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1997 UBC Earthquake Design
Introduction
Seismic forces are a particularly important consideration for
engineers working in the Western U.S. where the frequency
of earthquake occurrences is common.
Seismic building forces are the result of the sudden
movement and rupturing of crustal plates along fault lines.
There are more than 160 known active faults in
California alone.
New faults continued to be discovered, usually whenan unexpected earthquake occurs.
When a fault slip occurs suddenly, it generates seismic
shock waves that travel through the ground in a
manner unlike that of tossing a pebble onto the
surface of calm water.
These seismic waves cause the ground to shake.
The effect of this dynamic ground motion can be simply
modeled using a cereal box standing upon a piece of sand
paper.
Upon yanking the paper, the box topples in the direction
opposite of the yank, as if a pushing force had been applied to the box.
The heavier the box, the greater the apparent applied force
which is called an inertia force.
As the ground moves suddenly, the building attempts to
remain stationary, generating the inertia induced seismic
forces that are approximated by the static lateral force
procedure covered here.
This procedure is introduced in UBC '97 1629.8.3 and
discussed in detail in UBC '97 1630.
The static force procedure is limited to use with regular structures less than 240 feet in height.
And, also to irregular structures £ 65 feet or 5 stories in
height.
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See UBC '97 1629.8.3 for exact definition of
limitations.
Regular structures are symmetric, without
discontinuities in plan or elevation.
The building plan is generally rectangular.
The mass is reasonably uniform throughout the
building's height.
The shear walls line up from story to story.
Irregular structures include both vertical irregularities
(UBC Table 16-L) or plan irregularities (UBC Table
16-M). These irregular features include:
Reentrant corners.
Large openings in diaphragms.
Non-uniform distribution of mass or stiffness
over building height (e.g. soft story).
Basic premise of seismic code provisions:
Earthquake Damage to Structure
Minor None
Moderate Some damage to non-structural elements
Major Maybe severe damage, but not collapse.
Seismic zones in U.S. (UBC '97 Figure No. 16-2):
Zones Damage to Structure MMI* Scale
0 No Damage -----
1 Minor V, VI
2 Moderate VII
3 Major ³ VII
4 Major -----
*MMI = Modified Mercalli Intensity scale of 1933.
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1997 UBC Earthquake Design
Modeling Forces
1997 UBC static lateral method considers both horizontal
movement and vertical ground movement.
The vertical component may be taken as zero,
however, when using the allowable stress design
procedure.
We statically model the inertial effects using Newton's 2nd
law of motion:
Rewrite equation (1) as:
Compare (2) to UBC base shear design equations, as given
below, where each equation is a function of the building
weight and some form of an acceleration factor.
Each acceleration factor is somewhat equivalent to
a/g, except they account for factors like underlying
soil, the structural system, and building occupancy.
Where:
V= base shear force. The horizontal seismic force
acting at the base of the structure as modeled by the"yank" of the paper in the previous cereal box
example. It is important to note that this force was
developed for the strength design methodology and
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1997 UBC Earthquake Design
Base Shear Terms
In this section, the various terms of the static base shear equation
are examined in more detail.
Z = seismic zone factor.
Effective peak ground accelerations with 10%
probability of being exceeded in 50 yrs.
Given as a percentage of acceleration due to gravity.
For example, consider zone 4, where Z = .4 Þ
horizontal ground acceleration is predicted at .4g
at bedrock.
Doesn't account for building dynamic properties or
local soil conditions.'97 UBC Figure 16.2 Þ seismic zone map.
Table 16.I Þ Z values as given below:
Zone Z
0 0
1 .075
2A .15
2B .20
3 .30
4 .40
I = importance factor.
Classifying buildings according to use and importance.
Essential facilities, hazardous facilities, special
occupancy structures, standard occupancy
structures, miscellaneous structures.
Essential facilities mean that the building must
remain functioning in a catastrophe.
Essential facilities include: hospitals,
communication centers, fire and police stations.
Design for greater safety.'97 UBC Table 16-K.
I = 1.25 for essential and hazardous facilities.
I = 1.0 all others.
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T = building's fundamental period of vibration.
Fundamental period of vibration is the length of time,
in seconds, it takes a structure to move through one
complete cycle of free vibration in the first mode.
There are two methods to estimate T:
Method A:
Method B: (an iterative approach not generally
used in regular structures)
Using Method A, the fundamental period of
vibrations for masonry buildings is estimated at:
Height (ft) Period (seconds)
20 .19
40 .32
60 .43
120 .73
160 .90
Ca and Cv = seismic dynamic response spectrum values.
Accounts for how the building and soil can amplify the
basic ground acceleration or velocity.
Ca and Cv are determined from respectively '97 UBC
tables 16-Q and 16-R as a function of Z, underlying
soil conditions, and proximity to a fault.
Using method A,
Soil profile type:
The soil layers beneath a structure effects the
way that structure responds to the earthquake
motion.
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When the period of vibration of the building is
close to the period of vibration of the underlying
soil, the bedrock motion is amplified. The
building experiences larger motions than that
predicted by Z alone. The following are
generalizations about building response as a
function of building flexibility and underlying
soil stiffness.
Building
Description
Soil
Description
Induced
Seismic Force
Flexible (Large
T's)Soft (big S) Higher
Flexible Stiff Lower
Stiff Soft Higher
Flexible Stiff Lower
The soil profile types are:
Description Type
Hard Rock SA
Rock SB
Very dense soil and soft rock SC
Stiff soil SD
Soft soil SE
See '97 UBC 1629.3.1 SF
Specific details about each type can be found in
'97 UBC Table 16-J and '97 UBC 1629.3.1.
In the absence of a geotechnical site investigation, use
SD. This is in accordance with '97 UBC 1629.3
Do not confuse this requirement with the one
stated in '97 UBC 1630.2.3.2 which applies
ONLY when using the simplified design base
shear procedures of '97 UBC 1630.2.3. This website is NOT using these simplified procedures,
but is using 1630.2.1.
R = response modification factor.
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A judgement factor that accounts for building ductiltiy,
damping, and over-strength.
Ductility = ability to deform in the inelastic
range prior to fracture:
Damping = resistance to motion provided by
internal material friction.
Over-strength = the extra or reserve strength inthe structural system. It comes from the practice
of designing every member in a group according
to the forces in the most critical member of that
group.
Structural systems with larger R = better seismic
performance.
In '97 UBC Table 16-N, R range from 2.8 (light steel
frame bearing walls with tension bracing) to 8.5
(special SMRFS of steel or concrete and some dual
systems).For bearing wall systems where the wall elements
resist both lateral and vertical loads:
Wood shear panel buildings with 3 or less
stories: R = 5.5
Masonry shear walls: R = 4.5.
Nv and Na = near source factors that are applicable in only
seismic zone 4. They account for the very large ground
accelerations that occur near the seismic source (the fault).
Nv is generally used with Cv for structures located <
9.3 miles (15km) from the fault.
Nv is found in '97 UBC Table 16-T
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Na is used with Ca for structures located < 6.2 miles
(10 km) from the fault.
Na is found in '97 UBC Table 16-S.
Both Na and Nv are based upon the type of seismic
source, A-C. This source type, and location of fault,
must be established using approved geotechnical data
like a current USGS survey.
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1997 UBC Earthquake Design
Distribution of Seismic Forces to Primary LFRS
Now that we have the base shear force, what type of
induced forces act through the height of the building?
How to model the inertial force that acts opposite to
yank of paper on the cereal box?
Recall for wind loads
First, calculate loads/pressures over the height of
building.Then developed base values.
These values are at the allowable stress level.
In contrast, with seismic -
First, determine base force.
Then determine and distribute forces over the height
of the building, called story forces, Fx.
There are two different sets of story forces distributed
to the primary LFRS:
For vertical elements, use Fx.
For horizontal elements, use F px
.
Recall that the primary LFRS for a box building
= horizontal diaphragms and vertical shear
walls.
Then adjust these strength level forces by a
redundancy/reliability factor, r, and an allowable
stress factor of 1.4 discussed further in item d, below.
Story forces for vertical elements.
Used in design of shear walls and shear wall anchorage
at the foundation.
Determined before F px's.Applied simultaneously at all levels.
Results in a triangular distribution of forces over a
multi-story building that has approximately equal floor
masses.
and
a.
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Where:
Ft = roof level force accounting for whiplash
effect.
Ft{.07TV £ .25V or
0 if T £ .7 sec.
wx, wi = tributary weights at levels x and i.
hx, hi = height above base to levels x and i.
further detail can be found in '97 UBC 1630.5.
Story forces for horizontal elements.
At roof level, F px = Fx.
At other levels, F px > Fx.
Accounting for the possibility that larger instantaneous
forces can occur on individual diaphragms.
Applied individually to each level for the design of
that diaphragm.
where w px = weight of diaphragm and elements
tributary to it at level x.
For masonry buildings (and concrete) supported by
flexible diaphragms, the R factor used to determine V
must be reduced to 4.0 from 4.5 ('97 UBC 1633.2.9.3).
For more information see '97 UBC 1630.6.
b.
The single story building is a special case.
In most cases, T £ .7 and Ft then is taken as zero.
c.
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From equation 30-15:
From equation 33-1:
Consequently, F1 = F p1 = V for the case of wood
frame buildings.
For masonry buildings, F p, is based upon a slightly
larger V due to R changing from 4.5 to 4.0 according
to '97 UBC 1633.2.9.3. In this case, then: F1 = V and
F p1 = 1.125 V.
Redundancy/reliability factor and the 1.4 ASD adjustment:
In the load combination equations as discussed in the
last sub-module in the load module of this site, all
earthquake forces are generically called E.
Where:
Eh = load developed from V, (like Fx or F px) or
F p, (the design force on a part of a structure).
Ev = 0 for ASD
r = redundancy/reliability factor, discussed
below.
E is at strength level and must be divided by 1.4 for
use in allowable stress design.
The application of 1.4 and p are shown in
example one of this sub-module.
The redundancy/reliability factor penalizes structuresin seismic zones 3 and 4 that do not have a reasonable
number and distribution of lateral force resisting
elements, such as shear walls. These structures with a
limited number of shearwalls are referred to as
non-redundant structures where the failure of one wall
loads to the total collapse of the structure.
Where:
AB = the ground floor area of the structure in
d.
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ft2.
r max = maximum element-story shear ratio, r i,
occurring at any story level in bottom 2/3 of the
structure. r max identifies the least redundant
story.
r i = R wall/R story(10/lw)
Where:
R wall = shear in most heavily loaded wallR story = total story force, Fx
lw = length of most heavily loaded shear
wall.
r = 1 when in seismic zones 0, 1, or 2.
r = 1 when calculating drift.
Upon careful inspection of the r and r i equation
with application to a single story, regular
building, we see:
To maintain a r = 1.0, the minimum length
of the most heavily loaded shear wall isfixed as:
If a flexible diaphragm, a common
controlling case will be when R wall/R story
= .5.
In this case then to keep r =1.0.
Although the Breyer, et al book uses the subscript "u"
to distinguish strength-level vs. allowable stress-level
loads, I have opted for a different convention that I
believe is simpler.
Upon modifying the various Eh values by r and
1.4, Eh becomes E'h. For our single story
building, the shear wall forces and diaphragm
forces at ASD level would look like:
F'1 = rF
1 (1/1.4)
F'1 = rF p1 (1/1.4)
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1997 UBC Earthquake Design
Example 1
Develop the applicable seismic forces for a one-story, box-type industrial
building located in Southern California. Assume partially grouted CMU
walls weighing 61 lb/ft2,
a roof dead load of 9 psf, and the building is not
located near (further than 9.3 miles) a seismic source. No geotechnical
investigation was completed.
Base shear coefficient, V.
The base shear equation(s) are quite cumbersome to use,
unless on knows beforehand which equation governs.
Recall that middle equation is for buildings medium to
long fundamental T's. The left-hand equations are lower
bound values. The right-hand equation is for short (stiff)
T buildings.
You can determine if its the right-hand equation quickly
by comparing the building's T to Ts:
TS is a limiting period of vibration that is used to
differentiate between stiff and flexible buildings.
The seismically-induced forces in stiff buildings
are related to the bedrock acceleration. The
forces in flexible buildings are related more to
bedrock velocity.
1.
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