Calculation of compressed elements with mesh reinforcement at eccentric application of load at low eccentricities for a rectangular section (ℓ0 <017h) is carried out according to the formula
N≤mgφ1RskbA (1-2ℓ0 / h) ω, (19)
where Rskb≤R2 is the calculated resistance of reinforced masonry under eccentric compression, determined with a grade of solution 50 and higher by the formula
Rskb = R + 2μRs / 100 (1-2 l 0 / y). (20)
For eccentricities in rectangular sections ℓ0 <0.17h, as well as for λh> 15 or λ i > 53, mesh reinforcement should not be used. The percentage of reinforcement of masonry with mesh reinforcement is limited and should not exceed
μ = 50R / (1-2ℓ0 / y) Rs≥0.1.
Task 2.8. determine the carrying capacity of a brick pillar with a size in plan of 64 × 77 cm with an estimated height of Net = 8.4 m. the calculated longitudinal force, taking into account the reliability coefficient for the purpose N = 1200kN. Eccentricity of load application ℓ0 = 5 cm; height of the beam supported on the pole, 30 cm. Brick plastic extrusion brand M 200, solution brand M 75. Ng = 90kN-long-acting load.
Decision. The area of the column A = 64 * 77 = 4930 cm2. Elastic masonry characteristics according to the table. 3. equal to a = 1000; λh = 840/64 = 13,125 and table. 2.5 φ = 0.81. the calculated resistance of masonry (according to table. 1). R = 25 kg / cm2 = 2.5 MPa. The ultimate force in unreinforced masonry is determined by the formula (12)
N = mgωφAR (1-2ℓ0 / h) = 0.81 * 1.08 * 0.995 * 4930 * 2.5 (1-2 * 5/64) =
= 905.4 kN <1200 kN;
ω = 1 + ℓ0 / h = 1 + 5/64 = 1.08 <1.45;
η determined by the table. 6 with the percentage of longitudinal reinforcement 0.1;
mg = 1-ηNg / N = 1-0.062 * 90/1200 = 1-0.00465 = 0.995.
The strength of the masonry is not provided, so it must be reinforced with nets. Accept the grid of reinforcement class BP-I (used with a coefficient γs = 0.6). The value of the elastic characteristics for masonry with mesh reinforcement is calculated by the formula (2.6.)
Ask = a * Ru / Rsku; Rsku = kR + 2Rsnμ / 100.
We take in the first approximation the percentage of reinforcement μ = 0.15, then
Rsku = 2 * 2.5 + 2 * 350 * 0.15 / 100 = 6.05MPa <1.8 * Ru = 9MPa.
We calculate a sk = 1000 5.0 = 826.
6.05
With a sk = 826λh = l0 / h = (840-30) / 64 = 12.65
φ1 = 0.805.
Estimated compressive strength of the mesh-reinforced masonry,
Rsk = R + 2μRs / 10 = 2.5 + 2 * 0.15 350 = 3.55 MPa.
100
The bearing capacity of the column is determined by the formula (2.11)
N≤N sech = mgφ1RAcω;
N≤Nsech = 0.995 * 0.805 * 0.355 * 64 * 77 * 1.08 = 1401.3кН> 1200кН,
Accept rebar ø 4mm with f a = 0,126 cm2, mesh size 5 cm. When μ = 2 f a / cs = 0.15, the grid spacing is equal to
s = 2 f a / μc = 2 * 0.126 100 = 33.6 cm
0.15 * 5
Grid set through two rows of brickwork.
Table 1. Baseline data for task 1
Option number | Geometrical dimensions | HeightH, m | Brand solution | Type of masonry | Brand of stone | Type of overlap or method of support | |
a cm | b, cm | ||||||
one 2 3 five 6 7 eight 9 ten eleven 12 13 14 15 | 51 64 51 39 79 51 59 51 51 59 64 51 51 64 | 64 64 77 79 79 64 80 77 64 80 77 64 77 51 | 4.2 6.4 7.4 5.3 8.7 6.5 4.0 5.2 3.9 8.2 6,6 4.5 5.6 7,6 | 25 50 50 25 50 100 25 75 50 75 50 100 25 75 | Silicate Pressed plastic clay Ceramic Stone Concrete Concrete Silicate Cellular concrete Clay hollow Plastic pressing Concrete with voids Semi-dry clay pressing Silicate Ceramic Stone Plain Clay Plastic Molding | 150 250 125 75 100 125 100 300 125 75 100 200 50 125 | Articulated Precast Concrete Monolithic overlap Articulated Free-standing construction Precast Concrete Articulated Partial clamping on supports Monolithic overlap Articulated Free-standing construction Partial overlap Precast Concrete |
Table 2. Initial data for task 2
Option number | Geometrical dimensions a, cm | Floor height H, m | LoadN, kN | Type of overlap or method of support | Type of brick (stone) | Mark brick (stone) |
one 2 3 four five 6 7 eight 9 ten eleven 12 13 14 15 | 51 64 51 51 39 79 51 59 51 51 59 64 51 59 39 | 64 5.2 4.6 7.4 4.8 5.3 6.3 8.7 4.2 5.7 10.1 8.2 6,6 7.4 5.2 | 86 140 235 95 200 400 120 180 260 55 540 100 320 280 198 | Prefab Articulated Monolithic overlap Partial clamping on supports Articulated Also Free-standing construction Articulated Prefab Free-standing construction Articulated Monolithic overlap Articulated Articulated Articulated | Silicate Clay plastic pressing Ceramic Stone Ceramic hollow Concrete Also Silicate Cellular concrete Clay hollow semi-dry pressing Concrete with voids Semi-dry clay pressing Silicate Ceramic Stone Ceramic hollow Silicate | 150 250 125 100 75 100 125 100 300 125 75 100 200 100 150 |
Table 3. baseline data for task 3
Option number | Geometrical dimensions a, cm | Floor height H, m | Type of brick | Brand of brick | Brand solution | load | |
Long ng, kN | TotalN, kN | ||||||
one 2 3 four five 6 7 eight 9 ten eleven 12 13 14 15 | thirty 51 64 51 51 50 38 51 51 80 77 64 51 77 51 | 5.6 6.4 7.2 4.8 10.2 9.1 11.2 5.4 6.8 7.5 6.2 10.2 8.2 6.4 7.0 | Aerated Concrete Stone Silicate Clay plastic pressing Ceramic Stone Ceramic hollow Cellular concrete Clay hollow semi-dry pressing Clay hollow semi-dry pressing Silicate Concrete stones with voids Semi-dry clay pressing Silicate Clay hollow semi-dry pressing Semi-dry clay pressing Silicate | 75 200 250 100 75 50 200 125 150 125 100 300 125 100 200 | 25 50 25 75 100 75 100 50 25 50 25 100 75 50 75 | 230 140 70 70 180 240 40 90 80 120 100 250 110 87 160 | 450 240 95 120 300 420 80 160 100 350 180 510 180 210 320 |
Table 4. initial data for problem 4.
Option number | Geometrical dimensions, cm | LoadN, kN | Type of brick (stone) | Brand solution | Mark brick (stone) | |||||
b1 | h | h0 | d | b2 | ℓ0 | |||||
one 2 3 four five 6 7 eight 9 ten eleven 12 13 14 15 | 121 121 119 120 110 90 116 142 120 116 142 142 119 90 121 | 102 102 116 102 102 102 102 103 102 103 103 103 116 102 102 | 38 38 41 38 38 38 38 51 38 51 51 51 41 38 38 | 64 64 75 64 64 64 64 52 64 52 52 52 75 64 64 | 51 51 59 38 39 38 77 51 77 100 51 51 59 38 51 | 18 36 20 eight 14 12 22 thirty 15 12 eight ten sixteen 18 14 | 200 350 120 70 300 420 160 250 180 400 100 360 95 64 85 | Silicate Clay plastic pressing Aerated Concrete Stone Concrete stone Semi-dry clay pressing Silicate Clay hollow plastic extrusion Clay plastic pressing Ceramic Stone Ceramic hollow stone Aerated Concrete Stone Brick hollow semi-dry pressing Silicate Concrete stone Silicate | 50 25 25 50 100 75 50 25 100 50 25 50 75 50 25 | 125 200 75 150 100 300 100 250 150 100 50 150 100 150 150 |
Table 5. baseline data 5
Option number | Geometric dimensions of the cross section of the column, cm | Height H m | Loads | Eccentricity ℓ0, cm | Brand of brick | Brand solution | Dimensions of reinforced concrete slab, cm | ||
a | b | Ng, kN | N, kN | ||||||
one 2 3 four five 6 7 eight 9 ten eleven 12 13 14 15 | 51 64 51 51 39 79 51 59 51 51 59 64 51 51 64 | 64 64 77 51 79 79 64 80 77 64 80 77 64 77 51 | 4.8 7.2 6.4 5.2 10.2 8.3 9.6 11.5 8.6 6.8 7.5 4.2 5.4 6.0 8.2 | 230 140 70 70 180 240 40 90 80 120 100 250 1100 260 70 | 450 240 95 120 300 420 80 160 100 350 180 510 360 480 160 | eight five 12 7 four eight 15 ten 6 17 14 12 five eleven eight | 150 250 125 100 75 100 125 100 300 125 75 100 200 50 125 | 50 25 75 50 100 75 50 50 100 50 25 50 75 50 25 | 22 18 sixteen 20 20 26 thirty 24 22 sixteen 20 18 24 22 24 |
Table 6. baseline data 6.
Option number | Geometrical dimensions, cm | load | Floor height, N, m | Type of brick (stone) | Brand solution | Mark brick (stone) | |||||
b1 | h | h0 | d | b0 | N, kN | M, kN m | |||||
one 2 3 four five 6 7 eight 9 ten eleven 12 13 14 15 | 121 121 119 120 110 90 116 142 120 116 142 142 119 90 121 | 102 102 116 102 102 102 102 103 102 103 103 103 116 102 102 | 38 38 41 38 38 38 38 51 38 51 51 51 41 38 38 | 64 64 75 64 64 64 64 52 64 52 52 52 75 64 64 | 51 51 59 38 39 38 77 51 77 51 51 51 59 38 51 | 380 120 98 420 340 600 250 180 230 100 280 460 260 400 300 | 150 80 200 50 120 64 100 94 160 35 80 150 60 110 88 | 4.5 8.2 7,8 6.3 5.0 5.6 8.4 10.1 6.8 7.3 8.6 4.6 9.3 7.0 6.1 | Silicate Clay plastic pressing Cellular concrete Ceramic Stone Concrete stone Semi-dry clay pressing Silicate Clay hollow plastic extrusion Clay plastic pressing Ceramic Stone Ceramic hollow stone Also Aerated Concrete Stone Ceramic hollow semi-dry pressing Silicate | 125 50 25 75 50 50 25 75 100 50 25 25 25 50 75 | 125 200 50 150 75 300 100 150 250 150 100 100 50 150 75 |
Table 7. baseline data for task 7.
Option number | Floor height H, m | Load | The height of reinforced concrete slab, cm | Type of brick | Brand solution | |
N, kN | M, kN m | |||||
one 2 3 four five 6 7 eight 9 ten eleven 12 13 14 15 | 4.8 7.2 6.4 5.2 10.2 8.3 9.6 11.5 8.6 6.8 7.5 4.2 5.4 6.0 8.2 | 380 120 98 420 340 600 250 180 230 100 280 460 260 400 300 | 150 80 200 50 120 64 100 94 160 35 80 150 60 110 88 | 22 18 sixteen 20 26 thirty 24 22 sixteen 20 18 24 thirty 22 24 | Silicate, 125 Clay plastic molding, 200 Stone of cellular concrete, 75 Concrete Stone, 150 Clay semi-dry pressing, 100 Silicate, 300 Clay hollow plastic extrusion, 100 Clay plastic molding, 250 Ceramic Stone, 150 The stone is ceramic hollow, 100 Stone of cellular concrete, 50 Brick hollow semi-dry pressing, 150 Silicate, 100 Concrete Stone, 150 Silicate, 150 | 125 50 25 75 75 50 50 75 100 50 25 100 75 50 25 |
Task 7. Determine the bearing capacity of the stone pillar under central and eccentric loading according to the table. 7
Task 6. Determine the geometric dimensions of the stone column of rectangular cross-section with a different method of support according to the table. 6
Task 5. Determine the required brand of brick for masonry T-section eccentric-loaded according to the table. 5 (see fig. 2.2).
Task 3. Determine the strength of the laying of the inner bearing wall according to Table. 3
Task 4. Determine the strength of the eccentric-loaded masonry of the T-section according to the table. 4 with an eccentricity - in the direction of the edge (see figure 2.2).
Task 1. Determine the strength of a centrally loaded stone pillar with different support for it, taking into account the brutal design of the building according to the table. one
Task 2. Determine the width of the brick pier at a given thickness according to Table. 2
Questions for self-test
on the topic "Stone and Arkamkamen
constructions "
1. Materials for stone and reinforced stone structures.
2. Types of masonry and their characteristics.
3. Advantages and disadvantages of stone structures.
4. Types of artificial stones and characteristics and differences.
5. Types of natural stones, brand, scope.
6. Types of solutions, brand, method of application.
7. Requirements of strength and durability for stone materials.
8. Stages of masonry work in axial compression.
9. Factors affecting the strength of the masonry.
10. Determination of the average tensile strength (temporary resistance) of masonry in compression.
11. Deformative properties of masonry.
12. The modulus of deformation and its value.
13. The phenomenon of creep during prolonged loading masonry.
14. The work of masonry under tension and shear.
15. determining the temporal resistances.
16. What are the stresses experienced brick (stone) in the masonry during compression.
17. What are the stages of the work of the centrally compressed masonry.
18. Constructive strength of masonry and its dependence on the strength of the stone.
19. What are the deformation properties of masonry?
Determination of the modulus of deformation of the masonry.
20. Types of design limit states of the clutch.
21. How are the limits of strength and design resistance of masonry in compression, tension, shear and bending?
22. Determination of flexibility of compressed elements.
23. Accounting for the effect of flexibility on the carrying capacity of compressed elements.
24. The work of masonry in non-central compression.
25. What are the features of laying and bending?
26. Work masonry with local compression. As determined in this case, the calculated resistance of the masonry.
27. Types of reinforced structures, their characteristics and applications.
28. Mesh reinforcement.
29. Work of grids at the central and eccentric compression.
30. Longitudinal reinforcement. Features work masonry.
31. Calculation of longitudinal reinforcement.
32. How is the calculated resistance to compression of reinforced masonry determined?
33. How is the elastic characteristic and coefficient of buckling of the masonry with mesh reinforcement determined?
34. What are complex structures? Their device and work.
35. Ways to strengthen the clutch clips. Influence of clips on the work of masonry in compression?
36. Ways of making connections between elements of a building.
37. What are the signs distinguish buildings with a rigid structural scheme.
38. The actual and design scheme of the building with a rigid structural scheme.
39. How is the flexibility of walls and pillars determined?
40. The design scheme of the building with an elastic structural scheme.
41. In which cases the building is dismembered by temperature-shrinkable seams?
42. Construction of expansion joints.
43. Types of winter laying.
44. Features of winter laying.
45. Quality control and masonry effort.
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