Page 168 - Advanced Design Examples of Seismic Retrofit of Structures

160 Advanced Design Examples of Seismic Retrofit of Structures

l Connections
– Diaphragms-to-shear walls
– New shear walls-to-existing shear walls
l Foundation

3.5.2.1 RC Shear Walls
Flexural Design
The flexural design of the RC shear walls is according to Eq. (3.9) [8]. This
equation should be used for the eight aforementioned loads combinations under
100% of the most critical direction of ground motion, and 30% of the ground
motion in the orthogonal axis. Also, these controls should be made for the
Earthquake-1 and Earthquake-2 levels for satisfying LS and CP performance
levels, respectively. As a result, there are a total of 64 controls for each RC
shear wall.
2 2

M UD y
M UD x
+ 1 (3.9)
m x κM CE x m y κM CE y
where:
¼design bending moment about the x-axis for axial load P UF ;
M UD x
¼design bending moment about the x-axis for axial load P UF ;
M UD y
¼expected bending strength of a member about the x-axis;
M CE x
¼expected bending strength of a member about the y-axis;
M CE y
κ ¼a knowledge factor used to reduce component strength based on the level
of knowledge obtained for individual components during data collection;
m x ¼value of m for bending about the x-axis of a member; and
m y ¼value of m for bending about the y-axis of a member.
The significant scale of computations in this part led to development of a
MATLAB code, which automatically perform the tasks as follows:
(A) Receiving forces and moments in the shear walls from the numerical
model based on the expected values of concrete and steel as input data.
(B) Receiving forces and moments in the shear walls from the numerical
model based on the lower bound values of concrete and steel as input data.
(C) Development of the axial force-flexural moment interaction curves, i.e.,
(P-M) x and (P-M) y for the expected values of concrete and steel in four
is
main angles of 0 degree, 90 degree, 180 degree, and 270 degree (M UD x
is computed
computed based on angles 0 degree and 180 degree; M UD y
based on angles 90 degree and 270 degree).
(D) Determination of the expected value of flexural capacity of the applied
axial forces from force-controlled loads combinations about the x- and
y-axes under four main angles of 0 degree, 90 degree, 180 degree, and
270 degree. It is noteworthy that according to Section 10.7.2.3 of ASCE