reduced relative eccentricity ( m ef = mη);
r- radius;
t- thickness;
t f- thickness of the shelf (belt);
t w- wall thickness;
β f And β z- coefficients for calculating a fillet weld, respectively, for the weld metal and for the metal of the fusion boundary;
γ b- coefficient of connection operating conditions;
γc- coefficient of working conditions;
γn- reliability coefficient for the intended purpose;
γm- reliability coefficient for the material;
γ u- reliability coefficient in calculations based on temporary resistance;
η - coefficient of influence of the section shape;
λ - flexibility ( λ = lef / i);
Conditionalflex();
λ ef- reduced flexibility of the through-section rod;
Conditional reduced flexibility of a through-section rod ( 
);
Conditional flexibility of the wall ( 
);
The greatest conditional flexibility of the wall;
λ x; λ y- calculated flexibility of the element in planes perpendicular to the axes, respectively x-x and y-y;
v- coefficient of transverse strain of steel (Poisson);
σloc- local voltage;
σx; σy - normal stress, parallel to the axes, respectively x-x And y-y;
τ xy- shear stress;
φ (X, y) - buckling coefficient;
φ b- coefficient of reduction in design resistances for flexural-torsional buckling of beams;
φe- coefficient of reduction of design resistances during eccentric compression.
| 1. General provisions. 2 2. Materials for structures and connections. 3 3. Design characteristics of materials and connections. 4 4*. Taking into account operating conditions and purpose of structures. 6 5. Calculation of elements steel structures on axial forces and bending. 7 Centrally tensioned and centrally compressed elements.. 7 Bending elements.. 11 Elements subject to axial force with bending.. 15 Supporting parts. 19 6. Design lengths and maximum flexibility of steel structure elements. 19 Estimated lengths of elements flat trusses and connections. 19 Design lengths of elements of spatial lattice structures. 21 Design lengths of structural elements. 23 Design lengths of columns (racks) 23 Limit flexibility of compressed elements. 25 Ultimate flexibility of tensile elements. 25 7. Checking the stability of walls and waist sheets of bending and compressed elements. 26 Beam walls. 26 Walls of centrally eccentrically compressed and compressed-bending elements. 32 Belt sheets (shelves) of centrally, eccentrically compressed, compressed-bending and bendable elements. 34 8. Calculation of sheet structures. 35 Strength calculations. 35 Stability calculations. 37 Basic requirements for the calculation of metal membrane structures. 39 9. Calculation of steel structure elements for endurance. 39 10. Strength calculation of steel structure elements taking into account brittle fracture. 40 11. Calculation of connections of steel structures. 40 Welded joints. 40 Bolted connections. 42 Connections with high-strength bolts. 43 Connections with milled ends. 44 Chord connections in composite beams. 44 12. General requirements on design of steel structures. 45 Basic provisions. 45 Welded joints. 46 Bolted connections and connections with high-strength bolts. 46 13. Additional design requirements industrial buildings and structures. 48 Relative deflections and deviations of structures. 48 Distances between expansion joints. 48 Trusses and structural slabs. 48 Columns.. 49 Connections. 49 Beams. 49 Crane beams. 50 Sheet structures. 51 Mounting fasteners. 52 14. Additional requirements for the design of residential and public buildings and structures. 52 Frame buildings. 52 Hanging coverings. 52 15*. Additional support design requirements air lines power transmission, open structures distribution devices and lines of contact networks of transport. 53 16. Additional requirements for the design of structures of communication antenna structures (AC) with a height of up to 500 m. 55 17. Additional design requirements hydraulic structures river 58 18. Additional requirements for the design of beams with a flexible wall. 59 19. Additional requirements for the design of beams with a perforated wall. 60 20*. Additional requirements for the design of structures of buildings and structures during reconstruction. 61 Appendix 1. Materials for steel structures and their design resistances. 64 Appendix 2. Materials for connections of steel structures and their design resistances. 68 Appendix 3. Physical characteristics of materials. 71 Appendix 4*. Operating condition coefficients for a stretched single angle bolted to one flange. 72 Appendix 5. Coefficients for calculating the strength of steel structure elements taking into account the development of plastic deformations. 72 Appendix 6. Coefficients for calculating the stability of centrally, eccentrically compressed and compressed-bending elements. 73 Appendix 7*. Odds φ b for calculating beams for stability. 82 Appendix 8. Tables for calculating elements for endurance and taking into account brittle fracture. 85 Appendix 8, a. Determination of metal properties. 88 Appendix 9*. Basic letter designations quantities 89 |
The West Siberian Metallurgical Plant has mastered the production of shaped rolled products (equal-flange angles, channels, I-beams) with a flange thickness of up to 10 mm inclusive according to TU 14-11-302-94 “Shaped rolled products C345 from carbon steel modified with niobium”, developed by the plant, JSC Ural Institute of Metals" and agreed upon by the TsNIISK named after. Kucherenko.
Glavtekhnormirovanie reports that shaped rolled steel made of S345 steel categories 1 and 3 according to TU 14-11-302-94 can be used in accordance with SNiP II-23-81 “Steel structures” (Table 50) in the same structures for which it is provided rolled steel C345 categories 1 and 3 according to GOST 27772-88.
Head of Glavtekhnormirovaniya V.V. Tishchenko
Introduction
The metallurgical industry has mastered the production of rolled products for building metal structures and economically alloyed steel C315. Hardening, as a rule, is achieved by microalloying low-carbon mild steel with any of the elements: titanium, niobium, vanadium or nitrides. Alloying can be combined with controlled rolling or heat treatment.
The achieved volumes of production of sheets and shaped profiles from the new steel C315 make it possible to fully satisfy the needs of construction in rolled products with strength characteristics and cold resistance close to the standards for low-alloy steel according to GOST 27772-88.
1. Normative documents for hire
Currently, a series of technical specifications for rolled steel C315 has been developed.
TU 14-102-132-92 “Rolled shaped steel C315”. The holder of the original and the manufacturer of the rolled product is Nizhne-Tagil Metallurgical Plant, assortment - channels in accordance with GOST 8240, equal-flange corner profiles, unequal-flange corner profiles, ordinary I-beams and with parallel flange edges.
TU 14-1-5140-92 “Rolled products for building steel structures. General technical conditions". The original holder is TsNIICHM, the rolled product is manufactured by the Nizhne-Tagil Metallurgical Plant, the assortment is I-beams according to GOST 26020, TU 14-2-427-80.
TU 14-104-133-92 “High-strength rolled products for building steel structures.” The holder of the original and the manufacturer of the rolled metal is the Orsko-Khalilovsky Metallurgical Plant, assortment - sheets with a thickness of 6 to 50 mm.
TU 14-1-5143-92 “Sheet and rolled products of increased strength and cold resistance.” The original holder is TsNIICHM, the rolled product is manufactured by Novo-Lipetsk Iron and Steel Works, the product range is rolled sheets according to GOST 19903 with a thickness of up to 14 mm inclusive.
TU 14-105-554-92 “Rolled sheets of increased strength and cold resistance.” The holder of the original and the manufacturer of the rolled metal is the Cherepovets Metallurgical Plant, the assortment is sheet metal according to GOST 19903 with a thickness of up to 12 mm inclusive.
2. General provisions
2.1. It is advisable to use rolled products made from steel S315 instead of rolled products made from low-carbon steel S255, S285 according to GOST 27772-88 for groups of structures according to SNiP II-23-8I, the use of which in climatic regions of construction with a design temperature of minus 40 ° C is not allowed. In this case, it is necessary to use the increased strength of rolled steel C315.
3. Materials for structures
3.1. Rolled steel C315 is supplied in four categories depending on the requirements for impact bending tests (the categories are assumed to be the same as rolled steel C345 according to GOST 27772-88).
3.2. Rolled steel C315 can be used in structures, guided by the data in Table. 1.
Table 1
* For rolled products with a thickness of no more than 10 mm.
4. Design characteristics of rolled products and connections
4.1. Standard and calculated resistances of rolled steel C315 are taken in accordance with table. 2.
table 2
| Rolled thickness, mm | Standard resistance of rolled products, MPa (kgf/mm 2) | Design resistance of rolled products, MPa (kgf/mm 2) | ||||||
| shaped | sheet, broadband universal | shaped | ||||||
| Ryn | R un | Ryn | R un | Ry | R u | Ry | R u | |
| 2-10 | 315 (32) | 440 (45) | 315 (32) | 440 (45) | 305 (3100) | 430 (4400) | 305 (3100) | 430 (4400) |
| 10-20 | 295 (30) | 420 (43) | 295 (30) | 420 (43) | 290 (2950) | 410 (4200) | 290 (2950) | 410 (4200) |
| 20-40 | 275 (28) | 410 (42) | 275 (28) | 410 (42) | 270 (2750) | 400 (4100) | 270 (2750) | 400 (4100) |
| 40-60 | 255 (26) | 400 (41) | - | - | 250 (2550) | 390 (4000) | - | - |
4.2. Calculated resistances of welded joints of rolled steel C315 for various types connections and stressed connections should be determined according to SNiP II-23-81* (clause 3.4, table 3).
4.3. The calculated bearing resistance of elements connected by bolts should be determined according to SNiP II-23-81* (clause 3.5, table 5*).
5. Calculation of connections
5.1. Calculation of welded and bolted joints of rolled steel S315 is carried out in accordance with the requirements of SNiP II-23-81.
6. Manufacturing of structures
6.1. During production building structures made from steel C315, the same technology should be used as for steel C255 and C285 according to GOST 27772-88.
6.2. Materials for welding rolled steel S315 should be taken in accordance with the requirements of SNiP II-23-81* (Table 55*) for rolled steel S255, S285 and S345 - in accordance with GOST 27772-88, taking into account the calculated resistance of rolled steel S315 for different thicknesses .
On the use in construction of rolled plates of increased strength according to TU 14-104-133-92
The Ministry of Construction of Russia sent to ministries and departments Russian Federation, to the state construction agencies of the republics within the Russian Federation, design and research institutes, letter No. 13-227 dated November 11, 1992 with the following content.
The Orsko-Khalilovsky Metallurgical Plant has mastered the production of plates with a thickness of 6-50 mm according to the technical specifications TU 14-104-133-92 “High-strength rolled products for building steel structures”, developed by the plant, ITMT TsNIIchermet and TsNIISK im. Kucherenko.
The plant by microalloying low-carbon mild steel with titanium or vanadium (or both) with possible application heat treatment and controlled rolling conditions, a new highly efficient type of rolled metal was obtained from steels S315 and S345E, the properties of which are not inferior to those of rolled products made from low-alloy steels according to GOST 27772-88. The microalloying method, type of heat treatment and rolling modes are chosen by the manufacturer. Rolled products are supplied in four categories depending on the requirements for impact bending testing adopted in GOST 27772-88 and SNiP II-23-81*, as well as in the German standard DIN 17100 (on samples with a sharp notch). The category and type of impact bending test is indicated by the consumer in the order for rolled metal.
The Ministry of Construction of Russia reports that rolled steel S345E according to TU 14-104-133-92 can be used along with and instead of rolled steel S345 according to GOST 27772-88 in structures designed according to SNiP II-23-81* “Steel Structures”, without recalculation of sections of elements and their connections. The scope of application, standard and design resistance of rolled steel C315 according to TU 14-104-133-92, as well as the materials used for welding, design resistance of welded joints and crushing of elements connected by bolts, should be taken according to the recommendations of the TsNIISK im. Kucherenko, published below.
The Nizhny Tagil Iron and Steel Works has mastered the production of shaped rolled products - channels in accordance with GOST 8240, angles in accordance with GOST 8509 and GOST 8510, I-beams in accordance with GOST 8239, GOST 19425, TU 14-2-427-80, wide-flange I-beams in accordance with GOST 26020 according to the technical specifications TU 14-1 -5140-82 “High-strength shaped rolled products for building steel structures”, developed by the plant, TsNIIchermet im. Bardin and TsNIISK im. Kucherenko.
The plant due to rational selection chemical composition low-carbon steel, micro-alloying and saturating it with nitrides and carbonitrides with grain refinement during the rolling process, a highly efficient type of rolled product was obtained from steels C315, C345 and C375, the properties of which are not inferior to those of rolled products from low-alloy steels according to GOST 27772.
Rolled products are supplied in four categories depending on the requirements for impact bending testing adopted in GOST 27772-88 and SNiP II-23-81*, as well as in the German standard DIN 17100 (on samples with a sharp notch). The category and type of impact bending test is indicated by the consumer in the order for rolled metal.
The Gosstroy of Russia reports that rolled steel C345 and C375 in accordance with TU 14-1-5140-92 can be used along with and instead of rolled steel C345 and C375 in accordance with GOST 27772-88 in structures designed according to SNiP II-23-81* “Steel structures”, without recalculating the sections of elements and their connections. The scope of application, standard and design resistance of rolled steel C315 according to TU 14-1-3140-92, as well as the materials used for welding, design resistance of welded joints, crushing of elements connected by bolts, should be taken according to the “Recommendations” of the TsNIISK im. Kucherenko, which were published in the journal “Bulletin of Construction Technology” No. 1 for 1993.
Deputy Chairman V.A. Alekseev
Spanish Poddubny V.P.
GENERAL PROVISIONS
1.1. These standards must be observed when designing steel building structures of buildings and structures for various purposes.
The standards do not apply to the design of steel structures for bridges, transport tunnels and pipes under embankments.
When designing steel structures located in special conditions operation (for example, structures of blast furnaces, main and process pipelines, special-purpose tanks, structures of buildings exposed to seismic, intense temperature effects or exposure to aggressive environments, structures of offshore hydraulic structures), structures of unique buildings and structures, as well as special types structures (e.g. prestressed, spatial, suspended) should be observed Additional requirements, reflecting the operating features of these structures, provided for by the relevant regulatory documents, approved or agreed upon by the USSR State Construction Committee.
1.2. When designing steel structures, one must comply with SNiP standards for the protection of building structures from corrosion and fire safety standards design of buildings and structures. Increasing the thickness of rolled products and pipe walls in order to protect structures from corrosion and increase the fire resistance of structures is not allowed.
All structures must be accessible for observation, cleaning, painting, and must not retain moisture or impede ventilation. Closed profiles must be sealed.
1.3*. When designing maternity structures you should:
select optimal technical and economic schemes of structures and cross-sections of elements;
use economical rolled profiles and efficient steels;
apply for buildings and structures, as a rule, unified standard or standard designs;
use progressive structures (spatial systems made from standard elements; structures combining load-bearing and enclosing functions; pre-stressed, cable-stayed, thin-sheet and combined designs from different steels);
provide for the manufacturability of manufacturing and installation of structures;
use designs that ensure the least labor intensity of their manufacture, transportation and installation;
provide, as a rule, for the in-line production of structures and their conveyor or large-block installation;
provide for the use of progressive types of factory connections (automatic and semi-automatic welding, flanged connections, with milled ends, bolted connections, including high-strength ones, etc.);
provide, as a rule, installation connections on bolts, including high-strength ones; welded installation connections are allowed with appropriate justification;
comply with the requirements of state standards for structures of the corresponding type.
1.4. When designing buildings and structures, it is necessary to take design diagrams, ensuring strength, stability and spatial immutability of buildings and structures as a whole, as well as their individual elements during transportation, installation and operation.
1.5*. Steels and connection materials, restrictions on the use of steels S345T and S375T, as well as additional requirements for the supplied steel provided for state standards and CMEA standards or technical specifications, should be indicated in working (KM) and detailing (KMD) drawings of steel structures and in documentation for ordering materials.
Depending on the characteristics of the structures and their components, it is necessary to indicate the continuity class in accordance with GOST 27772-88 when ordering steel.
1.6*. Steel structures and their calculations must meet the requirements of GOST 27751-88 “Reliability of building structures and foundations. Basic provisions for calculations" and ST SEV 3972-83 "Reliability of building structures and foundations. Steel structures. Basic provisions for calculation."
1.7. Design schemes and basic calculation assumptions must reflect the actual operating conditions of steel structures.
Steel structures should generally be designed as unified spatial systems.
When dividing unified spatial systems into separate flat designs the interaction of elements with each other and with the base should be taken into account.
The choice of design schemes, as well as methods for calculating steel structures, must be made taking into account effective use COMPUTER.
1.8. Calculations of steel structures should, as a rule, be carried out taking into account inelastic deformations of steel.
For statically indeterminate structures, the calculation method for which taking into account inelastic deformations of steel has not been developed, the design forces (bending and torsional moments, longitudinal and transverse forces) should be determined under the assumption of elastic deformations of steel according to an undeformed scheme.
With an appropriate feasibility study, the calculation can be carried out using a deformed scheme that takes into account the influence of structural movements under load.
1.9. Elements of steel structures must have minimum cross-sections that meet the requirements of these standards, taking into account the range of rolled products and pipes. In composite sections established by calculation, the undervoltage should not exceed 5%.
Column is vertical element the load-bearing structure of a building, which transfers loads from the structures above to the foundation.
When calculating steel columns it is necessary to be guided by SP 16.13330 “Steel structures”.
For a steel column, an I-beam, a pipe, square profile, a composite section of channels, angles, sheets.
For centrally compressed columns, it is optimal to use a pipe or a square profile - they are economical in terms of metal weight and have a beautiful aesthetic appearance, however, the internal cavities cannot be painted, so this profile must be hermetically sealed.
The use of wide-flange I-beams for columns is widespread - when the column is pinched in one plane this type profile is optimal.
The method of securing the column in the foundation is of great importance. The column can have a hinged fastening, rigid in one plane and hinged in the other, or rigid in 2 planes. The choice of fastening depends on the structure of the building and is more important in the calculation because The design length of the column depends on the method of fastening.
It is also necessary to consider the method of fastening the purlins, wall panels, beams or trusses on a column, if the load is transmitted from the side of the column, then eccentricity must be taken into account.
When the column is pinched in the foundation and the beam is rigidly attached to the column, the calculated length is 0.5l, however, in the calculation it is usually considered 0.7l because the beam bends under the influence of the load and there is no complete pinching.
In practice, the column is not considered separately, but a frame or a 3-dimensional model of the building is modeled in the program, loaded, and the column in the assembly is calculated and selected required profile, but it can be difficult in programs to take into account the weakening of the section by bolt holes, so it may be necessary to check the section manually.
To calculate a column, we need to know the maximum compressive/tensile stresses and moments occurring in key sections; for this we construct stress diagrams. In this review, we will consider only the strength calculation of a column without plotting diagrams.
We calculate the column using the following parameters:
1. Central tensile/compressive strength
2. Stability under central compression (in 2 planes)
3. Strength due to joint action longitudinal force and bending moments
4. Checking the maximum flexibility of the rod (in 2 planes)
1. Central tensile/compressive strength
According to SP 16.13330 clause 7.1.1, strength calculation of steel elements with standard resistance R yn ≤ 440 N/mm2 with central tension or compression by force N should be fulfilled according to the formula
A n is the net cross-sectional area of the profile, i.e. taking into account its weakening by holes;
R y is the design resistance of rolled steel (depending on the steel grade, see Table B.5 SP 16.13330);
γ c is the operating conditions coefficient (see Table 1 SP 16.13330).
Using this formula, you can calculate the minimum required cross-sectional area of the profile and set the profile. In the future, in verification calculations, selection of the column section can only be done using the section selection method, so here we can set a starting point, less than which the section cannot be.
2. Stability under central compression
Stability calculations are carried out in accordance with SP 16.13330 clause 7.1.3 using the formula
A— gross cross-sectional area of the profile, i.e. without taking into account its weakening by holes;
R
γ
φ — stability coefficient under central compression.
As you can see, this formula is very similar to the previous one, but here the coefficient appears φ , to calculate it we first need to calculate the conditional flexibility of the rod λ (indicated with a line above).
Where R y—calculated resistance of steel;
E- elastic modulus;
λ — flexibility of the rod, calculated by the formula:
Where l ef is the design length of the rod;
i— radius of gyration of the section.
Estimated lengths l ef of columns (racks) of constant cross-section or individual sections of stepped columns according to SP 16.13330 clause 10.3.1 should be determined by the formula
Where l— column length;
μ — coefficient of effective length.
Effective length coefficients μ columns (racks) of constant cross-section should be determined depending on the conditions for securing their ends and the type of load. For some cases of fastening the ends and the type of load, the values μ are given in the following table:
The radius of inertia of the section can be found in the corresponding GOST for the profile, i.e. the profile must already be specified in advance and the calculation is reduced to enumerating the sections.
Because the radius of gyration in 2 planes for most profiles is different meanings on 2 planes (only the pipe and the square profile have the same values) and the fastening may be different, and consequently the design lengths may also be different, then stability calculations must be made for 2 planes.
So now we have all the data to calculate conditional flexibility.
If the ultimate flexibility is greater than or equal to 0.4, then the stability coefficient φ calculated by the formula:
coefficient value δ should be calculated using the formula:
odds α And β see table
Coefficient values φ , calculated using this formula, should be taken no more than (7.6/ λ 2) with values of conditional flexibility above 3.8; 4.4 and 5.8 for section types a, b and c, respectively.
With values λ < 0,4 для всех типов сечений допускается принимать φ = 1.
Coefficient values φ are given in Appendix D SP 16.13330.
Now that all the initial data are known, we perform the calculation using the formula presented at the beginning:
As mentioned above, it is necessary to make 2 calculations for 2 planes. If the calculation does not satisfy the condition, then we select a new profile with a larger value of the radius of gyration of the section. You can also change the design scheme, for example, by changing the hinged seal to a rigid one or by securing the column in the span with ties, you can reduce the design length of the rod.
It is recommended to strengthen compressed elements with solid walls of an open U-shaped section with planks or gratings. If there are no strips, then the stability should be checked for stability in case of flexural-torsional buckling in accordance with clause 7.1.5 of SP 16.13330.
3. Strength under the combined action of longitudinal force and bending moments
As a rule, the column is loaded not only with an axial compressive load, but also with a bending moment, for example from the wind. A moment is also formed if the vertical load is applied not in the center of the column, but from the side. In this case, it is necessary to make a verification calculation in accordance with clause 9.1.1 SP 16.13330 using the formula
Where N— longitudinal compressive force;
A n is the net cross-sectional area (taking into account weakening by holes);
R y—design steel resistance;
γ c is the operating conditions coefficient (see Table 1 SP 16.13330);
n, Cx And Сy— coefficients accepted according to table E.1 SP 16.13330
Mx And My- moments relative axes X-X and Y-Y;
W xn,min and W yn,min - sectional moments of resistance relative to the X-X and Y-Y axes (can be found in GOST for the profile or in the reference book);
B— bimoment, in SNiP II-23-81* this parameter was not included in the calculations, this parameter was introduced to take into account deplanation;
Wω,min – sectoral moment of resistance of the section.
If there should be no questions with the first 3 components, then taking into account the bi-moment causes some difficulties.
The bimoment characterizes the changes introduced into the linear stress distribution zones of section deplanation and, in fact, is a pair of moments directed in opposite directions
It is worth noting that many programs cannot calculate bi-torque, including SCAD which does not take it into account.
4. Checking the maximum flexibility of the rod
Flexibility of compressed elements λ = lef / i, as a rule, should not exceed the limit values λ u given in the table
Coefficient α in this formula is the profile utilization coefficient, according to the calculation of stability under central compression.
Just like the stability calculation, this calculation must be done for 2 planes.
If the profile is not suitable, it is necessary to change the section by increasing the radius of gyration of the section or changing the design scheme (change the fastenings or secure with ties to reduce the design length).
If the critical factor is extreme flexibility, then the lowest grade of steel can be taken because The steel grade does not affect the ultimate flexibility. The best option can be calculated using the selection method.
Posted in Tagged ,
