Effective depth of cross-section
Effective depth of cross-section is used for calculation of basic value of curvature and it is calculated according to clause 5.8.8.3(2) in EN 1992-1-1. The EN 1992-1-1 does not give rules when the reinforcement is not symmetrical but according to [4] the following rules are used for calculation effective depth:
- for symmetrical reinforcement and in case if all reinforcement is not concentrated on opposite sides, but part of it is distributed parallel
dy = 0,5 ∙ b + isy, dz = 0,5 ∙ h + isz
- for other cases (deign of reinforcement)
dy = b - asy, dz = h - asz
- for other cases (check) - the effective depth is calculated from plane of equilibrium or by simplified calculation, if this value cannot be calculated from this plane, see "Coefficient for calculation of effective depth of cross-section"
where
| isy(z) | the radius of gyration of the total reinforcement area in direction of y(z) axis of LCS |
| b | dimension of cross-section in centre of gravity in direction of y axis of LCS |
| h | dimension of cross-section in centre of gravity in direction of z axis of LCS |
| asy(z) | distance of centre of tensile reinforcement from tensile edge of css |
Calculation the radius of gyration of the total reinforcement and distance of centre of tensile reinforcement from tensile edge depends on shape of cross-section and if the internal forces are calculated for design of reinforcement or for checks. It means, this value can be different for design of reinforcement and for checks.
The user (real) reinforcement defined via REDES and free bars are not taken into account for calculation effective depth of cross-section for design reinforcement to column
Design of reinforcement for rectangular section
Total area of reinforcement
As = μs ∙ Ac
Calculation of ratio of reinforcement in y and z direction
ratioy = σy / (σy + σz), ratioz = σz / (σy + σz)
if σy = 0 MPa and σz = 0, then ratioy = ratioz = 0.5
Calculation area of reinforcement in direction of y(z) axis of LCS
As,y(z) = ratioy(z) ∙ As
Distance of centre of tensile reinforcement from tensile edge of cross-section
as = cnom + dss + 0,5 ∙dsm
Position of reinforcement from centroid of concrete cross-section in direction of y(z)
zs,y = 0,5 ∙ b - as, zs,z = 0,5 ∙ h - as
Second moment of reinforcement area
Is,y = As,y ∙ (zs,z)2 + 1 / 3 ∙ As,z ∙ (zs,z)2
Is,z = As,z ∙ (zs,y)2 + 1 / 3 ∙ As,y ∙ (zs,y)2
Radius of gyration of the total reinforcement area
is,y(z) = √(Is,z(y) / As)
where
| μs | estimation ratio of longitudinal reinforcement from recalculation internal forces for design, see "Estimation of ratio of longitudinal reinforcement" |
| Ac | cross sectional area of concrete |
| σy(z) |
the bending stress in concrete calculated for uncracked concrete cross-section according to formulas: σy(z) = M0Ed,y(z) / Wc,y(z) |
| My(z) | 1st order moment around of y(z) axis of LCS (in SCIA Engineer value My(z)) without imperfection and minimum value of eccentricity |
| Wc,y(z) |
section modulus of concrete cross-section around y(z) axis of LCS Wc,y = 1 / 6 ∙ b ∙ h2, Wc,z = 1 / 6 ∙ b2 ∙ h |
| b | width of rectangular cross-section |
| h | height of the rectangular cross-section |
| cnom | nominal concrete cover, see "Design Defaults" |
| dsm | diameter of longitudinal main reinforcement of the column, see "Design Defaults" |
| dss | diameter of transverse reinforcement (stirrup) of the column, see "Design Defaults" |
Design of reinforcement for circular section
Total area of reinforcement
As = μs ∙ Ac
Distance of centre of tensile reinforcement from tensile edge of cross-section
as = cnom + dss + 0,5 ∙ dsm
Position of reinforcement from centroid of concrete cross-section in direction of y(z)
zs = 0,5 ∙ D - as
Second moment of reinforcement area
Is,y = Is,z = As / 2 ∙ ((As / (4 ∙ π ∙ zs))2 + zs2)
Radius of gyration of the total reinforcement area
is,y(z) = √(Is,z(y) / As)
where
| μs | estimation ratio of longitudinal reinforcement from recalculation internal forces for design, see "Estimation of ratio of longitudinal reinforcement" |
| Ac | cross sectional area of concrete |
| D | diameter of circular cross-section |
| cnom | nominal concrete cover, see "Design Defaults" |
| dsm | diameter of longitudinal main reinforcement of the column, see "Design Defaults" |
| dss | diameter of transverse reinforcement (stirrup) of the column, see "Design Defaults" |
Design of reinforcement for other cross-sections
Total area of reinforcement
As = μs ∙ Ac
Area of reinforcement in each edge
As,i = As/nedge
Distance of centre of tensile reinforcement from tensile edge of cross-section
as = cnom + dss + 0,5 ∙ dsm
Position of reinforcement from centroid of concrete cross-section in direction of y(z)
zs,y(z)i = disty(z)i - as
Second moment of reinforcement area
Is,y(z) = ∑(As,i ∙ zs,z(y)i2)
Radius of gyration of the total reinforcement area
is,y(z) = √(Is,z(y) / As)
where
| μs | estimation ratio of longitudinal reinforcement from recalculation internal forces for design, see "Estimation of ratio of longitudinal reinforcement" |
| Ac | cross sectional area of concrete |
| nedge | number of edge of cross-section |
| disty(z) | distance from the middle of the i-th edge to centre of gravity of cross-section in direction of y(z) axis of LCS |
| cnom | nominal concrete cover, see "Design Defaults" |
| dsm | diameter of longitudinal main reinforcement of the column,see "Design Defaults" |
| dss | diameter of transverse reinforcement (stirrup) of the column, see "Design Defaults" |
Checks for all type of cross-sections
Total area of reinforcement
As = ∑Ai,s
Second moment of reinforcement area
Is,y(z) = ∑(As,i ∙ zs,z(y)i2)
Radius of gyration of the total reinforcement area
is,y(z) = √(Is,z(y) / As)
where
| Ai,s | the cross-sectional area of i-th bar of reinforcement |
| zs,y(z)i | the position of i-th bar of reinforcement from centre of gravity of cross-section in direction of y(z) axis of LCS |