The calculation of the foundations. Calculation example

is that the size of the base of the foundation, the depth of its foundation and the design height are determined.

The preliminary dimensions of the foundation can be determined using the conventional design resistance of the soil base R0. These values ​​of R0 relate to foundations with a width of B = 1 m and a depth of lay from the level of planning d0 = 2 m.

The dimensions of the basement sole are determined in the following sequence:

1) based on the results of engineering and geological surveys, the calculated values ​​of the characteristics of the soil are taken: the angle of internal friction, specific adhesion, deformation modulus and specific weight, as well as the turnover index of the porosity coefficient, the density of the soil

2) IV 1h. IV 2 p. 162- R0 designate the calculated design resistance of the soil base R0

3) determines the width of the sole by the formula

where N is the design load transferred to the foundation;

the m-ratio of the sides of the basement b / l;

at the central load m = 1, at the off-center. m = 1.2É1.5

- the averaged specific weight of the base material and the soil on its edges, taken to be 20 kN / m3 = 0.02 mN / m3

d is the depth of the foundation foot from the level of the layout.

Knowing the dimensions of the foundation, calculate its volume and weight Nf, as well as the weight of the soil on its trimming Nq and check the pressure on the sole:

4) P = (N + Nf + Ng) / BхL ≤ R (kPa)

5) P = P≤R (kPa)

Example 2

Determine the size of the basement under the column of an industrial building:

Initial data: a multistory building, frame in the form of reinforced concrete frames.

The vertical load on the foundation is N = 1390 kN

Depth of the foundation base d = 2m. Ground conditions are as follows:

soils - loams with a porosity ratio of e = 0.9; consistency index (turnover) IL = 0.5, the calculated angle of internal friction = 170, calculated specific cohesion CII = 15 kPa, specific gravity of the soil 17 kN / m3 ( )

Decision:

We take the shape of the foundation square. For these soils, the conventional design (pressure) soil resistance is 150 kPa = 0.15 mPa

the width of the basement found by the formula (3):

For a given depth of laying and the resulting width of the base of the foundation, by the formula (1) we determine the calculated resistance of the soil:

K = 1.1 (as we take the soil data according to the table).

C = 15 kPa

With this R, we calculate the width of the sole:

Finally take b = 2.8 m

check the pressure on the base of the foundation:

P = 1390 / 2.8 * 2.5 + 20 * 2 = 177.3 + 40 = 217.3 <220

those. the bearing capacity of the base is provided with a sole width of 2.8 m.

Example number 3.

Given: Industrial building, single-span with reinforced concrete columns. The depth of the foundation d = 2,5m. Vertical loads at the level of the edge of the basement N = 3500kn = 3.5 m.

The foundation of the foundations is a layer of semi-solid loams with a porosity coefficient e = 0.65, having the following design characteristics:

internal friction angle = 200, specific cohesion CII = 20kPa = 0.02 MPa, specific gravity of the soil = 17 kN / m3 = 0.017 mn / m3

Conditional design resistance of the soil R0 = 200 kPa = 0.02 MPa.

Decision:

We take the foundation square in plan.

The width of the foundation is:

For a given depth of laying and a preliminary width of the foundation, we determine the calculated resistance of the soil base:

Final basement width:

Conclusion: the bearing capacity of the base with a sole width of 3.5 m is provided.

Design of foundations

Calculation of centrally loaded foundations .

Calculation of the structures of centrally loaded foundations are carried out in the following sequence:

1) they carry out an inspection of the carrying capacity of the foundation for the design loads for the first group of limiting states:

2) carried out a foundation test for the formation of cracks in it under regulatory loads in accordance with the second group of limit states. Both of these calculations are similar to the calculation of reinforced concrete structures.

The calculation starts with the determination of stresses under the base of the foundation of the calculated loads.

Рсрр = (Nр + Gгрр + Gфр) / Af (1), where Nр is the calculated load at ground level.

Gp and Gfr are calculated loads of the weight of the soil, respectively, on the edges of the foundation and the foundation itself.

The foundation calculation is based on the premise that the outer parts of the basement under the influence of pressure gr-ba work like consoles embedded in an array of or-ba, and they are calculated according to this scheme in .... I - I - on the edge of the column; II-II- on the verge of the top ... ...

The shear force in sections I - I and II - II is equal to:

QI = Pptr * b * ℓ - ℓk / 2 (2)

QII = Ppcp * b * ℓ - ℓ1 / 2 (3)

Calculation of the effect of transverse forces do not produce, if the following conditions are met:

QI ≤ Yb3 * Rbt * b * ho (4)

QII ≤ Yb3 * Rbt * b * ho "(5)

Where Уb3 - coefficient taken for heavy concrete, equal to 0.6;

Rbt - calculated. concrete tensile strength;

ho = ha - the working height of the foundation.

a = 35É70mm - a protective layer of concrete;

70mm - for monolithic foundations and not <30mm for prefabricated

foundations.

If conditions (4) and (5) are not met, then it is necessary to install transverse reinforcement, or to increase the height of the cross section of the ledges of the foundation; in the practice of design, the latter method is most often resorted to.

In addition to conditions (4) and (5), the condition should be met that provides strength over an inclined section of the lower stage of the foundation from the condition of perception of transverse force Q by concrete:

Q = Pppr [0.5 (ℓ-ℓk) -c] * b ≤ 1.5 * Rbt * b * ho ׀ 2 / c (6), where the right-hand side of the inequality is assumed to be at least 0.6 * Rbt * b * ho and no more

2.5 Rbt * b * ho; c = 0.5 (ℓ-ℓk-2ho) is the length of the projection of the considered inclined section. If c <0, then an inclined crack does not form in the bottom stage of the f-th stage.

The height of the foundation and its individual steps are determined. calculation for pushing. When calculating, it is assumed that the foundation is being pushed along lateral faces, pyramids, the sides of which form an angle of 45 ° with the horizontal plane. In this case, the bottom of the pyramid

located at the level of the working longitudinal reinforcement, and the top - from the place of termination of the column.

The calculation of the foundation for pushing is performed according to the formula:

F ≤ Yb * Rbt * Um * ho (7), where

F is the calculated pressing force;

Yb - coefficient taken equal to 1 for heavy concretes;

Rbt is the calculated resistance. concrete tensile;

Um is the arithmetic average between the perimeters of the upper and lower bases of the pyramid forcing within the useful height of the basement ho.

For square foot foundations:

Um = 2 (bk + ℓk + 2ho) (8)

F = N - Ppcp * A (9)

Where A = (ℓk + 2ho) (bk + 2ho) (10) is the area of ​​the base of the pyramid forcing

If the longitudinal force <0, then the strength of the foundation for pushing provided.

The reinforcement of the foundation is carried out according to the result of the calculation of the normal sections on the action of bending moments in sections I - I and II and II, defined by the following formulas:

MI = 0.125 Ppcp (ℓ - ℓk) 2 * b (11)

MII = 0.125 Ppcp (ℓ - ℓ1) 2 * b (12)

The cross section of the working reinforcement for the entire width of the foundation is calculated by the formulas:

AsI = MI (13)

0.9 * ho * Rs

AsII = MII (14)

0.9 * ho ׀ * Rs where

Rs is the calculated resistance of the reinforcement to tension.

The percentage of reinforcement in the design section of the foundation should be no less than the minimum allowable percentage of reinforcement in bending elements:

µ = (As / b * h) * 100% ≥ 0.5%

The working reinforcement spacing is assumed to be 100-200 mm. Non-working (structural) rods of transverse reinforcement take a section of not less than 10% of the working reinforcement section and set them with a step of 250 ... 300 mm. The diameter of the working reinforcement should not be <10mm., Class A-III

Next, check the foundation for the second group of limit states - for crack resistance. The width of crack opening, and crc, determined by the formulas, are compared with the maximum allowable standards, in which the value of a crcu is assumed to be 0.2 mm for foundations that are below the groundwater level and 0.3 mm above the groundwater level.

If the condition a сrc ≤ a сrcu is met, then the calculation ends. If this condition is not fulfilled, it is necessary either to change the design of the foundation, or to increase the design class of concrete and to strengthen the reinforcement of the foundation, followed by adjustment of all calculations.

Questions for self-test.

1. Name the main types of foundations.

2. What are the parts of the calculation of the foundation?

3. From what conditions determine the shape and size of the sole of a separate foundation?

4. What loads are taken into account when determining the footing area of ​​the foundation?

5. From what conditions is the height of the foundation determined?

6. How to find the required amount of base reinforcement bottom?

7. How are reinforced strip and solid foundations?