- Timber structure
- Determination of the dimensions of the section of a wooden beam by formulas
- Calculation of a wooden beam according to the schedule
The choice of wood flooring is most often due to the environmental friendliness of the material and ease of installation. The overlap will last a long time and will be reliable if the beams are correctly calculated. The main condition for determining the required section dimensions is to ensure the strength of the structure.
Wooden flooring is inferior in terms of strength and stiffness to reinforced concrete, so it is suitable in residential buildings up to four floors. Beams are made from coniferous forests (pine, spruce, fir, etc.). The length of the beams is most often 5–6.5 m. In stone buildings, beams are laid at a distance (along the axis) that is a multiple of the size of bricks or blocks.
1. Blind termination. 2. Open termination. 3. Joining the beams butt. 4. Connecting the beams apart. a – brick wall, b – beam, c – internal support, d – metal plate e – waterproofing
Beams are sealed into the external stone walls with a deaf and open method. Regardless of the method of embedding, it is necessary to provide measures to prevent condensation of air vapors in the nests of the walls. This happens when they are less than two bricks thick. In thicker walls, condensation does not form in the nests.
The depth of the socket for supporting the beam in stone buildings, based on the compressive strength of the masonry, is taken as 0.6–0.8 h (h is the beam height). The minimum support size is 150 mm. Usually it is taken 180-200 mm. In this case, the beam should not reach the wall by 3–6 cm in order to provide air access to its end.
The floor beams are impregnated with antiseptic compounds, and the end is necessarily insulated with two layers of waterproofing (roofing paper, glassine). The space between the wall and the side surface of the beam is filled with mortar.
Every third beam must be anchored to the outer wall. The anchor is embedded into the wall at one end, and the arc end is attached to the beam. They are also connected to each other when resting on internal walls..
The subfloor is laid in two ways:
- Shields or boards are laid on the cranial bars using overhead strips.
- Continuous laying of shields (boards) directly on the cranial blocks.
Beams and logs are lined from below with shields made of thin boards, gypsum board, gypsum board, OSB or other sheet materials. Membrane insulation is laid on which a heat and sound insulating layer is laid. It can be bulk, slab or roll insulation, laid between the beams.
1. Floor beams. 2. Binder. 3. Rough floor. 4. Insulation 5. Vapor barrier
A vapor barrier layer is also arranged on the thermal insulation. Next, a clean floor is made, which can be attached to the logs or directly to the beams. The lags are laid on the floor beams. A gap is left between the insulation and the upper edge of the beams for air access to the wooden floor structures.
Floor and ceiling coverage depends on the performance of the room and the interior design solution. Almost any floor can be made on wooden beams (boardwalk, parquet, linoleum, ceramic tiles, etc.).
Beams are attached to each other using special metal products.
Determination of the dimensions of the section of a wooden beam by formulas
More often, the load-bearing elements of the interfloor or attic floor are beams with one span and free support on the load-bearing wall or pillar.
1. Round log. 2. A bar with two edges. 3. Beam, four edges. 4. Composite beam. 5. LVL timber. 6. Nascor beam 7. Board
They perceive the bending due to the weight of the entire floor and temporary payload (furniture, people, etc.). The required dimensions of the beam are determined by calculation. The prerequisite for this is the specified strength and stiffness of the supporting element..
To determine the loads on a beam, the density of coniferous wood for structures of premises with normal operation is taken to be 500 kg / m3. For wet rooms and outdoor structures – 600 kg / m3.
The flexural strength of softwood is 75 MPa. The stiffness index (elastic modulus E) determines its ability to deform under the action of any loads.
For normal operating conditions of structures under the action of loads:
- E = 10,000 MPa – along the fibers;
- across the fibers, the E index decreases by almost 50 times.
Temperature also affects the reliability of wood. In the case of its increase, the tensile strength and the elastic modulus decrease. This increases the fragility of wood products. The same happens when exposed to negative temperatures..
For the calculation of any structure, standard and design loads are determined. The design load is obtained by multiplying the value of the standard load by n – the coefficient of reliability (overload), which takes into account the conditions under which the structure operates.
The strength of the beam is checked by the action of the maximum bending moment:
? = M / WR ? Rand
- ? – tension in the beam;
- WR – calculated moment of resistance;
- Rand – design bending resistance, which for coniferous wood is 13 MPa.
Section selection is calculated based on the required moment of resistance Wtr:
Wtr = M / Rand
For a rectangular section:
For round sections:
The stiffness is checked for the action of the standard loads:
- f is the ultimate deflection of the beam;
- l – design beam span in cm;
- f / l – relative deflection, which should not exceed: 1/250 – for floors between floors; 1/200 – for attic floors;
- J – moment of inertia in cm4;
- qn – standard load in kg / running. cm;
- E = 10,000 MPa, 100,000 kg / cm2 – modulus of elasticity of wood;
- c is the maximum permissible coefficient for the ratio l / h, where h is the height of the beam section: 18.4 – for interfloor floors; 23.0 – for attic floors.
In the case when l? ch, the beams are only checked for strength. If l > ch, they are checked only for hardness.
For example, let’s calculate the wooden beam of the interfloor ceiling. Span l = 4.5 m; floor weight – g = 200 kg / m2; live load p = 150 kg / m2; the distance in plan between the axes of the beams is a = 0.9 m; beam material – pine Rand = 130kg / cm2; m coefficient of working conditions – 1.0.
Estimated load for 1 running. m element:
q = (gnn + pnn1) · A = (200 • 1.1 + 150 • 1.4) • 0.9 = 387 kg / running. m
- n, n1 – reliability factors of permanent and temporary payloads.
The moment of resistance that is required is determined from the strength condition:
Table of moments of resistance W in cm3 rectangular sections
b h 8 nine ten eleven 12 13 fourteen 21 588 661 735 808 882 955 1029 22 645 726 807 887 968 1049 1129 23 705 793 882 970 1058 1146 1234 24 768 864 960 1056 1152 1248 1344 25 833 937 1041 1146 1250 1354 1458 26 901 1014 1127 1239 1352 1465 1577
According to specially calculated tables, you can choose a rectangular section of the element – bхh. We accept a beam 8×24 cm (W = 768 cm3). In the case under consideration, the ratio l / h = 450: 24 = 18.75, and the maximum allowable c = 18.4 – for interfloor floors. Based on this, the calculation for the deflection is not performed..
Calculation of a wooden beam according to the schedule
For the convenience of the selection of wooden floor beams according to the above formulas, graphs have been drawn up, according to which, having the values of l and q, the width and height of the beam are found. The horizontal line a – a defines the boundary where the calculation is carried out either for strength or deflection.
If the point of intersection of l and h is below the line a – a, the calculation is carried out for strength according to the calculated load, above the line a – a – the calculation is carried out for deflection according to the standard load. This graph has the following indicators:
E = 130 kg / cm2; f = 1/250 l; E = 100,000 kg / cm2; mn = 1.0.
When these values change, the relative increase or decrease in the received data is found. For example, for a bar with a cross section of more than 14 cm, the coefficient of operating conditions will be 1.15 and, accordingly, the calculated resistance Rand = 150 kg / cm2, and for a log, the coefficient of operating conditions is 1.25, while Rand = 160 kg / cm2.
As an example, consider the following option: l = 6.1 m; b = 26 cm; l / h = 610: 26 = 23.4 > 18.4, therefore, the calculation is carried out for the deflection.
For a standard load according to the schedule qн = 360 kg / m according to the schedule b = 18.3 cm.
f = 1/200 l. Since the graph was drawn up for the beams of the attic floor, we specify it for an interfloor floor with a relative deflection f / l = 1/250. 200/250 = 0.8; b = 0.8 • 18.3 = 14.64 cm. Finally, you can take a beam for a floor beam 15×260 cm.
The height of the beams when selecting the section should be greater than the width, since in this position they work better for bending. Correctly selected size of floor beams will provide real savings in material while ensuring the reliability and durability of the entire structure.