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niversity of California at Berkeley
ivil and Environmental Engineering
Instructor: Stephen A. Mahin
Spring Semester 2006
CEE 227  Earthquake Resistant Design
Homework Assignments
Problem 13 (sort of optional)
Carry out a static pushover analysis of the 3 story building that was designed using the
1994 UBC using the method suggested by FEMA 356 and described in the class.
Continue the analysis until you get to a roof lateral displacement until you get to 1.5
times the roof displacement you predicted in Problem 12 (this will be the same as C
0
C
1
S
d
(assuming C
2
and C
3
are 1). FEMA 350 requires you to check at the target roof level, but
to continue the analysis beyond this point so you know how close to the displacement
capacity of the structure you are. You may use any computer program you are familiar
with that does this type of analysis.
a. Plot roof displacement vs. base shear.
b. Convert your system to an equivalent SDOF system as described in class, and plot
the lateral displacementlateral load response of the SDOF system and tabulate the
mass, stiffness, yield strength, and other relevant properties for this SDOF system.
(Regardless of whether you do the actual nonlinear pushover analysis, you need to
know how to do part b.
Typical modeling assumptions:
•
Use centerlinetocenterline dimensions. Do not model the panel zone region as a
rigid link! Assuming a rigid panel zone is unconservative. The beam plastic
hinges may be at the ends of the members. We will discuss modeling the inelastic
behavior of the panel zone later
•
You may represent plastic hinge regions by concentrated nonlinear rotational
springs having the flexural capacity of the beams and columns with a modest
amount of rotation hardening (perhaps 3% of the rotational stiffness of your
element under imposed end moments that produce a antisymmetric deformed
shape).
•
For this problem, you can ignore the effects of axial loads on the members.
Problem 14
Using virtual work or other similar method, develop an analytic relation for the braced
industrial subassemblies shown below in terms of E, L
col
, L
girder
, and A
brace
for ONE of
the two braced subassemblages shown below between the applied lateral force Q and:
a. The axial stress in the braces, and
b. The interstory drift.
Outline a design method where you seek to pick the area of the brace where it remains
elastic and does not displace more than a set limit for a frequent event, and can achieve a
specified target ductility and maximum lateral displacement for a very rare event.
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View Full Document In both braced frames, the period of the structure may be assumed to be in the
“displacement preserved” range. The beams and columns may be assumed pin connected
and axially inextensible. Buckling of the braces is not to be considered and they have
equal compression and tension capacities (as if bucklingrestrained braces are to be used).
Based on an examination of these relations (or some sample calculations), comment in
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This note was uploaded on 08/09/2009 for the course CEE 227 taught by Professor Mahin during the Spring '06 term at University of California, Berkeley.
 Spring '06
 Mahin

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