Truss – a through lattice structure, consisting of separate straight rods connected to each other at the nodes. This system is geometrically unchanged even if all real nodal connections are replaced by ideal hinges ( Fig. 2.11 ).
Rice. 2.11 Farm scheme:
1 – upper belt; 2 – lower belt; 3 – brace; 4 – rack; 5 – support brace;
6 – support post; 7 – reference node; 8 – ridge knot
Trusses are the foundations of many rod systems and are diverse in purpose. They are used in the construction of building coverings (truss, truss trusses), interfloor ceilings, as contour diaphragms of shells, folds, etc.
Farms are made of steel, aluminum alloys, wood, reinforced concrete. Sometimes these materials are combined in order to make the most rational use of their properties.
The truss works in bending from an external vertical load, usually applied at the nodes. Due to this, axial tensile and compressive forces occur in the truss elements, which ensures a more complete use of the material’s load-bearing capacity compared to beams.
Farms can be two-support (cut), multi-support (continuous) and cantilever. Continuous trusses, unloaded in the span as a result of the action of support moments, are lighter than split ones. However, they are more difficult to manufacture, install and are more sensitive to the settlement of supports. continuous and cantilever trusses are not typified and are rarely used, mainly for unique coverings of large spans.
Roof trusses can have a variety of shapes that meet the architectural and functional requirements of the designed object. The geometric scheme of the farm is determined by the outline of the belts and the type of lattice. According to the outline of the belts, truss trusses are quadrangular (with parallel and non-parallel belts), pentagonal (trapezoidal), polygonal (polygonal), segmental (circular and parabolic), triangular (with a straight or broken lower belt), single and double slope ( Fig. 2.12 ).
Rice. 2.12 Geometric diagrams of trusses:
a – triangular; b, c – quadrangular with parallel and non-parallel belts; g – pentagonal (trapezoidal); e – polygonal (polygonal);
e – segmented (arched); g – lenticular (fish-shaped); h – flattened
The outlines of the upper belt of trusses are determined mainly by the architecture of the building and are linked to the roofing material and slope. The line of the lower belt is determined by the presence of a false ceiling and the requirements of the interior.
Trusses with parallel belts and trapezoid are the simplest in form and manufacture, therefore they are widely used in civil and industrial buildings for various purposes, having a small building height compared to other types of trusses.
In public buildings, lenticular and fluted trusses are most widely used, and in industrial buildings – trusses with parallel belts and support at the nodes of the upper belt, etc.
Gridless trusses are used in intermediate floors, when the inter-truss space is used as an operated floor. Such a truss is devoid of the property of geometric invariability and can exist provided that its hinge joints are replaced by rigid ones, that is, it is turned into a frame. The disadvantages of these trusses include the occurrence of significant bending moments in the chords and struts, which lead to an increase in their sections and the need to make the nodes more rigid, and, consequently, to an increased consumption of steel.
The optimal height of the truss from the condition of the minimum mass and the required rigidity is obtained with the ratio of its height to the span: h / l = 1/4 … 1/5 (relative height of the truss). The larger it is, the less effort in the belts. however, in this case, the trusses, having a considerable height, are inconvenient in transportation and installation, overestimate the volume of the building. Therefore, the recommended truss heights are less than optimal.
Metal trusses usually cover spans of more than 24m. Sometimes they reach 100m, but starting from 60…70m it is more expedient to use arches or frames.
Wooden trusses are used to cover spans 9 … 36m. Nevertheless, examples of the use of trusses with a span of 70 m are known in world practice. In our country, industrial-made wooden trusses are used – segmented, polygonal, trapezoidal, triangular and trussed (glued, block). For the most part, they have a lower belt made of profiled or round steel, and therefore they are called metal-wooden. In such trusses, the properties of wood, which works well in compression in the upper chord, and steel in the stretched lower chord, are favorably combined.
Almost any geometric scheme of a truss can be implemented in reinforced concrete . However, in modern construction, the most rational types are used: segmental, with parallel belts and trapezoidal gables with a straight or broken lower belt ( Fig. 2.13 ).
The spans of typical trusses are 18.24.30 m at a step of 6 … 12 m. For spans over 30 m, metal trusses, reinforced concrete arches or thin-walled spatial structures are more economical.
Reinforced concrete trusses are characterized by a large dead weight, exceeding the weight of steel and wooden trusses by 2-3 times. This disadvantage is compensated by their increased fire resistance and steel savings (up to 50%).
Rice. 2.13 Schemes of reinforced concrete trusses:
a – triangular; b – trapezoid; c – single-sided; g – with parallel belts;
d – the same, bezraskosnaya; e – the same, combined; g – polygonal;
h – segment; and – bezraskosnaya; k – polygonal with a broken lower belt
An arch is a curvilinear design. Its defining feature is the thrust caused by the immovability of its supports. The outline of the axis of the arch can be parabolic, circular, elliptical. There are box arches (multi-center), “creeping” (supports are located at different levels), as well as triangular spacer systems ( Fig. 2.21 ).
Rice. 2.21 The outlines of the axes of the arches:
a – parabolic; b – circular; c – elliptical;
g – box; e – triangular; e – “creeping”
Arch spans – from 30 to 60 m (depending on the material), and unique arched coverings – up to 100 m. They can be used both as planar load-bearing structures and as part of spatial coatings as shell diaphragms.
Depending on the size of the lifting boom, the arches are divided into flat f= (1/8…1/6) l and lifting f= (1/4…1/2) l.
According to static work, three-hinged, two-hinged and hingeless arches are distinguished ( Fig. 2.22 ).
Rice. 2.22 Design schemes of arches and diagrams of bending moments:
a – three-hinged; b – two-hinged; c – hingeless
The three-hinged arch is statically determinable, it is not sensitive to displacements of supports and temperature fluctuations; easy to install and transport in the form of semi-arches. However, due to the uneven distribution of bending moments along its length, it is the most material-intensive.
A two-hinged arch is once statically indeterminate. Its thrust is less than that of a three-hinged arch. It is distinguished by a more favorable distribution of bending moments along its length, which is why it has become most widespread.
A hingeless arch is three times statically indeterminate. Pinching it in the supports contributes to a more uniform distribution of moments along the length, so that the design is lightweight. However, this factor makes it sensitive to the settlement of supports and temperature effects. Such an arch requires a reliable foundation and strong foundations, which is not always feasible for technical and economic reasons.
In the constructive solution, the arches are of a solid profile (solid-walled) or through (lattice). The contours of the arches, outlined by their belts, can be segmental, sickle-shaped, or have a constant height ( Fig. 2.23 ).
The thrust in the arches is perceived by puffs, foundations or rigid supporting structures ( Fig. 2.24 ). Sloping arches, as a rule, have puffs. Lifting arches, installed on a soil base, transfer thrust to foundations, buttresses. In case of weak soils or insignificant expansion forces, in order to avoid shifting the foundation, an additional tightening is arranged in the plane of the floor or under it. The position of the arch, the greater the spread.
Rice. 2.23 Structural schemes of arches:
a, b, c – solid profile; d, e, f – through
Rice. 2.24 The main ways of perceiving the spacing of arches:
a – puff; b – soil base and puff; c – adjoining building
Metal arches can cover spans from 30 to 150m.
Solid-walled arches with spans up to 60 m have a section height of 1/50 … 1/80 of the span. The cross section of the belts of arches of small spans is usually made of rolled profiles, and more powerful arches – in the form of I-beam or box-shaped profiles ( Fig. 2.25 a – c ). Stiffeners are installed at distances approximately equal to the height of the arch section. Such arches count on strength as compressed-curved elements.
Sometimes, for functional reasons, systems are designed from two rectilinear elements ( see Fig. 2.25 e ). the height of their section is taken equal to 1/15 … 1/20 of the span. Compared with curved arches, such structures are ineffective.
Rice. 2.25 Sections of belts of metal arches:
a – c – solid-walled; Ms. – through
Through (lattice) arches are used for spans of more than 60m. They are designed mainly with parallel chords. The cross-sectional height of such arches is 1/30…1/60 of the span, since they have less rigidity. The arch belts are made up of corners, channels, I-beams, pipes. With large spans and efforts, through arches are made spatial with a triangular or quadrangular cross section ( Fig. 2.25 df ). The lattice made of single profiles is usually triangular, often with additional posts that reduce the length of the compressed panels.
Cross-sections of solid and through arches are recommended to be taken constant along the entire length. Sometimes two- and three-hinged arches, in order to save metal, are designed as sickle-shaped or segmented.
Wooden arches can cover spans from 12 to 100m. For technological reasons, solid-walled arches are usually made with a constant radius of curvature. Lifting boom f= 1/4…1/10 span l.
The cross section of the curved arch is assembled from a package of glued boards up to 33mm thick (glued-laminated arches). Rectangular sectional shape with aspect ratio h/b ≤4 is preferred. Arch section height h= (1/30…1/50) l.
Reinforced concrete arches can be used starting from a span of 18m, but they become more economical than trusses with spans of more than 30m. it is most expedient to cover spans from 36 to 80 m with them.
The axis of the arch can have a parabolic or circular shape (to simplify manufacturing). The most common are double-hinged arches with a span of up to 36m. they are performed flat with a lifting boom f= (1/6…1/8) l. The thrust is usually perceived as a puff.
Long-span lifting arches have a more complex axis shape. They are usually made three-hinged (two semi-arches). The thrust is transferred to the foundations and foundation soils. In case of weak soils, a puff is arranged below the floor level ( Fig. 2.26 ).
Arches can be prefabricated in the form of mounting blocks with a length of 6 to 12 m or monolithic. They are made of concrete classes B30 and B40. step arches 6 … 12m. Reinforced concrete roof panels are laid along the arches, fastened by welding embedded parts and also performing the functions of horizontal ties.
Rice. 2.26 Options for supporting reinforced concrete arches
and ways to pay off the dispute:
a – puff; b – buttress; c – frame; d – foundation; 1 – arch; 2 – puff;
3 – column; 4 – pylon; 5 – frame; 6 – foundation; 7 – underfloor tightening
3. SPATIAL BEARING STRUCTURES OF COATINGS