Calculation of a triangular truss online calculator. Truss from a profile pipe: we calculate and make with our own hands. We calculate a truss from a steel profile pipe

Truss Calculation is a program used to calculate flat trusses.

Usage

Thanks to this software, you will be able to determine the load for structures of the selected type (even wooden ones are supported), as well as assess the level of their strength and stability. This will help to identify all the shortcomings and errors that sometimes "slip" unnoticed at the design stage.

Functional

This solution is an improved version of the program, which we talked about in another review. It is from the Crystal that the mode for calculating the trusses is borrowed. However, of course, the "farm" has much more advanced, improved functionality than its predecessor. For example, a developer has used in his product those prototypes that are most common in this field of activity. In addition, much more options have been added to the catalog of cross-section bars than were in Kristall. Also, the selection window has become more user-friendly.

Working with the program The calculation of trusses occurs in automatic mode. The user does not have to independently generate a farm model, since the calculation will be performed according to the ready-made template selected from the catalog. The construction of the calculation scheme of efforts and the geometric scheme takes place in AutoCad, which is much more convenient for a specialist than an ordinary report in a text editor. In addition to creating a farm in this program, you can also import projects here created in other software (DFX format).

Key features

calculation of flat trusses of any structures from the selected material;
use of ready-made prototypes, which eliminates the need to "draw" the farm yourself;
full calculation of formulas with detailed descriptions and with reference to SNiPs;
support for computers with any version of Windows;
simple and intuitive interface (completely in Russian);
compatibility with all established standards;
free distribution.

In various sectors of construction, trusses from a profile pipe are often used. Such trusses are structurally metal structures, consisting of individual rods and having a lattice shape. The trusses differ from structures made of solid beams in lower cost and greater labor intensity. Both the welded method and rivets can be used to connect shaped pipes.

Metal profile trusses are suitable for creating any spans, regardless of their length - but in order for this to be possible, the structure must be calculated with the utmost accuracy before assembly. If the calculation of the metal truss was correct, and all the work on the assembly of the metal structures was carried out correctly, then the finished truss will only need to be lifted and installed on the harvested harness.

The advantages of using metal rafters

Profile pipe trusses have many advantages, including:

Low weight of the structure;
Long service life;
Excellent strength indicators;
The ability to create structures of complex configuration;
Reasonable cost of metal elements.

Classification of trusses from a profile pipe

All metal structures of the truss have several common parameters, which ensure the division of trusses into types.

These parameters include:

Number of belts. Metal trusses can have only one belt, and then the whole structure will lie in one plane, or two belts. In the latter case, the farm will be called hanging. The structure of the hanging truss includes two belts - upper and lower.
The form. There is an arched truss, straight, shed and gable.
Circuit.
Tilt angle.

Depending on the contours, the following types of metal structures are distinguished:

Parallel belt trusses... Such structures are most often used as a support for arranging a roof made of soft roofing materials. A parallel chord truss is created from identical parts with identical dimensions.
Single-pitched farms... Single slope designs are inexpensive because they require few materials to make. The finished structure turns out to be quite durable, which is ensured by the rigidity of the nodes.
Polygonal farms... These structures have a very good bearing capacity, but you have to pay for it - polygonal metal structures are very inconvenient to install.
Triangular trusses... As a rule, trusses with a triangular profile are used for the installation of roofs located at a large slope. Of the disadvantages of such farms, it is worth noting a large number of unnecessary costs associated with the mass of waste during production.

How to calculate the angle of inclination

Depending on the angle of inclination, trusses are divided into three categories:

22-30 degrees. In this case, the ratio of the length and height of the finished structure is 5: 1. Farms with such a slope, differing in their low weight, are excellent for arranging spans of short length in private construction. As a rule, trusses with this slope have a triangular outline.
15-22 degrees. In a design with such a slope, the length exceeds the height by seven times. Farms of this type cannot be more than 20 m in length. If it is necessary to increase the height of the finished structure, the lower chord is given a broken shape.
15 or less. The best option in this case would be metal rafters from a profile pipe, connected in the form of a trapezoid - short struts will reduce the effect of longitudinal bending on the structure.

In the case of spans longer than 14 m, braces have to be used. The upper belt must be equipped with a panel about 150-250 cm long. With an even number of panels, a structure consisting of two belts will be obtained. For spans longer than 20 m, the metal structure has to be reinforced with additional support elements connected by support columns.

If you need to reduce the weight of the finished metal structure, you should pay attention to the Polonso farm. It includes two triangular shaped systems that are connected by tightening. Using this scheme, you can do without large braces in the middle panels.

When creating trusses with a slope of about 6-10 degrees for pitched roofs, you need to remember that the finished structure should not be symmetrical.

Calculation of a metal truss

When calculating, it is necessary to take into account all the requirements for metal structures by state standards. In order to create the most efficient and reliable structure, it is necessary at the design stage to prepare a high-quality drawing, which will display all the elements of the truss, their dimensions and features of the connection with the supporting structure.

Before calculating a farm for a shed, it is worth deciding on the requirements for a finished farm, and then starting from savings, avoiding unnecessary costs. The height of the truss is determined by the type of floor, the total weight of the structure and the possibility of its further displacement. The length of the metal structure depends on the intended slope (for structures longer than 36 m, the calculation of the building lift will also be required).

The panels must be selected in such a way that they can withstand the loads that will fall on the farm. The braces can have different angles, therefore, when choosing panels, this parameter must also be taken into account. In the case of triangular gratings, the angle is 45 degrees, and in the case of diagonal gratings, 35 degrees.

The calculation of the roof from the profile pipe ends with the determination of the distance at which the nodes will be created relative to each other. As a rule, this indicator is equal to the width of the selected panels. The optimal indicator of the step of the supports of the entire structure is 1.7 m.

When calculating a shed truss, you need to understand that with an increase in the height of the structure, its bearing capacity will also increase. In addition, if necessary, it is worth supplementing the truss scheme with several stiffeners that can strengthen the structure.

Calculation examples

When choosing pipes for metal trusses, it is worth starting from the following recommendations:

For arranging structures with a width of less than 4.5 m, pipes with a section of 40x20 mm with a wall thickness of 2 mm are suitable;
With a construction width of 4.5 to 5.5 m, 40-mm square shaped pipes with a 2-mm wall are suitable;
For larger metal structures, the same pipes are suitable as in the previous case, but with a 3-mm wall, or pipes with a section of 60x30 mm with a 2-mm wall.

The last parameter, which is also worth paying attention to when calculating, is the cost of materials. First, you need to take into account the cost of pipes (remembering that the price of pipes is determined by their weight, not their length). Secondly, it is worth asking about the cost of complex work on the manufacture of metal structures.

Recommendations for the selection of pipes and the manufacture of metal structures

Before you cook farms and select the optimal materials for your future design, you should read the following recommendations:

Studying the assortment of pipes available on the market, it is worth giving preference to rectangular or square products - the presence of stiffeners significantly increases their strength;
When choosing pipes for the truss system, it would be best to opt for stainless steel products (the dimensions of the pipes are determined by the project);
When installing the main elements of the truss, tacks and double corners are used;
In the upper chords, I-beams with different sides are usually used to connect the frame, the smaller of which is necessary for joining;
For mounting the lower belt, corners with equal sides are quite suitable;
The main elements of large-sized structures are attached to each other with overhead plates;
The braces are mounted at a 45-degree angle and the struts are mounted at a 90-degree angle.
When the metal truss for the canopy is welded, it is worth making sure that each weld is reliable enough (read also: "");
After welding, metal structural elements are left to be coated with protective compounds and paint.

Conclusion

Profile pipe trusses are quite versatile and suitable for a wide range of tasks. The manufacture of trusses cannot be called simple, but if you approach all stages of work with all responsibility, then the result will be a reliable and high-quality design.

There are not so many structural elements of a frame building: the foundation, supports and a roof - but each of them must be strong and durable. The stability of the supports is provided not only by the foundation, but by special reinforcing structures - strapping trusses. The trusses are also responsible for the reliability of the roof, but already rafters.

To strengthen the frame of houses, outbuildings and small architectural forms from a professional pipe, special elements called trusses are used. They are used for the top and side connection of canopy supports, gazebos, stopping pavilions and summer cafes. Reinforcing elements are also used when installing visors above the entrance groups, if the distance between the walls or supports is large.

Thus, a truss is a reinforcing structure consisting of two belts connected by jumpers. Such a device provides the structure with rigidity and allows it to maintain its shape under any load.

Note! In addition to the functional purpose, the trusses can also be decorative, if the structure being erected does not have walls and gables or is sheathed with transparent material.

Types of belts

Belts define the shape of the part: segment, double arc, triangle, rectangle, or polygon. At the same time, solid pipes - straight or curved - act as the lower and upper belts in the segment, rectangle and arc.

In trusses of a more complex shape: triangular, convex and concave polygons, one or both chords are assembled from several pipes.

The shape of the truss belts is chosen in accordance with the purpose of the structure. For the lateral connection of the struts of the structure, strapping trusses are usually used with two parallel straight or arcuate belts or an upper straight belt and a lower arcuate.

The shape of the truss chords depends on the type of roof:

Roof type	Possible form of belts	Farm name
single-slope, hip-roof	straight lines forming a right triangle	shed
gable	straight lines forming an isosceles triangle: 2 straight lines form the upper belt, one - the lower;	triangular
	two pairs of straight lines forming parallel angles	polygonal
	two pairs of straight lines forming a pair of unequal angles	scissors
	5 straight lines: two form the upper belt, 3 - the lower	farm Polonso
attic	straight lines forming an isosceles pentagon with a wide base;	attic
arched	two parallel arcs	arched
	two parallel polygonal lines	polygonal
	arc and line forming a segment or semicircle	segmental
	upper arc, lower polyline	console

Jumper types

Bulkheads are short lengths of pipe, usually smaller than those used for chords, attached straight or at an angle to the main structural members. The bridging complex is referred to as an inner lattice.

Vertical lintels are called supports or posts. Typically, a farm has one or two main racks and several additional ones.

Inclined lintels are called struts or slopes, their number can be any. If the truss belts are connected by supports, then the supports are strengthened by the slopes. In addition, the internal grill can be made up of vertical or only inclined lintels.

Note! Farms for frame structures are made not only from pipes, but also from corners. Each element of such a structure is assembled from a pair of corners to ensure the required strength, which complicates the calculations and installation and increases the time spent.

The advantages of a profile pipe for the manufacture of frames

Frame construction from a professional pipe has gained popularity and is not losing ground. Profiled pipes allow you to create beautiful and strong structures for a wide variety of purposes - from an umbrella over a sandbox to a residential, industrial or commercial building.

Today, trusses from a profile pipe are rightfully considered an ideal solution for the construction of a garage, a residential building and outbuildings. Strong and durable, these designs are inexpensive, quick to build, and can be handled by anyone with a little knowledge of math and cutting and welding skills.

And how to choose the right profile, calculate the truss, make jumpers in it and install, we will now tell you in detail. To do this, we have prepared for you detailed master classes for making such trusses, video tutorials and valuable advice from our experts!

So what is a farm? It is a structure that ties the supports together into a single unit. In other words, the truss belongs to simple architectural structures, among the valuable advantages of which we highlight the following: high strength, excellent performance, low cost and good resistance to deformations and external loads.

Due to the fact that such trusses have a high bearing capacity, they are placed under any roofing materials, regardless of their weight.

The use in the construction of metal trusses from new or rectangular closed profiles is considered one of the most rational and constructive solutions. And for good reason:

The main secret is economy thanks to the rational shape of the profile and the connection of all elements of the grille.
Another valuable advantage of profile pipes for use in truss fabrication is equal stability in two planes, remarkable streamlining and ease of use.
With all their low weight, such trusses can withstand serious loads!

Truss trusses differ in the shape of the belts, the type of cross-section of the rods and the types of lattice. And with the right approach, you can independently weld and install a truss from a profile pipe of any complexity! Even this one:

Stage II. We acquire a high-quality profile

So, before drawing up a project for future farms, you first need to decide on such important points:

contours, size and shape of the future roof;
material for the manufacture of the upper and lower chord of the truss, as well as its lattice;

Remember one simple thing: a frame made of a shaped pipe has so-called equilibrium points, which are important to determine for the stability of the entire truss. And it is very important to choose high-quality material for this load:

Farms are built from a profile pipe of such types of sections: rectangular or square. These are available in different cross-sectional sizes and diameters, with different wall thicknesses:

We recommend those that are specially sold for small-sized buildings: these are up to 4.5 meters long and have a cross-section of 40x20x2 mm.
If you will be making trusses longer than 5 meters, then choose a profile with parameters 40x40x2 mm.
For the full-scale construction of the roof of a residential building, you will need profile pipes with the following parameters: 40x60x3 mm.

The stability of the entire structure is directly proportional to the thickness of the profile, therefore, for the manufacture of trusses, do not use pipes for which are intended only for welding racks and frames - here are other characteristics. Also pay attention to which method the product was manufactured: electrowelded, hot-deformed or cold-deformed.

If you undertake to make such trusses yourself, then take square-section blanks - the easiest way to work with them. Get a 3 to 5 mm thick square profile that is strong enough and similar in performance to metal bars. But if you are going to make the farm just something for the visor, then you can give preference to a more budgetary option.

Be sure to consider snow and wind loads in your area when designing. Indeed, when choosing a profile (in terms of load on it), the angle of inclination of the trusses is of great importance:

You can more accurately design a truss from a profile pipe using online calculators.

We only note that the simplest structure of a truss made of a profile pipe consists of several vertical posts and horizontal levels on which roof rafters can be attached. You can buy such a frame ready-made on your own, even on order in any city in Russia.

Stage III. We calculate the internal stress of trusses

The most important and responsible task is to correctly calculate the truss from the profile pipe and select the required format of the inner lattice. To do this, we need a calculator or other software similar to it, as well as some tabular data of SNiPs, which for this:

SNiP 2.01.07-85 (impact, load).
SNiP p-23-81 (data on steel structures).

Review these documents if possible.

Roof shape and angle of inclination

What kind of roof is needed for a farm? Mono-pitched, gable, domed, arched or hipped-roof? The easiest option, of course, is to make a standard lean-to canopy. But even quite complex farms, you are also able to calculate and manufacture yourself:

A standard truss consists of such important elements as the upper and lower chords, struts, braces and auxiliary struts, which are also called sprengels. There is a grid system inside the trusses; welded seams, rivets, special paired materials and kerchiefs are used to connect pipes.

And, if you are going to make a roof that is complex in shape, then such trusses will be the ideal option for it. It is very convenient to make them according to a template right on the ground, and only then lift them up.

Most often, in the construction of a small country house, garage or change house, the so-called polonso trusses are used - a special design of triangular trusses connected by puffs, and the lower belt comes out raised here.

In fact, in this case, in order to increase the height of the structure, the lower belt is made broken, and then it is 0.23 of the flight length. It is very convenient for the internal space of the room.

So, in total there are three main options for making a truss, depending on the slope of the roof:

from 6 to 15 °;
from 15 to 20 °;
from 22 to 35 °.

What is the difference you ask? For example, if the angle of the structure is small, only up to 15 °, then it is rational to make the trusses a trapezoidal shape. And at the same time, it is quite possible to reduce the weight of the structure itself, taking in height from 1/7 to 1/9 of the total flight length.

Those. be guided by this rule: the less weight, the higher the height of the truss should be. But if we already have a complex geometric shape, then you need to choose a different type of truss and lattices.

Types of trusses and roof shapes

Here is an example of specific trusses for each type of roof (pitched, gable, complex):

Let's take a look at the types of farms:

Triangular trusses are a classic for making the base for steep roof slopes or awnings. The cross-section of pipes for such trusses must be selected taking into account the weight of the roofing materials, as well as the operation of the building itself. Triangular trusses are good because they have simple shapes, are simple in calculation and execution. They are appreciated for providing natural light under the roof. But we also note the disadvantages: these are additional profiles and long rods in the central segments of the lattice. And also here you will have to face some difficulties when welding sharp seating corners.
The next view is polygonal trusses from a profile pipe. They are indispensable for the construction of large areas. Their welding is already of a more complex shape, and therefore they are not designed for lightweight structures. But such trusses are distinguished by greater metal savings and strength, which is especially good for hangars with large spans.
Strong is also considered parallel chord truss... Such a farm differs from others in that it has all the parts that are repetitive, with the same length of rods, belts and lattices. That is, there are a minimum of joints here, and therefore it is easiest to calculate and cook such from a profile pipe.
A separate view is single-slope trapezoidal truss supported by columns. Such a truss is ideal when rigid fixation of the structure is required. It has slopes (braces) on the sides and there are no long bars of the upper lathing. Suitable for roofs where reliability is especially important.

Here is an example of making trusses from a profile pipe as a universal option that is suitable for any garden buildings. These are triangular trusses, and you've probably seen them many times before:

A triangular truss with a crossbar is also quite simple, and is quite suitable for the construction of gazebos and change houses:

And here arched farms in manufacturing are already much more complicated, although they have a number of their valuable advantages:

Your main task is to center the metal truss elements from the center of gravity in all directions, in simple terms, to minimize the load and correctly distribute it.

Therefore, choose the type of farms that are more suitable for this purpose. In addition to those listed above, the scissor truss, asymmetric, U-shaped, double-hinged, parallel chord truss and attic truss with and without supports are also popular. And also the attic view of the farm:

Lattice types and point loading

It will be interesting for you to know that a certain design of the internal truss gratings is chosen not at all for aesthetic reasons, but for quite practical ones: for the shape of the roof, the geometry of the ceiling and the calculation of loads.

You need to design your farm in such a way that all forces are concentrated specifically in the nodes. Then there will be no bending moments in the chords, braces and sprengels - they will only work in compression and tension. And then the cross-section of such elements is reduced to the required minimum, while significantly saving on material. And the farm itself to everything, you can easily make a hinged one.

Otherwise, a force distributed over the bars will constantly act on the truss, and a bending moment will appear, in addition to the total stress. And here it is then important to correctly calculate the maximum bending value for each individual bar.

Then the cross-section of such rods should be larger than if the truss itself were loaded with point forces. To summarize: trusses, on which the distributed load acts evenly, are made from short elements with hinged nodes.

Let's see what is the advantage of this or that type of grid in terms of load distribution:

Triangular the lattice system is always used in parallel chord trusses and trapezoid trusses. Its main advantage is that it gives the smallest overall lattice length.
Diagonal the system is good for low truss heights. But the consumption of material for it is considerable, because here the entire path of effort goes through the nodes and rods of the lattice. And therefore, when designing, it is important to lay as many rods as possible so that long elements are stretched and the struts are compressed.
Another view - truss lattice. It is made in the case of loads of the upper chord, as well as when it is necessary to reduce the length of the lattice itself. Here the advantage is in maintaining the optimal distance between the elements of all transverse structures, which, in turn, allows you to maintain a normal distance between the girders, which will be a practical moment for the installation of roofing elements. But creating such a lattice with your own hands is a rather laborious task with additional metal costs.
Cruciform the lattice allows you to distribute the load on the truss in both directions at once.
Another type of lattice - cross where the braces are attached directly to the truss wall.
And finally half-bevel and rhombic lattice, the most rigid of the listed. Here, two systems of braces interact at once.

We have prepared an illustration for you, where we have collected all types of trusses and their trellises together:

Here is an example of how a triangular truss is made:

Making a truss with a diagonal lattice looks like this:

This is not to say that one of the types of trusses is definitely better or worse than the other - each of them is valuable for less material consumption, lighter weight, load-carrying capacity and method of fastening. The drawing is responsible for which load scheme will act on it. And the selected type of lattice will directly depend on the weight of the farm, the appearance and laboriousness of its manufacture.

We also note such an unusual option for making a farm, when it itself becomes a part or support for another, wooden:

Stage IV. We make and install farms

We will give you some valuable advice on how to independently weld such farms without any special difficulties right on your site:

Option one: you can contact the factory, and they will make to order according to your drawing all the necessary individual elements that you just have to weld on the spot.
Second option: purchase a ready-made profile. Then all you have to do is sheathe the inside of the trusses with boards or plywood, and in between, lay insulation if necessary. But this method will cost, of course, more.

For example, here is a good video tutorial on how to lengthen a pipe by welding and achieve perfect geometry:

Here's also a very helpful video on how to cut a pipe at a 45 ° angle:

So, now we come directly to the assembly of the farms themselves. The following step-by-step instructions will help you cope with this:

Step 1. Prepare the farms first. It is better to weld them in advance directly on the ground.
Step 2. Install vertical supports for future trusses. It is imperative that they are truly vertical, so test them with a plumb line.
Step 3. Now take the longitudinal pipes and weld them to the support legs.
Step 4. Lift the trusses and weld them to the longitudinal pipes. After that, it is important to clean all the joints.
Step 5. Paint the finished frame with a special paint, after cleaning and degreasing it. When doing this, pay special attention to the joints of the profile pipes.

What else do those who make such farms at home face? First, plan in advance the support tables on which you will place the truss. It is far from the best option to throw it on the ground - it will be very inconvenient to work.

Therefore, it is better to install small support bridges that will be slightly wider than the lower and upper truss chord. After all, you will manually measure and insert jumpers between the belts, and it is important that they do not fall to the ground.

The next important point: trusses from a profile pipe are heavy in weight, and therefore you will need the help of at least one more person. In addition, help will not hurt in such tedious and painstaking work as sanding metal before cooking. Also keep in mind that you will need to cut the farms a lot, for all elements, and therefore we advise you to either purchase or build a homemade machine like what's in our master class. This is how it works:

In this way, step by step, you will draw up a drawing, calculate the truss lattice, make blanks and weld the structure already in place. Moreover, you will also have the remnants of profile pipes in your expense, therefore, you will not need to throw anything away - all this will be needed for the secondary parts of the canopy or hangar!

Stage V. We clean and paint the finished trusses

After you install the trusses in their permanent place, be sure to treat them with anti-corrosion compounds and paint them with polymer paints. A paint that is durable and UV resistant is ideal for this purpose:

That's all, the profile pipe truss is ready! All that remains is the finishing work on the sheathing of the trusses from the inside with finishing and from the outside with roofing material:

Believe me, making a metal truss from a shaped pipe is actually not difficult for you. A competently drawn up drawing, high-quality welding of a truss from a shaped pipe and the desire to do everything correctly and accurately play a huge role.

Determining the internal efforts of the farm

Often we do not have the opportunity to use a conventional beam for a particular structure, and we are forced to use a more complex structure, which is called a truss.
although it differs from the calculation of the beam, it will not be difficult for us to calculate it. All that will be required of you is attention, basic knowledge of algebra and geometry, and an hour or two of free time.
So, let's begin. Before calculating the farm, let's ask some real-life situation that you might encounter. For example, you need to cover a garage 6 meters wide and 9 meters long, but you have no floor slabs or beams... Only metal corners of various profiles. Here we are going to build our farm from them!
Subsequently, the girders and corrugated board will rely on the farm. The support of the truss on the garage walls is articulated.

First, you will need to know all the geometric dimensions and angles of your truss. This is where we need our mathematics, namely geometry. The angles are found using the cosine theorem.

Then you need to collect all the loads on your farm (see the article). Suppose you have the following loading option:

Next, we need to number all the elements, the nodes of the truss and set the support reactions (the elements are marked in green, and the nodes in blue).

To find our reactions, we write down the equations of equilibrium of efforts on the y-axis and the equation of equilibrium of moments relative to node 2.

Ra + Rb-100-200-200-200-100 = 0;
200 * 1.5 + 200 * 3 + 200 * 4.5 + 100 * 6-Rb * 6 = 0;

From the second equation we find the reference reaction Rb:

Rb = (200 * 1.5 + 200 * 3 + 200 * 4.5 + 100 * 6) / 6;
Rb = 400 kg

Knowing that Rb = 400 kg, from the 1st equation we find Ra:

Ra = 100 + 200 + 200 + 200 + 100-Rb;
Ra = 800-400 = 400 kg;

After the support reactions are known, we must find the node where the least unknowns are (each numbered element is an unknown). From this point on, we begin to divide the truss into separate nodes and find the internal forces of the truss rods in each of these nodes. It is for these internal efforts that we will select the sections of our rods.

If it turns out that the forces in the rod are directed from the center, then our rod tends to stretch (return to its original position), which means that it itself is compressed. And if the efforts of the rod are directed towards the center, then the rod tends to compress, that is, it is stretched.

So, let's move on to the calculation. In node 1, there are only 2 unknown quantities, so we will consider this node (we set the directions of efforts S1 and S2 from our own considerations, in any case, we will get it right as a result).

Consider the equilibrium equations on the x and y axes.

S2 * sin82.41 = 0; - on the x-axis
-100 + S1 = 0; - on the y-axis

From the 1st equation, it can be seen that S2 = 0, that is, the 2nd bar is not loaded!
From the 2nd equation it can be seen that S1 = 100 kg.

Since the S1 value turned out to be positive, it means that we chose the direction of effort correctly! If it turned out to be negative, then the direction should be changed and the sign changed to "+".

Knowing the direction of effort S1, we can imagine what the 1st rod is.

Since one force was directed to the node (node 1), then the second force will be directed to the node (node 2). This means that our rod is trying to stretch, which means it is compressed.
Next, consider node 2. It had 3 unknown quantities, but since we have already found the value and direction of S1, then only 2 unknown quantities remain.

Yet again

100 + 400 - sin33.69 * S3 = 0 - on the y-axis
- S3 * cos33.69 + S4 = 0 - on the x axis

From the 1st equation S3 = 540.83 kg (rod # 3 is compressed).
From the 2nd equation S4 = 450 kg (rod # 4 is stretched).
Consider the 8th node:

Let's compose the equations on the x and y axes:

100 + S13 = 0 - per y-axis
-S11 * cos7.59 = 0 - on the x-axis

Hence:

S13 = 100 kg (rod # 13 compressed)
S11 = 0 (zero rod, there is no effort in it)

Consider the 7th node:

Let's compose the equations on the x and y axes:

100 + 400 - S12 * sin21.8 = 0 - on the y-axis
S12 * cos21.8 - S10 = 0 - on the x axis

From the 1st equation we find S12:

S12 = 807.82 kg (rod # 12 compressed)

From the 2nd equation we find S10:

S10 = 750.05 kg (rod # 10 stretched)

Next, consider node # 3. As far as we remember, the 2nd rod is zero, which means we will not draw it.

Equations on the x-axis and y-axis:

200 + 540.83 * sin33.69 - S5 * cos56.31 + S6 * sin7.59 = 0 - on the y-axis
540.83 * cos33.69 - S6 * cos7.59 + S5 * sin56.31 = 0 - on the x axis

And here we already need algebra. I will not describe in detail the method for finding unknown quantities, but the essence is as follows - from the 1st equation we express S5 and substitute it into the 2nd equation.
As a result, we get:

S5 = 360.56 kg (rod # 5 stretched)
S6 = 756.64 kg (rod # 6 compressed)

Consider node # 6:

Let's compose the equations on the x and y axes:

200 - S8 * sin7.59 + S9 * sin21.8 + 807.82 * sin21.8 = 0 - on the y-axis
S8 * cos7.59 + S9 * cos21.8 - 807.82 * cos21.8 = 0 - on the x axis

Just like in the 3rd node, we will find our unknowns.

S8 = 756.64 kg (rod # 8 compressed)
S9 = 0 kg (rod # 9 zero)

Consider node # 5:

Let's compose the equations:

200 + S7 - 756.64 * sin7.59 + 756.64 * sin7.59 = 0 - on the y-axis
756.64 * cos7.59 - 756.64 * cos7.59 = 0 - on the x-axis

From the 1st equation we find S7:

S7 = 200 kg (rod # 7 compressed)

As a check of our calculations, consider the 4th node (there are no efforts in the rod No. 9):

Let's compose the equations on the x and y axes:

200 + 360.56 * sin33.69 = 0 - on the y-axis
-360.56 * cos33.69 - 450 + 750.05 = 0 - on the x axis

In the 1st equation it turns out:

In the 2nd equation:

This error is permissible and is most likely associated with angles (2 decimal places instead of 3 ex).
As a result, we get the following values:

I decided to double-check all our calculations in the program and got exactly the same values:

Selection of cross-section of truss elements

At calculation of a metal truss after all the internal forces in the rods are found, we can proceed to the selection of the cross-section of our rods.
For convenience, we will summarize all the values in the table.