civ100 wind and earthquake

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Chevron Corporation 100-1 September 2000

100 Wind and Earthquake

Design Standards

Abstract

This section contains guidance for determining wind and earthquake loads on indus-

trial structures and equipment. It also includes design methods for avoiding wind-

induced vibration of steel stacks. It is based on ASCE 7-93 and the Uniform

Building Code (1997). Wind and earthquake loads on tanks, buildings, and offshoreplatforms are beyond the scope of this document. The Tank Manualcovers wind and

earthquake loads on tanks. Local building codes define lateral loads on buildings.

Finally, API RP-2A should be used for the design of offshore platforms.

Maps showing basic wind speeds and seismic zones for the United States are

included in this section.

Allowable stresses, foundation stability ratios, soil bearing pressures, and sample

calculations are also included.

This section can be used as a design guide for contractors responsible for seismic

and wind design of new or existing Company facilities. Copies of this section can be

obtained from CRTC Technical Standards Team. For additional guidance andrequirements, refer to Chevron Specification CIV-EG-5009-C, Structural Design

Criteria. This document can also be obtained from the CRTC Technical Standards

Team.

Contents Page

110 Design Standards 100-3

111 Introduction

112 General

113 Wind Design

114 Earthquake Design

115 Allowable Stresses, Soil Bearing, and Stability Ratios

120 Methods and Calculations 100-24

121 Natural Period of Vibration


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100 Wind and Earthquake Design Standards Civil and Structural Manual

September 2000 100-2 Chevron Corporation

122 Wind-Induced Vibration of Steel Stacks and Columns

123 Examples of Wind and Earthquake Load Calculations

Example 1Two-Story Concrete Vessel Support Structure

(Assume El Segundo, CA Location)

Example 2Uniform Cylindrical Column(Assume El Segundo, CA Location)

Example 3Column of Variable Cross Section

(Assume Salt Lake City, UT Location)

Example 4Braced-Column Spheres

(Assume Richmond, California Location)

Example 5Vertical Vessels with Unbraced Legs

(Assume Richmond, CA Location)

Example 6Stack Vibration and Ovalling

Example 7Stack Vibration130 References 100-53


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Civil and Structural Manual 100 Wind and Earthquake Design Standards


110 Design Standards

111 Introduction

It is important that a civil engineer be consulted whenever new facilities or existing

structures are being evaluated for seismic and wind loads. This section is for civil

engineers of all experience levels. Engineers from other disciplines might use this as

a reference to follow a civil engineers calculations.

This section gives the reader specific instructions for calculating wind and earth-

quake loads on structures. It does not describe how to use the loads to calculate

stresses and design/analyze a structure or piece of equipment. It does, however, give

allowable stresses and foundation stability information that must be used in wind

and earthquake design.

This section includes formulas for natural period of vibration, example load calcula-

tions, and a method of preventing wind-induced vibration of tall steel stacks.

Section 110 may be used as a design specification.

112 General

These requirements provide the basic criteria for calculating wind and seismic loads

for Company facilities. For further information and background material used in

formulating these provisions, a list of references is provided in Section 130.

For critical structures containing significant quantities of acutely hazardous mate-

rial whose failure could result in off-site consequences, more stringent require-

ments may be appropriate. Examples of critical structures are LNG tanks and

ammonia spheres. The CRTC Civil/Structural Technical Service Team may be

consulted in these cases.

Use of Building Codes

Where legal building code provisions are more stringent and more applicable to a

particular structure than the guidelines and requirements presented here, then the

more stringent provisions must necessarily govern the design.

These provisions apply primarily to framed industrial structures other than build-

ings and to industrial equipment.

Load Combinations

The basic principle of design for lateral forces involves determining the lateralforces due to wind and earthquake (not both at once) and designing for the most

adverse conditions. Wind or earthquake loads should be combined with all other

loads which may reasonably be expected to occur simultaneously with the design

lateral loads. Vessels and other equipment and their supports should be analyzed for

wind loads combined with gravity loads, both including and excluding the weight of

the normal contents of the equipment. Earthquake loads need be combined only


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with normal operating and gravity loads. Wind and earthquake loads need not be

combined with hydrostatic test loads.

Structures designed for wind and earthquake loads must also be capable of with-

standing all other conditions of loading. Stresses from other loads must not exceed

normal allowable stresses.

Load Direction

The wind or earthquake forces should be considered as acting in any direction, but

for analysis they can be resolved into components in the directions of the principal

axes of the structure.

Dynamic Effects

Both wind and earthquake effects are dynamic phenomena. However, for the design

of structures covered by this document, the use of equivalent static forces is

adequate. Wind design for some structures, e.g., for stacks or slender processing

columns, must consider dynamic behavior. For earthquake design, dynamic

behavior is considered to a limited extent in that the lateral force is based on thestructures natural period. For major structures or critical facilities, it may be desir-

able to use dynamic procedures to supplement the basic static approach.

Design Standard Basis

The wind design provisions are based on ASCE 7-93 and the 1997 UBC.1

The earthquake provisions are similar in form to those in Recommended Lateral

Force Requirements and Commentary (1997 7th Edition), Structural Engineers

Association of California, and to the 1997 Uniform Building Code.

Locations outside the US must determine whether these standards or their own (e.g.,

Canadas NBC) apply.

113 Wind Design

Design wind pressures are dependent on the Wind Speed Zone, which is defined for

Company locations in Figure 100-1. Use Figure 100-2 to determine the Wind Speed

Zone for other locations in the United States including Alaska and Hawaii. Increase

the Wind Speed Zone if warranted by local conditions or anomalies.

After determining the appropriate Wind Speed Zone, wind forces (Fw) on an

exposed structure can be calculated:

FW = (Shape Factor) (Basic Wind Pressure) (Projected Area) (Importance Factor)

(Eq. 100-1)

1. The wind load provisions of ASCE 7-95 were reviewed during this manual revision. ASCE 7-95 contains

changes from previous editions and utilizes 3-second gust wind speeds instead of fastest-mile. However, the

design wind forces using the ASCE 7-95 criteria are essentially the same as ASCE 7-93 and 1997 UBC criteria.


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Shape factors for various elements are defined in Figure 100-3. The wind impor-

tance factor IW shall be taken as 1.0 for normal non-critical oil industry structures.

For critical structures or structures housing or supporting acutely hazardous mate-

rials (AHMs) Iw shall be taken as 1.15.

Fig. 100-1 Wind Speed Zone for Company Locations

Location

Wind Speed Zone

(mph)

California

Bakersfield/Cymric/McKittrick/Kern River/Taft 70

Carpinteria/Gaviota 70

El Segundo 70

Richmond 70

Colorado

Rangely 70

Hawaii

Barbers Point/Honolulu 80

Louisiana

Venice/Leeville/Oak Point/Morgan

City/Cameron/St. James 100

Mississippi

Pascagoula 100

Ohio

Marietta 70

Oregon

Willbridge 75

Texas

El Paso 75

Cedar Bayou/Houston/Mont Belvieu 90

Orange 95

Port Arthur 100

Utah

Salt Lake City 70

Washington

Kennewick 75

Wyoming

Evanston 75

Rock Springs 80


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ChevronCorporation

100-6

September2000

Fig. 100-2 Basic Wind Speeds for the United States (from 1997 Ed. UBC) Reproduced from the 1997 edition of

1997, with the permission of the International Conference of Building Officials


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Basic Wind Pressures are defined in Figure 100-4 and are a function of exposures.

Exposure B has terrain which has buildings, forest or surface irregularities 20 feet or

more in height covering at least 20 percent of the area, extending one mile or more

from the site. Exposure C has terrain which is flat and generally open, extending

one-half mile or more from the site in any full quadrant. Exposure D represents the

most severe exposure in areas with basic wind speeds of 80 mph or greater and has

terrain which is flat and unobstructed facing large bodies of water over one mile or

Fig. 100-3 Shape Factors For Wind Load Calculation

The shape factor shall be 1.3 for structures 40 feet or less in height and 1.4 for structures over 40 feet

in height, except as specified below:

Spheres 0.65

Tanks, stacks (except for cooling towers or stacks with helical spoilers) andother cylindrical structures, excluding appendages

0.8

Induced draft cooling towers: 1.3 +(0.2N)

N = number of cells in direction of wind loading

Total design pressure shall not be less than 23 psf at any height.

Cooling tower stacks 0.9

Stacks with helical spoilers (projected area to include the spoilers, i.e., to

outside

diameter of spoilers)

1.2

Columns and vessels, including normal piping and platforms:

Under 4-ft diameter 1.4

4-ft to 8-ft diameter 1.7 (0.075D)

Over 8-ft diameter 1.1

D = Outside diameter, including insulation, ft

Elements of structures:

Applies to the projected framing area of the wind members on any elementexposed to the wind (i.e., consider both columns for a frame parallel to the

wind).

2.0

(Forces on equipment and piping supported on the structure shall be added.)

Flat or angular sections 1.3

Cylindrical members (including piping):

Two inches or less in diameter

Over two inches in diameter

1.0

0.8


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more in width. Exposure D extends inland from the shoreline .25 miles or 10 times

building height, whichever is greater.

Fig. 100-4 Basic Wind Pressures (psf) for Heights above Ground

HeightWind Speed (MPH)

Exposure

70 75 80 85 90 95 100 110

0-15 ft.

20

25

30

40

60

80

100

120

160

200

300

400

8

8

9

10

11

12

13

14

15

16

18

20

22

9

10

10

11

12

14

15

16

17

19

20

23

26

10

11

12

12

14

16

17

19

20

21

23

26

29

11

12

13

14

15

18

19

21

22

24

26

30

33

13

14

15

16

17

20

21

23

25

27

29

33

37

14

15

16

17

19

22

24

26

28

30

32

37

41

16

17

18

19

21

24

26

29

31

33

36

41

46

19

21

22

23

26

29

32

35

37

40

44

50

55

B

0-15 ft.

20

25

30

40

60

80

100

120

160200

300

400

13

14

15

16

16

18

19

20

21

2223

26

28

15

16

17

18

19

21

22

23

24

2627

30

32

17

18

19

20

21

23

25

26

27

2931

34

36

20

21

22

23

24

26

28

30

31

3335

38

41

22

23

25

26

27

30

32

33

35

3739

43

46

24

26

27

29

30

33

35

37

39

4143

47

51

27

29

30

32

33

37

39

41

43

4648

53

56

33

35

37

38

40

44

47

50

52

5558

64

68

C


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The values of basic wind pressures in Figure 100-4 include: Structure Importance

Factor for wind, Velocity Pressure Exposure Coefficient, and a Gust Response

Factor per ASCE 7-93.

Use the projected area of each element within each height zone for calculating the

force. The total force on the structure is the sum of the forces on all the elements,

including wind up-lift forces on the surfaces of horizontal projections. Apply all

forces at the centroids of the projected areas. For example calculations, demon-

strating wind design methodology, see Section 123, Examples of Wind and Earth-quake Load Calculations. Other wind design concerns include wind-induced

vibration of stacks, above-grade pipelines, or any slender element which can be

excited aerodynamically. See Section 122 for an analysis of this problem.

114 Earthquake Design

These requirements are intended only for use in designing ordinary industrial struc-

tures. They are not intended to cover offshore platforms or buildings.

These criteria are adequate for most conditions. However, specific sites may present

special seismic hazards, such as soil liquefaction, landslide, surface rupture, and

tsunami that require additional design considerations beyond the scope of this docu-ment.

These provisions shall apply to the structure as a unit and also to the individual parts

of a structure.

0-15 ft.

20

25

30

40

60

80

100

120

160

200

300

400

17

18

19

19

20

22

23

24

24

25

26

28

29

20

21

22

22

23

25

26

27

28

29

30

32

34

23

24

24

25

27

28

30

31

31

33

34

36

38

26

27

28

28

30

32

33

35

36

37

39

41

43

29

30

31

32

34

36

37

39

40

42

43

46

48

32

33

35

36

37

40

42

43

44

47

48

51

54

35

37

38

39

42

44

46

48

49

52

54

57

60

43

45

46

48

50

53

56

58

59

62

65

69

72

D

Note For regions between the hurricane oceanline and 100 miles inland, the basic wind pressures shall be determined by

linear interpolation. At the hurricane oceanline, the basic wind pressures shall be multiplied by 1.05. At 100 miles from

the hurricane oceanline, the basic wind pressures shall be multiplied by 1.00. Hurricane oceanlines are the Atlantic and

Gulf of Mexico coastal areas.

Fig. 100-4 Basic Wind Pressures (psf) for Heights above Ground (Contd.)

HeightWind Speed (MPH)

Exposure

70 75 80 85 90 95 100 110


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Structural Systems Similar to Buildings (SSSB)

A concentric braced frame is a braced frame in which the members are subjected

primarily to axial forces.

A shear wall is a wall designed to resist lateral forces parallel to the plane of the

wall (sometimes referred to as a vertical diaphragm).

A light-framed wall with shear panels is similar to a shear wall system except the

vertical diaphragm is usually light gage metal, i.e., similar to a refinery box furnace.

A moment-resisting space frame is a structural system in which the members and

joints are capable of resisting lateral forces primarily by flexure. An ordinary

moment-resisting space frame (OMRSF) is a moment-resisting space frame not

meeting special detailing requirements for ductile behavior. An intermediate

moment-resisting space frame (IMRSF) is a concrete space frame designed in

conformance with UBC Section 1921.8. A special moment-resisting space frame

(SMRSF) is a moment-resisting space frame specially detailed to provide ductile

behavior and comply with the requirements given in UBC Section 1921 for concrete

and UBC Chapter 22, Division IV or V for steel.

An induced draft cooling tower is typically a timber structure with some type of

internal brace system.

Nonbuilding-Type Structures

These structures include all self-supporting structures (equipment with integral

supports) other than buildings which carry gravity loads and resist the effects of

earthquake. Nonbuilding structures also include structures supporting equipment

with structural systems similar to buildings (SSSB).

Design Base Shear for Structures

The determination of design base shear is directly related to the structures

fundamental period of vibration, T. The fundamental period of a structure can be

determined by rational methods as demonstrated in Section 121, Natural Period of

Vibration. Structures with longer periods of vibration, such as stacks, frames, one-

column pipe supports, and vertical vessels, will typically be governed by

Equation 100-2 below. Rigid structures with a short period of vibration, such as

short horizontal vessel supports or pump foundations, will typically be governed by

Equation 100-6.

It is important to note that the earthquake design forces specified by the 1997

Uniform Building Code are based on strength design; whereas in past editions of the

UBC the design forces were based on allowable stress design. Because this section

is based on the 1997 UBC, the following equations will provide results which are

strength design based. If one desires to use allowable stress design, the earthquake

forces calculated using the following equations need to be divided by a factor of 1.4.

For structure systems similar to buildings (such as those listed in sections I and II of

Figure 100-11) the total design base shear in a given direction shall be:


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(Eq. 100-2)

With the conditions that:

(Eq. 100-3)

and

(Eq. 100-4)

In addition, for Seismic Zone 4,

(Eq. 100-5)

For nonbuilding structures (such as those listed in Sections III and IV of

Figure 100-11) and having a period, T, less than 0.06 seconds, the total design base

shear shall be:

(Eq. 100-6)

For flexible nonbuilding structures (such as those listed in sections III and IV of

Figure 100-11), Equation 100-2 and Equation 100-3 shall apply, with the additional

stipulations that:

(Eq. 100-7)

and additionally, for Seismic Zone 4,

(Eq. 100-8)

The coefficients used above are defined as follows:

V = Total base shear

Z = Seismic zone factor

I = Occupancy importance factor

Ca, Cv = Site-dependent seismic coefficients representing the ground

motion

Na, Nv = Near-source factors related to the proximity of the structure to

known faults in seismic zone 4

VCvI

RT--------W=

Vmax

2.5CaI

R---------------- W=

Vmin 0.11CaIW=

Vmin

0.8ZNvI

R--------------------W=

V 0.7CaIW=

Vmin 0.56CaIW=

Vmin

1.6ZNvI

R--------------------W=


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R = Structural system factor

T = Fundamental period of vibration, in seconds, of the structure in

the direction under consideration. See Section 121, Natural

Period of Vibration

W = Total seismic deadload plus operating weight

The Seismic Zone Factor, Z, shall be as specified below for the earthquake zone in

which the structure is located. The earthquake zone shall be as listed in Figure 100-5

and shown on Figure 100-6.

Seismic Zone

Corresponding Seismic Zone

Factor, Z

0 0

1 0.075

2A 0.15

2B 0.203 0.30

4 0.40

Fig. 100-5 Seismic Zone for Company Locations (1)

Location

Earthquake

Zone Na Nv

California

Bakersfield/Cymric/McKittrick/Kern

River/Taft 4 1.0 1.0

Carpinteria 4 1.3 1.6

El Segundo 4 1.1 1.33

Gaviota 4 1.1 1.33

Richmond 4 1.2 1.6

Colorado

Rangely 1

Hawaii

Barbers Point/Honolulu 2A

Louisiana

Venice/Leeville/Oak Point/Morgan

City/Cameron/St. James 0

Mississippi

Pascagoula 0

Ohio

Marietta 1


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ChevronCorporation

100-13

September2000

Oregon

Willbridge 3

Texas

Cedar Bayou/Houston/Mont

Belvieu/

Orange/Port Arthur 0

El Paso 1

Utah

Salt Lake City 3

Washington

Kennewick 2B

Wyoming

Evanston 2B

Rock Springs 1

(1) Near-source factors (Na and Nv) are given for Company locations found in Zone 4 only.

Fig. 100-5 Seismic Zone for Company Locations (Contd.)(1)

Location

Earthquake

Zone Na Nv


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The Occupancy Importance Factor, I, shall be taken as 1.0 for normal non-critical

oil industry structures. For critical structures or structures housing or supporting

acutely hazardous materials (AHMs), I shall be taken as 1.25. See Figure 100-12.

The seismic coefficients, Ca

and Cv, shall be determined using Figures 100-7 and

100-8:

Ca and Cv represent the ground motion, and are a function of the seismic zone (Z)

and the soil profile type (given in 100-9). In seismic zone 4 only, Ca and Cv are also

a function of the near source factors Na and Nv. Na and Nv factors are dependent on

the distance of the structure to known active large magnitude faults. The Na and Nv

factors for Company locations in seismic zone 4 are given in 100-5.

Fig. 100-6 Seismic Zone Map of the United States (from 1997 ed. of UBC) Reproduced from the 1997

edition of the Uniform Building Code 1997, with the permission of the International Confer-ence of Building Officials


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A review of the Design Response Spectra (shown in Figure 100-10) helps to illus-

trate how the seismic coefficients Ca and Cv define the seismic response throughout

the spectral range. There are two basic regions to the response spectrum-short

period

(T < TS) and long period (T > TS). Equation 100-2 represents the curved (long

period) portion of the response spectrum, while Equation 100-3 represents the flat(short period) portion of the spectrum.

The Structural System Factor, R, reflects the expected earthquake resistance for

different types of structures. It is a numerical coefficient which represents the

inherent global energy absorbing capability or ductility and overstrength in a

particular type of structural system. Values for R for a wide variety of structural

systems are presented in Figure 100-11.

Fig. 100-7 Seismic Coefficient Ca(Reproduced from the 1997 edition of the Uniform Building Code 1997, with the permission of the International Conference of Building Officials)

Seismic Zone Factor, Z

Soil Profile

Type Z = 0.075 Z = 0.15 Z = 0.2 Z = 0.3 Z = 0.4

SA 0.06 0.12 0.16 0.24 0.32Na

SB 0.08 0.15 0.20 0.30 0.40Na

SC 0.09 0.18 0.24 0.33 0.40Na

SD 0.12 0.22 0.28 0.36 0.44Na

SE 0.19 0.30 0.34 0.36 0.36Na

SF See Footnote(1)

(1) Site-specific geotechnical investigation and dynamic site response analysis shall be performed to determine seismic coeffi-

cients for Soil Profile Type SF.

Fig. 100-8 Seismic Coefficient Cv(Reproduced from the 1997 edition of the Uniform Building Code 1997, with the permission of the International Conference of Building Officials)

Seismic Zone Factor, Z

Soil Profile

Type Z = 0.075 Z = 0.15 Z = 0.2 Z = 0.3 Z = 0.4

SA 0.06 0.12 0.16 0.24 0.32Nv

SB 0.08 0.15 0.20 0.30 0.40Nv

SC 0.13 0.25 0.32 0.45 0.56Nv

SD 0.18 0.32 0.40 0.54 0.64Nv

SE 0.26 0.50 0.64 0.84 0.96Nv

SF See Footnote(1)

(1) Site-specific geotechnical investigation and dynamic site response analysis shall be performed to determine seismic coeffi-

cients for Soil Profile Type SF.


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Two major types of structural systems exist, e.g., structures similar to buildings, andnonbuilding-type structures, each having a different minimum design requirement.

Fig. 100-9 Site Coefficients (Reproduced from the 1997 edition of the Uniform Building Code 1997,with the permission of the International Conference of Building Officials)

Soil

Profile

Type

Soil Profile

Name/Generic Descrip-

tion

Shear Wave

Velocity Vs

feet/second

(m/s)

Standard Pene-

tration Test, N

[or NCH for cohe-

sionless soil

layers]

(blows/foot)

Undrained Shear

Strength SU psf

(kPa)

SA Hard Rock > 5,000

(1,500)

--- ---SB Rock 2,500 to 5,000

(760 to 1,500)

SC Very Dense Soil and Soft

Rock

1,200 to 2,500

(360 to 760)

> 50 > 2,000

(100)

SD Stiff Soil Profile 600 to 1,200

(130 to 360)

15 to 50 1,000 to 2,000

(50 to 100)

SE(1) Soft Soil Profile < 600

(180)

< 15 < 1,000

(50)

SF Soil Requiring Site-specific Evaluation. See Section 1629.3.1.

(1) Soil Profile Type SE also includes any soil profile with more than 10 feet (3048 mm) of soft clay defined as a soil with a

plasticity index,

PI> 20, wmc 40 percent and su < 500 psf (24 kPa). The Plasticity Index, PI, and the moisture content, wmc, shall bedetermined in accordance with approved national standards.


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Fig. 100-10Design Response Spectra (Reproduced from the 1997 edition of the

Uniform Building Code 1997, with the permission of the InternationalConference of Building Officials)

Fig. 100-11Structural System Factors (R Factors) (1 of 2)

Structural System Description

I. STRUCTURAL SYSTEMS SIMILAR TO BUILDINGS (SSSB) Structural System Factor,R

Steel Structures

Special moment resisting frame 5.6

Ordinary moment resisting frame 4.5

Braced frame

a. Eccentrically braced frame 5.6

b. Concentrically braced frame 4.5

Inverted pendulum type structure (cantilever column) 2.2

Concrete StructuresSpecial moment resisting frame 5.6

Intermediate moment resisting frame(1) 4.5

Ordinary moment resisting frame(2) 3.5

Shear wall 4.5

Inverted pendulum type structure (cantilever pier/column) 2.2


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II. PIPEWAYS

Steel


Ordinary moment resisting frame 4.5

Braced frame (CBF) 4.5

Cantilever column 2.9

Concrete


Intermediate moment resisting frame(1) 4.5

Ordinary moment resisting frame(2) 3.5

Cantilever column 2.9

III. EQUIPMENT BEHAVING AS STRUCTURES WITH INTEGRAL SUPPORTS

Vertical vessels/heaters, tanks, or spheres supported by:

Steel skirts 2.9

Steel skirt when tshell/tskirt > 1.5 2.2

Steel braced legs 2.9

Steel or concrete unbraced legs 2.2

Horizontal vessels

Flexible concrete support 2.2

Boilers

Light steel framed wall with shear panels 4.5

Steel braced frame where bracing carries gravity load 4.5

Steel ordinary moment frame 4.5

Chimneys, stacks, or truss covers

Steel guyed 2.9

Steel cantilever 2.9

Concrete 2.9

IV. COOLING TOWERS

Wood frame 5.6

Concrete 3.6

Notes: 1. Some R values are slightly different than those prescribed by the 1997 UBC. This is in accordance with the ASCE

Publication Guidelines for Seismic Evaluation and Design of Petrochemical Facilities.

2. For analysis of existing Moment-Resisting Frames, use R for an Ordinary Moment-Resisting Frame unless a different

value can be justified.

3. If assigning a value of R to a system not itemized in this table, in the absence of a detailed study, use R = 2.1. CRTCs

Civil/Structural Team is available for counsel on this subject.

(1) Prohibited in Seismic Zones 3 and 4, except as permitted in UBC Section 1634.2.

(2) Prohibited in Seismic Zones 2A, 2B, 3, and 4.

Fig. 100-11Structural System Factors (R Factors) (2 of 2)


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Vertical Distribution of Base Shear Force for Free StandingStructures

For structures having a natural period, T, greater than 0.7 sec., a portion of the total

base shear force, V, shall be applied at the top of the structure, as determined by the

following equation:

Ft = 0.07 TV (Eq. 100-9)

where:

Ft = Portion of base shear applied at the top of the structure.

T = Structure natural period of vibration, sec.

V = Total base shear from appropriate equation (Equation 100-2

through Equation 100-8)

Ft need not exceed 0.25V (applies when T is equal to or greater than 3.57 sec.). If T

is less than or equal to 0.7 sec., Ft shall be taken as zero.

The remainder of the total base shear force shall be distributed and applied to thevarious masses in the structure in accordance with the following equation:

(Eq. 100-10)

where:

Fx = Lateral force applied to a mass at level x.

Wx = Weight of the mass at level x.

hx = Height of level x above the base (normally the bottom of the base

plate of the structure or portion of the structure being analyzed)

V = Total base shear from appropriate equations (Eq. 100-2 through100-8)

Wh = The sum of the products of Wx and hx for all the masses withinthe structure.

Vertical Distribution of Base Shear Force for Guyed Structures

Where guys are used to provide lateral force resistance, the total lateral force shall

be distributed to the various masses in direct proportion to their weights and shall be

applied at their centers of gravity. See Section 300, Industrial Structures, for more

information on the design of guyed structures.

Horizontal Distribution of Base Shear ForceThe total shear in any horizontal plane shall be distributed to the various resisting

elements in proportion to their rigidities, considering the rigidity of the horizontal

bracing system or diaphragm as well as the rigidities of the vertical resisting

elements. Provision shall be made for the increase in shear resulting from the hori-

zontal torsion due to an eccentricity between the center of mass and the center of

rigidity. Negative torsional shears may be neglected. In addition, where the vertical

Fx V Ft( )Wxhx

Wh-------------=


20/56



resisting elements depend upon diaphragm action for shear distribution at any level,

the shear resisting element shall be capable of resisting a torsional moment assumed

to be equal to the shear at the level, acting with an eccentricity of not less than 5%

of the maximum structure plan dimension at that level.

Details of Earthquake Resistant DesignMuch of the damage sustained in past earthquakes could have been avoided through

proper detailing of structural elements and connections. It is important in earth-

quake-resistant design to give the structure the ability to absorb energy if loaded to

levels above the minimum design. This quality is best achieved by detailing the

structural frame, the members, and the connections so that overall structural defor-

mation will be ductile rather than brittle. This flexibility is particularly desirable for

reinforced concrete construction. Structures should also have a consistent stress

level, or margin of reserve strength throughout.

An increased force, Em, shall be used for the design of crucial structural

components in the lateral force resisting system such as collector elements, steel

connections, and elements supporting discontinuous systems. The symbol Em repre-sents the estimated maximum earthquake force that can be developed in a structure.

It is a function of the base shear and the system overstrength, which takes into

account factors such as material overstrengths, advantageous collapse mechanisms,

and the type of lateral force resisting system. For more information on this topic,

contact the CRTC Civil/Structural Team.

The following general comments apply to structures and components of structures.

1. Masonry StructuresAlways reinforce in accordance with Section 2106 of the

Uniform Building Code.

2. Reinforced Concrete StructuresConcrete frames in Seismic Zones 3 and 4

shall be Special Moment Resisting Space Frames (SMRSF). Concrete frames inSeismic Zones 2A and 2B shall be, as a minimum, an Intermediate Moment

Resisting Space Frame (IMRSF). Concrete shear walls, braced frames, or

moment resisting frames used to resist earthquake forces shall be designed in

accordance with Section 1921 of the Uniform Building Code.

3. Steel StructuresPay special attention to connections. At connections and

other points of high stress in rigid frame structures, follow the requirements of

the AISC Specification for plastic design regarding width-thickness ratios,

lateral bracing, web stiffening, and fabrication. Follow the provisions of

Chapter 22, Divisions IV or V of the Uniform Building Code.

4. Vessels, Columns and SpheresMinimize stress raisers and provide for conti-

nuity of reinforcement around openings. Use bracing effective in tension and

compression for braced legs of spheres and vertical vessels. Anchor bolts

should be sized to resist the maximum predicted earthquake forces. Use the

Standard Anchor Bolt Drawing (GD-Q68922) for bolt selection and spacing.

This drawing was developed based on a ductile failure criteria. Do not oversize

the anchor bolts as this will result in a non-ductile failure.


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5. FoundationsProvide tie beams, reinforced concrete slabs, or other equivalent

restraint interconnecting individual footings on piles when the surface soil does

not provide adequate lateral restraint.

See Sections 1626 through 1636 of the Uniform Building Code for general earth-

quake regulations.

Electrical and Mechanical Equipment

All equipment and equipment anchorage to foundations or supporting structures

shall be designed to resist a minimum lateral earthquake force acting at the center of

mass of the equipment. This provision includes such items as switch gear, trans-

formers, vessels supported in structures, control panels, etc.

For equipment supported by a structure:

(Eq. 100-11)

With the condition that:

(Eq. 100-12)

(Eq. 100-13)

where:

For rigid equipment supported at grade (such as a transformer, switchgear, etc.):

(Eq. 100-14)

Fp = Design lateral earthquake force

IP = Seismic importance factor (See Figure 100-12)

Wp = Total operating weight of equipment

ap = In-Structure Component Application Factor (from Figure 100-13)

Rp = Component Response Modification Factor (from Figure 100-13)

hx = element or component attachment elevation with respect to grade.

hx shall not be less than 0.0

hr = structure roof elevation with respect to grade

Fig. 100-12Seismic Importance Factor

Description I IP

Equipment required for life safety systems 1.25 1.5

Items containing sufficient quantities of acutely

hazardous material whose failure could result in off-site

consequences.

1.25 1.5

All other equipment or normal non-critical structures 1.0 1.0

Critical structures 1.25 1.5

Fp

apCaIp

Rp----------------- 1 3

hx

hr-----+

Wp=

Fpmin 0.7CaIpWp=

Fpmax 4.0CaIpWp=

Fp 0.7CaIpWp=


22/56



Direct anchorage through anchor bolts shall be provided where possible. For

shallow expansion anchor bolts, use Rp = 1.5. For nonductile or adhesive anchor

bolts, use Rp = 1.0. In situations where anchor bolt connections are impractical, a

welded ductile connection between equipment and support may be provided. A

ductile connection shall be defined as one that will undergo inelastic deformation

through yielding before the connection fails. The direct welding of rigid equipment

to a rigid foundation or support is not recommended.

Appendix H, Determination of Base Shear for Selected Structures, indicates the

appropriate base shear equations that should be used for many typical refinery struc-

tures and types of equipment. Appropriate R values are also included.

Displacement

There is no specific code requirement which limits the lateral displacement/drift in

industrial structures. However, it is recommended that the lateral displacement be

limited to a displacement that can be tolerated by the equipment being supported,

including the associated piping and other appurtenances.

The Maximum Inelastic Response Displacement, M, corresponds to the maximumdeformations of a structure responding in the inelastic range. In order to calculateM, the design level displacement (S) is simplified to the inelastic level using thefollowing equation:

(Eq. 100-15)

where:

M is as defined above

S is the displacement corresponding to the code-level design seismic forces

R is the structural system factor.

The analysis used to determine the Maximum Inelastic Response Displacement

(M) shall consider P effects. For guidance on this subject, contact the CRTCCivil/Structural Team.

Earthquake Loads

To design a structure, calculate the forces to be applied to each element of the

structure. The earthquake load (E) on an element of a structure is a result of the

Fig. 100-13Horizontal Force Factors (ap and Rp)

Equipment Description ap Rp

1. Vessels (including contents), and their support systems 1.0 3.0

2. Electrical, mechanical, and plumbing equipment and associated conduit

and ductwork and piping such as switchgears, transformers, pumps, andair-handling units.

1.0 3.0

NOTE:

Refer to UBC Table 16-0 for a more extensive listing of horizontal force factors.

M 0.7RS=
http://civ.pdf/http://civ.pdf/http://civ.pdf/http://civ.pdf/


23/56



combination of the horizontal component (Eh) and the vertical component (Ev), and

can be calculated using the following equation:

(Eq. 100-16)

where:

= redundancy/reliability factor

= 1.0 for nonbuilding structures and for structures in seismic zone

0, 1, or 2

1.0 for structural systems similar to buildings (SSSB) in seismiczone 3 or 4

Eh = earthquake load due to either the base shear (V) or the design

lateral force (Fp)

Ev = the load effect resulting from the vertical component of the earth-

quake ground motion

= 0.5CaID for Strength Design

= 0 for Allowable Stress Design

The intent of the factor is to encourage the design of redundant lateral forceresisting structures by penalizing non-redundant structures. There are a number of

important benefits to redundancy, one of the most evident being that the failure of

any single element in a non-redundant structure can produce global structural

collapse. Therefore, in order to obtain good seismic performance, the lateral resis-

tance should be distributed throughout the structure so that failure of any single

element will not result in collapse of the entire structure. The factor variesbetween 1.0 and 1.5, and takes into account the number of lateral force resisting

elements, the plan area of the structure, and the distribution of the forces to thelateral force resisting elements. For a structure with an adequate level of redun-

dancy, the factor would be equal to 1.0; whereas a structure with poor overallredundancy could have a factor of up to 1.5, resulting in design forces that are50% higher than otherwise required. Contact the CRTC Civil/Structural Team for

guidance on this subject.

Analysis of Existing Facilities

These Design Standards are intended to apply to the design of new facilities. In

general, structures and equipment properly designed in accordance with earlier

codes need not be redesigned to meet the present Wind and Earthquake Design

Standards. However, when any significant modification is made or weight is added

to an existing structure, the design should be reviewed. If required, the structure

should be modified to meet the requirements of the appropriate building code.

Although current building codes do not require the upgrading of existing facilities,

in keeping with Corporate Policy 530 for Safety, Fire, Health, and the Environment,

it may be appropriate to review the design of facilities in critical service. A portion

of that policy instructs management to conduct scientific hazard and risk assess-

E Eh Ev+=


24/56



ments, as needed, to identify, characterize, and safely manage any present or future

potential hazards of Company products and operations.

A critical facility is defined as one for which a major failure would cause one of the

following:

1. Develop a condition which would result in serious injury or death.

2. Result in damage to the environment significantly beyond that which the earth-

quake would cause at the site.

3. Result in appreciable loss of revenue.

To evaluate the risk of a critical facility, the following steps are recommended:

1. Determine the existing strength of the structures.

2. Make a judgment as to whether the existing strength is acceptable in light of

current conditions, including the types of risk factors previously noted.

The judgments required to determine acceptability should include evaluation ofstructural redundancy and reserve strength. The assessment of existing facilities for

earthquake capacity is not commodity engineering and should be done by qualified

personnel.

Since most assessments of existing facilities are voluntary efforts to mitigate

potential business risks, it is not always necessary or even beneficial to measure a

structures acceptability against the current building code requirements. CRTCs

Civil/Structural Technical Service Team has performed many seismic assessments

of Company owned facilities utilizing Proposed Guidance for Risk Management

and Prevention Program (RMPP) Seismic Assessments. This document was

developed in 1992 by a team of technical experts and industry professionals to aid

in the assessment of seismic risk at existing industrial facilities. In 1998, thisdocument was revised and renamed Proposed Guidance for California Accidental

Release Prevention (CalARP) Program Seismic Assessments.

Proposed Guidance for CalARP Seismic Assessments evaluates the ultimate

strength capacity of existing structures. The ultimate strength capacity of a structure

is defined here as the ability of a structure to perform inelastically while avoiding

failure. The ultimate strength must be compared to the expected structural demand

resulting from the expected levels of ground shaking at the site. The CalARP guide-

lines utilize the same level of acceptable risk as that defined in the current UBC, i.e.,

the level of ground motion associated with a 10 percent chance of exceedance in 50 years.

For facilities with unacceptably low strength, one of the following should be

considered:

1. Strengthen the facility

2. De-rate the facility to lower the risk of failure. For example, reduce the safe

operating height for tanks.

CRTCs Civil/Structural Technical Service Team is available for counsel regarding

these procedures and judgments.


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115 Allowable Stresses, Soil Bearing, and Stability Ratios

Allowable Stresses for Structural Members

The allowable stresses for structural members for loading conditions including wind

or earthquake loads shall be one-third greater than the stresses allowed for normal

conditions of loading by applicable structural design codes.

Stability Ratio

The stability ratio of the resisting moments about the edge of a foundation to the

overturning moment due to wind loads shall not be less than 1.5.

The stability ratio for earthquake loads shall not be less than 1.0 and the force Ft, if

applicable, may be omitted when determining the earthquake overturning moment

to be resisted at the foundation-soil interface.

Foundation Soil Bearing Pressures

Foundation soil bearing pressures for loading conditions including wind or earth-quake loads should be based on sound engineering principles taking into account the

nature of the subsoil and distribution of the load. In the absence of other criteria, the

allowable soil bearing pressures may be increased by one-third when considering

wind or earthquake forces acting alone or when combined with vertical loads.

Allowable Stresses in Pressure Vessel Shells and Skirts

See thePressure Vessel Manualfor allowable stresses in pressure vessels subject to

wind or earthquake loads. Allowable stresses for loading conditions including wind

or earthquake loads are typically higher than stresses allowed for normal conditions.

120 Methods and Calculations

121 Natural Period of Vibration

In the design of flexible structures for earthquake loads and wind-induced vibra-

tion, it is necessary to determine the first mode natural period of vibration of the

structure. The following figures (Figures 100-14 through 100-20), and their accom-

panying equations give the natural period of vibration for several types of industrial

structures. Texts about dynamics of structures tell how to find the periods of more

complex structures. Computer programs with dynamic structural analysis capabili-

ties can also determine periods of structural vibration.

The units used throughout the following formulas must be consistent except whereotherwise noted.

Equation 100-23 in Figure 100-20 is an approximate formula which is sufficiently

accurate for most non-uniform distillation columns and vertical vessels. If a vessel

has a lower section several times the diameter of the upper portions, and the lower

portion is short compared with the overall height (such as a vertical seal drum on

which is mounted a self-supporting flare or vent stack), the period can be more


26/56



accurately determined by finding the period of the upper portion, assuming that

displacement and rotation are fixed at its junction with the lower section. For

vessels where the shell diameter or thickness is large in comparison with the

supporting skirt, such as for high pressure reactors, the period calculated from

Equation 100-23 may be overly conservative for earthquake design, and more accu-

rate methods may be justified.

The equations presented in this section ignore the effects of soil-structure inter-

action. Soil-structure interaction can have a profound effect on the natural

period of large vertical vessels on individual pile-supported foundations. All

critical calculations for such vessels should consider this dynamic phenom-

enon. The CRTC Civil/Structural Technical Service Team may be consulted in

these cases.

Figure 100-14 gives the general formula for determining the natural period of

vibration, T, for a one mass structure.

Figure 100-15 gives the equation for determining the natural period of vibra-

tion for a one mass, Bending Type Structure.

Figure 100-16 gives the equations for a one mass, rigid frame-type structure.

Figure 100-17 gives the equation and parameters for determining the natural

period of vibration for a two mass structure.

Figure 100-18 gives the equation for a bending type structure of uniform

weight distribution and constant cross section.

Figure 100-19 gives the equation for the natural period of vibration for a

uniform vertical cylindrical steel vessel.

Figure 100-20 gives the equation for the natural period of vibration for a non-

uniform vertical cylindrical vessel.

Figure 100-21 lists the coefficients for determining the natural period of vibra-

tion of free-standing cylindrical shells with varying cross sections and mass

distribution.

Fig. 100-14Natural Period of Vibration - One Mass Structure

(Eq. 100-17)

where:

y = static deflection of mass resulting from a lateral load applied at the

mass equal to its own weight.

g = acceleration due to gravity.

See Examples 4 and 5 for application.

T 2 yg---

0.5=


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Fig. 100-15Natural Period of Vibration - One Mass, Bending Type Structure

Fig. 100-16Natural Period of Vibration - One Mass, Rigid Frame Type Structure

(Eq. 100-18)

(Eq. 100-19)


28/56



Fig. 100-17Natural Period of Vibration - Two Mass Structure

Fig. 100-18Natural Period of Vibration - Bending Type Structure, Uniform Weight Distribution and

Constant Cross Section

(Eq. 100-20)

(Eq. 100-21)


29/56

ChevronCorporation

100-29

September2000

Fig. 100-19Natural Period of Vibration - Uniform Vertical Cylindrical Steel Vessel

(Eq. 100-22)


30/56



Fig. 100-20Natural Period of Vibration - Non-uniform Vertical Cylindrical Vessel Courtesy of the James F.

Lincoln Arc Welding Foundation

(Eq. 100-23)


31/56



Fig. 100-21Coefficients for Determining Period of Vibration of Free-Standing Cylindrical Shells Having

Varying Cross Sections and Mass Distribution Courtesy of the James F. Lincoln Arc Welding

Foundation


32/56



122 Wind-Induced Vibration of Steel Stacks and Columns

Introduction

Welded steel stacks and other tall, cylindrical structures such as fractionating

columns are susceptible to large-amplitude oscillations during steady winds of

moderate velocity. These oscillations occur transverse to the mean wind direction

and are driven by the vortices which form the downstream wake. The amplitude of

the oscillations is inversely related to the mass and damping of the structure. Unac-

ceptable oscillations are most likely to be encountered with lightly damped struc-

tures, such as welded steel stacks on rigid foundations, and less likely with lined

stacks, riveted structures, concrete stacks, or columns containing process fluids.

The following is a method for design to avoid wind-induced oscillations for tall

cylindrical structures, including guyed stacks. The method is based on a conserva-

tive interpretation of available data, and will produce reliable results when used with

realistic estimates of structural damping.

Ovalling vibration of thin walled stacks must also be checked.

Critical Wind Velocity

The design objective is to have the Critical Wind Velocity (Uc) be greater than the

Design Wind Velocity (Ud), thereby eliminating wind-induced vibration.

The Critical Wind Velocity is the lowest velocity at which wind-induced oscilla-

tions occur. It is computed as follows:

1. Determine the natural fundamental period (T) of the structure (See Section 121,

Natural Period of Vibration).

2. Using the outside diameter of the stack (D), find the Critical Wind Velocity

(Uc):

(Eq. 100-24)

3. Determine the Mean Steady Wind Velocity (Um) at the site, sustained for

approximately 10 minutes. This wind velocity should be referenced to a

particular height above grade (Z), which is 30 feet in most meteorological data.

Note: This is not the Wind Speed Zone used in Section 113 or the Base Shear

Z used in Section 114.

4. Determine the Mean Steady Wind Velocity (Ut) at the top of the stack (H):

(Eq. 100-25)

5. Calculate the Design Wind, (Ud):

Ud = 3Ut (Eq. 100-26)

If Uc > Ud, then the stack is not susceptible to wind-induced oscillation. If Uc < Ud,

the following design check is required.

Uc4.7D

T------------=

Ut Um HZ----

0.28

=


33/56



Design Check

The design objective is to have the Design Damping Coefficient (Cd) be less than

the Structural Damping Coefficient (Cs) so wind-induced vibration amplitudes will

not exceed acceptable limits.

The Design Damping Coefficient (Cd) and the Structural Damping Coefficient (Cs)are determined as follows.

1. Select an allowable vibration amplitude, Ya, which represents the amplitude of

vibrations that could be sustained indefinitely without fatigue damage to the

stack. Use this method to find a good approximation for Ya.

a. Define allowable stress range (Fr) for infinite life. For shells with butt

welded circumferential joint, Fris 16 ksi. For shells with fillet welded

circumferential joint, Fris 5 ksi. For other types of connections, refer to the

tables in the AISC Manual of Steel Construction, Part 5, Appendix K4.

b. Determine stress per unit-deflection (Fm) for the fundamental mode shape

of the stack. This may be approximated by:

Fm = 1.2 Fw / Yw (Eq. 100-27)

where:

Fw = the maximum change in stress from a static condition due to

design wind load only.

Yw = The maximum deflection from a static condition due to the design

wind load only.

c. Let:

Ya = (Fr/2Fm) (Eq. 100-28)

Note that allowable stress range is divided by two to get single amplitudeallowable stress.

2. Compute Mr:

(Eq. 100-29)

w = Weight/unit length of the top one-third of the stack. If variable,

average the weight over the top one-third of the stack.

= Weight density of air times /4= 0.076 lb/ft3 x /4 = 0.06 lb/ft3

D = Diameter of the top one-third of the stack. If variable, take thesquare root of the length-weighted average of the squared values

of the diameters over the top one-third. For example, for two

sections:

(Eq. 100-30)

Mrw

D2----------=

DD1

2l1 D22l2+

l1 l2+( )------------------------------

0.5

=


34/56



3. Compute Design Minimum Required Damping Coefficient (Cd):

(Eq. 100-31)

= A shape factor; use 1.3 for the fundamental mode of cantilever

structures.

4. Select a Structural Damping Coefficient (Cs) by adding the appropriate frac-

tions listed below (other values for structural damping may be used if they can

be substantiated):

For example, a stack with refractory lining on a 2000 psf foundation would

have:

Cs = 0.003 + 0.002 + 0.002 = 0.007.

5. If Cd < Cs, then wind-induced vibration amplitudes will not exceed acceptable

limits. If Cd > Cs, then design alternatives must be considered.

Design Alternatives

1. Lower H/D or increase t, stack wall thickness (to raise Uc above Ud.)

2. Increase t or refractory line stack (to increase Mrand Cs.)

3. Attach helical spoilers to the top third of the stack. Conservative guidelines for

spoiler design are:

a. Spoilers shall consist of three helical strakes over the top third of the stack

with a pitch of 5D and a height of 0.12D.

b. A conservative estimate for Design Minimum Damping Fraction for a

stack with spoilers is:

(Eq. 100-32)

Cd0.45

Mr----------

DYa-------- 1.0

0.5=

Factor Incremental Damping Fraction

Basic Stack 0.003

Refractory 0.002

Basic Column

Empty 0.008

With Liquid Content 0.013Foundation soil strength:

less than 1500 psf 0.006

1500 psf to 3000 psf 0.002

greater than 3000 psf 0.0

Pile-supported stacks 0.0

Stacks supported atop structures 0.0

Cd0.30

Mr----------=


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Spoilers will be effective if Cs > Cd. A lower value of Cd may be used if it can

be justified.

Note that spoilers increase the effective area and shape factor for static wind

load, which must be accounted for in the design.

4. Attach a damping device to the stack. Several such devices have been used.Two proven alternatives are hydraulically tensioned guys, and chain impact

dampers.

If Design Minimum Damping is close to the required minimum, so that short dura-

tions of wind-induced vibration will not result in damage, then a reasonable alterna-

tive is to design an auxiliary damping system and provide attachments to the stack

(i.e., padeyes), but defer fabrication and installation of the dampers until after the

stack is erected and actual unacceptable vibration amplitudes have been observed.

Ovalling Vibration of Thin-walled Stacks

Thin-walled stacks are also susceptible to ovalling vibrations, i.e., oscillations

where the stack cross-section vibrates as a ring. The same aeroelastic phenomenadescribed in the introduction to this section create this mode of vibration. Ovalling,

however, can be directly prevented by the addition of circumferential stiffeners to

the stack.

Criteria for avoiding ovalling is:

If (Eq. 100-33)

where:

t = stack wall thickness, inch

R = stack radius, inch

Ud = Design Wind (see Equation 100-26), fps

If stiffeners are required:

1. Choose a spacing of stiffeners, L, such that:

(Eq. 100-34)

2. Calculate the required moment of inertia, Ir(in4), of the added stiffener section

about its center of gravity axis by

(Eq. 100-35)

where:

E = modulus of elasticity at operating temperature in psi

D = Diameter in feet

R = Radius in inches

t

R---

Ud

10200--------------- stiffeners are required 0.003 R (Eq. 100-36)

Example Calculations

See Section 123, Examples 6 and 7, for a demonstration of the methodology for

analyzing wind-induced vibration of steel stacks

123 Examples of Wind and Earthquake Load Calculations

Following are seven examples of wind and earthquake load calculations for several

different structures and supports. These examples are:

Note: Examples 1-5 are based on the 1997 edition of the UBC. The earthquake

design forces specified by the 1997 UBC are based on strength design; whereas in

past editions of UBC the design forces were based on allowable stress design.

Therefore, in order to be consistent with the 1997 UBC, examples 1-5 are strength

design based. If you want to use allowable stress design, the calculated earthquake

forces should be divided by a factor of 1.4.

Example 1Two-Story Concrete Vessel Support Structure(Assume El Segundo, CA Location)

Earthquake Forces (Transverse directionLoads on one bent)

W = 20 kips (includes structure weight)

Deflections from 1 kip at A and B (calculations not shown):

Caa = 0.0384 in., Cab = 0.0180 in., Cbb = 0.0157 in.

Example 1 Two-Story Concrete Vessel Support Structure


Example 2 Uniform Cylindrical Column


Example 3 Column of Variable Cross Section

(Assume Salt Lake City, UT Location)

Example 4 Braced-Column Spheres

(Assume Richmond, California, Location)

Example 5 Vertical Vessels with Unbraced Legs

(Assume Richmond, CA Location)

Example 6 Stack Vibration and Ovalling

Example 7 Stack Vibration


37/56



Use Equation 100-20

(Eq. 100-2)

Z = 0.40 (Seismic Zone 4)

I = 1.0

Assume Type Sc soil.

For El Segundo, Na = 1.1 and Nv = 1.33 (Figure 100-5)

Fig. 100-22Two-Story Concrete Vessel Support StructureSMRSF, EQ Zone 4, Wind Zone 70 MPH

T 2 3.14( )12 0.0384( ) 8 0.0157( ) 12 0.0384( ) 8 0.0157( )[ ]

24 12( ) 8( ) 0.0180( )

2+[ ]

0.5+ +

2 386( )---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

0.5

=

0.234 sec 0.06 sec>=

Use VCvI

RT--------W=

Ca 0.40Na 0.40 1.1( ) 0.44 (Figure 100-7)= = =

Cv 0.56Nv 0.56 1.33( ) 0.745= = = Figure 100-8( )


38/56



Check vs. Vmax:

(Eq. 100-3)

Note: If it is desired to use allowable stress design, the base shear value (V =

3.93K) should be divided by 1.4.

(Eq. 100-10)

Base Moment, Mo = (2.95) (20) + (0.98) (10) = 68.2 k-ft.

Wind Forces (Transverse directionLoads on one bent). Assume wind speedzone = 70, Exposure B.

Shape Factors: Vessels = 1.4; Open Framework Structures = 1.3

Base Overturning Moment = (0.64) (20) + (0.41) (10) = 16.9 k-ft

Therefore, the Earthquake Moment controls the design.

R 5.6 (Figure 100-11) Special Moment-Resisting Space Frame - Concrete=

VCvI

RT--------W

0.745( ) 1.0( )5.6( ) 0.234( )

------------------------------- 20( ) 11.17 kip Total Base Shear= = =

Vmax

2.5CaI

R---------------- W=

2.5( ) 0.44( ) 1.0( )5.6

---------------------------------------- 20( )=

3.93k

=

Vmax controls!

Use V 3.93k

=

T 0.7 sec., thereforeFt

0.0=

WA

hA

12 20( ) 240 WB

hB

; 8 10( ) 80 Wh; 320= = = = =

FA

VW

AhA

Wh---------------- 3.93( )

240

320--------- 2.95 kip FB

;W

BhB

Wh---------------- 3.93

80

320--------- 0.98 kip= = = = = =

FA

1.4 9( ) 4 202------

1.3 8( ) 1.5 112

------ 1.0 10

2------

++

1 000,-------------------------------------------------------------------------------------------------------------- 0.64 kip= =

FB

1.4 8( ) 2 152------

1.3 8( ) 1.5 112

------ 1.0

10

2------ 10+

++

1 000,-------------------------------------------------------------------------------------------------------------------------- 0.41 kip Total Shear 1.05 kip= = =


39/56



Example 2Uniform Cylindrical Column (Assume El Segundo,CA Location)

In most columns of constant diameter, the entire mass can be assumed uniformly

distributed over the height. Where there are large concentrations of mass or varia-

tions in cross-section, the analysis should be made as shown in Example 3.

Period of Vibration:

(Eq. 100-22)

Z = 0.4 (Zone 4); Importance Factor, I = 1.0

Na = 1.1; Nv = 1.33 (From Figure 100-5).

Assume Type Sc soil.

Fig. 100-23Uniform Cylindrical Column: Earthquake Forces

T7.78

106----------

100

6---------

2 12 600 60.25

------------------------------ 0.5 0.898 sec= =

tvessel

tsk ir t---------------

0.625

0.25------------- 2.5 and 2.5 1.5 therefore, useR 2.2= (from Figure 100-11),>= =


40/56



From Figures 100-7 and 100-8,

Ca = 0.40Na = 0.40(1.1) = 0.44

Cv = 0.56Nv = 0.56(1.33) = 0.745

(Eq. 100-2)

(Eq. 100-0)

Check Vmin:

(Eq. 100-7)

Also, for Zone 4:

(Eq. 100-8)

Note If it is desired to use allowable stress design, the base shear value

(V = 23.21k) should be divided by 1.4.)

T > 0.7 sec, therefore Ft = 0.07 TV = 0.07(0.898)(23.21) = 1.46 kip (Eq. 100-9)

V-Ft = 21.75 kip

W wH 600 lb ft( ) 100 ft( ) 60 000 lb, 60 kip= = = =

Base Shear, VCVI

RT---------W

0.745( ) 1.0( )2.2( ) 0.898( )

------------------------------- 60 kip( ) 22.63 kips= = =

CheckVmax

2.5CaI

R---------------- W

2.5( ) 0.44( ) 1.0( )2.2

---------------------------------------- 60( ) 30.0 kip= = =

Vmin 0.56CaIW=

0.56 0.44( ) 1.0( ) 60( )=

14.78kips=

Vmin

1.6ZNVI

R---------------------W=

1.6 0.4( ) 1.33( ) 1.0( )2.2------------------------------------------------ 60( )=

23.21kips=

Vmin controls! Use V 23.21 kips=


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When the weight is distributed uniformly along the height, the distribution of the

lateral force V-Ft given by Equation 100-10 resolves to the triangular distribution

shown in Figure 100-23.

The moment at the top of the skirt, or at any other elevation, can be found bydrawing a free body diagram. For example, M15 = 1,243 k-ft.

Wind Forces(Wind Zone = 70, Exposure C)

Diam. = 6 ft.-0 in. + 2 (2 in) = 6.33 ft.

Shape Factor = 1.7 - (0.075 D) = 1.7 - (0.075)(6.33) = 1.23

Fig. 100-24Uniform Cylindrical Column: Wind Forces

Base Moment,Mo FtH Fxhx+ 1.46 100( )2

3--- 21.75( ) 100( )+ 1 596 k-ft,= = =

Wind Base Shear, VW Wind Moment, MOW:

F1 = 1.23(13)(6.33)(15) = 1,520 M01 = 1,520(7.5) = 11,400

F2 = 1.23(14)(6.33)(5) = 550 M02 = 550(17.5) = 9,630

F3 = 1.23(15)(6.33)(5) = 580 M03 = 580(22.5) = 13,050

F4 = 1.23(16)(6.33)(15) = 1,870 M04 = 1,870(32.5) = 60,780

F5 = 1.23(18)(6.33)(20) = 2,800 M05 = 2,800(50) = 140,000

F6 = 1.23(19)(6.33)(20) = 2,960 M06 = 2,960(70) = 207,200

F7 = 1.23(20)(6.33)(20) = 3,110 M07 = 3,110(90) = 279,900

Vw = 13,390 lb Mow = 721,960 lb-ft = 722 k-ft


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Moment at top of skirt:

M15 = 1.23(14)(6.33)(5)(2.5) + 580(7.5)

+ 1,870(17.5) + 2,800(35)

+ 2,960(55) + 3110(75) = 532.5 k-ft.

Therefore, Earthquake Moment controls the design.

Wind and earthquake moments can be determined similarly at other sections.

Combine the larger of wind or earthquake moment with corresponding gravity

forces at each section and use allowable stresses to determine the required skirt and

shell thickness.

Example 3Column of Variable Cross Section (Assume SaltLake City, UT Location)

Period of VibrationUse Equation 100-23 (see Figure 100-20.)

Z = 0.30 (Zone 3); Occupancy Factor = 1.0

Fig. 100-25Column of Variable Cross Section: Natural Period of Vibration

1800

(lb/ft)

(lb)

D

3720 684.86

1200

8000

900

40

3760

1039.76

672.47

2397

2397


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Assume SD soil.

Therefore, from Figures 100-7 and 100-8, Ca = 0.36, and Cv = 0.54

W = 58.5(1.8) + 23.5(1.2) + 12(0.9) + 8.0 = 152.3 kips

(Eq. 100-2)

Check Vmin = 0.56CaIW = 0.56(0.36)(1.0)(152.3) = 30.7 kips (Eq. 100-7)

Therefore, use V = 33.83 kips.

Note If it is desired to use allowable stress design, the base shear value

(V=33.83 kips) should be divided by 1.4.

T > 0.7 sec; therefore Ft = 0.07TV = 0.07 (1.105) (33.83) = 2.62 kip (Eq. 100-9)

V - Ft = 31.21 kips

(Eq. 100-10)

Shear and Moments: Divide column into segments not exceeding 20% of height.

Base overturning moment, Mo = 2239.3 k-ft. See Figure 100-26.

Wind Forces (Wind Speed Zone = 70, Exposure B)

Base overturning moment, Mo = 499 k-ft. See Figure 100-27. The shape factor and

projected area are based on the outside diameter including the insulation. M(Figure 100-27) is calculated for each section by multiplying average shear in

section by height of section. (Area under shear diagram.) Therefore, M is theincremental moment at each section, while Mx is the total moment at each section.


tvessel

tsk ir t---------------

0.625

0.25------------- 2.5 and 2.5> 1.5, therefore, use R 2.2 (from Figure 100-11)= = =

Base Shear, VCvI

RT--------W

0.54( ) 1.0( )2.2( ) 1.105( )

------------------------------- 152.3( ) 33.83 kips= = =

Fx V Ft( )

Wxhx

Wh-------------31.21

7672.7----------------Wxhx= =


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Fig. 100-26Column of Variable Cross Section: Earthquake Forces

Fig. 100-27Column of Variable Cross Section: Wind Forces

62 62

11.7

11.7

11.7

11.7

11.7

21.06

21.06

21.06

21.06

21.06

88.15

76.45

64.75

53.05

41.35

1856.44

1610.04

1363.64

1117.23

870.83

7.55

6.55

5.55

4.54

3.54

10.17

16.72

22.27

26.81

30.35

6.40

13.45

19.49

24.54

28.58

74.83

157.32

228.08

287.11

334.42

74.83

232.15

460.22

747.34

1081.76

5.875

5.875

5.875

7.05

7.05

7.05

32.56

26.69

20.81

229.57

188.15

146.73

0.93

0.77

0.60

31.29

32.05

32.65

33.14

33.57

33.83

30.82

31.67

32.35

32.89

33.35

33.70

181.07

186.06

190.07

0.0

195.94

404.38

1262.83

1448.89

1638.96

1638.96

1834.90

2239.28

5.875 7.05 14.94 105.31

0.49

0.43

0.26

60

73

106

179

192

34

226

22248

37285

39

32441

365

26391

108

499


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Example 4Braced-Column Spheres (Assume Richmond, Cali-forniaLocation)

The recommended bracing system for spheres consists of x-bracing connecting

adjacent pairs of columns as illustrated in Figure 100-28. In accordance with Details

of Earthquake Resistant Design in Section 114, the bracing for large spheres subjectto earthquake loads should be effective both in tension and compression to better

resist the lateral forces. The lateral forces are transmitted into the shell by a

balcony girder.

The shear in each panel and the maximum panel shear may be found by the

formulas:

Fig. 100-28Recommended Bracing System for Spheres


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(Eq. 100-37)

(Eq. 100-38)

where:

Vp = panel shear

Vpmax = maximum panel shear

V = total lateral force

n = number of panels (equal to number of columns)

= angle between the plane of the panel and the direction of thelateral force.

Earthquake ForcesPeriod of Vibration:

The period of vibration is found using the general formula for one-mass structure in

Section 121, Equation 100-17. The static deflection, y, is found by determining the

change in length of the bracing resulting from a total lateral load equal to the weight

of the sphere. Deformation of the columns and balcony girder are usually neglected

for one-story structures.

(Eq. 100-17)

Z = 0.4, Zone 4; Occupancy Factor I = 1.0, R = 2.9 (Figure 100-11)

From Figure 100-5, Na = 1.2 and Nv = 1.6.

Assume SE Soil (site over Bay mud)

Therefore, from Figures 100-7 and 100-8,

Vp2V

n------- cos=

Vpmax2V

n-------=

P Maximum force in brace1

2---

2 15006

--------------------- 36.0

20.0----------

450 kip= = =

Change in length of brace PLEA------- 450( ) 36.0( ) 12( )

29 000,( ) 8.0( )---------------------------------------- 0.838 in.= = = =

y

sin----------- 0.838( ) 36.0

20----------

1.51 in.= = =

Period of Vibration, T 2 yg---

0.5=

T 2 1.5132.2 12( )---------------------

0.5 0.393 sec= =


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Ca= 0.36Na = 0.36(1.2) = 0.43

Cv= 0.96Nv = 0.96(1.6) = 1.54

(Eq. 100-2)

Check Vmax:

(Eq. 100-3)

Note If it is desired to use allowable stress design, the base shear value (V = 556

kips) should be divided by 1.4.

Fig. 100-29Wind Forces for Braced-Column Spheres

Wind Forces (Wind Speed Zone = 70, Exposure C)

Description Projected Area ft2 Shap

e

factor

Wind

Pressure

psf

Force

k

Sphere Above 40 Elev. 246 0.65 18 2.9

Sphere Between 30 and 40 Elev. 382 0.65 16 4.0




Sphere Below 15 Elev. 92 0.65 13 0.8

Columns & Bracing Above 25 Elev. (1/6)[4(1)(30)+6(.5)(36

)]=38

2.0 16 1.2

Columns & Bracing Between 20 and 25Elev. (1/6)[228]=38 2.0 15 1.1

Columns & Bracing Between 15 and 20

Elev.

(1/6)[228]=38 2.0 14 1.1

Columns & Bracing Below 15 Elev. (1/2)[228]=114 2.0 13 3.0

Total Wind Force, VW = 19.4

Note In computing the slenderness ratio of bracing in an x-braced frame, the effective length may be taken as one-half the

total

length about both axes of the member. Braces should be attached at their point of intersection.

Base Shear, VC

vI

RT---------W

1.54( ) 1.0( )2.9( ) 0.393( )

------------------------------- 1500( ) 2026.8 kips= = =

Vmax

2.5CaI

R---------------- W=

2.5 0.43( ) 1.0( )2.9

----------------------------------- 1500( )= 556.0 kips=

Vmax controls.

Use V 556.0 kips=


48/56



Therefore, earthquake forces control the design.

Example 5Vertical Vessels with Unbraced Legs (Assume Rich-mond, CA Location)

Vertical vessels are often supported with legs rather than skirts as represented in

Figure 100-30. Where the legs are braced, earthquake and wind loads may be deter-mined as in Example 4. Small vessels are frequently supported on legs without

bracing. Usually the legs are considered fixed at the vessel shell and pinned at their

bases. For these cases, the shell must be adequate to resist the bending moments

applied by the legs, or must be adequately stiffened.

Earthquake Forces


Since the stiffness of the shell is usually large compared with that of the legs, the

period of vibration can be found using the general formula for a one-mass structure

in Section 121 (Equation 100-17) assuming the deflection, y, equals the deflectionof the legs resulting from a total lateral force equal to the weight of the vessel. For a

vessel supported on three or more legs symmetrically spaced about the center, y

may be determined from the formula:

(Eq. 100-39)

where:

N = number of legs

Ix + Iy = sum of moments of inertia of one leg about the perpendicular axis

L = length of legs from base to shell attachment

For example shown:


(Eq. 100-17)

Zone 4; Z = 0.40, Occupancy Factor, I = 1.0; Assume SE soil

From Figure 100-5, Na = 1.2; Nv = 1.6

y2WL3

3NE Ix Iy+( )-------------------------------=

y2( ) 15.0( ) 5 12( )3

3( ) 4( ) 29000( ) 2.45 2.45+( )-------------------------------------------------------------------- 3.80 in= =

T 2 yg---

0.5 2 3.8032.2 12( )---------------------

0.5 0.623 sec= = =


49/56



Fig. 100-30Vertical Vessel with Unbraced Legs


50/56



(Eq. 100-2)

Check Vmax:

(Eq. 100-3)

Vmax controls.

Note If it is desired to use allowable stress design, the base shear value (V = 7.33

kips) should be divided by 1.4.

T < 0.7, therefore Ft = 0.0

Considering the weight, W, uniformly distributed along the shell length, the force V-

Ft given by Equation 100-10 resolves to a trapezoid, the extended non-parallel sides

of which intersect at the base as shown in the sketch in Figure 100-30.

Earthquake Base Overturning Moment:

For the distribution noted above, the base overturning moment, Mo, can be deter-

mined by the formula:

(Eq. 100-40)

for design example,

Wind Forces (Wind Speed Zone = 70, Exposure B)

Wind Base Moment Mo = 0.53(10) + 0.067(2.5) = 5.47 k-ft.


R 2.2 (Figure 100-11)=

From Figure 100-7, Ca 0.36Na 0.36 1.2( ) 0.43= = =

From Figure 100-8, Cv

0.96Nv

0.96 1.6( ) 1.54= = =

Base Shear, VC

vIW

RT--------------

1.54( ) 1.0( ) 1.5( )2.2( ) 0.623( )

---------------------------------------- 16.85 kips= = =

Vmax

2.5CaI

R---------------- W=

2.5 0.43( ) 1.0( )

2.2

----------------------------------- 15( )=

7.33 kips=

use V 7.33 k=

M0 FtH2

3--- V Ft( )

H3 L3

H2 L2-------------------+=

M0

2

3--- 7.33( ) 15

3 53( )

152 52( )------------------------- 79.4 k-ft.= =


51/56



The axial loads may be determined using the vessel weight and governing base

overturning moment. The bending moment in the legs at the shell about each prin-

cipal axis (axes of maximum and minimum moment of inertia) may be determined

using the governing base shear.

Example 6Stack Vibration and Ovalling

Check the susceptibility to large-amplitude oscillation and also determine the

required circumferential stiffener size and spacing for the following stack:

H = 180 ft

D = 15.0 ft

t = 0.50 in.

Um = 15 fps at elev. + 30 ft

Use Figure 100-19, Uniform Vertical Cylindrical Steel Vessel, for determining

period of vibration.

(Eq. 100-22)

(Eq. 100-24)

(Eq. 100-25)

(Eq. 100-26)

Fig. 100-31Base Shear for Vertical Vessels with Unbraced Legs

Item Projected Area (ft2) Shape Factor Wind Pressure

Force

(lb)

Shell 5' 10' = 50 1.7-(0.0755) = 1.33 8 532

Legs 5' 0.84' = 4.2 2.0 8 67Base Shear = 599 lb

w4--- 180( )2 179( )2( )

1

144--------- 490 959 lb/ft.= =

T7.78

106----------

180

15---------

2 12 959 150.50

--------------------------------- 0.5 0.66 sec.= =

Uc4.7D

T------------

4.7( ) 15( )0.66

----------------------- 106.8 fps= = =

Ut UmH

Z----

0.28 15( ) 18030

--------- 0.28 24.8 fps= = =

Ud 3Ut 3( ) 24.8( ) 74.4 fps= = =


52/56


September 2000 100-52 Chevron C

civ100 wind and earthquake

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