A.3.1 Design assumptions
(1)P In analysing a cross-section to determine its ultimate resistance, the design sizes are taken as the nominal sizes.
The assumptions given below shall be used:
a) Plane sections remain plane.
b) Tensile strength (including the flexural strength) of the AAC is ignored for the design of structurally reinforced AAC components. For non-structurally reinforced wall components with bending from non- permanent transverse load see A.5.
c) For cross-sections subject to pure longitudinal compression, the strain of the AAC is limited to |-0,002|.
d) For cross-sections not fully in compression, the strain in the compressed zone is limited to |-0,003|. In intermediate situations, the strain in the compressed zone is limited to |-0,002| at a level of 1/3 of the height of the section from the most compressed face.
e) The cross section shall have sufficient rotation capacity which is fulfilled if the tensile strain of the reinforcement is greater than 0,001, and thus achieving ductile failure.
f) Adoption of the above assumptions leads to the range of possible strain diagrams shown in Figure A.4.
g) Effect of longitudinal reinforcement present in the compression zone shall not be taken into account when calculating the axial loadbearing capacity, unless the reinforcing bars are sufficiently restrained to the principal reinforcement in the tension zone, e.g. by stirrups.
h) In the analysis of a cross-section which has to resist bending combined with a small longitudinal compression force, the effect of the design ultimate longitudinal force may be ignored if the corresponding longitudinal stress, due to the longitudinal load, does not exceed 0,08 fck.
i) Local reduction in the effective depth shall be considered in the cross-sectional analysis.
A.3.2 Stress-strain diagram for AAC
(1)P The design value of the compressive strength of AAC is defined by Formula (A.1):
fcd = fck /γc (A.1)
where
fcd is the design value of the compressive strength of the AAC;
fck is the characteristic compressive strength of the AAC;
γc is the partial safety factor of AAC for ductile or brittle failure.
NOTE 1 The value of γc for use in a country may be found in its national application document. The recommended values for use are given in Table D.4.
(2) The stress-strain diagram for AAC for cross-sectional design is given in Figure A.2. Other established stress-strain diagrams may be also used if they are equivalent with respect to the amount and position of the resulting compression force in the cross section.
Key
1 Idealised diagram 2 Design diagram
Figure A.2 — Bi-linear stress-strain diagram for AAC in compression for cross-sectional design (3) The factor α in Figure A.2 is a coefficient taking into account the long term effects on the compressive strength and of the unfavourable effects resulting from the way the load is applied.
NOTE 2 The value of α for use in a country may be found in its national application document. The recommended value of α for use is 0,85.
A.3.3 Stress-strain diagram for reinforcing steel
(1)P The design value of the yield stress of reinforcing steel is defined by Formula (A.2):
fyd = fyk/γs (A.2)
where
fyd is the design value of the yield stress of reinforcing steel;
fyk is the characteristic yield stress of reinforcing steel;
γs is the partial safety factor for reinforcing steel.
NOTE The value of γs for use in a country may be found in its national application document. The recommended value for use is given in Table D.4.
(2) The design stress-strain diagram for reinforcing steel is given in Figure A.3. Other established stress- strain diagrams may be used. Es is the modulus of elasticity of reinforcing steel (e.g. 2 × 105 MPa).
Key
1 Idealised diagram 2 Design diagram
Figure A.3 — Design stress-strain diagram for reinforcing steel
Key
1 Neutral axis
Figure A.4 — Strain diagrams in the ultimate limit state
A.3.4 Minimum reinforcement
(1)P For structural reinforced components the characteristic bending capacity of the cracked cross- section shall be greater than the characteristic cracking moment, in order to avoid brittle failure at the formation of the first crack. This shall be ensured by providing a minimum content of reinforcement to be determined by calculation. The tensile strength shall be taken as the flexural strength according to 4.2.5 in the uncracked cross-section, but shall be ignored in the calculation of the cracked cross-section.
(2) Unless a more rigorous calculation shows a lesser area to be adequate, the required minimum area of structural reinforcement may be calculated from Formula (A.3):
Asmin = k Ac ƒcflm / ƒyk (A.3)
where
Asmin is the minimum reinforcement area;
Ac is the area of AAC within the tensile zone;
ƒcflm is the mean flexural strength of AAC, determined by Formulae (5)a) and (5b) for bending. For pure tension determined by Formulae (4)a) and (4b);
fyk is the tensile strength of the reinforcement;
k is a coefficient which takes into account the nature of the stress distribution.
In case of pure tension in the whole cross-section k = 1,0.
In case of pure bending without normal compressive force k = 0,4.
(3)P For AAC beams a minimum shear reinforcement is required. In wall, floor and roof components, and in components with minor structural importance the minimum shear reinforcement may be omitted.
(4) For beams the minimum cross-sectional area of shear reinforcement within length s may be calculated from Formula (A.4):
( )( ) ( )
( )
⋅ +
⋅
⋅
⋅ ⋅
⋅ +
⋅ ⋅ +
−
⋅
=
s s
swd Sd
s s
w swd 1 Rd
swmin
sin cot
1 1 ,1
sin cot
240 1 1 1000 / 83 , 0 1 1 ,1 min
α α
s
α α
ρ s t
d
s V
b s d
A (A.4)
where
Aswmin is the minimum cross-sectional area of shear reinforcement within length s, in millimetres;
τRd is the design value of the basic shear strength, in Megapascals; see A.4.1.2.1;
fyk is the characteristic yield strength of the shear reinforcement, in Megapascals;
d is the effective depth in millimetres;
ρ1 is the reinforcement ratio;
s is the spacing of the shear reinforcement, in millimetres;
bw is the minimum width of the section, in millimetres;
VSd is the design value of shear force, in Newtons;
σswd is the design value of the steel stress in the shear reinforcement, in Megapascals;
αs is the angle of the shear reinforcement with the longitudinal axis, see Figure A.5.