When selecting sections of beams, the correct choice of their height is important. The weight and vertical rigidity of the superstructure, the conditions for its manufacture, transportation and installation depend on the height of the beams.
In many cases, when driving on top, the height of the embankment at the approaches to the bridge depends on the height of the beams, and, consequently, the cost of these approaches.
Since when the beam is working for bending, its material is most fully used in the chords and much less at the neutral axis, then when selecting the cross-section of the beam, it is advantageous to take the wall high and thin, placing the material mainly in the chords.
The minimum permissible wall thickness of riveted beams is 10 mm; welded main beams - 12 mm. These limitations are caused by the desire to slow down the noticeable weakening of sheets by corrosion, and for welded beams, in addition, to reduce welding deformations.
For a given design bending moment M, the cross-sectional area of the beam F and, therefore, its theoretical weight can be represented as a function of the beam height h and the thickness of its wall b. You can find the minimum of this function by equating the derivative to zero.
In many cases, the height of the beams is assigned less than the optimal weight in terms of weight, in an effort to reduce the building height of the superstructure or to facilitate the conditions for its manufacture, transportation and installation.
The minimum permissible height of the beams is determined by the requirements for the vertical stiffness of the superstructure.
In existing road bridges with split main beams, which have solid walls, the ratio of the height of the beams to the span ranges from V12 to V20.
Accordingly to the increased rigidity of continuous beams, their minimum permissible height in the middle of the spans can be reduced in comparison with split beams.
The choice of the cross-sectional shape and dimensions of the chords of the main beams is of serious importance. Beams that do not work in conjunction with a reinforced concrete or steel slab are usually given a symmetrical I-section.
The dimensions of the flange corners in riveted beams should be related to the capacity of the horizontal sheet packages attached by the corners to the wall.
The thickness of the package of horizontal sheets, including the flanges of the belt corners and lining in the joints, should not exceed 4.5 diameters of the rivet hole, and the number of riveted bodies in the package should not exceed 7 with a rivet diameter of 23 mm and 8 - with a rivet diameter of 26 mm.
When riveting in two pneumatic hammers, one of which replaces the support, or on the bracket, the thickness of the package can be increased to 5.5 diameters, and the number of riveted bodies increased to 8 with rivets d = 23 mm and up to 9 with rivets d = 26 mm ...
The thickness b of the flange sheets of welded carbon steel beams should not be more than 50 mm, and of low-alloy steel - 40 mm.
The width of the unbordered overhang of the compressed belt of welded beams with a ride on top should not exceed 10 6 and 0.3 m in railway bridges;
in road and city bridges - 15 b and 0.4 m. Here b is the thickness of the belt.
If the limiting thickness and width of a single chord sheet do not provide the required chord area, and an increase in the beam height is undesirable, one of the ones shown in Fig. 337 belt shapes.
The area of the belt corners that attach the horizontal sheets to the wall should correspond to the area of the latter, accounting for approximately 30% of the entire area of the belt.
When this recommendation in cases of powerful beams is difficult to implement due to the limited range of angle bars, part of the required area of the beam can be placed in the form of vertical sheets (lamellas) between the beam wall and the flange corners or go to double-wall beams.
The width of the upper chords of the longitudinal and main beams of railway bridges with a ride on wooden crossbars, according to the working conditions of the crossbars for crushing, should be at least 240 mm.
The width of the overhang a of the belt package of riveted beams, counting from the outer row of rivets of the belt corners to the edges of carbon steel sheets, should be no more than 12 26, where 26 is the thickness of the package. With low-alloy steel sheets, a should be no more than 10 26.
To ensure the density of the package of belt sheets, the distance L from the edge of the package to the nearest row of rivets should be no more than 120 mm and 86, where 6 is the thickness of the thinnest sheet of the package.
The thickness of the sheets in riveted beams should be no more than 20 mm according to the conditions for punching holes on punching machines.
A well-chosen cross-section of the beam must meet the requirements of strength, endurance, manufacturability (ease of manufacture and installation) and, ultimately, cost-effectiveness in terms of material and labor costs with guaranteed operational reliability.
The design bending moments along the length of the beam change. The selection of the section of the beam is carried out, first of all, in the section with the maximum bending moment. As the bending moments decrease, the cross-section of the beam is reduced mainly due to the area of the chords.
In welded beams, the thickness and width of horizontal sheets are reduced; in riveted beams - the number of sheets in belt packs. The possibility of such a reduction should be provided for when selecting the section of the beam at the place of maximum bending moment, where the chords must be sufficiently powerful.
The sections of the beam, starting from which their area can be safely reduced, are usually determined graphically using a material diagram.