« Combinations of actions Exercise »

Effects of actions

Effects of actions (E) are deformations (displacements, rotations etc.) and tensions (moments, shears/axial forces, stressesetc.) and refer to structural elements (slabs, beams, columns, footings etc.) [EC0, 6.4.3]. The effects of the design action ( Ed) ensure the structural integrity, provided that they do not exceed the corresponding design resistances (Rd) (the general condition is Ed<Rd). Design action effects (E d) are considered in two families of combinations of actions, i.e. with or without earthquake action.

All combinations of the following actions are examined:

Σ(γ G · G k )+γ Q · Q 1 +Σ(γ Q · ψ 0 · Q i ), i>1[EC 0, 6.4.3.2. expression 6.10]
Factors γ, involved in each design combination, are received from the table of the §2.2.2.1 [EC0, table A1.2(B)].

Note

If verification of static equilibrium (EQU) [EC0, 6.4.1.] is required, then γg,sup=1.10 (factor of unfavorable actions) and γg,inf=0.90 (factor of favourable actions). However, in buildings [*] NoteIn individual elements subjected to horizontal actions, e.g. as in a retaining walls, equilibrium verification is essential. , usually there is no need for EQU, particularly for combinations without earthquake.

Definition of tensions-deformations of a structure for combinations of seismic (or accidental) actions

All seismic combinations of the following gravity actions are examined:

ΣG k +A Ed +Σ(ψ 2 · Q i ), i ≥1 [EC0, 6.4.3.4. expression 6.12b]

Verification of static equilibrium (EQU) may be omitted in buildings with plain frame function or of mixed frame and wall systems having more than one frames on both principle directions. This happens because in these structures the vertical forces due to horizontal seismic actions on footings are distributed alternatively to all supports of the base, usually avoiding the problem of static equilibrium. In any case the danger of loss of static equilibrium of a structure, for any actions combination, is concluded from the analysis results by checking the significant tensile axial forces in the columns at the foundation level. In this case EQU is mandatory.

Definition of tension - deformation envelope

The envelope of all stress resultants in structural element level (e.g. beam bending moment) and in storey level (e.g. displacements of diaphragm) are produced by the two combination families, i.e. without and with earthquake. These values in each structural element (e.g. Beam design moments) will be compared to the respective moments of resistance of the element.

Strength of structural elements

The use and participation of materials (concrete, steel) composing reinforced concrete, in order to obtain the adequate strength for the structural elements is being described in Chapter 1.4 of volume Α'.

The design strength of structural elements should be calculated using the material partial factors γC and γS, given in the following table.

 Design states γC (concrete) γS (reinforcing steel) Permanent & Variable 1.5 1.15 Accidental 1.2 1.0

Table 2.4: Partial factors for materials for ultimate limit states

Effects of actions (E) are deformations (displacements, rotations etc.) and tensions (moments, shears/axial forces, stressesetc.) and refer to structural elements (slabs, beams, columns, footings etc.) [EC0, 6.4.3]. The effects of the design action ( Ed) ensure the structural integrity, provided that they do not exceed the corresponding design resistances (Rd) (the general condition is Ed<Rd). Design action effects (E d) are considered in two families of combinations of actions, i.e. with or without earthquake action.

All combinations of the following actions are examined:

Σ(γ G · G k )+γ Q · Q 1 +Σ(γ Q · ψ 0 · Q i ), i>1[EC 0, 6.4.3.2. expression 6.10]
Factors γ, involved in each design combination, are received from the table of the §2.2.2.1 [EC0, table A1.2(B)].

Note

If verification of static equilibrium (EQU) [EC0, 6.4.1.] is required, then γg,sup=1.10 (factor of unfavorable actions) and γg,inf=0.90 (factor of favourable actions). However, in buildings [*] NoteIn individual elements subjected to horizontal actions, e.g. as in a retaining walls, equilibrium verification is essential. , usually there is no need for EQU, particularly for combinations without earthquake.

Definition of tensions-deformations of a structure for combinations of seismic (or accidental) actions

All seismic combinations of the following gravity actions are examined:

ΣG k +A Ed +Σ(ψ 2 · Q i ), i ≥1 [EC0, 6.4.3.4. expression 6.12b]

Verification of static equilibrium (EQU) may be omitted in buildings with plain frame function or of mixed frame and wall systems having more than one frames on both principle directions. This happens because in these structures the vertical forces due to horizontal seismic actions on footings are distributed alternatively to all supports of the base, usually avoiding the problem of static equilibrium. In any case the danger of loss of static equilibrium of a structure, for any actions combination, is concluded from the analysis results by checking the significant tensile axial forces in the columns at the foundation level. In this case EQU is mandatory.

Definition of tension - deformation envelope

The envelope of all stress resultants in structural element level (e.g. beam bending moment) and in storey level (e.g. displacements of diaphragm) are produced by the two combination families, i.e. without and with earthquake. These values in each structural element (e.g. Beam design moments) will be compared to the respective moments of resistance of the element.

Strength of structural elements

The use and participation of materials (concrete, steel) composing reinforced concrete, in order to obtain the adequate strength for the structural elements is being described in Chapter 1.4 of volume Α'.

The design strength of structural elements should be calculated using the material partial factors γC and γS, given in the following table.

 Design states γC (concrete) γS (reinforcing steel) Permanent & Variable 1.5 1.15 Accidental 1.2 1.0

Table 2.4: Partial factors for materials for ultimate limit states

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