Main content: In engineering practice, we often encounter the safety calculation of equipment foundation, the calculation of the thickness of the brick membrane, etc. This article mainly describes the strength calculation of masonry, and on this basis, the relevant calculation can be carried out with a little extension. Without further ado, the text is sent:
1. Calculation of masonry compressive strength
In our daily work, the compressive strength of masonry is often replaced by the compressive strength of the block, which is actually inaccurate. Masonry is made of blocks flattened with mortar, so its compression work is very different from that of homogeneous monolithic structural components. Due to the deviation of the thickness of the ash joint, the uneven degree of compactness, and the interaction between the block and the mortar, the compressive strength of the masonry is lower than that of the block. The compressive strength of masonry is calculated as follows:
where: fm: average axial compressive strength of masonry;
f1: the value or average value of the compressive strength grade of the block (brick, stone, block);
f2: average compressive strength of mortar. Units are all in MPa;
K1、K2：系数，取值见表1。
Table 1: Masonry axial compressive strength average value calculation coefficient value table:
| Types of masonry | k1 | A | k2 |
| Sintered ordinary bricks, sintered perforated bricks, autoclaved lime sand bricks, autoclaved fly ash bricks | 0.78 | 0.5 | 当f2＜1时，k2=0.6+0.4f2 |
| Concrete blocks | 0.46 | 0.9 | When f2=0, k2=0.8 |
| Wool stone | 0.79 | 0.5 | 当f2＜1时，k2=0.6+0.4f2 |
| Rubble | 0.22 | 0.5 | 当f2＜2.5时，k2=0.4+0.24f2 |
| 1. K2 is equal to 1 when it is outside the conditions listed in the table. 2. The average value of the axial compressive strength of concrete block masonry, when f2 >10MPa, the multiplier coefficient is 1.1~0.01f2, and the masonry of MU20 should be multiplied by the coefficient of 0.95, and meet the requirements when f1≥f2, f1≤20MPa. |
2. Calculation of tensile strength of masonry
Characteristics of masonry axial tension failure: when the masonry axis is tensioned, there are three failure modes depending on the direction of tensile force. When the axial tension acts parallel to the horizontal ash joint of the masonry, the masonry may fail along the mortar joint section, and the failure surface is toothed, which is called the axial tension of the masonry along the tooth joint section section. Masonry may also fail along the block and vertical mortar joint section, and the failure surface is relatively neat, which is called masonry tension along the axis of the block section. When the axial tension acts perpendicular to the horizontal mortar joint of the masonry, the masonry may be along the through-joint cross-section, which is called the masonry tension along the axial of the horizontal through-joint section. Among them, the axial tensile strength along the through-seam section is very low and should be avoided.
Calculation of the average value of axial tensile strength:
（K3：系数，取值见表2）
Table 2: Table of calculation coefficients for the average value of axial tensile strength, tensile resistance and shear strength of masonry
| Types of masonry | k3 | k4 | K5 | |
| along the gap between the teeth | along the through seams | |||
| Sintered ordinary bricks, sintered perforated bricks | 0.141 | 0.250 | 0.125 | 0.125 |
| Autoclaved lime sand bricks, autoclaved fly ash bricks | 0.09 | 0.18 | 0.09 | 0.09 |
| Concrete blocks | 0.069 | 0.081 | 0.056 | 0.069 |
| Rubble | 0.075 | 0.113 | -- | 0.188 |
3. Calculation of bending tensile strength of masonry
There are also three failure modes of masonry bending and tension. When the tensile stress in the cross-section causes the masonry to fail along the tooth gap section, it is called masonry bending and tension along the tooth gap section; If the masonry is destroyed along the block section, it is called masonry bending and tensioning along the block section; If the masonry is damaged along the through-joint cross-section, it is called masonry bending and tensioning along the through-joint cross-section.
Average flexural tensile strength
(K4：系数，取值见表2）
4. Calculation of shear strength of masonry
Because the strength of the masonry after shearing essentially depends on the bond strength between the mortar and the block, the shear strength of the masonry is mainly determined by the strength of the mortar.
Average shear strength
(K5：系数，取值见表2）
5. Standard value of masonry strength
The standard value of masonry strength is the basic representative value of strength used in structural design, which is determined by the 0.05th quantile of the probability distribution.
Calculation of standard values of masonry strength:
Attached: Other calculation parameters
Schedule 3: Standard value of compressive strength of brick masonry fk(MPa)
| Brick strength grade | Mortar strength grade | Mortar strength | ||||
| M15 | M10 | M7.5 | M5 | M2.5 | ||
| MU30 | 6.30 | 5.23 | 4.69 | 4.15 | 3.61 | 1.84 |
| MU25 | 5.75 | 4.77 | 4.28 | 3.79 | 3.30 | 1.68 |
| MU20 | 5.15 | 4.27 | 3.83 | 3.39 | 2.95 | 1.50 |
| MU15 | 4.46 | 3.70 | 3.32 | 2.94 | 2.56 | 1.30 |
| MU10 | 3.64 | 3.02 | 2.71 | 2.40 | 2.09 | 1.07 |
Schedule 4: Standard value of compressive strength fk (MPa) of concrete block masonry
| Block strength grade | Mortar strength grade | Mortar strength | |||
| M15 | M10 | M7.5 | M5 | ||
| MU20 | 9.08 | 7.93 | 7.11 | 6.30 | 3.73 |
| MU15 | 7.38 | 6.44 | 5.78 | 5.12 | 3.03 |
| MU10 | -- | 4.47 | 4.01 | 3.55 | 2.10 |
| MU7.5 | -- | -- | 3.10 | 2.74 | 1.62 |
| MU5 | -- | -- | -- | 1.90 | 1.13 |
Schedule 5: Standard value of compressive strength of wool stone masonry fk(MPa)
| Stone strength grade | Mortar strength grade | Mortar strength | ||
| M7.5 | M5 | M2.5 | ||
| MU100 | 8.67 | 7.68 | 6.68 | 3.41 |
| MU80 | 7.76 | 6.87 | 5.98 | 3.05 |
| MU60 | 6.72 | 5.95 | 5.18 | 2.64 |
| MU50 | 6.13 | 5.43 | 4.72 | 2.41 |
| MU40 | 5.49 | 4.86 | 4.23 | 2.16 |
| MU30 | 4.75 | 4.20 | 3.66 | 1.87 |
| MU20 | 3.88 | 3.43 | 2.99 | 1.53 |
Schedule 6: Standard value of compressive strength of rubble masonry fk(MPa)
| Rubble strength grade | Mortar strength grade | Mortar strength | ||
| M7.5 | M5 | M2.5 | ||
| MU100 | 2.03 | 1.80 | 1.56 | 0.53 |
| MU80 | 1.82 | 1.61 | 1.40 | 0.48 |
| MU60 | 1.57 | 1.39 | 1.21 | 0.41 |
| MU50 | 1.44 | 1.27 | 1.11 | 0.38 |
| MU40 | 1.28 | 1.14 | 0.99 | 0.34 |
| MU30 | 1.11 | 0.98 | 0.86 | 0.29 |
| MU20 | 0.91 | 0.80 | 0.70 | 0.24 |
Schedule 7: Standard values of axial tensile strength ft,k, standard values of flexural tensile strength ftm,k and standard values of shear strength fv,k(MPa) when failing along the section of masonry mortar joints:
| Intensity category | Destruction characteristics | Types of masonry | Mortar strength grade | |||
| ≥M10 | M7.5 | M5 | M2.5 | |||
| Axial tension | along the gap between the teeth | Sintered ordinary bricks, sintered perforated bricks, autoclaved lime sand bricks, autoclaved fly ash bricks, concrete blocks, rubble | 0.300.190.150.14 | 0.260.160.130.12 | 0.210.130.100.10 | 0.15--0.07 |
| Flexural tensile strength | along the gap between the teeth | Sintered ordinary bricks, sintered perforated bricks, autoclaved lime sand bricks, autoclaved fly ash bricks, concrete blocks, rubble | 0.530.380.170.20 | 0.460.320.150.18 | 0.380.260.120.14 | 0.27--0.10 |
| along the through seams | Sintered ordinary bricks, sintered perforated bricks, autoclaved lime sand bricks, autoclaved fly ash bricks, concrete blocks, rubble | 0.270.190.12 | 0.230.160.10 | 0.190.130.08 | 0.13-- | |
| Shear resistance | Sintered ordinary bricks, sintered perforated bricks, autoclaved lime sand bricks, autoclaved fly ash bricks, concrete blocks, rubble | 0.270.190.150.34 | 0.230.160.130.29 | 0.190.130.100.24 | 0.13--0.17 |