Manual for the design of foundations on a natural basis. Calculation of a columnar foundation under a column under the action of a vertical load and a moment in one direction

6.1. CALCULATION OF REINFORCED CONCRETE FOUNDATIONS ON A NATURAL BASE FOR COLUMNS OF BUILDINGS AND STRUCTURES

6.1.1. General provisions

The dimensions of the sole and the depth of the foundations are determined by the calculation of the base given in Ch. 5. Calculation of the foundation structure (slab part and under-column) is carried out according to strength and crack opening and includes: punching test and “reverse” moment, determination of reinforcement sections and crack opening width, as well as calculation of the strength of the cross-section of the under-column.

The initial data for the calculation are: dimensions of the sole of the slab part; foundation depth and foundation height; sectional area of ​​the column; combinations of design and standard loads from the column at the level of the foundation edge.

The calculation of foundations for strength and crack opening is carried out for the main and special combinations of loads. When calculating the foundation for strength, the design forces and moments are taken with a load safety factor according to the instructions of the current SNiP, and when calculating crack opening - with a load safety factor equal to one.

When checking the strength of the slab part of the foundation for the reverse moment, it is necessary to take into account the loads from the material and equipment stored on the floor.

When calculating foundations in terms of strength and crack opening, the forces arising in them from temperature and similar deformations are taken to vary vertically from their full value at the level of the foundation edge to a half value at the level of the foundation sole.

Design characteristics of concrete and steel are given in Ch. 4 and are accepted taking into account the corresponding coefficients of working conditions [ , ].

6.1.2. Calculation of foundations for punching

The calculation for punching is carried out from the condition that the acting forces are perceived by the concrete section of the foundation without installing transverse reinforcement: with a monolithic interface of the column with the slab part - from the top of the latter (Fig. 6.1, a), with a monolithic interface of the under-column with the slab part, regardless of the type of connection columns with a sub-column (monolithic or glass) with a distance from the top of the slab part to the bottom of the column H 1 ≥ (b uc - b c)/2 - from the top of the slab part (Fig. 6.1, b), and with a smaller H 1 - from the bottom of the column (Fig. 6.1, c).

Rice. 6.1.

a - monolithic interface of the plate part with the column; b - the same with a high sub-column; c - the same, with a low column; 1 - column; 2 - slab part; 3 - sub-column

This condition is verified in both directions.

Guidelines for the design of concrete and reinforced concrete structures made of heavy concrete (without prestressing)

Guidelines for the design of foundations on a natural basis for columns of buildings and structures of industrial enterprises

SNiP 52-01-2003 Concrete and reinforced concrete structures

When calculating the foundation for punching, the minimum height of the slab part is determined h and the number and dimensions of its steps are assigned, or the bearing capacity of the slab part is checked for a given configuration. When calculating for punching from the top of the slab part, it is assumed that the punching of the foundation under central loading occurs along the side surfaces of the pyramid, the sides of which are inclined at an angle of 45 ° to the horizontal (see Fig. 6.1).

The square foundation is calculated for punching from the condition

F ≤ kR bt b a h 0

where F— design pushing force; k— coefficient taken equal to 1; Rbt- design tensile strength of concrete; b a is the arithmetic mean of the perimeters of the upper and lower bases of the punching pyramid formed within the working height of the section h 0 , (distance from the top of the plate part to the middle of the reinforcement).

Rice. 6.2.

Quantities F and b a are determined by the formulas:

b a = 2(l c + b c + 2h 0);

F=A 0 p,

where R- pressure on the soil without taking into account the weight of the foundation and soil on its ledges;

A 0 = A-Ap;

here A- the area of ​​​​the base of the foundation; Ap is the area of ​​the lower base of the punching pyramid.

For centrally loaded rectangular and eccentrically loaded square foundations, a scheme is adopted in which the strength condition of one face parallel to the smaller side of the foundation base is considered (Fig. 6.2). The strength condition is checked by formula (6.1).

The calculation is made on the action of a vertical force N applied along the edge of the foundation, and the moment at the level of the sole M. In this case, the force and size of the side of the punching pyramid will be:

F=A 0 p; F=A 0 p max ,

A 0 = 0,5b(l-l c - 2h 0) - 0,25(b-bc - 2h 0) 2 ;

b p = b c + h 0 ;

p, p max- the average or maximum edge pressure on the soil from the design loads:

Under central loading

p = N/A;

For eccentric loading

p max = N/A + M/W,

here W is the moment of resistance of the base of the foundation.

b-bc < 2h 0 ,

bp = 0,5(b-bc),

A 0 = 0,5b(l-l c - 2h 0).

The number and height of the steps are assigned depending on the total height of the slab part h in accordance with the table. 4.25 and taking into account modular dimensions.

First, it is determined (see Ch. 4) the removal of the lower step of the foundation With 1 (Fig. 6.3) and check the condition

F ≤ R bt h 01 bp,

where h 01 - working height of the lower step of the foundation.

Rice. 6.3.

Power F and b p calculated by the formulas:

F=A 01 pmax;

b p = b 1 + h 01 ,

where A 01 - polygon area a 1 b 1 c 1 d 1 e 1 g 1 ;

A 01 = 0,5(l - l 1 - 2h 01) - 0,25(b-b 1 - 2h 01) 2 ,

if b-b 1 < 2h 01 , then

A 01 = 0,5b(l - l 1 - 2h 01).

Rice. 6.4. To determine the height of steps

Removal of the lower stage c 1 is taken no more than the values ​​\u200b\u200bspecified in table. 4.28 taking into account modular dimensions.

The minimum dimensions of the remaining steps of the foundation in the plan are determined after setting the offset of the lower step c 1 line crossings AB with lines limiting the heights of the steps (Fig. 6.4). For two-stage and three-stage foundations, these dimensions must be at least:

l 1 ≥ l - 2c 1 ;

b 1 ≥ ml 1 ;

l 2 ≥ (l - 2c 1 - lc)h 3 / (h 2 + h 3) + lc;

b 2 ≥ ml 2 + lc;

here m- the ratio of the smaller side of the foundation to the larger one, taken equal to 0.6-0.85.

The final dimensions of the steps are assigned taking into account the unification of the dimensions of the foundations (see Chapter 4).

It must be borne in mind that the removal of steps, especially the lower one, determines the amount of reinforcement. In this regard, the sizes of steps assigned according to the above method can be adjusted from the condition of reinforcement efficiency.

With some characteristic ratios of the dimensions of the steps, the bearing capacity of the slab part is checked as follows.

For centrally and eccentrically loaded rectangular foundations with an upper step, one side of which l 1 > lc + 2h 2 , and another b 1 ≤ bc + 2h 2 (Fig. 6.5), the calculation for punching is made from the condition

F ≤ Rbt(h 01 b 1p + h 2 b 2p).

Meaning F b 1R and b 2R- according to the formulas:

b 1p = b 1 + h 01 ;

b 2p = (b 1 + bc)/2.

Polygon area abcdeg

A 0 = 0,5b(l-l c - 2h 0) - 0,25(b-b 1 - 2h 01) 2 .

Rice. 6.5.

Rice. 6.6. Scheme of formation of a punching pyramid for rectangular foundations having a different number of steps in two directions

If b - b 1 < 2h 01 , then A 0 is determined by formula (6.12).

For centrally and eccentrically loaded rectangular foundations that have a different number of steps in two directions (Fig. 6.6), the calculation for punching is carried out according to the formula

F ≤ Rbt[(h 0 - h 3)b 1p + h 3 bc].

Meaning F is determined by formula (6.5), b 1R- according to the formula

The columnar foundation consists of a slab and a sub-column, which has a recess (glass) for embedding the prefabricated reinforced concrete column or performed without it (when pairing the foundation with a metal or reinforced concrete half-timbered column).

The design of the foundation for a reinforced concrete column begins with determining the dimensions of the column and the glass. It is recommended to take typical dimensions of the top of the foundation (depending on the section of the column). For columns with a cross-sectional size of 400x300 mm, 400x400 mm, take the section of the under-column 900x900 mm; for columns with a cross section of 500x400 mm, 500x500 mm, 600x400 mm, 600x500 mm, take the section of the under-column 1200x1200 mm, and for columns with a cross section of 700x400 mm, 800x400 mm, 800x500 mm - 1500x1200 mm. The depth of the glass is

The dimensions of the foundation must be modular, in plan and in height a multiple of 300 mm, while the height of the steps is 300 and 600 mm (Fig. 1).

The design of the stepped foundation is first performed in a plane of a larger size l. To do this, at the mark (-0.150), the corresponding size of the column is set aside symmetrically to the axis of the foundation. The number of steps is from one to three. In this case, the departure of steps in size must be no less than the height of the step (300, 450, 600 and 900 mm). Similarly, the foundation is constructed in the direction of the short side b. As a result, the number of steps on both sides should not differ by more than one. Preferably the same number.

On the construction site it is preferable to use columnar foundations made of monolithic heavy concrete of classes B10, B12.5, B15, B20 (with a minimum frost resistance grade of F50).

The slab part of the foundation is checked by the punching calculation /10/. In this case, the pushing force must be absorbed by the concrete section, as a rule, without setting transverse reinforcement.

Rice. 1. Columnar foundation for the last ordinary column

It is necessary to distinguish between two schemes of calculation for punching:

when pairing a prefabricated column with high foundation with height

a column that satisfies the condition hc f - dp ≥ 0.5(l c f - l c ), where hc f is the height of the column; dp is the depth of the glass; l c f is the length of the cross section of the column; l c - length of the cross section of the column (in this case, the punching of the slab part is considered from the bottom of the sub-column to the action of the longitudinal force N and the bending moment M);

when pairing a prefabricated column with a low foundation (in this case, the calculation is carried out for punching by the column from the bottom of the glass under the action of only the longitudinal force N).

The foundation is reinforced as follows: the slab - with a C1 mesh of class AIII rods and a diameter of at least 10 mm along the side with a size of up to 3 m and 12 mm with a size of more than 3 m in increments of 200 mm (Fig. 1); under-columns - two grids C2 from rods of class AI and AIII. Longitudinal working reinforcement of class AIII with a diameter of at least 10 mm is placed with a step of 200 mm, and transverse reinforcement of class AI with a diameter of at least 6 mm with a step of 600 mm. The selection of the diameter of the reinforcement is carried out as a result of the calculation of the foundation for strength when guided by the manual /10/.

In addition, the glass of the columnar foundation is reinforced. transverse

the reinforcement is designed constructively in the form of grids C-3 of paired rods 8 AIII with six grids at the highest value of eccentricity (e>l c /2) and with five grids in other cases. The grid spacing in the first variant is 50+2x100+2x200, in the second variant 50+2x100+200. The upper mesh is deepened from the edge by 50 mm, the lower one is placed above the end of the column by at least 50 mm. An example of constructing a columnar foundation is given in Appendix 1.

Under the foundation, as a rule, preparation is made of concrete B 3.5 with a thickness of 100 mm (with a release beyond the edge of the foundation slab by at least 150 mm). In this case, the thickness of the concrete protective layer is assumed to be 35 mm. Preparation can be omitted on coarse soils, in which case the protective layer of concrete has a thickness of 75 mm.

To support the outer walls and the construction of the base, it is necessary to provide foundation beams (Table 15). Their dimensions depend on the pitch of the columns, the width of the outer walls and the dimensions of the pedestal.

For buildings with hinged panels and a column spacing of 6 m, it is recommended to use beams 2BF and 3BF, and for a column spacing of 12 m - beams 5BF and 6BF.

Foundation beams, as a rule, rest on concrete columns, the width of which must be at least the maximum width of the beam, and the edge at the mark - 0.35 m or - 0.65 m (depending on its height).

In this article, we will consider the calculation of the foundation for the column according to the 1st limit state when the foundation is loaded with a vertical load and a horizontal load with a bending moment acting in the same plane.

Initial data

The initial data for calculating the foundation will be the loads coming to the foundation from the column and engineering and geological surveys.

As a result of the calculation of the frame in the calculation program, the following loads on the foundation were obtained:

Mx=14.8 t*m (bending moment)

My=0, Qy=0 (I will consider the calculation under the action of moments in 2 planes separately in the following articles)

I want to note that it is best to check 2 calculated combinations:

1. Full wind, snow, structure weight, evenly distributed
2. Complete wind and weight structures

The fact is that one of the calculation conditions is to prevent the edge of the foundation from being separated from the ground, and in the absence of snow load, the vertical load will be less and, accordingly, less resistance to the bending moment.

Engineering and geological surveys:

Depth of seasonal freezing - 1.79 m;

Level ground water 1.6 m;

Soil properties:

The strength properties of soils are determined by engineering and geological surveys. To do this, we are looking for an engineering-geological section under the right foundation and a table with normative and calculated characteristics of soils. For the calculation according to the 1st limit state (strength calculation), it is necessary design characteristics at α=0.95 (confidence probability of calculated values), according to clause 5.3.17 of SP 22.13330.2016.

EGE-1 - bulk soil - sand of different sizes c incl. construction waste up to 15-20%, loam lumps, railroad debris slabs (does not participate in the calculation because the mark of the bottom of the foundation is below this soil layer);

EGE-2 - sand of medium size, medium density, water-saturated: (e=0.65, ρ=1.8 t/m³, E=30 MPa, ϕ=35°, C=1 kPa).

EGE-3 - sand of medium size, with rare interlayers of fluid sandy loam, loam, clay of medium density, water-saturated: (e=0.6, ρ=1.82 t/m³, E=35 MPa, ϕ=36°, С=1, 5 kPa).

Groundwater level 1.8 m from ground level.

Foundation calculation

The scheme for applying loads to the foundation is as follows:

Foundation depth

The depth of the foundation is determined depending on the maximum depth of seasonal freezing, which is given in the report on engineering and geological surveys. In my case, the standard depth of seasonal freezing is d fn = 1.79m.

The estimated depth of seasonal freezing is calculated according to formula 5.4 of SP 22.13330.2016

where k h is the coefficient taking into account the influence of the thermal regime of the structure, taken for the external foundations of heated structures - according to table 5.2 of SP 22.13330.2016; for external and internal foundations of unheated structures k h =1.1, except for areas with a negative average annual temperature;

In our case, the building is unheated, so

d f =1.1*1.79=1.969≈2 m

The depth of the foundation should not be higher than the estimated freezing depth (according to Table 5.3 of SP 22.13330.2016). For heated buildings, it is allowed to build foundations inside the building (not under external walls) above the freezing depth, but it must be guaranteed that the building will be heated during the cold season. If it is assumed that the building can be mothballed or the heating turned off, then the internal foundations must also be laid to the estimated freezing depth.

Preliminary dimensions of the foundation

We preliminarily determine the area of ​​\u200b\u200bthe base of the foundation.

The preliminary dimensions of the foundation are determined by the formula:

N - vertical load from the column, which we received when calculating the frame of the building (N = 21.3 t = 213 kN);

R 0 - design soil resistance, intended for preliminary calculation, are given in Appendix B to SP 22.13330.2016 (in our case, Table B.2 for sand of medium size and average density R 0 = 400 kPa, for clay and other soils, see other tables in the appendix B);

Table B.2 - Design resistances R 0 sands

ȳ - average value specific gravity foundation and soil on its edges, previously accepted ȳ=20 kN/m³;

d - depth of foundation (in our case d = 2 m)

A \u003d N / (R 0 -ȳd) \u003d 213.246 / (400-20 * 2) \u003d 0.6 m²

20% as foundation eccentrically compressed 0.72 m²

The dimensions of the base of the foundation are assigned in increments of 0.3 m, with a size of at least 1.5x1.5 m (Table 4 of the Manual for the design of foundations on a natural basis)

Table 4 Guidelines for the design of foundations on a natural basis

We preliminarily assign a foundation of 1.5x1.5 \u003d 2.25 m², which is more than the preliminary minimum of 0.72 m².

Calculation of maximum and minimum edge pressure

The maximum and minimum edge pressure is found by the formula 5.11 SP 22.13330.2016

Where N \u003d 21.3t \u003d 213 kN is the vertical load from the column in kN;

A f \u003d 2.25 m² - foundation area, m²;

γ mt – weighted average specific gravity foundation bodies, soils and floors, assumed 20 kN/m³;

d=2 - foundation depth, m;

M-moment from the resultant of all loads, acting on the base of the foundation in kN * m, we find by the formula:

М=Mx+Qx*d=14.8+2.8*2=20.4t*m=204kN*m

W is the moment of resistance of the base of the foundation, m³. For a rectangular section, it is found by the formula W=bl²/6 where in our case b is the side of the base of the foundation along the letter axis, l is the length of the side of the base of the foundation along the digital axis (see the picture below).

Because previously we adopted a foundation with dimensions of 1.5x1.5 m, then

W= bl²/6=1.5*1.5²/6=0.5625 m³

Under action vertical load on the foundation, together with the bending moment, we can have 3 options for soil pressure diagrams:

1. Trapezoidal

1. triangular

1. Triangular with separation of the edge of the foundation

The separation of the foundation must not be allowed, i.e. Pmin must always be ≥0.

In our case Pmin<0, поэтому нужно увеличить ширину фундамента таким образом, чтобы Pmin стал больше или равен нулю. Далее увеличиваем размеры фундамента методом подбора. При этом шаг изменения размера фундамента равен 300 мм.

We assign the foundation according to the modular dimensions in increments of 0.3 m. It is better to use a rectangular foundation 2.1x1.8 m (l=2.1m, b=1.8m)

A f \u003d 2.1 * 1.8 \u003d 3.78 m² - foundation area, m²;

W= bl²/6=1.8*2.1²/6=1.323 m³

The rest of the parameters remain the same.

Pmin again<0, снова увеличиваем размеры фундамента:

We assign a foundation with a size of 2.4x1.8 m (l=2.4m, b=1.8m)

A f \u003d 2.4 * 1.8 \u003d 4.32 m² - foundation area, m²;

W= bl²/6=1.8*2.4²/6=1.728 m³

Pmin again<0, как вы уже поняли мы будем увеличивать размер фундамента до тех пор, пока Pmin не станет больше или равен нулю.

As a result of the selection, we got that the foundation should have dimensions of 3.0x2.4 m (l=3.0m, b=2.4m)

A f \u003d 3.0 * 2.4 \u003d 7.2 m² - foundation area, m²;

W= bl²/6=2.4*3.0²/6=3.6 m³

For foundations of columns of buildings equipped with overhead cranes with a lifting capacity of more than 75 tons and more, as well as for foundations of columns of open crane racks with a lifting capacity of more than 15 tons, for tower-type structures, as well as for all types of structures with a design soil resistance of the base R<150кПа размеры фундамента нужно назначать такими, чтобы эпюра давлений была трапециевидной и Pmin/Pmax≥0.25 (п.5.6.27 СП 22.13330.2016). В нашем случае мы должны проверить расчётное сопротивление грунта, и если оно будет меньше 150кПа, то нужно ещё увеличить размеры фундамента.

Soil resistance calculation

The design soil resistance of the base is calculated according to the formula 5.7 of SP 22.13330.2016

γ с1 =1.4 (table 5.4 of SP 22.13330.2016)

γ с2 =1.2 (table 5.4 of SP 22.13330.2016)

Table 5.4 SP 22.13330.2016

k= 1 k=1.1, if they are taken from the tables of Appendix A).

My=1.68 (Table 5.5 of SP 22.13330.2016)

Mq=7.71 (Table 5.5 of SP 22.13330.2016)

Mc=9.58 (Table 5.5 of SP 22.13330.2016)

Here I want to pay attention, despite the fact that we rely on the EGE-3 soil, the EGE-2 soil has lower strength characteristics and it is laid below the EGE-3 soil, so we consider the bearing capacity of the foundation according to EGE-2.

Table 5.5 SP 22.13330.2016

k z =1 b<10 м);

b=2.4 (foundation width);

γ II - (averaged (see 5.6.10) calculated value of the specific gravity of soils lying below the base of the foundation (in the presence of groundwater, it is determined taking into account the weighing effect of water), kN/m³) to a depth equal to z=b/2=0.75 m. To put it simply, the specific gravity of the soil is the density of the soil in kN / m³. To convert soil density in t / m³ to kN / m³, the value is multiplied by 10 (1.8 t / m³ \u003d 18 kN / m³).

Because we have water-saturated soils, then in our case we determine taking into account the weighing effect of water according to formula 36 of the Handbook for the design of foundations for buildings and structures

γ sb = (γ s – γ w)/(1 + e))

where γ w is the specific gravity of water, equal to 10 kN/m³,

e=0.65 is the porosity coefficient, taken according to the data of engineering and geological surveys,

γ II = (γ s – γ w)/(1 + e)) =(18-10)/(1+0.65)=4.84 kN/ m³;

γ' II - (calculated value of the specific gravity of soils lying above the base of the foundation). In our case, this will be backfilling, so the specific gravity of the soil without taking into account the weighing effect of water is 16 kN / m³.

The porosity coefficient is set to at least 0.65. The depth of groundwater is 1.6 m from the surface of the earth. Therefore, the specific gravity of the soil, taking into account the weighing effect of water

γ sb = (γ s – γ w)/(1 + e)) \u003d (16-10) / (1 + 0.65) \u003d 3.64 kN / m³ (at a depth of 2 to 1.6 m, i.e. the thickness of the layer is 0.4 m);

The calculated value is calculated as the average value of the specific gravity of the soil according to the formula

γ’ II =Σ γ’ i *h/Σhi=(3.64*0.4+16*1.6)/2=13.528 kN/m³;

d 1 \u003d 2.0m (depth of foundation from the planning level);

d b \u003d 0 (basement depth, in its absence it is equal to zero according to note 5 to clause 5.6.7 of SP 22.13330.2016);

C II \u003d 1 kPa (calculated value of the specific adhesion of the soil lying directly under the foundation, taken according to survey data, or in accordance with Appendix A of SP 22.13330.2016);

We calculate the calculated resistance of the soil under the base:

Under the action of a bending moment on the foundation, the edge pressure is Rmax=R/1.2=0.330 MPa (clause 5.6.26 of SP 22.13330.2016).

Pmax=127kPa< R=330кПа

We also see that R>150 kPa, so there is no need to increase the size of the foundation.

Therefore, the foundation satisfies the requirements for the bearing capacity of the foundation.

After that, you need to design a foundation, assign dimensions, reinforcement, concrete, which I will definitely consider in future articles.

Calculation program in Excel can be downloaded from the link