seismic upgrade strategies for a historical building in

SEISMIC UPGRADE STRATEGIES FOR A HISTORICAL BUILDING IN

PLACERVILLE, CALIFORNIA

A Project

Presented to the faculty of the Department of Civil Engineering

California State University, Sacramento

Submitted in partial satisfaction of

the requirements for the degree of

MASTER OF SCIENCE

in

Civil Engineering

(Structural Engineering)

by

Yash Kandhari

FALL

2019

ii

© 2019

Yash Kandhari

ALL RIGHTS RESERVED

iii



A Project

by

Yash Kandhari

Approved by:

__________________________________, Committee Chair

Dr. Benjamin Fell, PE

____________________________

Date

iv

Student: Yash Kandhari

I certify that this student has met the requirements for format contained in the University

format manual, and this project is suitable for shelving in the library and credit is to be

awarded for the project.

__________________________, Graduate Coordinator ___________________

Dr. Ghazan Khan Date

Department of Civil Engineering

v

Abstract

of



by

Yash Kandhari

This report summarizes a seismic structural retrofit to an existing unreinforced masonry

(URM) building in Placerville, California, presenting two different structural systems as

alternatives. The first system is a more traditional approach using a Special Steel Moment

Resisting Frame (SMRF), while the second features a newer approach of coating the walls

in Fiber Reinforced Cementitious Matrix (FRCM). The various failure modes and concerns

of URM buildings or components subjected to earthquake excitation are presented, along

with the different design methodologies of the two retrofit strategies. A comprehensive

literature review is presented to establish the design methodology and material

characteristics for the FRCM to determine the upgraded strength of the masonry structure.

For both systems, the diaphragms are also detailed according to the varying seismic forces

developed from each lateral load resisting system.

_______________________, Committee Chair

Dr. Benjamin Fell, PE

________________________

Date

vi

ACKNOWLEDGEMENTS

I would like to thank Prof. Benjamin Fell, my project advisor for all the knowledge

and guidance he has provided me through this project. He has been very supportive and

has led me with care and caution throughout the project.

I would like to thank Burne Engineering for presenting this project which gave depth

to my understanding in many aspects.

I would also like to thank my parents, Pooja and Gopal for their constant support and

love and making me believe that I can accomplish anything when I put my mind to it and

always reminding me to chase my dreams.

I would also like to thank my friends for their support and for standing by my side in

worst times and let me up.

Lastly, I would like to thank the Department of Civil Engineering, Prof. Benjamin

Fell for giving me this wonderful opportunity to learn and grow and always encouraging

to do things which I never thought of doing.

vii

TABLE OF CONTENTS

Page

Acknowledgements .................................................................................................. vi

List of Tables ......................................................................................................... viii

List of Figures ........................................................................................................... x

Chapter

1. INTRODUCTION ................................................................................................. 1

2. BACKGROUND ................................................................................................... 3

3. FABRIC-REINFORCED CEMENTITIOUS MATRIX (FRCM) ........................... 5

4. NEW STEEL SPECIAL MOMENT FRAMES .................................................... 20

5. DIAPHRAGMS .................................................................................................. 31

6. SUMMARY ........................................................................................................ 43

Appendix A. Excel Calculations .............................................................................. 44

References ............................................................................................................... 64

viii

LIST OF TABLES

Tables Page

1. Vertical distribution of forces (FRCM)………………………………………... 7

2. Mechanical properties (FRCM)………………………………………………... 8

3. FRCM reinforcement properties……………………………………………….. 8

4. Loading information (1st story) ………………………………………………. 10

5. Loading information (2nd story) …………………………………………….... 10

6. Nominal shear capacity of the CMU wall panel (1st story) …………………... 12

7. Nominal shear capacity of the CMU wall panel (2nd story) ………………….. 13

8. Shear capacity of the FRCM strengthened wall (1st story) …………………... 15

9. Shear capacity of the FRCM strengthened wall (2nd story) …………………. 16

10. Design shear strength of the strengthened wall (1st story) …………………... 17

11. Design shear strength of the strengthened wall (2nd story) …………………... 17

12. Dead load (roof)………………………………………………………………. 25

13. Dead load (floor)…………………………………………………………….... 26

14. Wall weights……………………………………………………………………26

15. Vertical distribution of forces (SMF)………………………………………..... 27

16. Story drift (building 1) ……………………………………………………….. 29

17. Story drift (building 2) ……………………………………………………….. 30

18. Diaphragm forces (FRCM-1st story)………………………………………….. 33

19. Diaphragm unit shear (FRCM-roof) …………………………………………. 34

20. Diaphragm unit shear (FRCM-2nd floor) …………………………………….. 35

ix

21. Diaphragm detailing (FRCM)………………………………………………… 36

22. Chord force & chord unit shear (FRCM-roof) ……………………………….. 36

23. Chord force & chord unit shear (FRCM-2nd floor) …………………………… 37

24. Diaphragm forces (SMF)……………………………………………………... 38

25. Diaphragm unit shear (SMF-roof) …………………………………………… 39

26. Diaphragm unit shear (SMF-2nd floor) ………………………………………. 40

27. Diaphragm detailing (SMF)…………………………………………………... 41

28. Chord force & chord unit shear (SMF-roof) ………………………………… 41

29. Chord force & chord unit shear (SMF-2nd floor) ……………………………... 42

x

LIST OF FIGURES

Figures Page

1. Building layout……………………………………………………………….. 3

2. Vertical distribution of forces (FRCM)……………………………………….. 7

3. In-plane shear contribution (FRCM: north-south walls)

(a) 1st story (b) 2nd story…………………………………………………….... 18

4. In-plane shear contribution (FRCM: east-west walls)

(a) 1st story (b) 2nd story……………………………………………………….19

5. Typical local buckling of beam flanges and web……………………………...20

6. ATC hazards by location (seismic report) ……………………………….…...24

7. Vertical distribution of forces (SMF)………………………………………... 27

8. Confidence engine company hall mastan2 elastic analysis………………….. 29

9. Emigrant jane building mastan2 elastic analysis…………………………...... 30

10. Diaphragm behavior…………………………………………………………. 32

11. Diaphragm force resisting walls (FRCM)

(a)North-South Walls (b)East-West Walls…………………………………... 34

12. Diaphragm force resisting walls (SMF)

(a)north-south walls (b)east-west Walls………………………………………39

13. (a) Excel calculation sheet (20.125ft wall) (1st story) ……………………….. 44

(b) Continued excel calculation sheet (20.125ft wall) (1st story) ……………. 45

14. (a) Excel calculation sheet (20.125ft wall) (2nd story) ………………………. 46

(b) Continued excel calculation sheet (20.125ft wall) (2nd story) …………… 47

xi

15. (a) Excel calculation sheet (22.125ft wall) (1st story) ………………………. 48

(b) Continued excel calculation sheet (22.125ft wall) (1st story) ……………. 49

16. (a) Excel calculation sheet (22.125ft wall) (2nd story) ………………………. 50

(b) Continued excel calculation sheet (22.125ft wall) (2nd story) …………… 51

17. (a) Excel calculation sheet (51.42ft wall) (1st story) ………………………… 52

(b) Continued excel calculation sheet (51.42ft wall) (1st story) ……………... 53

18. (a) Excel calculation sheet (51.42ft wall) (2nd story) ………………………... 54

(b) Continued excel calculation sheet (51.42ft wall) (2nd story) …………….. 55

19. (a) Excel calculation sheet [middle wall (49ft)] (1st story) …………………. 56

(b) Continued excel calculation sheet [middle wall (49ft)] (1st story) ……… 57

20. (a) Excel calculation sheet [middle wall (49ft)] (2nd story) ……………….... 58

(b) Continued excel calculation sheet [middle wall (49ft)] (2nd story) ……… 59

21. (a) Excel calculation sheet [corner wall (49ft)] (1st story) …………………... 60

(b) Continued excel calculation sheet [corner wall (49ft)] (1st story) ………. 61

22. (a) Excel calculation sheet [corner wall (49ft)] (2nd story) …………………. 62

(b) Continued excel calculation sheet [corner wall (49ft)] (2nd story) ……… 63

1

1. INTRODUCTION

Unreinforced masonry (URM) structures are prevalent building types, but the

combination of their large seismic mass and lower tensile strength makes these structures

prone to earthquakes. Considering the large number of URMs in high seismic areas, this is

an important topic for the structural engineering community to assess the vulnerabilities of

the buildings and to develop economical methods to ensure life safety during an earthquake

event. The lack of reinforcement in these structures is the primary concern for seismic

behavior and can lead to a very brittle failure mechanism. Other issues include minimal

structural detailing at the connections between the floor system and walls, and weak

diaphragm systems to accommodate the full seismic load. Thus, the selected seismic

retrofit strategy for URMs should primarily focus on shear strengthening of the wall

systems but should also consider the full load transfer mechanism.

This study includes a historical building built in 1860’s, that requires retrofitting which

aims not just to evaluate seismic capacity of the existing masonry historical building

constructed, but to improve their capacity using different alternatives which would also

broaden our thinking over the traditional retrofitting techniques (moment frames, timber

shear walls, etc.). A new retrofitting material FRCM (Fabric-Reinforced Cementitious

matrix) has a different design approach compared to the traditional methods. FRCM design

is a modern-day design with new and different types of construction materials, design

procedures, workmanship, installation process with high nominal compressive strength.

On the other hand, new steel special moment frames are designed using equivalent lateral

force procedure and section designing is done in Mastan2. Thus, main motive of

2

considering two retrofit methods is to provide a better designing approach based on all the

aspects such as designing techniques, material properties and wall capacities obtained

through different systems.

This study also involves re-sheathing at the floor and roof levels, so diaphragm checks

were done with the same two methods FRCM and steel moment frames. Due to different

lateral forces affecting the buildings in both the systems, different sort of diaphragms such

as unblocked diaphragms, blocked diaphragms and blocked diaphragms (high load

diaphragms) were considered for full load transfer mechanism. Selection of diaphragms

involves common nail size, fastener penetrations, nominal panel thickness, nominal width

and nail spacing at diaphragm boundaries. All these factors are taken into consideration for

both the systems, performing required design calculations which provides the best

alternative for diaphragm design and re-sheathing at floor and roof levels.

3

2. BACKGROUND

Over the last few decades, traditional retrofit methods such as moment frames,

timber shear walls are into practice. So, to adapt a new method known as Fiber-

Reinforced Cementitious Matrix (FRCM) which may add a different outcome for

retrofitting is researched. By comparing the results achieved from moment frames and

FRCM, an effort is made to reach a better alternative for this project.

Historical buildings were provided by Burne Engineering which were Confidence

Engine Company Hall and Emigrant Jane Building built in 1860s, with an idea of three

retrofitting options which were rehabilitate and strengthen existing URM shear walls,

new timber shear walls and new steel special moment frames. Along with that a

requirement of re-sheathing was stated. Out of these three alternatives, one alternative

of new steel special moment frames was selected.

Figure 1. Building layout

4

A research was done to find a different material which has a different designing

style than the traditional retrofit methods. FRCM was considered as this new material

because of its high tensile strength, sprayable nature, fast installation and maybe a cost-

effective solution. FRCM is suitable to masonry as it matches substrate, provides

protective barrier and repairs walls while adding strength. Thus, benefits of FRCM, its

compatibility with masonry and its different or new age style of retrofitting persuaded

me to select this material as one of my retrofitting alternatives.

Many different design considerations were made for both the methods, as

information available for FRCM was limited. Moment frames were designed according

to the design provisions in ASCE 7-10, to select section properties and to check

deformations, moment frames were modelled in Mastan2. While, FRCM was designed

according to the design provisions in ACI 549.4r-13 and the material properties were

considered from AC 434. As FRCM has limited information, some assumptions were

made at the start to keep the buildings behavior elastic. Thus, some of these

considerations may lead to different results as seismic demand, story forces and wall

capacity obtained through these methods.

To fulfill the requirement of re-sheathing, diaphragm had to be designed to get the

required diaphragm shear force. Diaphragm design was provided with the same two

alternatives which is FRCM and steel moment frames to obtain a cost-effective

alternative. Diaphragms were designed using code AWC-SDPWS 2015. This code

helped to select which diaphragm is more suitable for the given buildings, as it provides

an idea of the cost for each method.

5

3. FIBER-REINFORCED CEMENTITIOUS MATRIX (FRCM)

3.1 INTRODUCTION

Unreinforced masonry historical buildings built without enough in-fill frame separation

have been consistently reported in reconnaissance reports to undergo in-plane shear

damage. Typical earthquake damage patterns in masonry infills include cracking along the

in-fill frame interface, toe crushing, diagonal cracking through masonry or mortar joints,

and bed joint sliding. It is widely accepted that cracking at infill-frame interface initiates

at low magnitude of lateral loading that leads to decrease in stiffness, following which it

continues to exhibit linear behavior until toe crushing leads to sudden stiffness

deterioration. It was noted from the review of structural drawings of existing buildings in

the Gulf, Asia, USA, Europe and New Zealand that majority of buildings built prior to the

introduction of modern seismic provisions in 1960s have unreinforced clay brick masonry

or hollow concrete masonry infill panels. These masonry panels, without strengthening,

exhibit low shear strength and are likely to undergo damage during a moderate to large

earthquake.

Therefore, a modified system is developed consisting of a cement-based matrix and a

dry fiber reinforced grid referred to as fabric reinforced cementitious matrix (FRCM) that,

when applied in a strengthening application, acts as externally bond reinforcement. The

dry fiber reinforced grids are made of two- or three-dimensional strands of individually

coated fibers rather than being bound together in an organic polymeric resin. The FRCM

system has also been referred to as textile-reinforced matrix or cementitious matrix grid

6

systems. FRCM is preferably applied on both sides of the wall to achieve symmetry and

effectiveness.

3.2 Vertical Distribution of forces

To find the lateral forces at each story for Fiber Reinforced Cementitious Matrix

(FRCM) there isn’t any specific method provided or stated, so in this report equivalent

lateral force procedure is followed to find the vertical distribution of forces.

Firstly, seismic response coefficient is calculated using the site coordinates, latitude:

38.72976389 and longitude: -120.7995222, risk category “II” and site class “D”. But for

FRCM, there are no design coefficients and factors available, so response modification

coefficient (R), overstrength factor (Ωo) and deflection amplification factor (Cd) all are

equal to one to keep the design elastic and avoid deformations. Once all the considerations

are made, we obtain a seismic response coefficient of 0.449.

Secondly, to calculate the base shear, effective seismic weight of the building is

calculated which accounts for dead loads and weight of the walls. Weight of the entire

building is calculated to obtain a force which can move the entire structure from the ground.

This force is the seismic demand according to which a retrofit method can be practiced,

and design can be proposed accordingly. Base shear of the FRCM system is:

Effective seismic weight = 850 kips

Seismic Response Coefficient = 0.449

𝑉 = 𝐶𝑠 ∗ 𝑊 (ASCE7-10: 12.8.1)

7

V= 382 kips

Base shear is distributed among the floors of the building which is also known as vertical

distribution of forces. This process helps to determine lateral forces affecting at each story

which will later affect the story displacements and story drifts which are basically designed

to make the floors in a building stronger and resistible.

• Vertical Distribution of Forces

K=1 as Ta < 0.5 sec

𝐶𝑣𝑥 = (𝑤𝑥ℎ𝑥𝑘)/(∑ 𝑤𝑖ℎ𝑖

𝑘)𝑛𝑖=1 (ASCE7-10: 12.8-12)

Table 1. Vertical distribution of forces (FRCM)

Level W (k) H (ft) WHK Cvx Fx (k)

Roof 247 29.52 7284 0.45 172

2nd Floor 603 14.76 8903 0.55 210

Total 850 16187 382

Figure 2. Vertical distribution of forces (FRCM)

172

kips

380 kips

210

kips

14

.76

ft

14.7

6ft

29

.52ft

8

3.3 Material Properties

Mechanical Properties

Table 2. Mechanical properties (FRCM)

Properties Strength References

Nominal Compressive strength

(f'm ) (lb/in2)

1500 ACI 530-11 (MSJC)

Compressive Ultimate Strength

(mu)

0.0025 (maximum usable

starin)

NCMA TEK 14-4B

Masonry elastic modulus

(Em=900fm’) (lb/in2)

1350000 NCMA TEK 14-4B

Lower-bound shear strength

(vtL=0.05fm’) (lb/in2)

7

5

NCMA TEK 14-4B

FRCM systems for wall shear are installed as:

C10: Carbon fiber fabric for masonry structural reinforcement

M25: Stabilized inorganic matrix for cementitious material

FRCM matrix reinforcement properties

Table 3. FRCM reinforcement properties

Properties Strength Reference Area of mesh reinforcement

by unit width (Af) (in2/ft)

0.022 AC 434

Tensile Modulus of elasticity (Ef) (ksi)

10061 AC 434

Ultimate Tesnile Strength (fd) 0.004 AC 434

9

Ultimate tensile strength

(ffd=Ef*fd) (ksi)

40.244 AC 434

3.4 In-plane Shear Design

The FRCM composite material bonded to surfaces of masonry are used to enhance the

design shear strength in the plane of the wall by acting as shear reinforcement. FRCM is

applied on both sides of the wall for symmetry and effectiveness. Nominal shear strength

is the contribution of unreinforced masonry and FRCM composite material.

In-plane shear design consists of following steps:

1. Loading information from the existing URM walls

2. Compute the nominal shear capacity of the CMU wall panel

3. Compute the nominal shear capacity of the FRCM strengthened wall

4. Compute the design shear strength of the strengthened wall

Step1. Loading information from the existing URM walls

Firstly, to check the wall capacity for each wall, new ultimate shear for every wall

should be calculated to meet the seismic demands.

Secondly, superimposed dead load is calculated for each wall using the arbitrary area

for each wall and considering the dead loads on that story. Once we get the dead load value

it is divided by the length of that wall to get per foot value for that wall.

Thirdly, lower bound axial compressive force due to gravity loads consider the dead

loads and live loads acting on each wall. Product of the dead/live loads and arbitrary area

10

for each wall gives us the axial compressive force on that wall and dividing that by the wall

length gives the axial force per foot value.

Afloor = 2123.80 ft2

Aroof = 2287.57 ft2

• 1st Story

Table 4. Loading information (1st story)

North-South Direction East-West Direction

List 51.42ft

Wall

Middle

Wall (49ft)

Corner

Wall (49ft)

20.125ft

Wall

22.125ft Wall

Tributary Area

(At) (ft2) 591 986 472 247 284ii8ufe3w2``

At/Af/r 0.278 0.464 0.222 0.116 0.134

New ultimate

shear force (Vu)

(kip)

106 177 85 44 51

Superimposed

dead load (PD)

(lbf/ft)

424 742 355 451 473

Lower-bound

axial

compressive

force due to

gravity load (QG)

(lbf/ft)

1183 2070 990 1260 1322

• 2nd Story

Table 5. Loading information (2nd story)


List 51.42ft

Wall

Middle

Wall (49ft)

Corner Wall

(49ft)

20.125ft

Wall

22.125ft

Wall

Tributary Area

(At) (ft2)

591 986 472 247 284

At/Af/r 0.258 0.431 0.206 0.108 0.124

New ultimate

shear force

(Vu) (kip)

44 74 35 19 21

11

Superimposed

dead load (PD)

(lbf/ft)

234 410 196 249 262

Lower-bound

axial

compressive

force due to

gravity load

(QG) (lbf/ft)

418 732 350 445 467

Step 2. Compute the nominal shear capacity of the CMU Wall (ACI 549.4r-13)

Concrete masonry elements can be designed by several methods such as empirical

design, strength design or allowable stress design.

Lower-bound masonry shear strength

𝑣𝑚𝐿 = 0.75 ∗𝑣𝑡𝐿+(

𝑃𝐷𝐴𝑛

)

1.5

where,

vtL = lower-bound shear strength

PD = superimposed dead load

An = section area

Compute the desired lateral capacity of the wall

𝑉𝑚𝐸 = 0.9 ∗ 𝛼 ∗ 𝑃𝐷 ∗ 𝐿𝑊 ∗ (𝐿𝑤

ℎ𝑒𝑓𝑓)

where,

α = 1.0 is a factor accounting for boundary conditions

Lw = length of the wall

12

heff = clear height of the wall

Compute the lower-bound lateral capacity of the wall

Lower bound shear capacity is computed as:

𝑉𝑚𝐿 = 𝑣𝑚𝐿 ∗ 𝐴𝑛 ∗ 𝐿𝑤

The shear capacity due to toe crushing is computed as:

𝑉𝑡𝑐 = 𝛼 ∗ 𝑄𝐺 ∗ (𝐿𝑤

ℎ𝑒𝑓𝑓) ∗ (1 − (

𝑓𝑎

0.7𝑓𝑚′ )) ∗ 𝐿𝑤

where,

QG = lower-bound axial compressive force due to gravity loads

𝑓𝑎 = 𝑎𝑥𝑖𝑎𝑙 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑙𝑜𝑎𝑑𝑠 =𝑄𝐺

𝐴𝑛

fm’ = nominal compressive strength

The lower-bound lateral capacity is computed as:

𝑉𝑚𝐿𝐵 = min(𝑉𝑚𝐿 , 𝑉𝑡𝑐)

• 1st Story

Table 6. Nominal shear capacity of the CMU wall panel (1st story)

North-South Direction East-West Direction List 51.42ft

Wall Middle

Wall (49ft) Corner

Wall (49ft) 20.125ft

Wall 22.125ft

Wall Lower-bound

masonry

shear strength

vmL (lb/in2)

29 28 28 29 29

13

Desired shear

capacity of

URM VmE (lbf)

126053 200318 95805 32909 41740

Lower-bound

shear

capacity

VmL (lbf)

843899 811969 802490 330567 363665

Shear-

capacity due to toe

crushing Vtc (lbf)

390145 619093 296620 101844 129160

Lower-bound

lateral

capacity

VmLB (lbf)

390145 619093 296620 101844 129160

• 2nd Story

Table 7. Nominal shear capacity of the CMU wall panel (2nd story)

North-South Direction East-West Direction List 51.42ft

Wall Middle

Wall (49ft) Corner

Wall (49ft) 20.125ft

Wall 22.125ft

Wall Lower-bound

masonry

shear strength

vmL (lb/in2)

28 29 28 28 28

Desired shear

capacity of

URM VmE (lbf)

69611 110623 52907 18174 23051

Lower-bound

shear

capacity

VmL (lbf)

630770 605384 600149 247027 271713

Shear-

capacity due

to toe

crushing Vtc (lbf)

138031 219202 104925 36034 45702

Lower-bound

lateral

capacity

VmLB (lbf)

219202 219202 104925 36034 45702

14

Step3. Compute the shear capacity of the FRCM strengthened wall (ACI 549.4r-13)

Select the number of FRCM plies and width of the FRCM strip

The number of plies of FRCM should exceed the maximum number of plies to be used

for flexural strengthening.

Number of plies = nf

In this project, a width of 12in is considered.

Width of FRCM strip, wf = Lw

A continuous layer of FRCM reinforcement is applied on both sides of the wall.

Calculate the FRCM design tensile strain and strength

Design tensile strain, fv = min(fd,0.004)

Design tensile strength, 𝑓𝑓𝑣 = 𝜀𝑓𝑣 ∗ 𝐸𝑓

Calculate the FRCM design tensile strain and strength

The total force per unit width that the FRCM system can transfer to the masonry

substrate is computed as:

𝑉𝑓 = 2 ∗ 𝑛𝑓 ∗ (𝐴𝑓 ∗ 𝑓𝑓𝑣) ∗ 𝐿𝑤

Compute the nominal shear capacity of the strengthened wall

15

The nominal shear capacity of the unstrengthened masonry wall is the minimum

between the expected lateral capacity and the lower-bound lateral capacity.

𝑉𝑚 = min(𝑉𝑚𝐸 , 𝑉𝑚𝐿𝐵)

The nominal shear strength of the strengthened unreinforced masonry wall is

computed according to:

𝑉𝑓𝑑 = min(𝑉𝑓 , 1.5𝑉𝑚)

𝑉𝑛𝑠1 = 𝑉𝑚 + 𝑉𝑓𝑑

Additionally, Vns1 cannot be larger than Vtc (shear capacity due to toe crushing)

𝑉𝑛𝑠 = 𝑉𝑛𝑠1 𝑖𝑓 𝑉𝑛𝑠1 ≤ 𝑉𝑡𝑐

= 𝑉𝑡𝑐 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

• 1st Story

Table 8. Shear capacity of the FRCM strengthened wall (1st story)


List 51.42ft

Wall

Middle

Wall

(49ft)

Corner

Wall

(49ft)

20.125ft

Wall

22.125ft

Wall

No. of FRCM

plies nf

1 1 1 2 2

FRCM shear

strength Vf

(lbf)

91051 86766 86766 71272 78355

Nominal shear capacity of

unstrengthened

masonry wall

Vm (lbf)

126053 200318 95805 32909 41740

Vfd (lbf) 91051 86766 86766 49364 62610

Vns1 (lbf) 217104 287084 182571 82273 104350

16

Nominal shear strength of the strengthened unreinforced

masnry walls (Vns) (lbf)

217104 287084 182571 82273 104350

• 2nd Story

Table 9. Shear capacity of the FRCM strengthened wall (2nd story)


List 51.42ft

Wall

Middle

Wall (49ft)

Corner

Wall (49ft)

20.125ft

Wall

22.125ft

Wall No. of FRCM

plies nf

1 1 1 1 1

FRCM shear

strength Vf

(lbf)

91051 86766 86766 35636 39178

Nominal shear

capacity of unstrengthened

masonry wall

Vm (lbf)

69611 110623 52907 18174 23051

Vfd (lbf) 91051 86766 79361 27261 34576

Vns1 (lbf) 160662 197390 132268 45434 57626 Nominal shear strength of the strengthened unreinforced

masonry wall

Vns (lbf)

138031 197390 104925 36034 45702

Step4. Compute the design shear strength of the strengthened wall (ACI 549.4r-13)

The nominal shear strength Vn, is obtained as the minimum of the nominal shear strength

as determined in previous step.

This nominal shear strength is the wall capacity for every wall which should meet the

seismic demand for every wall (new ultimate shear force) found in step1 to prove that the

shear check meets the designing requirements and is OK.

𝑉𝑢 = 𝛷𝑣 ∗ 𝑉𝑛𝑠

17

where,

Φv = strength reduction factor = 0.75

• 1st Story

Table 10. Design shear strength of the strengthened wall (1st story)


List 51.42ft

Wall

Middle

Wall (49ft)

Corner

Wall (49ft)

20.125ft

Wall

22.125ft

Wall New ultimate

shear force Vu

(kips)

106 177 85 44 51

Design shear

strength of

strengthened

wall Vu (kips)

163 215 137 62 78

Check_Shear OK OK OK OK OK

• 2nd Story

Table 11. Design shear strength of the strengthened wall (2nd story)


List 51.42ft

Wall

Middle

Wall (49ft)

Corner

Wall (49ft)

20.125ft

Wall

22.125ft

Wall New ultimate

shear force Vu

(kips)

44 74 35 19 21

Design shear

strength of

strengthened

wall Vu (kips)

104 148 79 27 34

Check_Shear OK OK OK OK OK

18

• North-South Walls

FRCM Strip

Wall Capacity

Seismic Demand

Figure 3. In-plane shear contribution (FRCM: north-south walls)

19

• East-West Walls

FRCM Strip

Wall Capacity

Seismic Demand

Figure 4. In-plane shear contribution (FRCM: east-west walls)

20

4. NEW STEEL SPECIAL MOMENT FRAMES

4.1 Introduction

Even in areas of very excessive seismic danger, like California and Alaska, extreme

earthquakes are rare activities, affecting usual buildings at common intervals of loads of

years. Given this, it's far economically impractical to layout systems to resist such extreme

however rare earthquakes without damage. Instead, the building codes have adopted a

design philosophy meant to offer protection by way of keeping off earthquake-prompted

fall apart in severe occasions, whilst allowing tremendous structural and nonstructural

harm. Inelastic behavior in steel special moment frames system is supposed to be

accommodated through the formation of plastic hinges at beam-column joints and column

bases. Plastic hinges form through flexural yielding of beams and columns and shear

yielding of panel zones. These modes are associated with frame behavior, include the

following criteria: beam behavior, joint panel zone behavior, column behavior, column

splices, column bases, structure P-delta effects and sideway collapse.

Figure 5. Typical local buckling of beam flanges and web

21

The most important advantage of moment frame structures is that they do no longer

have structural partitions or vertically oriented diagonal braces. They consequently provide

architectural freedom in layout, permitting open bays and unobstructed view lines. The

trade-off for those benefits is that second frames can be greater luxurious to assemble than

braced body or shear wall systems. The introduced price outcomes from the usage of

heavier sections within the moment resisting frames, requiring multiplied metal utilization

and more labor-intensive connections than is common in braced structures. However,

second frames usually impose smaller forces on foundations than do different structural

structures, ensuing in incredibly more most economical foundation systems.

Seismic design requirements are given in chapter 12 of the ASCE7-10 Code. For

computing the base shear of a building using the equivalent lateral force method, the code

gives an alternative way to compute the natural period of the system before the design.

However, the validity of this procedure needs to be checked for structures prone to high

seismic risks. Therefore, in this project the actual natural period is found to get the total

base shear to design a 2-D steel special moment frame (SMF) in high seismic zones. Steel

special moment frames are often used as a part of the seismic force resisting systems in

buildings designed to resist earthquakes with substantial inelastic energy dissipation.

Design requirements for steel special moment frames can be found in a series of U.S.

building codes. ASCE 7-10 sets the basic load requirements for special moment frames

with associated lateral drift limits. AISC 360 is the main AISC specification that provides

design and detailing requirements for all steel buildings. In addition, AISC 341-05 gives

detailed design requirements related to materials, framing members, connections, and

22

construction quality assurance and quality control. It is worth mentioning that the ASCE

7-10 permits to use three types of analyses to determine member design forces and design

drifts namely: equivalent lateral force, modal response spectrum, and seismic response

history analysis. Equivalent lateral force analysis is the simplest procedure; however, it can

lead to a conservative design.

4.2 Equivalent Lateral Force Procedure

The SMF is a part of a two-story historical buildings located in Placerville, CA, USA.

Four special moment frames (SMFs) are considered for the east-west direction of the

building. The building geometry is shown in Figure (). The bay width in the east west

direction is 20.125 ft while it is 49 ft for the north-south direction for Emigrant Jane

building. The bay width in the east west direction is 22.125 ft while it is 51.42 ft for the

north-south direction for Confidence Engine Company Hall. A typical 14.76 ft floor-to-

floor heights is considered. The first story height is 14.76 ft.

For the seismic analysis, the frame is analyzed according to the ELF to get the base

shear. The base shear calculations require finding the effective seismic weight of the

building and the seismic response coefficient. From a report on “Upper Broadway Bike

Lanes-City of Placerville, Vs30 value of 1164.70 ft/s is obtained and if the VS30 value is

between 600ft/s and 1200 ft/s, the soil conforms to site class D. The two buildings share a

common wall and a internal hallway and door and have been utilized as a single tenant

office buildings which falls under risk category “II”. The calculations are provided in detail

in this paper.

23

Equivalent Lateral Force Procedure (ELFP), as outlined in ASCE 7-10, is a technique

for developing and distributing equivalent lateral loads on a structure to account for the

horizontal seismic load effect.

Equivalent Lateral Force Procedure includes following steps:

1. Calculation of Seismic Response Coefficient

2. Seismic Base Shear

3. Vertical Distribution of Forces

Step1. Calculation of Seismic Response Coefficient

To start this procedure, firstly, a seismic site report is prepared with the help of ATC

hazards by location whose main purpose is to provide site-specific hazard information that

can be used to determine design loads for buildings and other structures using the following

site information:

1) Site Coordinates: latitude= 38.72976389 and longitude= -120.7995222

2) Reference Document: ASCE 7-10

3) Risk Category: II

4) Site Class: D

With the help of the above inputs, following report is generated specifying the site details:

24

Figure 6. ATC hazards by location (seismic report)

25

Response Modification Factor R=8

Overstrength Factor Ωo = 3.0

Deflection Amplification Factor = 5.5

Approximate Fundamental Period Ta = Ct * hnx = 0.468 sec (ASCE 7-10:Table 12.8-2)

Calculation of Seismic Response Coefficient consists of three equations:

1) 𝐶𝑠 =𝑆𝑑𝑠

𝑅

𝐼𝑒

= 0.056 (ASCE 7-10:Eqn. 12.8-2)

2) 𝐶𝑠𝑚𝑎𝑥 =𝑆𝑑1

𝑇(𝑅

𝐼𝑒) = 0.078 (Ta<TL) (ASCE 7-10:Eqn. 12.8-3)

3) 𝐶𝑠𝑚𝑖𝑛 = 0.044𝑆𝑑𝑠𝐼𝑒 = 0.020 (S1<0.6) (ASCE 7-10:Eqn. 12.8-5)

As, Csmin < Cs < Csmax

Cs = 0.056

Step2. Seismic Base Shear

Seismic Base shear is the force to move the whole structure from the ground. It is a product

of the seismic response coefficient and the total effective seismic weight of the building.

Total seismic weight of the building includes total dead load and weight of the walls.

• Dead Load (Roof)

Table 12. Dead load (roof)

List Dead load (psf)

Raptors 2*12” @ 16” o.c. 3.0

5/8” sheathing (gypsum sheathing) 2.0

1/4” shingles (asphalt shingles) 2.0

Other (mechanical/electrical) 3.0

Three ply ready roofing 1.0

Rigid insulation ½” 0.75

Balt Insulation 1.1

26

Ceiling (2 layers of gypsum board) 5.5

Miscellaneous 2

Total 20.35

(ASCE 7-10: Table C3.1)

• Dead Load (Floor)

Table 13. Dead load (floor)

List Dead Load (psf)

Joists 2*10 (16” spacing) 6

Tongue-and-groove paneling 1.5

MEP 3

Wood studs,2*4, unplastered 4

Miscellaneous 3

Total 16.5

(ASCE 7-10: Table C3.1)

• Live loads (floor) = 50 psf

• Live loads (roof) = 16psf

• Wall Weights

Table 14. Wall weights

List Weight (kips)

Roof 200.21

Floor 568.11

Total 768.32

Arearoof = 2287.57 ft2

Areafloor = 2123.80 ft2

Total effective seismic weight = (DLroof * Aroof) +(Wallsroof) + (DLfloor * Afloor)

+(Wallsfloor)

Total effective seismic weight = 849.91 kips

Seismic Base Shear = Cs*W (ASCE 7-10:

12.8-1)

Therefore, Seismic Base Shear V = 48 kips

27

Step3. Vertical Distribution of Forces

Once we obtain seismic base shear, vertical distribution of forces is done to distribute the

base shear among the floors of the structure.

Table 15. Vertical distribution of forces (SMF)

Level W (k) H (ft) WHK Cvx Fx (k)

Roof 247 29.52 7284 0.45 22

2nd Floor 603 14.76 8903 0.55 26

Total 850 16187 1.0 48

K=1 as Ta < 0.5 sec

Cvx = vertical distribution factor (ASCE 7-10: 12.8-12)

Figure 7. Vertical distribution of forces (SMF)

22

kips

48 kips

26

kips

14

.76

ft

14.7

6ft

29.5

2ft

28

4.3 Design

The lateral load is equally distributed among the four SMFs. The calculations are shown in

the subsequent sections. The drift limits are achieved by applying only the horizontal

seismic forces. The self-weight of the members is ignored for the analysis. The moment of

inertia of the beams is considered as the average of the positive and negative moment of

inertias according to AISC specification. The positive moment of inertia represents the

long-term moment of inertia for the composite beam section, while the negative moment

of inertia represents the moment of inertia of the steel section.

The analysis is done using Mastan2 and the elastic story drift for each story is exported.

The elastic drift is then multiplied by Cd/Ie to back calculate the plastic story drifts, where

Cd is the deflection amplification factor and Ie is the seismic importance factor. The

deflection amplification factor Cd is 5.5 for a steel special moment frame as per Table 12.2-

1 of ASCE 7-10 Code. The plastic story drifts are checked with the allowable story drifts

(Δa) provided by ASCE 7-10 Code, Table 12.12-1. Elastic analysis is applied in Mastan2

which is used to design beam/column sections which will give the most significant effects

on the drifts. This requires several iterations until the plastic story drift satisfy the allowable

story drift of ASCE 7-10.

Importance of story drift is to design partition or curtain walls, as they must be designed to

accommodate story drift, or they will be crack. Before getting story drift at every story,

story displacement is obtained at every story, which is the absolute value of displacement

of the story under action of lateral forces. Story drift is the difference of these displacements

obtained between two consecutive stories divided by the height of the story. This process

29

will give us a story drift in percentage which should be less than 0.025% from ASCE7-10

table 12.12-1.

Building1 (Confidence Engine Company Hall):

Beam 1: W30x99

Beam 2: W30x108

Columns: W21x147

Table 16. Story drift (building1)

Figure 8. Confidence engine company

hall mastan2 elastic analysis

Story () a () Check

1st

Story

0.023 0.025 OK

2nd

Story

0.008 0.025 OK

Beam 2

Co

lum

ns

Beam 1

30

Building2 (Emigrant Jane Building):

Beam 1: W30x90

Beam 2: W30x99

Columns: W21x132

Table 17. Story drift (building2)

Figure 9. Emigrant jane building

mastan2 elastic analysis

Story () a () Check

1st

Story

0.023 0.025 OK

2nd

Story

0.008 0.025 OK

Co

lum

ns

Beam 2

Beam 1

31

5. DIAPHRAGMS

5.1 Introduction

Diaphragm partitions are cellular walls composed of two wythes of masonry with a

massive hollow space or void, the wythes of that are bonded together with masonry ribs or

go partitions. The ribs are related to the wythes in this type of way that the two wythes act

compositely, thereby giving a completely composite section.

A diaphragm is a structural element designed to transfer in-plane shear forces to other

elements. Diaphragms connect exterior walls of a building providing rigidity against

racking and bowing from earthquakes and wind loads. Diaphragms are typically horizontal

but can be sloped such as in gable roof. They are like horizontal version of a shear wall.

All edges of a diaphragm shall be supported by a boundary element such as chords, drag

struts, collectors, shear walls and frames. Wall top plates typically function as both

diaphragm chords and drag struts.

Valuable characteristics of unreinforced diaphragm walls are that the net section

properties are easily calculated and that they have a large moment of inertia. Given that

they may be thick, unreinforced diaphragm partitions are powerful at resisting out-of-plane

loads and are inherently very stiff. Unreinforced walls, however, regularly crack before

deflections control the overall performance.

32

Figure 10. Diaphragm behavior

5.2 FRCM (Fiber-Reinforced Cementitious Matrix)

5.2.1 Diaphragm Force

Diaphragm forces are obtained from self-weight of the diaphragms and

element/component weights that depend on the diaphragm for lateral support. Roof and

floor diaphragms are designed to resist design seismic forces from the structural analysis

part. Forces shall not be less than the following equation:

𝐹𝑝𝑥 = (∑ 𝐹𝑖/ ∑ 𝑤𝑖𝑛𝑖=𝑥 ) ∗ 𝑊𝑝𝑥𝑛

𝑖=𝑥 (ASCE7-10: 12.10-1)

Minimum diaphragm force:

𝐹𝑝𝑥𝑚𝑖𝑛 = 0.2 ∗ 𝑆𝐷𝑆 ∗ 𝐼𝑒 ∗ 𝑊𝑝𝑥 (ASCE7-10: 12.10-2)

Maximum diaphragm force:

𝐹𝑝𝑥𝑚𝑎𝑥 = 0.4 ∗ 𝑆𝐷𝑆 ∗ 𝐼𝑒 ∗ 𝑊𝑝𝑥 (ASCE7-10: 12.10-3)

33

Table 18. Diaphragm forces (FRCM-1st story)

Level W (kips) Fx (kips) Fpx Fpxmin Fpxmax

Roof 247 172 172 22 44

2nd Floor 603 210 271 54 108

Total 850 382

The diaphragm design force at Roof and 2nd Floor is 172 kips and 271 kips respectively,

but it exceeds the maximum diaphragm design force. So, the design diaphragm force for

both the stories is the maximum diaphragm force.

Design Diaphragm Force: Roof = 44 kips

2nd Floor = 108 kips

5.2.2 Diaphragm Demand Shear

Diaphragms are transverse stiffeners which may serve many purposes like transverse

shear capacity.

Transverse shear capacity means diaphragms help in load sharing between different

girders, so reduced bending/shear demands on the girders is achieved due to not only

vertical loads but also horizontal loads.

Diaphragm Shear:

Max Shear = Diaphragm Reaction at Shear wall

Diaphragm Unit Shear = 𝑅𝑒𝑎𝑐𝑡𝑖𝑜𝑛

𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝐷𝑖𝑎𝑝ℎ𝑟𝑎𝑔𝑚 (plf)

34

(a) north-south walls (b) east-west walls

Figure 11. Diaphragm force resisting walls (FRCM)

• Diaphragm Unit Shear

Roof

𝑓 =𝐹𝑝𝑥(𝑟𝑜𝑜𝑓)

𝐴𝑟𝑒𝑎

Table 19. Diaphragm unit shear (FRCM-roof)


Diaphragm

Length

51.42ft Wall 49ft Wall 20.125ft Wall 22.125 Wall

Reaction

(RA/B) (kips)

11.95 10.35 10.36 11.93

Diaphragm

Unit Shear

(ra/b)

(k/ft)

0.232 0.211 0.515 0.539

35

2nd Floor

𝑓 =𝐹𝑝𝑥(2𝑛𝑑𝑓𝑙𝑜𝑜𝑟)

𝐴𝑟𝑒𝑎

Table 20. Diaphragm unit shear (FRCM-2nd floor)


Diaphragm

Length


Reaction

(RA/B) (kips)

29.02 25.15 25.14 29

Diaphragm

Unit Shear

(ra/b)

(k/ft)

0.564 0.513 1.249 1.310

Maximum shear is in the east-west direction at the second floor.

Therefore, Maximum shear = maximum reaction at shear wall = 29 kips

Diaphragm length = 22.125ft

Maximum Unit Shear = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛

𝑑𝑖𝑎𝑝ℎ𝑟𝑎𝑔𝑚 𝑙𝑒𝑛𝑔𝑡ℎ =

29 𝑘𝑖𝑝𝑠

22.125 𝑓𝑡

Maximum Unit Shear (Vs)= 1310 plf

According to AWC-SDPWS 2015, Table 4.2B, Blocked Diaphragms (high load

diaphragms), have diaphragm shear range of 605plf <Vs<1565plf.

Therefore, the Design Diaphragm Shear = 1320 plf

36

• Diaphragm Detailing (AWC-SDPWS 2015, Table 4.2B)

Table 21. Diaphragm detailing (FRCM)

Sheathing Grade Structural I

Common Nail Size 10d

Minimum Fastener Penetration in Framing

Member or Blocking (in)

1-½

Minimum Nominal Panel Thickness (in) 19/32

Minimum Nominal Width of Nailed Face

at Adjoining Panel Edges and Boundaries

(in)

4

Nail spacing at diaphragm boundaries (in) 4

5.2.3 Chord Forces & Chord Unit Shear

Maximum Chord Force occurs at the location of maximum moment.

Chord Force = Tension or Compression

𝐶ℎ𝑜𝑟𝑑 𝐹𝑜𝑟𝑐𝑒 =𝑀𝑚𝑎𝑥

𝐷𝑖𝑎𝑝ℎ𝑟𝑎𝑔𝑚 𝐷𝑒𝑝𝑡ℎ =

𝑓𝐿2

8𝑑

𝐶ℎ𝑜𝑟𝑑 𝑈𝑛𝑖𝑡 𝑆ℎ𝑒𝑎𝑟 =𝐶ℎ𝑜𝑟𝑑 𝐹𝑜𝑟𝑐𝑒


• Roof

Table 22. Chord force & chord unit shear (FRCM-roof)


Diaphragm

Length


Chord Force

(kips)

1.29 1.12 6.31 6.93

Chord Unit

Shear (plf)

25 23 313 313

37

• 2nd Floor

Table 23. Chord force & chord unit shear (FRCM-2nd floor)


Diaphragm

Length


Chord Force

(kips)

3.12 2.58 15.30 16.85

Chord Unit

Shear (plf)

61 53 760 762

Maximum chord force is in the east-west direction at the second floor.

Therefore, Maximum chord force = 16.85 kips


Chord Unit Shear = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑐ℎ𝑜𝑟𝑑 𝑓𝑜𝑟𝑐𝑒


16.85 𝑘𝑖𝑝𝑠

22.125 𝑓𝑡

Maximum Chord Unit Shear = 762 plf

5.3 New Steel Special Moment Frames

5.3.1 Diaphragm Force

Roof and floor diaphragms are designed to resist design seismic forces from the structural

analysis part. Forces shall not be less than the following equation:

𝐹𝑝𝑥 = (∑ 𝐹𝑖/ ∑ 𝑤𝑖𝑛𝑖=𝑥 ) ∗ 𝑊𝑝𝑥𝑛

𝑖=𝑥 (ASCE7-10: 12.10-1)

Minimum diaphragm force:

38

𝐹𝑝𝑥𝑚𝑖𝑛 = 0.2 ∗ 𝑆𝐷𝑆 ∗ 𝐼𝑒 ∗ 𝑊𝑝𝑥 (ASCE7-10: 12.10-2)

Maximum diaphragm force:

𝐹𝑝𝑥𝑚𝑎𝑥 = 0.4 ∗ 𝑆𝐷𝑆 ∗ 𝐼𝑒 ∗ 𝑊𝑝𝑥 (ASCE7-10: 12.10-3)

Table 24. Diaphragm forces (SMF)

Level W (kips) Fx (kips) Fpx Fpxmin Fpxmax

Roof 247 22 22 22 44

2nd Floor 603 26 34 54 108

Total 850 48

The diaphragm design force at Roof and 2nd Floor is 22 kips and 34 kips respectively, but

it is less than the minimum diaphragm design force. So, the design diaphragm force for

both the stories is the minimum diaphragm force.

Design Diaphragm Force: Roof = 22 kips

2nd Floor = 54 kips

5.3.2 Diaphragm Demand Shear

Diaphragms are transverse stiffeners which may serve many purposes like transverse

shear capacity.

Transverse shear capacity means diaphragms help in load sharing between different

girders, so reduced bending/shear demands on the girders is achieved due to not only

vertical loads but also horizontal loads.

39

Diaphragm Shear:

Maximum Shear=Diaphragm Reaction at Shear wall

Diaphragm Unit Shear = 𝑅𝑒𝑎𝑐𝑡𝑖𝑜𝑛


(a) north-south walls (b) east-west walls

Figure 12. Diaphragm force resisting walls (SMF)

• Diaphragm Unit Shear

Roof

𝑓 =𝐹𝑝𝑥(𝑟𝑜𝑜𝑓)

𝐴𝑟𝑒𝑎

Table 25. Diaphragm unit shear (SMF-roof)


Diaphragm

Length


Reaction

(RA/B) (kips)

5.69 4.93 4.93 5.68

40

Diaphragm

Unit Shear

(ra/b)

(k/ft)

0.111 0.101 0.245 0.257

2nd Floor

𝑓 =𝐹𝑝𝑥(2𝑛𝑑𝑓𝑙𝑜𝑜𝑟)

𝐴𝑟𝑒𝑎

Table 26. Diaphragm unit shear (SMF-2nd floor)


Diaphragm

Length


Reaction

(RA/B) (kips)

14.82 12.82 14.50 12.57

Diaphragm

Unit Shear

(ra/b)

(k/ft)

0.288 0.262 0.655 0.625

Maximum shear is in the north-south direction at the second floor.

Therefore, Maximum shear = maximum reaction at shear wall = 14.82 kips


Maximum Unit Shear = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛



51.42 𝑓𝑡

Maximum Unit Shear (Vs)= 288 plf

According to AWC-SDPWS 2015, Table 4.2C, Unblocked Diaphragms, have diaphragm

shear range of 0plf <Vs<320plf.

Therefore, the Design Diaphragm Shear = 290 plf

41

• Diaphragm Detailing (AWC-SDPWS 2015, Table 4.2B)

Table 27. Diaphragm detailing (SMF)

Sheathing Grade Sheathing and Single-Floor

Common Nail Size 10d

Minimum Fastener Penetration in

Framing Member or Blocking (in)

1-½

Minimum Nominal Panel Thickness (in) 15/32

Minimum Nominal Width of Nailed Face

at Adjoining Panel Edges and Boundaries

(in)

3

Nail spacing at diaphragm boundaries (in) 3

5.3.3. Chord Forces & Chord Unit Shear

Maximum Chord Force occurs at the location of maximum moment.

Chord Force = Tension or Compression

𝐶ℎ𝑜𝑟𝑑 𝐹𝑜𝑟𝑐𝑒 =𝑀𝑚𝑎𝑥

𝐷𝑖𝑎𝑝ℎ𝑟𝑎𝑔𝑚 𝐷𝑒𝑝𝑡ℎ =

𝑓𝐿2

8𝑑

𝐶ℎ𝑜𝑟𝑑 𝑈𝑛𝑖𝑡 𝑆ℎ𝑒𝑎𝑟 =𝐶ℎ𝑜𝑟𝑑 𝐹𝑜𝑟𝑐𝑒


• Roof

Table 28. Chord force & chord unit shear (SMF-roof)


Diaphragm

Length


Chord Force

(kips)

1.06 0.96 3.00 3.30

Chord Unit

Shear (plf)

21 20 149 149

42

• 2nd Floor

Table 29. Chord force & chord unit shear (SMF- 2nd floor)


Diaphragm

Length


Chord Force

(kips)

1.59 1.32 7.65 8.43

Chord Unit Shear

(plf)

31 27 380 381

Maximum chord force is in the east-west direction at the second floor.

Therefore, Maximum chord force = 8.43 kips


Chord Unit Shear = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑐ℎ𝑜𝑟𝑑 𝑓𝑜𝑟𝑐𝑒



22.125 𝑓𝑡

Maximum Chord Unit Shear = 381 plf

43

6. SUMMARY

6.1 Conclusions

In-plane shear checks with two different alternatives (moment frame v. FRCM) would

provide building owner with different alternatives to consider based on performance and

aesthetics. Diaphragm design illustrated a possible cost savings for moment frame

alternative due to lesser quantities of sheathing material (due to smaller forces).

Deformations are significant with moment frame design – which would lead to a worse

damage state during an earthquake.

6.2 Future Work

In depth cost analysis of FRCM versus Steel moment frames to be presented to the

building owners. To start a research on FRCM displacement codes and to learn design

accordingly, which would allow to design with different methods and sections. If allowed,

to perform an on-field material testing to obtain precise material and reinforcing properties

for this buildings.

44

Appendix A.

Excel Calculations

1. East-West Direction (20.125 ft wall - 1st Story)

Figure 13. (a) Excel calculation sheet (20.125ft wall) (1st story)

45

Figure 13. (b) Continued excel calculation sheet (20.125ft wall) (1st story)

46

2. East-West Direction (20.125 ft Wall – 2nd Story)

Figure 14. (a) Excel calculation sheet (20.125ft wall) (2nd story)

47

Figure 14. (b) Continued excel calculation sheet (20.125ft wall) (2nd story)

48

3. East-West Direction (22.125 ft Wall – 1st Story)


49


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4. East-West Direction (22.125 ft Wall – 2nd Story)


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5. North-South Direction (51.42 ft Wall – 1st Story)


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6. North-South Direction (51.42 ft Wall – 2nd Story)


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7. North-South Direction [Middle Wall (49 ft) – 1st Story]

Figure 19. (a) Excel calculation sheet [middle wall(49ft)] (1st story)

57

Figure 19. (b) Continued excel calculation sheet [middle wall(49ft)] (1st story)

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8. North-South Direction [Middle Wall (49 ft) – 2nd Story]

Figure 20. (a) Excel calculation sheet [middle wall(49ft)] (2nd story)

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Figure 20. (b) Continued excel calculation sheet [middle wall(49ft)] (2nd story)

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9. North-South Direction [Corner Wall (49 ft) – 1st Story]

Figure 21. (a) Excel calculation sheet [corner wall (49ft)] (1st story)

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Figure 21. (b) Continued excel calculation sheet [corner wall (49ft)] (1st story)

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10. North-South Direction [Corner Wall (49 ft) – 2nd Story]

Figure 22. (a) Excel calculation sheet [corner wall (49ft)] (2nd story)

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Figure 22. (b) Continued excel calculation sheet [corner wall (49ft)] (2nd story)

64

References

1. Designing methods and in-plane shear checks using FRCM:

ACI 549.4r-13 Guide to design and construction of externally bonded fabric- reinforced

cementitious matrix (FRCM) systems for repair and strengthening concrete and masonry

structures.

2. Material properties for FRCM:

AC 434 Design criteria report for ruredil FRCM composite systems

3. Mechanical properties for Masonry:

ACI 530-11 Building code requirements and specification for masonry structures

4. FRCM behavior, application, benefits and webinar slides:

https://www.strongtie.com/products/rps/css/frcm-applications

5. Equivalent Lateral Force Procedure and Diaphragm Forces:

ASCE 7-10 Minimum design loads for buildings and other structures

6. Diaphragm Design:

AWC – SDPWS 2015 Special design provisions for wind and seismic

7. U.S. Seismic Design Maps. United States Geographical Survey.

http://earthquake.usgs.gov/designmaps/us/application.php

8. To find Vs30 which gives soil class for these buildings

https://www.cityofplacerville.org/upper-broadway-bike-lanes

https://www.strongtie.com/products/rps/css/frcm-applications

http://earthquake.usgs.gov/designmaps/us/application.php

https://www.cityofplacerville.org/upper-broadway-bike-lanes

seismic upgrade strategies for a historical building in

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