How many lumber 150x150 in a cube: solve the problem of

19-07-2018

Building

How many cubed timber is 150x150? How much does a house weigh from this bar? How many piles do you need for a screw foundation of a house of known area?

We will devote today's article to solving simple mathematical problems that confront the builder in the process of building a private house with their own hands.

Construction begins with purchases. Purchases - with the calculations.

Reference data

In the beginning - some useful information and reference data that will help us in the decision.

Density

Density бруса из лиственницы оценивается в 680 килограмм на кубометр.
Density сосны примерно равна 530 кг/м3.
El - 460 kg / m3.
Cedar - 440 kg / m3.
Fir - 390 kg / m3.
Oak - 720 kg / m3.
Beech - 650 kg / m3.
Birch - 640 kg / m3.
Lipase - 540 kg / m3.
Aspen - 500 kg / m3.

It is necessary to clarify: the average values are given. The actual density depends on the moisture content of the wood, on the region of its growth, on the salinity of the soil and on the mass of additional factors. The scatter for one breed can reach 20 percent.

Thermal conductivity

Requirements for thermal resistance of walls are set out in SNiP 23-02-2003.

We give some values for different cities of Russia.

For Petropavlovsk-Kamchatsky, the rated thermal resistance of the walls should be 3.33 m2 * C / W.
For Anadyr - 4.89 m2 * C / W.
Verkhoyansk - 5.6 m2 * C / W.
Krasnoyarsk - 3.59 m2 * C / W.
Salekhard - 4.46 m2 * C / W.
Murmansk - 3.68 m2 * C / W.
Kursk - 2.9 m2 * C / W.
Moscow - 3.15 m2 * C / W.
St. Petersburg - 3.06 m2 * C / W.
Sochi - 1.83 m2 * C / W.

What is the thermal conductivity of popular building materials?

The thermal conductivity of reinforced concrete is estimated at 1.69 W / (m * s).

Curiously: thermal conductivity is often estimated in other terms - W / (m * K). Let it not confuse the reader: there is no practical difference between the Celsius scale and the Kelvin scale in our case.

As you can see, there is no practical difference when changing the temperature difference.

Thermal conductivity красного глиняного кирпича равна 0,56 Вт/(м*С).
Foam concrete has a thermal conductivity of 0.09 - 0.28 W / (m * s). The exact value depends on the percentage of porosity.
For wood, heat conduction is distinguished across and along fibers. So, for spruce across the fiber, it is 0.09 W / (m * C), then along it is twice as large.
For oak, these values are 0.12 and 0.23 W / (m * C), respectively.
The thermal conductivity of mineral wool at a packing density of 100 kg / m3 is estimated at 0.056 W / (m * s). At a density of 50 kg / m3, the thermal conductivity decreases to 0.048 W / (m * C): the best heat insulator, as we remember, is air.
For foam, a value of 0.03 W / (m * C) is usually taken. However, dense extruded polystyrene foam (150 kg / m3) has a thermal conductivity as low as 0.05 W / (m * s).

How, knowing the characteristics of materials and requirements for the wall, calculate its minimum thickness? The instruction is simple: you just need to multiply the calculated thermal resistance by the thermal conductivity of the material.

Practical tasks

Volume

How many cubes in a log are 150x150 in running meters?

Or, if you slightly complicate the task - how many pieces are in a cube of a bar 150x150x6000?

Volume одного погонного метра - 1х0,15х0,15=0,025 м3.
The answer to the question of how much timber in 1 cube is 150 150 is reduced to solving a simple arithmetic division problem: the number of meters is 1 / 0.025 = 40.
To find out how many pieces in a cube is 150 by 150, you only need to divide the total number of meters by the length of one beam. So, for six-meter segments, we get 40/6 = 6.7; for a timber 3.5 meters long - 40 / 3.5 = 11.4.

What will be the total volume of the external walls of the house in two floors, if its size is 8x8 meters with a floor height of 3 meters?

Material - all the same timber 150x150 mm.

Like other lumber, timber is usually sold in cubic meters.

The total length of the walls is 8x4 = 32 meters.
The height of the outer walls is 3x2 = 6 meters. Area - 32 * 6 = 192 m2.
As we remember, the thickness of the timber is 15 centimeters, or 0.15 m. Accordingly, the total volume required for the construction of the wall of the timber is 192x0.15 = 28.8 m3.

Please note: in practice, the timber is purchased with a margin of at least 10 percent. In addition, the calculations are usually somewhat more complicated: the beam goes not only on the walls, but also on the gables, and on the supporting beams of the floors.

Load on the foundation

The foundation calculation begins with a rough estimate of the load. It is the mass of the building that determines the requirements for the strength of the foundation itself, and the depth of its laying; for screw piles, it is necessary to estimate their approximate quantity.

How to calculate how much the house weighs? Detailed assessment of the mass of all structures, property, residents, snow on the roof and other factors is quite problematic. However, it has long been noticed that a more or less balanced design has a total mass of approximately twice the mass of external bearing walls.

Thus, to estimate the load on the foundation, we only need to calculate the mass of the walls at a known density of the material and multiply it by two.

Let us, as an example, calculate the mass of a one-story house with an area of 100 m2 square in plan. The height of the floor is the same three meters as in the previous example; material - cedar timber section 150x150 millimeters.

Cedar is chosen by us for its resistance to decay; at the same time, the price for a cubic meter is about half that of a slightly more resistant larch.

With a square-shaped house of 100 m2, the length of each wall, if its thickness is neglected, will be 10 meters.
The total length of the walls is 10 + 10 + 10 + 10 = 40 meters.
The area of three-meter walls is 40x3 = 120 m2.

Pay attention, we need an approximate, estimated calculation. We deliberately neglect the area of the gable roof gables, which will increase the load on the foundation, and the area of the openings (door and window), which will reduce it.

Volume материала стены равен 120х0,15=18 кубометров.
With a cedar wood density of 440 kg / m3, the total mass of external walls can be estimated at 18x440 = 7920 kg.
The total weight of the house will be approximately 16 tons.

The carrying capacity of the most popular screw piles of 108/300 section (pipe / blade) depends on the type of soil and is usually 2-4 tons per piece. In our case, no more than 8 piles will be required.

In practice, however, their number is influenced not only by the carrying capacity, but also by the layout of the house: piles are installed at all corners and under the crossings of the internal partitions. In addition, with a wall length of 10 meters, she will definitely need at least two additional supports in the middle.

Warming

How to calculate the required thickness of the wall and find out whether it needs additional insulation?

If reference data is available, it all comes down to a simple mathematical task. It is not much more difficult than calculating how much cubed timber is 150 by 150 by 6 meters.

The formula mentioned above: the wall thickness in meters is equal to the product of the rated thermal resistance and the thermal conductivity of the material. Let's do as an example a simple calculation of the minimum wall thickness for Anadyr.

The material will be pine timber.

In the photo - winter in Anadyr. In January, the temperature drops to -45 degrees.

The target thermal resistance is 4.89 m2 * C / W.
Since the direction of heat exchange with the street will be perpendicular to the wood fibers, we can proceed from the thermal conductivity of pine at 0.09 W / (m * s).
The minimum wall thickness of the timber for Anadyr is 4.89 x0.09 = 0.4401 meters.

Но в нашем распоряжении только брус размером 150х150! Что делать? Класть его в три ряда? В этом случае стоимость строительства станет запредельной, да и надежная перевязка слоев стены будет проблематичной…

The exit is simple: the wall from a single bar is warmed outside. The crate is packed on it, into which is placed mineral wool or any other vapor-permeable insulation. Then the insulation is closed by a windproof membrane and is sewn with wooden lining, vinyl siding, professional sheet or any other material at the discretion of the builder.

What should be the thickness of the insulation? Let's calculate.

With a thickness of 0.15 meters, the beam will give a thermal resistance of 0.15 / 0.09 = 1.67 m2 * C / W. Insulation should provide 4.89-1.67 = 3.22 m2 * C / W.

If we use mineral wool with a density of 50 kg / m3 (thermal conductivity of 0.048 W / m * C) as a thermal insulation material, its minimum thickness will be 3.22 x 0.048 = 0.154 meters.

Taking into account the additional protection that the cladding will provide, it is possible with a light heart to recommend 150 mm insulation mats for timber. If you want to be safe, it is permissible to use two layers of 100 mm with overlapping seams.

External warming of walls from a bar. Mineral wool is protected from wind blowing.

Conclusion

As you can see, with the availability of reference data calculations are not too complicated. And the video in this article will complement our narrative with visual information. Successes in construction!