As stone materials from which buildings are erected, they use solid, lightweight and hollow brick, brick blocks and blocks of natural stone. Concrete blocks are used for basement walls. The most common use in construction is ceramic common brick of grades 75-125 and silicate brick of grades 75-250, as well as hollow brick grades 75-150, ceramic hollow and concrete hollow or solid stones from heavy concrete of class 50-200 and on porous aggregates of grades 25 -100, natural stones (limestone, tuffs), rubble stone for the construction of foundations and walls below ground level and soil concrete.
Solutions used to connect individual bricks or stones with each other, ensure their joint work, uniform load transfer over the masonry, and maintenance of the heat and humidity regime of the room in use. By type of binders, the solutions can be clay, lime, cement or composite (for example, clay-cement, cement-lime, etc.). The brand of the solution (compression resistance at 28 days of age) varies between 0.4-20.0 MPa and depends on the age, type of binder and hardening conditions.
The main design characteristics of strength and deformability for natural and artificial stone products and mortar binding solutions are given in table. 1 ÷ 4. '
When determining the design characteristics (Table 1 ÷ 4 ), it is necessary to consider the following ratios of working conditions γс:
a) for pillars and walls with a cross-sectional area of 0.3m2 and less - 0.8;
b) for elements of circular cross-section, not reinforced with mesh reinforcement, made of ordinary bricks -0.6;
c) for masonry compression when the solution hardens for more than a year - 1.15;
g) for laying of silicate bricks on mortars
with the addition of potash -0.85.
For the reinforcement of masonry, reinforcement of classes А-I and Вр-I is used for mesh reinforcement and AI; BP-I and A-II for longitudinal and transverse reinforcement, anchors and connections, and the coefficient of working conditions must be considered depending on the type of reinforcement γcs in accordance with SNiP 2.03.01-84.
Modulus of elasticity (initial strain modulus) for unreinforced masonry
Ео = aRu, (1)
for reinforced masonry
Ea = aa Rshu, (2)
where a and aa are the elastic characteristics of the masonry taken on the table. 3,
Ru - the average tensile strength (temporary resistance) of the masonry in compression
Ru = R, (3)
where R is the calculated resistance of the masonry taking into account the coefficients of the conditions of work of the masonry; k - coefficient equal to 2 for laying of bricks and stones of all kinds (except for large and small blocks of cellular concrete); RSu - the average tensile strength (temporary resistance) to compression of reinforced masonry from brick or ceramic stones, determined by:
For masonry with mesh reinforcement
Rshu = kR + 2 Rsn μ / 100 (4)
For masonry with longitudinal reinforcement
Rshu = kR + Rsn μ / 100 (5)
μ = As / Ak * 100 (5 a )
where A, Ak -, respectively, the cross-sectional area of reinforcement and masonry;
Rsn - normative resistance of reinforcement in masonry; μ is the percentage of reinforcement. The percentage of reinforcement for masonry with retina reinforcement is μ = υs / υk × 100, where υs and υk are the volumes of reinforcement and masonry, respectively. For masonry with longitudinal reinforcement μ = As / Ak × 100, where As and Ak are the areas of reinforcement and masonry, respectively. Rsn = 240; 300 and 350 MPa, respectively, for steel classes AI, A-II and Bp-I.
The value of the elastic characteristics for masonry with longitudinal reinforcement is taken as for unreinforced masonry, and for masonry with mesh reinforcement, a sk is determined by the formula
ask = aRu / Rsku (6)
The value of the strain modulus when determining stresses in the masonry in the calculations for the limiting states of the first group E = 0.5 E0 and the limiting states of the second group E = 0.8 E0; masonry shear modulus G = 0.4 E0 (E0 modulus of elasticity in compression).
Table 1. Calculated resistances to compression of all types of brick masonry and ceramic stones with slit-like vertical voids up to 12 mm wide with a height of a row of masonry 50-150 mm on heavy mortars
Brand of brick or stone | Design resistance R, MPa | |||||||||
With a brand of solution | When the strength of the solution | |||||||||
200 | 150 | 100 | 75 | 50 | 25 | ten | four | 0.2 | null | |
300 250 200 150 125 100 75 50 35 | 3.9 3.6 3.2 2.6 | 3.6 3.3 3.0 2.4 2.2 2.0 | 3.3 3.0 2.7 2.2 2.0 1.8 1.5 | 3.0 2.8 2.5 2.0 1.9 1.7 1.4 1.1 0.9 | 2.8 2.5 2.2 1.8 1.7 1.5 1,3 1.0 0.8 | 2.5 2.2 1.8 1.5 1.4 1,3 1.1 0.9 0.7 | 2.2 1.9 1.6 1,3 1.2 1.0 0.9 0.7 0.6 | 1.8 1.6 1.4 1.2 1.1 0.9 0.7 0.6 0.45 | 1.7 1.5 1,3 1.0 0.9 0.8 0.6 0.5 0.4 | 1.5 1,3 1.0 0.8 0.7 0.6 0.4 0.35 0.25 |
Notes: 1. The calculated resistance of masonry to compression is taken into account taking into account
coefficients: 0,85-when applying hard (without the addition of clay or lime), and light cement mortars, as well as lime mortars under the age of three months; 0.9-for cement mortars (without lime or clay) with organic plasticizers.
2. The calculated resistance of masonry of ceramic stones with voids more than 12mm wide are taken from experimental data.
Table 2. Calculated resistances R to compression of masonry from large concrete solid blocks and blocks from natural stone, captured or clean tesky at the height of the masonry row 500-1000mm
Brand of concrete or stone | Design resistance R, MPa | |||
With a brand of solution | At zero strength of the solution | |||
50 | 25 | ten | ||
1000 800 600 500 400 300 250 200 150 100 75 50 35 25 | 16.5 13.8 11.4 9.8 8.2 6.5 5.7 4.7 3.9 2.7 2.1 1.5 1.1 0.9 | 15.8 13.3 10.9 9.3 7.7 6.2 5.4 4.3 3.7 2.6 2.0 1.4 1.0 0.8 | 14.5 12.3 9.9 8.7 7.4 5.7 4.9 4.0 3.4 2.4 1.8 1.2 0.9 0.7 | 11.3 9.4 7.3 6.3 5.3 4.4 3.8 3.0 2.4 1.7 1,3 0.85 0.6 0.5 |
Table 3. Elastic characteristic of masonry a
Type of masonry | Elastic masonry characteristic | ||||
With the marks of the solution | When the strength of the solution, MPa | ||||
25-200 | ten | four | 0.2 | null | |
From large blocks made of heavy and coarse-porous concrete on heavy aggregates and heavy natural stone (180kN / m3) From stones made of heavy natural stones, heavy concrete and buta From large blocks made of concrete on porous aggregates and porous porous concrete on light aggregates of dense silicate concrete and from light natural stone From large blocks made of cellular concrete type BUT…………………………………. B ………………………………… .. From stones from cellular concrete of a look BUT…………………………………. B ………………………………… .. Of ceramic stones From ceramic brick of plastic extruded full-bodied and hollow, from hollow silicate stones, from stones made of concrete on porous aggregates and porous, from light natural stones Made of brick silicate corpulent and hollow From a ceramic brick of semi-dry pressing of corpulent and hollow | 1500 1500 1000 750 500 750 500 1200 1000 750 500 | 1000 100 750 750 500 500 350 1000 750 500 500 | 750 750 500 500 350 350 200 750 500 350 350 | 750 500 500 500 350 350 200 500 350 350 350 | 500 350 350 500 350 200 200 350 200 200 200 |
Table 4. Calculated resistances R to compression of hollow concrete stone masonry at a height of a series of masonry 200-300mm
Brand of stone | Design resistance R, MPa | |||||||
With a brand of solution | When the strength of the solution | |||||||
100 | 75 | 50 | 25 | ten | four | 0.2 | null | |
100 75 50 35 25 | 2.0 1.6 1.2 | 1.8 1.5 1.15 1.0 | 1.7 1.4 1.1 0.9 0.7 | 1.6 1,3 1.0 0.8 0.65 | 1.4 1.1 0.9 0.7 0.55 | 1,3 1.0 0.8 0.6 0.5 | 1.1 0.9 0.7 0.55 0.45 | 0.9 0.7 0.5 0.4 0.3 |
Table 5. The coefficients of buckling φ for different values of the elastic characteristics of the masonry a
Flexibility | Elastic masonry characteristics | |||||||
a h | λ i | 1500 | 1000 | 750 | 500 | 350 | 200 | 100 |
four five 6 7 eight 9 ten eleven 12 13 14 15 sixteen 17 18 20 22 24 26 28 thirty 32 34 36 38 40 42 46 50 54 | 14 17 21 24 28 31 35 38 42 45 49 52 56 59 63 69 76 83 90 97 104 111 118 125 132 139 146 160 173 187 | one 0.99 0.98 0.96 0.95 0.93 0.92 0.90 0.88 0.86 0.85 0.83 0.81 0.79 0.77 0.73 0.69 0.65 0.61 0.57 0.53 0.49 0.44 0.40 0.36 0.33 0.29 0.21 0.17 0.13 | one 0.98 0.96 0.94 0.92 0.90 0.88 0.86 0.84 0.81 0.79 0.77 0.74 0.72 0.70 0.65 0.61 0.56 0.52 0.49 0.45 0.42 0.38 0.35 0.31 0.27 0.25 0.18 0.15 0.12 | one 0.97 0.95 0.93 0.9 0.87 0.84 0.81 0.79 0.76 0.73 0.7 0.68 0.65 0.63 0.58 0.53 0.49 0.45 0.42 0.39 0.36 0.32 0.29 0.26 0.23 0.21 0.16 0.13 0.1 | 0.98 0.94 0.91 0.88 0.85 0.82 0.79 0.75 0.72 0.69 0.66 0.63 0.59 0.56 0.53 0.48 0.43 0.39 0.36 0.34 0.32 0.29 0.26 0.24 0.21 0.19 0.17 0.13 0.1 0.08 | 0.94 0.91 0.88 0.84 0.8 0.76 0.72 0.68 0.64 0.50 0.57 0.55 0.50 0.47 0.45 0.40 0.35 0.32 0.29 0.27 0.25 0.23 0.21 0.19 0.17 0.16 0.14 0.1 0.08 0.06 | 0.9 0.86 0.81 0.76 0.7 0.65 0.6 0.56 0.51 0.47 0.45 0.40 0.37 0.35 0.32 0.28 0.24 0.22 0.20 0.18 0.17 0.16 0.14 0.13 0.12 0.11 0.09 0.07 0.05 0.04 | 0.82 0.75 0.68 0.81 0.54 0.48 0.43 0.38 0.34 0.31 0.28 0.25 0.23 - - - - - - - - - - - - - - - - - |
Notes: 1. The coefficient φ at intermediate values of flexibilities is determined by interpolation.
2. The coefficients of φ for ratios λh exceeding the limiting ones should be taken when determining φс in the case of a calculation for an eccentric compression with a large eccentricity.
3. For each masonry with mesh reinforcement, the values of the elastic characteristics determined by formula 6 can be less than 200.
Table 6. The coefficient η for masonry of various stone materials
λ h | λ l | Masonry coefficient η | |||
From ceramic bricks, from stones and large blocks, from heavy concrete, from natural stones of all kinds | From silicate bricks, from stones and large blocks, from light and cellular concrete | ||||
With a percentage of longitudinal reinforcement | |||||
0.1 or less | 0.3 and more | 0.1 or less | 0.3 and more | ||
ten 12 14 sixteen 18 20 22 24 26 28 thirty 32 34 36 38 40 | 35 42 49 56 63 70 76 83 90 97 104 111 118 125 132 139 | 0 0.04 0.08 0.12 0.15 0.20 0.24 0.27 0.31 0.34 0.38 0.42 0.46 0.49 0.53 0.57 | 0 0.03 0.07 0.09 0.13 0.16 0.20 0.23 0.26 0.29 0.32 0.35 0.38 0.42 0.45 0.48 | 0 0.05 0.09 0.14 0.19 0.24 0.29 0.33 0.38 0.42 0.47 0.52 0.57 0.61 0.66 0.71 | 0 0.03 0.08 0.11 0.15 0.19 0.22 0.26 0.30 0.33 0.37 0.41 0.44 0.48 0.52 0.56 |
Note. For unreinforced masonry, the values of the coefficient η are accepted as for masonry with a reinforcement of 0.1% or less. When the percentage of reinforcement is more than 0.1% and less than 0.3%, the coefficients η are determined by interpolation.
Table 7. The coefficient of buckling φ with a = 1000
λhnp | λ i np | Buckling coefficient φ | λhnp | λ i np | Buckling coefficient φ |
four five 6 7 eight 9 ten eleven 12 13 14 15 | 14.0 17.5 21.0 24.5 28.0 31.5 35.0 38.5 42.0 45.5 49.0 52.5 | 1.00 0.98 0.96 0.94 0.92 0.90 0.88 0.86 0.84 0.81 0.79 0.77 | sixteen 18 20 22 24 26 28 thirty 32 34 36 38 40 | 56.0 63.0 70.0 76.0 83.0 90.0 97.0 104.0 111 118 125 132 139 | 0.74 0.70 0.65 0.61 0.66 0.52 0.49 0.45 0.42 0.38 0.35 0.31 0.27 |
Table 8. calculated height of walls and pillars
Structural scheme of the building | Type of construction and method of support | Estimated height |
Tough | Articulated bearing Partial clamping on supports Bearing on the wall of precast concrete floor Relying on the wall of the monolithic overlap on four sides | H 0,8N 0.9N 0,8N |
Elastic | Multi-span building Single span building | 1.25H 1.5N |
Free-standing construction | 2.0H | |
Note. The value of H with reinforced concrete precast or monolithic ceilings embedded in masonry, is equal to the height of the floor minus the thickness of the reinforced concrete flooring slab or floor panel. In other cases, the value of H is equal to the height of the floor.
Table 9. The coefficient ω
Type of masonry | Ω value for sections | |
Arbitrary shape | Rectangular section | |
For all types of masonry, except those specified in paragraph 2 From stones and large blocks made of cellular and large-pore concrete, from natural stones (including rubble), from ceramic stones with large voids | 1+ e 0/2 y≤1.45 one | 1+ e 0 / h≤1.45 one |
Note. If 2y <h, then when determining the coefficient ω take the value of h instead of 2y.
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