Page 177 - Advanced Design Examples of Seismic Retrofit of Structures

Example of an RC Building Retrofitted by RC Shear Walls Chapter 3 169

(E) Determination of the ratio of the shear force to the shear capacity of the
segment.
(F) Comparison of the values of the ratios in the previous step and determina-
tion of the most critical ratio.
Some retrofitting stages of the vulnerable shear wall P 1L are presented in
Figs. 3.32–3.34.

3.5.2.2 Diaphragms
All the diaphragms are assumed to be force-controlled members, and hence the
force-controlled loads combinations are used for their evaluation. The controls
for the diaphragms include the following.

In-Plane Shear
For evaluation the shear adequacy of the diaphragms, the shear forces in the
diaphragms under various loads combinations are calculated and compared
to the shear capacity of the section which is as follows.
p ffiffiffiffi
v c ¼ 0:53 f c 0
p ffiffiffiffiffiffiffiffi (3.11)
¼ 0:53 170 ¼ 7kg=cm 2
A sh f y
v s ¼
bd

2
20 10 ð 300Þ 2 (3.12)
¼ 3:0 MPa,A sh ¼ 2 φ18@25 cmð Þ ¼ 20cm
¼ 2 2
100 10 20 10
v n ¼ v c + v s ¼ 0:7+ 3:0 ¼ 3:7 MPa;use v n ¼ 3:0MPa
As an example, the shear stresses at the roof of story 2 are compared with
the assumed value of 3.0MPa (see Fig. 3.35). The areas where these stresses
exceed 3.0MPa are concentrated at the vicinity of the columns’ ends. Because
of the wedge shape of the column ends with the average thickness of two time of
the diaphragm’s thickness (50cm), the shear capacity of the section is larger
than the shear demands.

Connection of Diaphragms
The connection of the new shear walls to the diaphragms and also the connec-
tion of the diaphragms at the connection line between the two building parts are
assumed to be made by two layers of crossed φ16@20 cm.
2
A s ¼ 2000 mm =m, f y ¼ 400 MPa
The shear capacity of the connection line is:
A s f y ¼ 2000 400 ¼ 800 kN=m
which is considerably larger than the shear forces in the diaphragms (deter-
mined from the results of the model) in all the stories.