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To design the raft foundation properly, it's essential to understand the load it will bear from the weight of roofs, walls, and any additional imposed loads. A simpler model assumes that each element does not deform and behaves like a rigid body. This allows for calculating how the various forces are literally channeled towards the walls in contact with the raft foundation.

In particular, the following components are considered for:

Walls:

• SIP panel

• Exterior siding

• Interior drywall

Mezzanine forming the ceiling for the first floor:

• SIP panel

• Interior drywall

• Warehouse and hallway overburden

Roof:

• SIP panel

• Zinc colonial tile

>Model

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The original specification of the raft foundation is summarized in cross-section M1:

and in cross-sections M2 and M3:

which can be summarized as:

• Continuous foundation

• Reinforcement bars Fi 12 mm

• Subbase

• Concrete footing G17

• Raft foundation of 15 cm concrete G17

• Polyethylene ground cover

• Compacted base

• Acma C92 mesh

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The walls of the house that are in contact with the raft foundation are shown in the following diagram:

The vast majority of walls (all except those on the northwest, northeast, and the interior west and east) are 4.5 meters long, 2.45 meters high, and 11.4 centimeters wide.

The northwest and northeast walls have an upper part that is not horizontal and can be up to 2.4 meters higher than at the other end.

All walls outside the north, northwest, and northeast orientations support the mezzanine. In the case of the west-northwest, southwest, west-west, west-south, east-northeast, southeast, east-east, and east-south walls, there is a triangle that sits above the mezzanine and supports the roof.

Additionally, there are internal walls in the left (west) and right (east) modules.

Finally, there are both central beams and roof supports covering all three modules.

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The basic shapes of the SIP panels forming the walls are:

The SIP panel consists of two pressed wood sheets and a core of plastic foam for insulation, as shown in the image:

The width of each element is measured between the outer edges of the two pressed wood sheets and is utilized in thicknesses of 90 mm, 114 mm, and 162 mm.

The vast majority of the walls are of the type 114 mm wide, 4.5 m long, and 2.45 m high. With a density of 20.81 kg/m2, their respective masses are 229.43 kg. In twelve cases (WN, W, WW, WS, WE, S, EW, ES, EE, E, EN, and N), they are external walls, so they have siding typically weighing 9 kg/m2 on one side and gypsum board typically weighing 7.1 kg/m2 on the other side. In two cases (SW and SE), the walls are internal, so they have gypsum board on both sides. In summary, the weights are:

Two of the walls that do not border the mezzanine (NW and NE) are of the type 114 mm wide, 4.5 meters long, and 2.45 meters high on one side and 4.85 meters on the other. With a density of 20.81 kg/m2, their respective masses are 341.80 kg. Since they are external walls, they have siding of typically 9 kg/m2 on one side and gypsum board of typically 7.1 kg/m2 on the other side. In summary, the weights are:

In eight of the cases (walls WN, SW, WW, WS, SE, EN, EE, and ES), there are triangular elements that go over the mezzanine and are of the type 114 mm wide, 4.5 meters long, and 2.384 meters high. In six cases, they are external walls, so they have siding of typically 9 kg/m2 on one side, but being part of the loft, they do not have gypsum board on the inside. In two cases, they are internal, but they only have gypsum board covering typically 7.1 kg/m2 on one side. In summary, the weights are:

Finally, there are two groups of internal walls that only support the mezzanine. They are of the type 90 mm wide with 2.45 meters high and, in the case of the west wall, a total length of 15.62 meters and, in the case of the east wall, a total length of 14.76 meters. Therefore, the surfaces are 38.27 m2 and 36.16 m2, with the SIP contributing to the mass with 19.85 kg/m2 in addition to the gypsum board covering typically 7.1 kg/m2 on both sides. In summary, the weights are:

In summary

When all values are grouped by type of wall or the wall that supports them (triangular elements on their rectangular base), the following masses are obtained:

The two vertical beams (i) of the central module are included (see Beams).

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The mezzanine covers most of the habitable area, forming its ceiling. Only in the living-dining area, where the ceiling is higher, the structure is not covered:

It is composed of SIP162 panels covering both side modules with 52.6 m2 each and the central one with 26.3 m2. To its own mass of 22.65 kg/m2, a gypsum board panel of typically 7.1 kg/m2 is added to the entire lower surface, and in the center, in a 1.2 m strip, a floating floor of typically 6.5 kg/m2. In summary, we have:

* Only in 10.8 m2

The loads of the different sections of the mezzanine are distributed over the exterior walls, the internal walls, and the two beams in the central module. In a non-rigid model, the distribution is calculated directly from the deformation of the supporting elements (Finite Element Analysis FEA). In the rigid case, it must be modeled in a simpler way, resulting in a loss of the effect of the rigidity of the horizontal elements, making the calculation less precise. The simplest approach is:

• In the lateral modules, the load is distributed according to their vertical lengths, namely the 27 meters of the exterior wall and internal elements between modules, as well as the 15.62 meters of the left module and 14.76 meters of the right module.
• In the central module, the load is distributed according to the supporting vertical elements, three in total, and the two vertical beams.

The result can be added to the previous total table, giving the following values:

Summary

It is important to note that:

Warning: In the rigid modeling, the supports for bending rigidity are not considered, leading to higher values for some elements compared to reality, as they have to bear the entire weight of the assigned section.

It is important to note that:

In the rigid modeling, the supports for bending rigidity are not considered, leading to higher values for some elements compared to reality, as they have to bear the entire weight of the assigned section.

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For the roof, SIP 162 panels are used, which have a mass of 22.65 kg/m2, on which the zinc roof imitation colonial tile is typically placed, weighing about 10 kg/m2. Additionally, it should be considered that in the central front part (nn) and in a strip on the lower panel (ns), a gypsum board ceiling, typically weighing 7.1 kg/m2, is installed. For the calculation, it should be noted that the following diagram shows the projection on the plane, and each panel has a slope of 54.5%, or 28.6 degrees:

If we simplify the calculation assuming that the figure is composed of six equal panels, which is not entirely accurate because the peak is slightly offset backward, we find that each one occupies a horizontal projection of 28.41 m2. This means that, with an inclination of 28.6°, the actual surface area of each panel is 32.36 m2.

In summary, we have:

* Only in 12.3 m2 (projection of the same 10.8 m2 above)

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Finally, we can examine the beams supporting the roof. For this, we distinguish four types:

i) The two vertical beams located in the center of the central module, supporting the beam at the top, with dimensions of 6"x8" and a length of 4850 mm.
ii) The two horizontal beams at the top of the central module and to the right, measuring 3"x8" and 9000 mm in length.
iii) A beam similar to the previous one but 1 meter longer to support the pulley for raising/lowering items to/from the loft.
iv) A total of 30 beams extending from the central beams at the top to the walls.

Assuming a density of 800 kg/m3, the following masses are obtained:

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In the rigid body model, where different parts do not deform and distribute their weight onto supporting elements, we begin with the weight of the roof (SIP panels and zinc), estimating how the forces associated with the masses are distributed to the walls through the beams. The process includes estimating how the mezzanine is supported by the walls, and with that, along with the contact surfaces of the walls with the slab, we can calculate the pressure on it.

In a model where the roof is supported by the beams and not entirely by the walls on which it rests, we can assume that the weight of a section is distributed over the beams and the ceilings parallel to them in equal parts, i.e., in 7 parts. In this way, we can assume in a simplified manner the following distribution of the load:

The load of each panel is distributed over five beams (5x1/7) and over the two side walls (2x1/7). Then, half of the load of the beam rests on the bottom wall (5/14) and the other half on the top beam (5/14). The sum of the load on the central beam may or may not consider the vertical beams. If not considered, it rests only on the two points where three walls converge, and in the opposite case, a total of four support points can be considered.

Since each beam is exposed on both sides to the load, the total load per central beam is obtained as follows:

In this way, we can calculate for both cases (with and without support on the vertical beams) the load represented by the roof on the foundation, summing over all fractions:

The result is summarized as follows:

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If we add up the weights of all elements for each of the base elements, we calculate the force $F$ by multiplying the mass $M$ by the gravitational acceleration $g$, so that

$F = M g$

and dividing by the contact area of the element with the slab $S$, we obtain the pressure exerted on it:

$p = \displaystyle\frac{F}{S}$

Additionally, we can calculate the maximum pressure assuming a safety factor of 1.5.

In this case, we study both the scenario where the vertical beam supports the horizontal beam (blue circle) and where it does not. In both cases, it supports part of the mezzanine (red circle), transferring the load to the ground at the slab support (orange circle):

Alternatives for the vertical beam

Thus, for the case where the vertical beam supports:

and

In both cases, the weight due to the overload on the slab has been included, which, according to the NCh1537 standard, was assumed to be 200 kg/m2. Thus, the weight of the house, including the overload, would be 72.3 t or 108.4 t with the safety factor (without the weight of the slab and the foundations themselves).

In summary, the main support is required on the red lines (between 30 and 40 kPa; between 45 and 60 kPa with safety margin) as well as on the orange lines (around 53 kPa; 80 kPa with safety margin), which have a higher load due to the effect of combining the load of the side modules with that of the center:

Definition of the foundations

There are doubts about the supports of the vertical beams. By assuming a rigid element, there is an overestimation of the load at this point, so it is important to know the rigidity of the mezzanine. If this rigidity is high, the pressure on the base of the beams may become negligible, while if it is low, it may even reach values at the indicated level. Similarly, it is important to know how much of the load of the roof beam should be supported by the vertical beam.

In summary:

• If the vertical beam needs to support the roof beam, the foundation should consider massive support for it (around 153 kPa; 230 kPa with safety margin).
• If the vertical beam only needs to support the mezzanine, its support can be less if it is sufficiently rigid, and finally, a local foundation may be necessary to support additional load (around 115 kPa; 172 kPa with safety margin).

In summary, the support of the vertical beams depends on the design of the mezzanine and the SIP roof. Creating a small separate foundation could at least reduce the risk of future slab breakage.

In practice, defining the foundations that will support the house leads to the creation of trenches where the foundations will be created:

Result on the ground (here the cavities for the foundations that will support SW and SE still need to be excavated).

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