Example 3: Column strengthening - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 118

Table 8.3 Axial loads and bending moments for the relevant load combinations.

Load combination N M

— kN kNm

Load case 3; ULS 6469.8 48.5

Load case 3; SLS, quasi-permanent 2764.7 20.7

8.2 Internal forces
The above loads result in the axial loads on the column as given in Table 8.3, which also
lists the moments due to axial load and eccentricity of loading.

8.3 Determining the cross-sectional values
The cross-sectional values of the column are required at several points in order to
determine its load-carrying capacity. First of all, we need the modular ratio and the area
of the concrete cross-section:

E s
E cm

200
33

α s 6 : 1

A c D 2 = 4 ? π 250 2

? π 1964 ? 10 2 mm 2

Using these values it is possible to calculate the idealized area of the cross-section
according to DAfStb guideline [1, 2] part 1, RV 6.1.4.2, Eq. (RV 6.85):

? A s 1964 ? 10 2 ? 58 : 9 ? 10 2 2264 ? 10 2 mm 2

A i A c α s 1

6 : 1 1

To calculate the idealized second moment of area, we first need the second moment of
area of the gross concrete cross-section:

16 ? 4 ? 4 D 4 250 4 0 ? 10 6 mm 4 I c = 3068 :

DAfStb guideline [1, 2] part 1, RV 6.1.4.2, Eq. (RV 6.87) is used to calculate the
idealized second moment of area:

? X j z j 2

? A s

I i I c α s 1

s

As can be seen from the equation, z s and A s must be determined. This is carried out
below according to Figure 8.3.
First of all we must determine the positions of the bars, or rather the radii to the centres of
the reinforcing bars. This depends on the concrete cover and the diameter of the links
ϕ sw and the bars ϕ s .