Page 83 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter 2 75

2.7.5 Capacity Forces Calculations
Where evaluating the behavior of deformation-controlled actions, the expected
strength, Q CE , shall be used. Q CE is the expected strength of a deformation con-
trolled action of an element at the deformation level under consideration and is
defined as the mean value of resistance of a component at the deformation level
anticipated for a population of similar components, including consideration of
the variability in material strength and strain hardening and plastic section
development [2].
Where evaluating the behavior of force-controlled actions, a lower-bound
estimate of the component strength, Q CL , shall be used. Q CL is the lower-bound
estimate of the strength of a force-controlled action of an element at the defor-
mation level under consideration and is defined as the mean minus one standard
deviation of the yield strengths, Q y , for a population of similar components.

2.7.5.1 Deformation-Controlled
Expected in-plane strength of URM walls shall be the lesser of rocking strength
or bed-joint sliding strength in “Expected In-Plane Rocking Strength of URM
Walls and Piers” and “Expected In-Plane Bed-Joint Sliding Strength of URM
Walls and Piers” sections, respectively.

Expected In-Plane Rocking Strength of URM Walls and Piers
Based on ACE41-13 [2], the expected lateral strength, Q CE , of URM walls or
pier components for rocking failure mode shall be calculated in accordance with
Eq. (2.31):
L
Q CE ¼ V r ¼ 0:9 αP D +0:5P W Þ (2.31)
ð
h eff
where:
h eff ¼height to resultant of seismic force;
L ¼length of wall or wall pier;
P D ¼superimposed dead load at the top of the wall or wall pier under
consideration;
P W ¼self weight of the wall pier;
V r ¼strength of wall or wall pier based on rocking; and
α ¼factor equal to 0.5 for fixed-free cantilever wall, or equal to 1.0 for
fixed-fixed wall pier.
Note that Code 360 [10] does not include the effects of wall’s or pier’s
self-weight into account. As a result, the equation in this code is similar to
the previous version of ASCE 41, that is, ASCE 41-06 [15]. This results in zero
capacity for rocking failure mode in walls and piers which carries no vertical
loads from the roof; hence, it can significantly underestimate the rocking capac-
ity for such walls.