1) Plate; 2) equal-shelf angle; 3) unequal-shelf angle; 4) channel
5) channel with parallel sides of shelves; 6) normal girder; 7) girders with parallel shelf edges; 8) brand; 9) welded beam; 10) round tube; 11) bent channel; 12) bent C-shaped channel; 13) bent equal-shelf angle; 14) bent unequal-shelf angle; 15) figuratively joist; 16) bent Z-shaped profile; 17) square bent-welded profile; 18) rectangle bent-welded profile; 19) wavy deck; 20) trapezoid profiled sheet.
Quiz:
What are the basic requirements for MC?
What advantages have MC?
What is the approximate annual use of steel in construction?
What time did applying of steel in building structures begin?
What metals are used in the construction MC?
What is gauge?
What are the advantages of closed sections?
What is the chemical structure and variations of the aluminum alloys?
Theme3. Calculation of Elements of Steel Constructions
1. Calculation of elements of metal designs for limit states.
2. Standard and rated steel resistance.
3. Calculation of metal construction elements for the central stretching.
4. Calculation of metal construction elements for the central pressure.
5. Calculation of metal construction elements for a bend.
1. Calculation of metal construction elements for limit states
1.1. The structure of rated formulas
Calculation for limit conditions of the first group is made always for all elements bearing loading.
Loss of bearing ability can happen owing to destruction of a material, loss of stability, fatigue development. The structure of settlement formulas is identical to the most part of limit conditions of the first group.
The condition is the basis for calculation of durability: destruction won't come if the greatest tension doesn't exceed settlement resistance:
Inner effort r γс
Strain=geometrical factor <γn
Where R - the settlement resistance of steel;
γс - the coefficient of working conditions, considers adverse influences of environment and other circumstances which aren't reflected in calculations by a direct way; γп - reliability coefficient to destination designs.
The effort in a counted element is defined by a type of loading (at stretching — the normal force of N, at a bend — the bending moment of M etc.).
The geometrical factor is determined by nature of distribution of tension by the cross section of an element (at uniform distribution — the area and, at the linear law of distribution — the moment of resistance of W etc.).
Inner effort R γс
Strain =geometrical factor <γn
The structure of formulas for check of the general stability is similar, but settlement resistance is multiplied by decreasing coefficient which depends on kind of work of an element (at the central compression applied р - coefficient of a longitudinal bend).
Stability condition:
So, formulas for check of stability differ from formulas for durability check by existence in a coefficient denominator φ.
1.1. Standard and settlement resistance.
For standard resistance take the minimum values:
a) Limit of fluidity of Ryn = σT;
b) Temporary resistance of Run = σв.
At steel works the limit of fluidity and temporary resistance control selectively. Therefore, the material can get to MC with the worst properties, than it is established to SS therefore settlement resistance to stretching, for rolling steel are equal to compression and a bend standard, divided into reliability coefficient on a material γm.
Distinguish settlement resistance:
a) On fluidity limit: Ry = Ryn/γm,
b) On temporary resistance: Ru = Run/γm.
The second of them apply very seldom, only to the elements which operation is possible and after achievement of a limit of fluidity.
In table 51 II-23-81* Construction Norms and Regulations settlement resistance are accepted individually for each brand of steel.
1.3. Calculation for the second group of limit states.
Calculation essence — it has to exclude excessive deformations (deflections, angles of rotation) and fluctuations of designs. Usually calculation is reduced to deflection check (often speak - to rigidity check).
These calculations can be not carried out when it is obvious that deformations of a design are insignificant.
Always check rigidity of bent elements (but often enough only to be convinced that the accepted height of a beam is more min). It is necessary to check a deflection for low farms, which belts are executed from high-strength steel.
Relative limit deflection [f/l] the greatest relative deflection resolved by norms for this type of MK. Relative limit deflections are established by norms in flight shares individually for each type of metal designs.
The settlement formula turns out from a rigidity condition: the relative deflection of a beam from standard loading fn/l calculated on formulas of resistance of materials shouldn't exceed a relative deflection [f/l] established by norms for this type of MC. Rigidity condition:
2. Calculation of elements on the central stretching.
Completely very few designs work for stretching, more often all design, and its separate elements is stretched not. The stretched elements share on central stretched and is non-central the stretched. Central stretched the elements the stretching force on which works on the section center of gravity (elements of farms, inhaling of arches, walls of tanks, suspension brackets) are considered.
We will consider work of the central stretched element on the example of a steel strip. At calculation it is necessary that at the central stretching of a strip in its section there is uniform stretching tension σ. However existence of openings or cuts in a strip reduces the area of cross section and at the same time leads to that near openings (cuts) there is a concentration of tension (increase in tension in comparison with average size σ). Concentration of tension can lead to destruction. Openings (cuts) have to be carried out without acute angles, with smooth contours as it promotes reduction of concentration of tension.
Destruction of the central stretched elements happens on section to the smallest area — An. In case easing (openings, cuts) is absent, the area net is equal to the area gross And.
Calculation of durability of the central stretched steel element is conducted on a formula:
Where N — the greatest stretching effort operating on an element;
An — the section area net, An = And - Aosl;
Ry — the settlement resistance of steel taken on a limit of fluidity;
γс — working condition coefficient.
γп - responsibility coefficient to destination buildings.
The long stretched elements can change the initial form (to be bent) as a result of excessive flexibility and it can complicate their further application. Therefore flexibility of the stretched elements is limited to norms and depends on purpose of elements and character of operating loadings (static or dynamic).
Where lef - the settlement length of an element;
i - Radius of inertia of section;
[λ] - limit flexibility (tab. 20 * II-23-81 Construction Norms and Regulations).
At calculation of the central stretched elements usually there are following types of tasks: selection of section of the stretched element (type 1) and check of durability of the accepted or available element (type 2).
