Flat trusses

An example of solving problems on the equilibrium of a system of bodies (see § 18) is given by the calculation of trusses. A truss is a rigid structure made of straight rods connected at the ends by hinges. If all the rods of a truss lie in the same plane, the truss is called flat. The connection points of the truss rods are called nodes. All external loads on the truss are applied only at the nodes. When calculating a truss, friction at the nodes and the weight of the rods (compared to external loads) are neglected or the weights of the rods are distributed among the nodes. Then each of the truss rods will be acted upon by two forces applied to its ends, which, in equilibrium, can only be directed along the rod. Therefore, we can assume that the truss rods work only in tension or compression. Let us limit ourselves to considering rigid flat trusses without extra rods formed from triangles. In such trusses, the number of rods k and the number of nodes are related by the relation

In fact, in a rigid triangle formed from three rods there will be three nodes (see, for example, below in Fig. 74 the triangle ABD formed by rods 1, 2, H). Attaching each subsequent node requires two rods (for example, in Fig. 74, node C is connected by rods 4, 5, node E by rods 6, 7, etc.); therefore, all other nodes will require rods. As a result, the number of rods in the truss. With a smaller number of rods, the truss will not be rigid, and with a larger number, it will be statically indeterminate.

The calculation of a truss comes down to determining the support reactions and forces in its rods.

Support reactions can be found using the usual methods of statics (see § 17), considering the truss as a whole as a solid body. Let's move on to determining the forces in the rods.

Knot cutting method. This method is convenient to use when you need to find the forces in all the rods of the truss. It comes down to a sequential consideration of the conditions of equilibrium of forces converging at each of the nodes.

We will explain the calculation process using a specific example.

Let's consider the one shown in Fig. 73, and a truss formed from identical isosceles right triangles, the forces acting on the truss are parallel to the axis and are numerically equal:

In this truss, the number of nodes is the number of rods. Therefore, relation (38) is satisfied and the truss is rigid without extra rods.

Compiling the equilibrium equations (29) for the truss as a whole, we find that the reactions of the supports are directed as shown in the figure and are numerically equal.

Let's move on to determining the forces in the rods. Let's number the truss nodes with Roman numerals, and the rods with Arabic numerals. Let us denote the required forces as S, (in rod), (in rod 2), etc. Let us mentally cut off all the nodes together with the rods converging in them from the rest of the truss. We replace the action of the rejected rods with forces that will be directed along the corresponding rods and are numerically equal to the required forces. We depict all these forces in the figure at once, directing them from the nodes, i.e., considering all the rods stretched (Fig. 73, a; the picture depicted must be imagined for each node as shown in Fig. 73, b for node III). If, as a result of the calculation, the value of the force in any rod turns out to be negative, this will mean that this rod is not stretched, but compressed. Letter designations for forces acting along the rods in Fig. 73 we do not introduce, since it is clear that the forces acting along rod 1 are numerically equal along rod 2 - equal, etc.

Now for the forces converging at each node, we compose sequentially the equilibrium equations (12):

We start from the node where two rods meet, since from the two equilibrium equations only two unknown forces can be determined.

Compiling the equilibrium equations for the node, we obtain:

From here we find:

Now, knowing, let's move on to node II. For it, the equilibrium equations are given from where

Having determined, we compose in a similar way the equilibrium equations, first for node III, then for node IV. From these equations we find:

Finally, to calculate, we create an equilibrium equation for the forces converging at node V, projecting them onto the axis. We get from here

The second equilibrium equation for node V and two equations for node VI can be constructed as test equations. To find the forces in the rods, these equations were not needed, since instead of them three equilibrium equations for the entire truss as a whole were used in the determination (see § 181.

The final calculation results can be summarized in a table

As the signs of effort show, rod 5 is stretched, the remaining rods are compressed; rod 7 is not loaded (zero rod).

The presence of zero rods in the truss, similar to rod 7, is immediately detected, since if three rods converge in a node not loaded by external forces, two of which are directed along the same straight line, then the force in the third rod is equal to zero. This result is obtained from the equilibrium equation in projection onto the axis perpendicular to the two rods mentioned. For example, in the truss shown in Fig. 74, in the absence of force RA, rod 15 will be zero, and therefore 13. In the presence of force, one of these rods is not zero.

If during the calculation you encounter a node for which the number of unknowns is more than two, then you can use the section method.

Method of sections (Ritter method). This method is convenient to use to determine the forces in individual truss rods, in particular for verification calculations. The idea of ​​the method is that the truss is divided into two parts with a section passing through three rods in which (or in one of which) the forces need to be determined, and the equilibrium of one of these parts is considered. The action of the discarded part is replaced by corresponding forces, directing them along the cut rods from the nodes, i.e., considering the rods to be stretched (as in the method of cutting nodes). Then the equilibrium equations are composed in the form (31) or (30), taking the centers of the moments (or the axis of projections) so that only one unknown force enters each equation.

A truss is a rod system that remains geometrically unchanged after the conditional replacement of its rigid nodes with hinged ones. Trusses have essentially the same purpose as solid beams, but are used to span significant spans when the design of solid beams (for example, I-beams) becomes economically unprofitable due to incomplete use of the wall material, the stress in which is less than in the flanges ( see the diagram of normal stresses in the cross sections of the beam in Fig. 4.1), and the need to thicken the vertical wall due to the possibility of its buckling (with a significant wall height).

In such cases, a solid beam is replaced by a rod system - a truss, the elements of which (rods), under the action of concentrated loads applied at the nodes, work mainly in central compression or tension. This makes it possible to use the truss material much better, since the normal stress diagrams in the cross sections of each of its rods practically look like rectangles. Therefore, the truss is lighter than a beam with a solid wall that has the same span and height. An example of a farm is the system shown in Fig. 4.2.

In addition to flat trusses, in which the axes of all rods are located in the same plane, spatial trusses are used, the axes of the elements of which do not lie in the same plane (Fig. 4.3). In many cases, the calculation of a spatial truss can be reduced to the calculation of several flat trusses.

The distance between the axes of the truss supports (Fig. 4.4, a) is called the span; the rods located along the outer contour of the truss are called chord rods and form chords, the rods connecting the chords form the lattice of the truss and are called: vertical - racks, inclined - braces.

The distance between adjacent nodes of any chord of a truss (usually measured horizontally) is called the panel.

We will classify farms according to the following five characteristics: 1) the nature of the outline of the external contour; 2) type of grating; 3) type of truss support;

4) purpose of the farm; 5) driving level.

Based on the nature of the outline, trusses are distinguished with parallel chords (Fig. 4.4, a) and with a broken or so-called polygonal arrangement of belts. The latter include, for example, trusses with parabolic

the outline of the upper chord (Fig. 4.4, b) and a triangular truss (Fig. 4.4, c).

According to the type of lattice, trusses are divided into: trusses with a triangular lattice (Fig. 4.5, a); trusses with a diagonal lattice (Fig. 4.5, b) trusses with a semi-diagonal lattice (Fig. 4.5, c); trusses with a rhombic lattice (Fig. 4.5, d); double-lattice (Fig. 4.5, e), multi-lattice (Fig. 4.5, f).

According to the type of support, trusses can be: fixed, at both ends - beam (Fig. 4.6, a) or arched (Fig. 4.6, e, f); cantilever - fixed at one end (Fig. 4.6, b); beam-cantilever (Fig. 4.6, c, d).

Depending on the purpose, there are trusses (Fig. 4.7, a), crane trusses (Fig. 4.7, b), tower trusses (Fig. 4.7, c), bridge trusses (Fig. 4.8), etc.

Depending on the ride level, bridge trusses are divided into trusses with a ride at the bottom (Fig. 4.8, a), trusses with a ride at the top (Fig. 4.8, b) and trusses with a ride in the middle (Fig. 4.8, c).

The study of these issues is necessary in the future to study the dynamics of the movement of bodies taking into account sliding and rolling friction, the dynamics of the movement of the center of mass of a mechanical system, kinetic moments, to solve problems in the discipline “Strength of Materials”.

Calculation of farms. Farm concept. Analytical calculation of flat trusses.

Fermoy called a rigid structure of straight rods connected at the ends by hinges. If all the bars of a truss lie in the same plane, the truss is called flat. The connection points of the truss rods are called nodes. All external loads on the truss are applied only at the nodes. When calculating a truss, friction at the nodes and the weight of the rods (compared to external loads) are neglected or the weights of the rods are distributed among the nodes.

Then each of the truss rods will be acted upon by two forces applied to its ends, which, in equilibrium, can only be directed along the rod. Therefore, we can assume that the truss rods work only in tension or compression. We will limit ourselves to considering rigid flat trusses, without extra rods formed from triangles. In such trusses, the number of rods k and the number of nodes n are related by the relation

The calculation of a truss comes down to determining the support reactions and forces in its rods.

Support reactions can be found using conventional statics methods, considering the truss as a whole as a rigid body. Let's move on to determining the forces in the rods.

Knot cutting method. This method is convenient to use when you need to find the forces in all the rods of the truss. It comes down to a sequential consideration of the conditions of equilibrium of forces converging at each of the nodes of the truss. We will explain the calculation process using a specific example.

Fig.23

Let's consider the one shown in Fig. 23,a a truss formed from identical isosceles right triangles; the forces acting on the truss are parallel to the axis X and are equal: F 1 = F 2 = F 3 = F = 2.

The number of nodes in this farm is n= 6, and the number of rods k= 9. Consequently, the relationship is satisfied and the truss is rigid, without extra rods.

Compiling the equilibrium equations for the truss as a whole, we find that the reactions of the supports are directed, as shown in the figure, and are numerically equal;

Y A = N = 3/2F = 3H

Let's move on to determining the forces in the rods.

Let's number the truss nodes with Roman numerals, and the rods with Arabic numerals. We will denote the required efforts S 1 (in rod 1), S 2 (in rod 2), etc. Let us mentally cut off all the nodes together with the rods converging in them from the rest of the truss. We will replace the action of the discarded parts of the rods with forces that will be directed along the corresponding rods and are numerically equal to the required forces S 1 , S 2.

We depict all these forces at once in the figure, directing them from the nodes, i.e., considering all the rods to be stretched (Fig. 23, a; the picture depicted should be imagined for each node as shown in Fig. 23, b for node III). If, as a result of the calculation, the magnitude of the force in any rod turns out to be negative, this will mean that this rod is not stretched, but compressed. There are no letter designations for the forces acting along the rods in Fig. 23 not inputs, since it is clear that the forces acting along rod 1 are numerically equal S 1, along the rod 2 - equal S 2, etc.

Now for the forces converging at each node, we compose the equilibrium equations sequentially:

We start from node 1, where two rods meet, since only two unknown forces can be determined from the two equilibrium equations.

Compiling the equilibrium equations for node 1, we obtain

F 1 + S 2 cos45 0 = 0, N + S 1 + S 2 sin45 0 = 0.

From here we find:

Now knowing S 1, go to node II. For it, the equilibrium equations give:

S 3 + F 2 = 0, S 4 - S 1 = 0,

S 3 = -F = -2H, S 4 = S 1 = -1H.

Having determined S 4, we compose in a similar way the equilibrium equations, first for node III, and then for node IV. From these equations we find:

Finally, to calculate S 9 we compose an equilibrium equation for the forces converging at node V, projecting them onto the By axis. We get Y A + S 9 cos45 0 = 0 from where

The second equilibrium equation for node V and two equations for node VI can be compiled as verification equations. To find the forces in the rods, these equations were not needed, since instead of them, three equilibrium equations for the entire truss as a whole were used to determine N, X A, and Y A.

The final calculation results can be summarized in a table:

As the signs of effort show, rod 5 is stretched, the remaining rods are compressed; rod 7 is not loaded (zero rod).

The presence of zero rods in the truss, similar to rod 7, is immediately detected, since if three rods converge in a node not loaded by external forces, two of which are directed along one straight line, then the force in the third rod is equal to zero. This result is obtained from the equilibrium equation in projection onto the axis perpendicular to the two rods mentioned.

If during the calculation you encounter a node for which the number of unknowns is more than two, then you can use the section method.

Method of sections (Ritter method). This method is convenient to use to determine the forces in individual truss rods, in particular, for verification calculations. The idea of ​​the method is that the truss is divided into two parts with a section passing through three rods in which (or in one of which) the force is required to be determined, and the equilibrium of one of these parts is considered. The action of the discarded part is replaced by corresponding forces, directing them along the cut rods from the nodes, i.e., considering the rods stretched (as in the method of cutting nodes). Then they compose equilibrium equations, taking the centers of moments (or the axis of projections) so that each equation includes only one unknown force.

Graphic calculation of flat trusses.

Calculation of a truss using the method of cutting out nodes can be done graphically. To do this, first determine the support reactions. Then, sequentially cutting off each of its nodes from the truss, they find the forces in the rods converging at these nodes, constructing the corresponding closed force polygons. All construction is carried out on a scale that must be selected in advance. The calculation begins with the node at which two rods converge (otherwise it will not be possible to determine the unknown forces).

Fig.24

As an example, consider the farm shown in Fig. 24, a. The number of nodes in this farm is n= 6, and the number of rods k= 9. Consequently, the relation is satisfied and the truss is rigid, without extra rods. We depict the support reactions for the truss under consideration along with the forces and as known.

We begin to determine the forces in the rods by considering the rods converging at node I (we number the nodes with Roman numerals, and the rods with Arabic numerals). Having mentally cut off the rest of the truss from these rods, we discard its action and mentally replace the discarded part with forces and , which should be directed along rods 1 and 2. From the forces converging at node I, we build a closed triangle (Fig. 24, b).

To do this, we first depict a known force on a selected scale, and then draw straight lines through its beginning and end, parallel to rods 1 and 2. In this way, the forces and acting on rods 1 and 2 will be found. Then we consider the equilibrium of the rods converging at a node II. We mentally replace the action on these rods of the discarded part of the truss with the forces , , and , directed along the corresponding rods; at the same time, the force is known to us, since by the equality of action and reaction.

By constructing a closed triangle from the forces converging at node II (starting with the force ), we find the quantities S 3 and S 4 (in this case S 4 = 0). The forces in the remaining rods are found similarly. The corresponding force polygons for all nodes are shown in Fig. 24, b. The last polygon (for node VI) is constructed for verification, since all the forces included in it have already been found.

From the constructed polygons, knowing the scale, we find the magnitude of all efforts. The sign of the force in each rod is determined as follows. Having mentally cut out a node along the rods converging in it (for example, node III), we apply the found forces to the edges of the rods (Fig. 25); the force directed from the node (in Fig. 25) stretches the rod, and the force directed towards the node (and in Fig. 25) compresses it.

Fig.25

According to the accepted condition, we assign the sign “+” to tensile forces, and the sign “-” to compressive forces. In the example considered (Fig. 25), rods 1, 2, 3, 6, 7, 9 are compressed, and rods 5, 8 are stretched.

MINISTRY OF EDUCATION OF THE REPUBLIC OF BELARUS

Educational institution " BELARUSIAN STATE UNIVERSITY OF TRANSPORT"

Department of Structural Mechanics

D. V. Leonenko

CALCULATION OF FLAT TRUSSES

Educational and methodological manual for students of construction specialties

Approved by the methodological commission of the PGS faculty

Gomel ■ 2006

ÓÄÊ 539.3 (075.8) ÁÁÊ 38.112

REVIEWER – Candidate of Technical Sciences V.V. Taletsky (EI “BelSUT”)

Leonenko, D. V.

L47 Calculation of flat trusses: educational method. manual for students of construction specialties / D. V. Leonenko. – Gomel: EE “BelSUT”, 2006. – 57 p.

ISBN 985-468-075-4

Brief theoretical information on the calculation of trusses for static moving and stationary loads is presented. Methods for determining forces in trusses are considered. Detailed examples of solving typical problems are given.

The manual corresponds to the currently existing program in structural mechanics. Intended for students of construction specialties of all forms of study.

ÓÄÊ 539.3 (075.8) ÁÁÊ 38.112

ISBN 985-468-075-4

© Leonenko D. V., 2006

© Decor. EE "BelGUT", 2006

1 BRIEF THEORETICAL INFORMATION 1.1 The concept of a farm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Kinematic analysis of trusses. . . . . . . . . . . . . . . . . . . . 10 1.4 Calculation of trusses for a stationary load. . . . . . . . . . . . . 13 1.5 Analysis of the stress state of trusses

under stationary vertical load. . . . . . . . . . . . 19 1.6 Calculation of trusses for moving loads. . . . . . . . . . . . . . . 21 1.7 Determination of efforts along lines of influence. . . . . . . . . . . . 27 1.8 The concept of truss trusses. . . . . . . . . . . . . . . . . 29 1.9 Kinematic method for constructing lines of influence. . . . . 31

2 EXAMPLES OF SOLVING PROBLEMS 2.1 Calculation of trusses by cutting out nodes. . . . . . . . . . . . . 34

2.2 Calculation of trusses using the section method. . . . . . . . . . . . . . . . . . . . 43 2.3 Calculation of trusses for moving loads. . . . . . . . . . . . . . . 46 2.4 Calculation of truss trusses. . . . . . . . . . . . . . . . . . . . . 51 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

1 BRIEF THEORETICAL INFORMATION

1.1 Concept of a farm

A rod system with a rigid or hinged connection of rectilinear elements at nodes, which remains geometrically unchanged after the conditional replacement of its rigid nodes with hinged ones, is called a truss (Figure 1.1,a).

The scope of application of trusses is very diverse: floors of long-span buildings, bridges, television towers, etc. The rationality of these structures has led to their widespread use today.

Calculation diagram of the farm. In real trusses, the rods are rigidly connected to each other. When making calculations, it is always assumed that all nodes are ideal hinges, and the loads are transferred through the system of auxiliary structures to the truss nodes (Figure 1.1, b, c).

In rigid truss nodes, slight bending of individual elements occurs, but the stresses from bending are small compared to the stresses from the axial force, so they are neglected. At the same time, in some cases (for example, in reinforced concrete trusses)

the calculation is carried out taking into account the rigidity of the nodes, since if the influence of bending moments is ignored, significant errors in determining the stress state of massive elements are possible. In this case, the nature of the truss is similar to that of frame structures.

 In reality, the loads are applied not only to the nodes, but also to individual rods, i.e., the design diagrams of the trusses differ significantly from real structures. However, even in this case it is applicable to them with a sufficient degree of approximation hinge-rod design scheme.

The idealization of calculation schemes, while making it possible to simplify calculations, has a slight effect on their accuracy. The applicability of the hinge-rod scheme to real trusses has been confirmed experimentally.

 In some cases, especially when reconstructing existing structures, it may turn out that in addition to the nodal load, extra-nodal load is inevitable. In this case, the rods taking up the extra-nodal load will experience bending with tension or compression. These rods are separately designed for local bending load.

Basic elements of a farm. The distance between the axes of the truss supports (Figure 1.2) is called the span. The rods are located

those placed along the outer contour of the truss are called belt and form belts. The set of truss rods between its lower and upper chords is called a lattice. The lattice, as a rule, consists of vertical (uprights) and inclined (braces) rods.

If you mentally move along the braces from the supports of the farm to the middle, then along some braces you will have to go down, “descend”, along others - up, “ascend”. In accordance with this, braces are divided into descending and ascending.

Figure 1.2

The part of the truss located between adjacent chord nodes is called a panel, and the distance between these belt nodes is the length of the panel, the largest distance between the chords is the height of the truss.

Design practice shows that optimal trusses are obtained with a ratio of height to span dimensions of approximately 1/8 ... 1/10.

1.2 Classification

Farms are classified according to several criteria.

Depending on the nature of the structure, trusses are divided into flat and spatial. If all truss elements lie in the same plane, they are called flat. Spatial are called trusses in which the axes of all the rods, including the supporting ones, do not lie in the same plane. In what follows we will consider only flat trusses.

According to their purpose, farms are divided into:

on the trusses of bridge spans (Figure 1.3, a); rafters used as load-bearing structures for coverings of industrial and civil buildings (Figure 1.3, b), as well as crane trusses; tower trusses (Figure 1.3, b), automobile and other cranes;

truss-masts of power transmission lines (Figure 1.3,г) and äð.

Figure 1.3

According to the outline of the belts, farms are divided (Figure 1.4): into trusses with parallel belts; triangular trusses; trapezoidal trusses;

farms with curved belts (polygonal).

For polygonal trusses, either one or both chords can be non-horizontal. The nodes in the upper and lower chords are usually located along some kind of curve - parabolic, elliptical, box or circle. The rods of such belts are straight and are chords of the curve on which the nodes are located.

Figure 1.4

According to the type of lattice, trusses are divided into trusses with simple

è complex lattices.

Ê farms with simple grille(Figure 1.5) include:

trusses with a braced lattice, which is a continuous zigzag with alternating braces and posts;

a truss with a triangular lattice, which is formed by only one brace with an alternating slope. Trusses with a triangular lattice and additional racks belong to the same class;

trusses with semi-diagonal lattice. The grids of such trusses are formed by replacing the braces with half-braces. Each panel has two different directional braces leading to the rack.

Truss with triangular lattice and additional posts

Truss with half-diagonal lattice

Figure 1.5

Complex lattices are those that are obtained by superimposing two or more simple lattices on top of each other. Trusses with such gratings (Figure 1.6) are divided into:

on trusses with a two-braced lattice. Through each panel (except for the extreme ones) of this truss there are two braces of the same direction;

double-lattice and multi-lattice trusses;

truss farms. Their lattice is formed by introducing into

a regular lattice of additional elements - trusses. The springs perceive local load applied outside the nodes of the main truss. They reduce the length of the compression chord panels, resulting in increased stability of the compression bars.

Truss trusses

Multi-lattice truss

Figure 1.6

Based on the direction of the support reactions, a distinction is made between non-thrust and spaced trusses.

In supports non-thrust trusses When a vertical load is applied to them, only vertical support reactions occur. The horizontal component of the support reactions (thrust) in the hinged-fixed support is zero.

Non-thrust trusses (Figure 1.7), depending on the location of the supports, are divided into beam, cantilever-beam (trusses on two supports), as well as cantilever trusses, one end of which is supported, the other is free.

Note that a truss with the same structure, but with different supports, can belong to different classes. Thus, the truss shown in Figure 1.9, a, is a spacer, and in Figure 1.9, b - non-space.

Figure 1.9

Depending on the ride level, bridge trusses are divided into trusses with a ride on the bottom, trusses with a ride on the top and trusses with a ride in the middle (Figure 1.10).

Figure 1.10

The classification considered is not exhaustive. It indicates the most typical design schemes of flat trusses that are used in construction practice.

1.3 Kinematic analysis of trusses

Any truss used in construction must be designed so that it is geometrically immutableè fixedly attached to the ground. To ensure the invariability of the truss, a kinematic analysis is carried out. In this case, the main concepts are the disk - an unchangeable element of the structure and the number of degrees of freedom W - the number of independent geometric parameters that determine the position of the disk or structure on the plane.

Kinematic analysis consists of the following steps:

à) determining the number of degrees of freedomW of the system and checking the necessary analytical condition of invariability;

b) structural analysis of the structure and verification of the sufficient condition of immutability.

Disks and methods of connecting them. The simplest disk is an articulated triangle. By attaching nodes to it using two rods, the axes of which do not lie on the same straight line,

A truss is a geometrically constant hinge-rod structure.
A truss is called flat if all the truss rods lie in the same plane.
The certainty or stability of a truss reflects the dependence of the number of nodes and rods of the truss:
Farm defined, sustainable
K = 2N - 3 ;
The truss is undefined and has extra rods
K > 2N - 3 ;
The farm is unstable and is a mechanism
K< 2N - 3 .
When calculating a truss, friction at the nodes and the weight of the rods are neglected, or the weight of the rods is distributed among the nodes.
All external loads (forces) are applied to the truss only at the nodes, so all the truss rods experience either compression or tension.
The calculation of a truss comes down to determining the support reactions and forces in its rods.
To determine the reactions of the supports, three equilibrium equations are compiled and solved, considering the truss to be an absolutely rigid body under the action of known external loads (active forces) and unknown reactions of the supports (reactive forces).
There are 2 methods for determining forces in truss rods.

Knot cutting method
The method of cutting out nodes is to mentally cut out the nodes of the truss, applying to them the appropriate external forces, reactions of the supports and reactions of the rods, and create an equilibrium equation for the forces applied to each node.
A node with 2 unknown forces is cut out, since in each node a converging system of forces is formed, respectively, two equilibrium equations are formed
It is conventionally assumed that all the rods are stretched, i.e. the reactions of the rods are directed away from the nodes.

Ritter method
Ritter's method is that the truss is divided into two parts by a section passing through three rods in which the forces need to be determined, and the equilibrium of one of the parts is considered. The action of the discarded part is replaced by corresponding forces, which are directed along the cut rods from the nodes.
Then they create an equilibrium equation for a plane arbitrary system of forces
The Ritter point (center of moments) is a point for each of three dissected rods at which two other rods of a given section intersect, for example, point K is the Ritter point for determining the force in rod 6.
With respect to the Ritter point, an equation is drawn up for the sum of the moments of the selected part of the truss.
In case the rods do not have an intersection point, i.e. are parallel, an equilibrium equation is drawn up in the form of the sum of the projections of all the forces of the selected part of the truss onto an axis perpendicular to these rods.

A flat truss rests on fixed and movable hinges. Loads are applied to the truss nodes. [ 1 ]

A flat truss rests on fixed and movable hinges. Two vertical loads P and two inclined loads - Q and F are applied to the truss nodes. Dimensions are given in meters. [ 2 ]

Flat trusses that have three connections with the foundation and meet the conditions of rigid fastening are called externally statically definable. If we discard the supporting connections and replace their action with forces equal in value to the forces arising in these connections under the action of an external load, then the equilibrium of the truss will not be disturbed and we will get a truss that is in equilibrium under the action of external forces and three unknown forces in the discarded connections - so called bond reactions. [ 3 ]

Flat trusses formed by adding each of the subsequent triangles to the base triangle 1 - 2 - 3 (Fig. 3.16) by attaching two non-collinear rods and one node are called simple trusses. They have the property of geometric immutability, and for them condition (3.29) turns out to be necessary and sufficient. [ 4 ]

The flat truss shown in the figure has frictionless hinges at the nodes and is supported at A and C. The rods AB, BC, DE have the same length and are absolutely rigid. The four inclined elements are identical in both length and elastic properties. [ 5 ]

A flat truss in the shape of a regular polygon with sides Af is connected by radial rods. Radial rods connect the center to each of the nodes. [ 6 ]

A through flat truss has low horizontal rigidity from the plane and therefore acquires stability only in a spatially rigid block with another truss. [ 7 ]

Flat trusses of steel transmission tower structures are usually simple trusses or formed by superimposing two simple trusses on top of each other. [ 8 ]

The simplest flat truss is the three-bar ABC truss shown in Fig. 5.24, a; it contains three nodes. By adding new nodes in the same way, as shown in Fig. 5.24, b with a dashed line, many more complex trusses can be formed. [ 9 ]

A simple flat truss is a truss that can be obtained from a triangular one by successively connecting each new node using two new rods. [ 10 ]

A flat rod truss is a system formed by straight rods connected to each other in a certain sequence by hinges located at the ends of the rods. When rods are connected with such hinges and exposed to loads applied at the nodes, only axial forces arise in the rods - tensile or compressive. [ 11 ]

Rods flat trusses located along its upper contour are called the upper chord, located along the lower contour are called the lower chord. [ 12 ]

For flat trusses L S - 2U 3, if the truss is attached, and L S - 2U, if the truss is free. [ 13 ]