ubc earthquake design

8/9/2019 UBC Earthquake Design

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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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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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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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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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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.

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ubc earthquake design

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