master's project writeup 9-29

REPURPOSING THE PIERS OF THE OLD

SAN FRANCISCO-OAKLAND BAY BRIDGE:

A REPORT DISCUSSING PROJECT FEASIBILITY,

DEVELOPMENT OF ALTERNATIVES, AND DESIGN

Michael Grant Martin

Issue Date: September 30, 2016

Table of Contents

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TABLE OF CONTENTS

Abstract .......................................................................................................................................... 4

Chapter 1: Purpose and Need ...................................................................................................... 6

1.1 Background ....................................................................................................................................... 6

1.2 Purpose............................................................................................................................................... 6

1.3 Need .................................................................................................................................................... 7

Chapter 2: Project Alternatives ................................................................................................. 10

2.1 Development of Alternatives .......................................................................................................... 10

2.2 Alternatives Considered ................................................................................................................. 11

2.2.1 Alternative 1: No Build Alternative – Leaving the Piers in the Bay .......................................... 11

2.2.2. Alternative 2: No Build Alternative – Removing the Piers from the Bay ................................ 11

2.2.3 Alternative 3: Floating Concrete Bridge .................................................................................... 12

2.2.4. Alternative 4: Constant depth, precast concrete I-girder bridge ............................................... 14

2.2.5. Alternative 5: Variable-depth, precast concrete box-girder bridge ........................................... 17

2.2.6. Alternative 6: Concrete slab-on-piles bridge ............................................................................ 20

2.3 Comparisons of Alternatives’ Characteristics.............................................................................. 22

2.3.1. Funding ..................................................................................................................................... 22

2.3.2. Costs .......................................................................................................................................... 23

2.3.3. Constructability & Schedule ..................................................................................................... 24

2.3.4. Public Access ............................................................................................................................ 24

2.3.5. History ....................................................................................................................................... 25

2.3.6. Climate Change & Sea Level Rise ............................................................................................ 26

2.3.7. Environmental Impact/Advantages ........................................................................................... 27

2.3.8. Economic Stimulus/Jobs ........................................................................................................... 28

2.4 Selecting a Preferred Alternative .................................................................................................. 28

2.5 Construction Process of the Preferred Alternative ...................................................................... 30

Full Construction Staging of Preferred Alternative ............................................................................ 30

2.6 Bridge or Barge? ............................................................................................................................. 34

Chapter 3: Loading Demands .................................................................................................... 35

3.1 Vertical Loads ................................................................................................................................. 35

3.1.1 Load Paths .................................................................................................................................. 35

3.1.2. Longitudinal Loading Configurations ....................................................................................... 36

3.1.3. Transverse Loading Configurations .......................................................................................... 38

3.2 Lateral Loading Considerations .................................................................................................... 39

3.2.1. Seismic Loading ........................................................................................................................ 39

3.2.2. Wave Loading ........................................................................................................................... 40

Chapter 4: Design and Calculations .......................................................................................... 42

4.1 Design ............................................................................................................................................... 42

4.1.1. Floating Box Design - Longitudinal ......................................................................................... 42

4.1.2. Floating Box Design – Transverse ............................................................................................ 43

4.1.3. New Pier Caps Design .............................................................................................................. 44

4.1.4. ADA Ramp ............................................................................................................................... 44

4.2 Hand Calculations ........................................................................................................................... 46

Table of Contents

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4.2.1. Positive Longitudinal Moment Capacity .................................................................................. 46

4.2.2. Negative Longitudinal Moment Capacity ................................................................................. 47

4.2.3. Transverse Moment Capacity ................................................................................................... 48

4.2.3. Longitudinal Shear Capacity ..................................................................................................... 48

4.2.4. Transverse Shear Capacity ........................................................................................................ 49

4.2.4. Punching Shear Strength ........................................................................................................... 49

4.2.5. Crack Width and Crack Control ................................................................................................ 51

Chapter 5: Model and Results ................................................................................................... 53

5.1 Model Setup ..................................................................................................................................... 53

5.1.1 Longitudinal Model.................................................................................................................... 53

5.1.2. Transverse Model ...................................................................................................................... 53

5.1.3. Verifying Model Validity .......................................................................................................... 53

5.2 Results of Analysis .......................................................................................................................... 56

5.2.1. Longitudinal Model – Structural Analysis Results ................................................................... 59

5.2.2. Transverse Model ...................................................................................................................... 59

Chapter 6: Looking forward ...................................................................................................... 61

Appendix ...................................................................................................................................... 64

A.1 Longitudinal Load Combinations ................................................................................................. 64

A.2 Transverse Loading Combinations .............................................................................................. 72

A.3 Plan Sheets ...................................................................................................................................... 78

A.4 Architectural Renderings .............................................................................................................. 81

Works cited .................................................................................................................................. 84

Abstract

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ABSTRACT

The San Francisco-Oakland Bay Bridge has been a fixture of the Bay Area since its erection in

1936. In the past, the bridge carried both trucks and trains across the bay, and as needs of the Bay

Area changed, so did the bridge. In 1958, the rail line was removed to make room for increasing

automobile traffic demands. In the 1989 Loma Prieta earthquake, a section of the eastern span

upper deck fell onto the lower deck, resulting in loss of life, and was quickly replaced. As traffic

demands on the bridge continued to increase and fears of the next “big one” loomed, Caltrans

decided that replacement of the eastern span was the proper course of action. Construction began

on the new eastern span in 2002 on a project that would reflect the Bay Area’s past and future, and

its culture ingenuity, and spirit.

Even before the new bridge was open, the State of California began the demolition of the piers that

supported the old eastern span of the Bay Bridge. Beginning in November 2015 with a controlled

implosion on the largest support, E3, in an important shipping channel, the state showed it is

possible to remove these piers from the Bay and have arranged do so for the remaining piers, with

a few exceptions. The piers scheduled to be left behind are piers E19-E23 near the Oakland

approach and pier E2 near Yerba Buena Island. This report will focus on building a pedestrian

walkway bridge between piers E21-E23.

Repurposing these piers instead of removing them has benefits threefold. Firstly, there will be

minimal environmental impact when constructing the pedestrian walkway compared to the

environmental cost of removing them. The San Francisco Bay Conservation and Development

Commission (BCDC) has very stringent regulations on what is built in the bay and how old

structures are removed. Although the removal of pier E-3 went smoothly, reducing the number of

pier that need to be demolished clearly results in a smaller environmental impact.

A major benefit to this project is creating public access to the San Francisco Bay. Plans are already

underway to turn the old Oakland approach into a public park for the surrounding community, and

a pedestrian walkway out over the Bay could act as a venue for numerous activates. Since the

closing of the Berkeley Pier, citizens of the East Bay have been searching for another location to

fish without needed a boat. The walkway could also serve other hobbyists as well, like as a launch

point for kayakers, kite surfers, or windsurfers. The walkway could also be made available for rent

to private parties that need to accommodate large crowds. Most importantly, the park and walkway

could serve as a place for the community to gather and enjoy the beauty of the San Francisco Bay

and the breathtaking architecture of the new eastern span.

As plans to develop the land on the old Bay Bridge Oakland-side approach evolve, it is important

to recognize the piece of history being left behind. The old piers are relics of the Bay Area’s past

and should be honored and preserved. The Bay Bridge opened almost 80 years ago and served

countless passengers in its lifetime. The Bay Bridge was envisioned back in the days of

California’s gold rush but was seen as an impossibility for many years due to the length of the

traverse and the depth of the bay. We should celebrate the incredible triumphs of chief engineer

Abstract

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Ralph Modjeski and his crew should by preserving pieces of the past instead of casually discarding

them.

A final advantage to repurposing the old piers is the financial cost. Based on current costs of

removing the piers in the deeper waters, it would cost a few million dollars to remove each pier in

the shallower water. If piers E19 and E20 are left as bird sanctuaries and piers E21-E23 become

the foundations for the pedestrian walkway, the roughly $15 million could instead be spent on

building the walkway or the nearby park. Rather than spending huge sums to destroy the existing

piers, it would certainly be a better use of funds to create something that people from all around

the Bay Area can enjoy both as leisurely diversion or to soak up a piece of California’s history.

As the old Bay Bridge piers are removed from bay waters, there is a unique opportunity to preserve

history, save money, reduce environmental impact, and most importantly, provide public access

to the Bay. As the Bay area continues to increase its population, it is necessary to create more

public areas for the community to come together. With the closing of the Berkeley Pier, new public

works providing access to the Bay are needed now more than ever. This work proposes the

construction of a new pedestrian walkway out over the San Francisco Bay using the piers that

previously supported the old eastern span of the San Francisco-Oakland Bay Bridge (SFOBB).

Chapter 1: Purpose and Need

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CHAPTER 1: PURPOSE AND NEED

1.1 Background

Since the completion of the new eastern span of the Bay Bridge, the Bay Area Toll Authority

(BATA), in partnership with many environmental resource agencies, particularly the Bay Area

Conservation and Development Commission (BCDC), has been in the process of dismantling the

old eastern span of the SFOBB. The final and most environmentally challenging pieces to remove

are the piers in the water that supported the columns and superstructure. This Masters of Science

project is to determine feasibility and design an unusual bridge structure that reuses these piers. In

an effort to save money, preserve the bay environment and history, and provide maximum public

access to the bay, this project proposes the construction of a pedestrian and bicycle walkway out

onto the two piers nearest the Oakland approach, E21-E23, on the future site of the Gateway Park.

Adjacent to interstate 80, this location will be easily accessible by the public and provide incredible

views of the San Francisco Bay and all she holds.

The bridge piers are about 300 feet apart, so an elevated bridge span would be pushed to its

practical engineering limits. This is one of the most significant challenges facing the design of this

bridge. As the depth of the water changes, so do the sizes of the piers, though E21-E23 are similar

in size and are quite large in order to carry the previous demands of ten traffic lane loads and a

train load, approximately 75 feet by 25 feet—slightly smaller than the piers E19 & E20 which are

about 100 feet by 50 feet. Clearly the axial loads on these piers will never be reached again with a

structure so small in comparison to what they originally carried, however the loads must be applied

carefully as piers are basically a reinforced concrete box with a hollow interior. To ensure that the

piers will not fail in their centers where it is basically a reinforced concrete slab with fixed supports

on all sides, an extra slab will be poured on top of what is already there. This procedure will also

allow for customized connections for the bridge spans, including the necessary shear keys to

prevent motion of the deck. Much of the concrete needed for this pedestrian and bicycle bridge

itself will be cured off-site in a casting yard to avoid wet concrete over bay waters minimize the

environmental impact.

The design should be effective for the functions stated above, but also practical in its construction

and maintenance. The bridge and repurposed piers should pay respect to the historic old bridge

structure while simultaneously complementing the new structure in both style and scale.

1.2 Purpose

The goal of this project is to repurpose some of the old Bay Bridge piers that could be left in the

water after the old span is disassembled. A pedestrian and bicycle bridge will be erected between

the existing piers. This structure itself should be a worthy destination, open to the public, allowing

for increased access to the bay waters along with a safe and comfortable place for the community


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to come together as individuals or as a group for organized events. It should be a resource to the

local community and its visitors, not only a location to view the region, but also a way to

experience the bay. The area could be capable of holding public and private parties, which could

serve as a revenue source for the park and help fund maintenance.

As part of the future Gateway Park, a public bridge with bay access could provide wonderful

education opportunities for the public. It could hold events teaching members of the community

about activities like boating, sailing, and kayaking. The old piers would also be a perfect location

for educating the public about the bay’s history. Plaques and signs could explain the history of the

old Bay Bridge and the transition to the new eastern span. A small science lesson may even spark

the minds of some future structural engineers!

The tertiary objective in constructing a pedestrian/bicycle bridge is to simultaneously provide a

valuable communal resource while minimizing possible environmental impacts to the bay and

costs to the public. BATA has allocated approximately $50 million to remove the piers in the bay,

and if some of the piers can remain, it could be a great financial boon. A portion of the funds that

would be spent on demolition could instead be used to erect a bridge open to the public. This could

potentially save millions of dollars while providing a safe place where the public can gather. Due

to the inherent communal value in opening up access to the bay for the public to use and the

financial cost of removing the piers, building the walkway is arguably more economically

advantageous.

The main purpose of this structure should be to bring the community closer to the bay. The

Gateway Park should make the public feel like a part of the bay, and a pedestrian bridge over the

water will really drive that feeling home. The bridge should bring park patrons right down to the

bay water, if possible, and create a full sensory experience.

1.3 Need

There are many needs for this project with varying degrees of importance. Perhaps the most

fundamental needs that must be provided are those that provide public use and access for the

community. One of the main goals of this project is to create a safe place that is a part of the

community and can provide access to the bay. Per legal requirement, the walkway needs to be

compliant with the Americans with Disabilities Act to ensure that it is accessible to the entire

community. The Americans with Disabilities Act (ADA) of 1990 is a labor law that prohibits

discrimination based on disability. The ADA also requires that all new public projects reasonably

accommodate persons with disabilities. Among the common features to fulfill ADA requirements

is a wheelchair ramp for persons with disabilities with a slope no greater than 1:12. Inclusivity is

an emphasis for this project, and that extends beyond the minimum legal requirements.

In an effort to draw more traffic, the walkway could serve as a point of historical education and

interest. Since the bridge will be immediately adjacent to the new Bay Bridge, it is the perfect


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place to view and admire the architecture and design that the people of the Bay so proudly wanted

displayed in their community. The piers themselves could open up to allow people to walk around

them and view the Bay Bridge and experience all the bay has to offer. The pedestrian bridge and

old piers could also serve as a viewpoint for birdwatching, as there are current considerations to

repurpose the next two piers, E19 & E20, as sanctuaries for birds to lay eggs out of reach of land

predators. Tower viewers/binoculars mounted on the piers would also provide an excellent, close-

up view of the new structure and the bird sanctuaries. These are not only an attraction, could be a

small source of revenue to maintain the park by charging a few cents to get a closer look.

Another way to draw out more of the community is to build a bridge that allows for a range of

activities. With safe, legitimate water access, people could have a launch point for kayaking,

windsurfing, or kitesurfing. These hobbyists would have access to the bay as a whole and could

get closer and more unique views of the beautiful bridge or observe wildlife settling on the bird

sanctuaries. The pedestrian bridge could also cater to other hobbyists like fishermen. Since the

Berkeley pier closed down, the need for a new fishing spot is greater than before. With the

development of the Gateway Park as a whole, this could be a much safer and more secure location

than the Berkeley pier had been in the years before its closure.

Aesthetics are quite important to any structure erected next to something as striking and

monumental as the new eastern span of the Bay Bridge. The pedestrian and bicycle bridge must

follow the same architectural motif as the Bay Bridge without conflicting or competing with it in

any way; the Bay Bridge is the still the main focus. In an effort to follow this vision, the pedestrian

walkway will use the same railings, light fixtures, and concrete color as the Bay Bridge. The

walkway must also stay low to the water so as not to challenge the majesty and size of the Bay

Bridge. Following these guidelines, the pedestrian bridge will only complement the Bay Bridge

rather than steal away any attention. However, in keeping the bridge low and small, other

engineering challenges arise, like how to span such the roughly 300 feet between piers. The

inelegant solution would be to reduce the span length by placing more foundations in the water.

This solution must immediately be discarded, both because the BCDC would likely not allow that

much disruption in the bay for a small project like a pedestrian bridge, and because any new

supports in the water would very likely clash with the elegance of the Bay Bridge. These

architectural and structural needs are very important to the project due to its proximity to a

landmark as gorgeous and important as the Bay Bridge.

One of the main concerns in erecting any piece of infrastructure that must be addressed is the

financial cost. This project, however, has a unique financial situation. The many environmental

and governmental bodies that regulate bay development require that the piers in the bay be

removed in an attempt to revert the bay to its original state. Unfortunately, the cost in removing

these piers is tremendous, costing millions of dollars each. This project should serve as a potential

balance between returning the bay to its original state, providing public access to the bay, and the

financial cost of each respective function. Instead of spending money to remove these piers, some

portion of this money would be better spent providing something new for the community. With

proper project option selection, this could become a financial gain for the community instead of a

cost. Though a lofty goal, one of the needs of this project is to actually save and make money. By


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selecting an inexpensive alternative, this need may not be so improbable. There are also ways for

the pedestrian bridge to generate revenue. The Gateway Park and the new walkway could be rented

out for private functions such as weddings, corporate parties, or small concerts. A temporary,

mobile shelter would be pulled over the walkway in the event of foul weather like rainstorms or a

particularly hot and sunny afternoon. As previously mentioned, tower viewers could provide an

additional continuous, albeit small, source of revenue for the park.

Each new function that this pedestrian bridge serves brings along new loading scenarios. The dead

load of the concrete, railings, lighting, and any other aesthetic features must of course be accounted

for. The most common, everyday loading that the bridge will feel will come from pedestrians

walking out on it. This bridge needs to hold a minimum pedestrian live load of 85 psf at every

location along the bridge and also in the specific locations that create the largest moment and shear

loads. It will be a rare occurrence for the bridge to be fully loaded, but if any events are to be held

over the water, the bridge must be capable of holding large numbers of people. In addition to

pedestrians, the bridge should also be able to carry a single vehicle. Although the bridge will not

carry vehicular loads in general, exceptions should be made for small emergency and maintenance

vehicles. At the very minimum, emergency workers should be able to safely approach the bridge

and easily allow stretchers out over the water for quick access. Another minimum loading

requirement is the need to carry a small maintenance vehicle out on the bridge deck to the piers.

Light fixtures will need repair and fresh paint will need to be applied regularly, and for

maintenance to be efficient, workers will need a vehicle. The bridge must be able to carry the 4-

point load of a single, heavily loaded maintenance truck loaded with work equipment at any

location along the span.

This bridge must also serve the community for a reasonable amount of time in the future. Although

this pedestrian bridge does not fall under AASHTO regulations, it is prudent to use AASHTO as

a guideline. Therefore, this bridge will have a design life of at least 75 years. Structures built on

or over water with long design lives face a new, pressing challenge, climate change. This bridge

must be capable of surviving rising sea levels and the damage associated with it. In order to ensure

that no part of the bridge ever falls below the water surface, more concrete must be added on top

of the piers to increase their height. After the tops of the piers are sufficiently raised, any bridge

fixed to the piers will stay above the sea level for its lifetime.

Chapter 2: Project Alternatives

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CHAPTER 2: PROJECT ALTERNATIVES

2.1 Development of Alternatives

Demolition and removal of the largest pier, E3, took place in November 2015. Investigation of

project alternatives to avoid complete removal of all piers began in March 2016. Various agencies,

stakeholders, and members of the public have a vested interest in turning the old Oakland approach

into a public park. Many alternatives are present in this report, each with advantages and

disadvantages that address various needs of the project. Ideally, the public will have a chance to

voice their opinions on the alternatives and help select one that best fits their needs and desires.

Without public input, the best way to analyze the alternatives was to assign a numerical value to

each alternative’s ability to fulfil the needs of the project. Each considered alternative’s ability to

complete the project needs are outlined in Table 1, shown later. From the results of this table, an

alternative has been selected that best fits the needs of the project and community. Below are a

variety of project alternatives, weighed against each other and one of them is selected as the

preferred alternative.

1. No build alternative—no walkway construction; the piers will need to be removed from the water

per BCDC regulations

2. No build alternative—do nothing; leave the piers in the bay water

3. Floating concrete bridge that connects to the piers

4. Precast concrete I-girder bridge with precast reinforced concrete slab deck lain transversely on

girders

5. Variable-depth, precast concrete box girder

6. Concrete slab-on-piles bridge


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2.2 Alternatives Considered

2.2.1 Alternative 1: No Build Alternative – Leaving the Piers in the Bay

The no build alternative is the option for members of the community who are entirely unconcerned

with development of public land. About twenty years ago, during planning stages for the new

eastern span, the State of California, Caltrans, and the Metropolitan Transportation Commission

committed to removing the piers from the San Francisco Bay after the old bridge was dismantled.

By leaving the piers in the water without repurposing them, the state is reneging on the promise

without putting forth a better option. This alternative fails to achieve almost all of the needs of the

project. The only advantages to this option are that it comes at no additional financial cost to the

community, or with minimal investment, bird sanctuaries could be placed on the piers.

2.2.2. Alternative 2: No Build Alternative – Removing the Piers from the Bay

Much like the previous no build alternative, this option falls short of many of the goals of the

project. It will not provide any increased public access to the bay, which is the primary objective

of this project. Should the rest of the Gateway Park come to exist, it will lack a feature attraction

like the pedestrian bridge. Even the view of the Bay Bridge will seem less impressive from the

shore compared to a vantage point from over the water.


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Alternative 2 does have a few upsides, however. By removing the piers, the State of California

follows through on its promise from twenty years ago and appeases the BCDC’s goal of restoring

the bay to its natural state by removing any foreign objects. The task would also require a

significant amount of labor and specialized workers, creating jobs and injecting capital into the

community. Additionally, once the piers are removed from the bay, the stunning new eastern span

of the SFOBB would stand alone without any other structures distracting viewers or detracting

from its beauty.

2.2.3 Alternative 3: Floating Concrete Bridge

Proposed Bridge Type

Floating concrete bridges are becoming popular public assets around the world. Alternative 2 is

the least inexpensive bridge alternative outlined here. They can be easily transported via most

waterways and are simple to assemble. Floating concrete bridges can span extremely long distance

due to continuous support from the water beneath them. Spans lengths are mostly limited by forces

acting transversely on the structure, like ocean waves. Floating concrete bridges can rise and fall

with the tidal action but must have a special connection to the land and piers to allow pedestrian

access during in all conditions.

Bridge Geometry


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The proposed bridge must span the length between each pier, just under 300 feet center-to center.

The walkway will be 30 feet wide which should provide ample space for people to walk around

and to sit down and spend some time over the water. The bridge must be about six feet deep in

order to create sufficient buoyant force to support the self-weight of the bridge and the live load

of any pedestrians and/or vehicles on the bridge.

Project Seismic Design Criteria

Even though the San Francisco Bay Area is highly seismically active, the unique nature of the

floating concrete bridge gives it a great seismic advantage over traditional bridges. The piers will

feel forces from the bottom of the bay and will shake the bridge, but because it is continuously

supported by water, which cannot sustain or transfer any shear whatsoever, seismic forces on the

bridge itself are entirely eliminated.

Aesthetic Recommendations

Aesthetic details on the floating concrete bridge will match the new eastern span of the Bay Bridge

as closely as possible. The bridge will use the same white railings were possible and will have the

same light fixtures and will be located on the piers. The concrete in the bridge can also be carefully

colored to match the color scheme of the bicycle path on the Bay Bridge so that pedestrians and

cyclists can look down from the Bay Bridge and appreciate the matching style.

Purpose & Need

Alternative 3 address the main Purpose of the project by proving public access out over the bay

and repurposing the old bridge piers so they don’t need to be removed. The floating bridge is also

an inexpensive construction option which can actually save money for the community compared

to the millions of dollars associated with removing the piers. Additionally, what money is spend

to construct the bridge would stay in the community. The floating bridge sections can be built in a

local concrete yard and floated out to the construction site. This creates jobs for the concrete

workers in the yard, the tug operators moving the pieces, and of course the construction workers

on the job site.

The floating bridge alternative also does an exceptional job of addressing many of the needs of the

project. Floating concrete bridges and similar structures like floating concrete docks are fixed to

the land and other permanent structures by ramps that can rotate with rising and falling water

levels. The ramp simply needs to be sufficiently long and properly installed to ensure the slope is

ADA compliant in all tidal conditions.

This kind of bridge also offers unparalleled bay access. Since the bridge floats just above the water,

it can serve as an easy launch point for water-sport enthusiast like kayakers or windsurfers. Certain

locations can feature gates or temporary railings to allow quick entry and exit. Even the citizens

that stay on the bridge will be in much closer proximity to the water and may even be able to reach

down and touch it, further strengthening the connection to the bay. The floating concrete bridge

also has the unique aspect of touching the water, which allows pedestrians to actually feel waves


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from the bay beneath them. It may seem minor, but it could be an exceptional experience for many

members of the community. Fishermen will also be able to cast lines from the floating bridge or

the piers, a much needed feature after the closure of the Berkeley Pier.

Another way to connect the park and bridge to the community is to hold events. The floating

concrete bridge is capable of carrying a load of 100 psf, larger than the AASHTO required 85 psf.

This is to allow event planners to have some extra wiggle room in arranging what attractions be

held or what equipment can rest on the bridge. During inclement weather, portable, floating

awnings can be pulled out over the bridge to shelter the event and the guests.

In order to justify the effort put into repurposing the old bay bridge piers, the pedestrian bridge

must serve the community for years to come. The floating concrete bridge has a design life of 75

years; what is typically expected for non-critical, non-building structures. One of the newest

challenges when designing structures that connect to the ocean is the effect of rising sea level due

to climate change. Fortunately, the floating bridge is automatically equipped to handle this

problem. The bridge already rises and falls with the tides and would similarly behave with any

permanent changes in sea level. The piers themselves will need their heights slightly bolstered, but

refinishing the surface is already necessary to give it enough traction over water.

Repurposing the piers also preserves a piece of one of California’s most important historical

structures. The pylons that carried the entire bridge load are mounted on the piers and will remain

in place for this design. Members of the community will have a window into California’s past and

an opportunity to learn about the incredible feat of engineering that helped shape the Bay Area and

the state. Educational stations and plaques will give the public a new appreciation for their home

and its history.

Leaving the four piers allow for not only a pedestrian bridge but also a small bird sanctuary. Piers

E19 and E20, which are further out into the Bay, will remain in place as a location on which birds

can settle. With some small amount of work, environmentalists can shape the piers into a suitable

breeding ground and sanctuary for avian life in the Bay. This could go a long way to offset and

potential harm caused by leaving the piers in the water.

Of course any development in the Bay will have some negative environmental impacts. Moving

the bridge into place will disrupt fish and other wildlife during the process. Pouring the new surface

for the piers also carries potential risk of spillage and dripping. These risks certainly must be

considered, but seem relatively diminutive compared to many other options. Further environmental

studies are necessary to make a fully informed decision.

2.2.4. Alternative 4: Constant depth, precast concrete I-girder bridge



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Precast I-girder bridges are attractive because they are a very common, very well-known design.

Since contractors and concrete workers have so much experience constructing concrete I-girder

bridges, they are relatively inexpensive. The long span length required is a challenge and will

require deep beams in order to carry such a large moment load, but it is certainly achievable.

Bridge Geometry



and to sit down and spend some time over the water. The bridge must be sufficiently deep in order

to create sustain the large bending moment that such a long span creates.


The highly seismic nature of the San Francisco Bay Area presents a challenge for the concrete I-

girder bridge. In order to avoid exceptionally large beams requiring extra concrete and reinforcing

steel, seismic isolation bearings can be installed on the piers to reduce the earthquake forces in the

bridge. Although these bearings are expensive, the cost is recouped by reducing the material

needed in the superstructure.


Aesthetic details on the concrete I-girder bridge will match the new eastern span of the Bay Bridge

as closely as possible. The bridge will use the same white railings were possible and will have the

same light fixtures and will be located on the piers. The concrete in the bridge can also be carefully


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colored to match the color scheme of the bicycle path on the Bay Bridge so that pedestrians and

cyclists can look down from the Bay Bridge and appreciate the matching style.

Unfortunately, even with aesthetic considerations, this bridge may still clash with the eastern span

of the SFOBB. Near the pedestrian bridge site, the SFOBB has a varying depth between the

supports. This look does not mesh well with the constant depth of the concrete I-girder bridge and

may cause some complaints. It is important to note, however, that very few people will be able to

compare the two bridges simultaneously; an observer would have to be out in a boat or a kayak

over the water to be able to see the underside of both bridges at the same time. Still, architectural

elements must be considered when erecting a new bridge so close to such an iconic structure.

Purpose & Need


and repurposing the old bridge piers so they don’t need to be removed. The concrete I-girder bridge

is also an inexpensive construction option which can actually save money for the community

compared to the millions of dollars associated with removing the piers. Additionally, what money

is spend to construct the bridge would stay in the community. The girders and deck can be built in

a local concrete yard and floated out to the construction site on barges. Then the pieces can be

lifted into place using two cranes on another barge. This creates jobs for the concrete workers in

the yard, the tug and barge operators moving the pieces, crane operators assembling the bridge,

and of course the remaining construction workers on the job site.

The concrete I-girder bridge alternative addresses many of the needs of the project. ADA

specifications must be followed absolutely for any public work. Fortunately, the concrete I-girder

bridge will stay at a constant elevation throughout its span from its initial launch point off of the

land. There should be no problems in keeping the pedestrian bridge accessible to all members of

the community.

Since the closure of the Berkeley pier, members of the East Bay have needed another site with bay

access. The concrete I-girder bridge would be a great addition to the community and to the

proposed Gateway Park. The public could walk out over the bay to enjoy the atmosphere and

admire the eastern span of the SFOBB. Fishermen will also be able to cast lines from the floating

bridge or the piers, a much needed feature after the closure of the Berkeley Pier.

Another way to connect the park and bridge to the community is to hold events. The concrete I-

girder bridge is capable of carrying a load of 100 psf, larger than the AASHTO required 85 psf.


held or what equipment can rest on the bridge.


must serve the community for years to come. The concrete I-bridge has a design life of 75 years;

what is typically expected for non-critical, non-building structures. Climate change that results in

rising sea levels poses a problem for structures near the ocean. In order to tackle this problem, the

piers will need an additional layer of concrete atop them to ensure they stay above the king tide


17

not only today, but in the event of sea level rise. Once the tops of the piers are sufficiently tall, the

concrete I-girders can lay atop them and be out of range of the water.






and its history.











2.2.5. Alternative 5: Variable-depth, precast concrete box-girder bridge


Precast box-girder bridges are also very common like I-girder bridges, but they require labor. The

variable depth of the bridge also increases the complexity. Skilled carpenters need to craft the

special formwork for a bridge like this, increasing labor times and cost. The long span length

required is a challenge and will require deep boxes in order to carry such a large moment load, but

it is certainly achievable.


18

Bridge Geometry



and to sit down and spend some time over the water. The soffit of the bridge is parabolic in shape

over the span length.


The highly seismic nature of the San Francisco Bay Area presents a challenge for the concrete

box-girder bridge. In order to avoid exceptionally large beams requiring extra concrete and

reinforcing steel, seismic isolation bearings can be installed on the piers to reduce the earthquake

forces in the bridge. Although these bearings are expensive, the cost is recouped by reducing the

material needed in the superstructure.


Aesthetic details on the variable depth, concrete box-girder bridge will match the new eastern span

of the Bay Bridge as closely as possible. The bridge will use the same white railings were possible

and will have the same light fixtures and will be located on the piers. The concrete in the bridge

can also be carefully colored to match the color scheme of the bicycle path on the Bay Bridge so

that pedestrians and cyclists can look down from the Bay Bridge and appreciate the matching style.

The concrete box-girder bridge also complements the look of the eastern span SFOBB. Since both

bridge spans would have variable depths, they would each appear to have been designed with the


19

other in mind. Architects of the SFOBB certainly prefer the pedestrian bridge to match their

original vision without distracting from it.

Purpose & Need


and repurposing the old bridge piers so they don’t need to be removed. The concrete box-girder

bridge design is well-known, but the variable depth requires that skilled carpenters make the forms,

increasing the cost. The box-girders can be built in a local concrete yard and floated out to the

construction site on barges. Then the pieces can be lifted into place using two cranes on another

barge. This creates jobs for the concrete workers in the yard, the tug and barge operators moving

the pieces, crane operators assembling the bridge, and of course the remaining construction

workers on the job site.

The concrete box-girder bridge alternative addresses many of the needs of the project. ADA

specifications must be followed absolutely for any public work. Fortunately, the concrete box-

girder bridge will stay at a constant elevation throughout its span from its initial launch point off

of the land. There should be no problems in keeping the pedestrian bridge accessible to all

members of the community.


access. The concrete box-girder bridge would be a great addition to the community and to the


admire the eastern span of the SFOBB. Fishermen will also be able to cast lines from the floating


Another way to connect the park and bridge to the community is to hold events. The concrete box-





must serve the community for years to come. The concrete box-girder bridge has a design life of

75 years; what is typically expected for non-critical, non-building structures. Climate change that

results in rising sea levels poses a problem for structures near the ocean. In order to tackle this

problem, the piers will need an additional layer of concrete atop them to ensure they stay above

the king tide not only today, but in the event of sea level rise. Once the tops of the piers are

sufficiently tall, the concrete box-girders can lay atop them and be out of range of the water.






and its history.


20











2.2.6. Alternative 6: Concrete slab-on-piles bridge


Concrete slab bridges are very simple to design and are quite common. The downside of concrete

slab bridges is that they can only span short distances and therefore need many supports. In order

to decrease the span length, piles must be driven beneath the bridge to support it. Driving piles in

the bay comes with many bureaucratic obstacles and can become quite costly.

Bridge Geometry



and to sit down and spend some time over the water. Rows of 5 piles must be driven into the bay

about every 30 feet longitudinally in order to support the slab.



21

The concrete slab-on-piles bridge additional seismic challenges compared to the other alternatives.

The additional piles that support the slab would transfer ground motion to the bridge deck, almost

certainly resulting in damage to the bridge deck.


Aesthetic details on the concrete slab-on-piles bridge will match the new eastern span of the Bay

Bridge as closely as possible. The bridge will use the same white railings were possible and will

have the same light fixtures and will be located on the piers. The concrete in the bridge can also

be carefully colored to match the color scheme of the bicycle path on the Bay Bridge so that

pedestrians and cyclists can look down from the Bay Bridge and appreciate the matching style.

The concrete slab-on-piles bridge has a very distinct look compared to the SFOBB. The long spans

of the SFOBB are very different from the near-continuously supported look of the pile bridge. One

of the aesthetic benefits to this bridge is that it can be positioned very low on the water, reducing

the visual impact of the piles and

Purpose & Need


and repurposing the old bridge piers so they don’t need to be removed. Concrete slab-on-piles

bridges are very common with a straightforward design. However, driving piles in the bay is not

as simple as it is on land. There are many regulations on development in the bay and they are quite

stringent. Drilling new piles in the bay would be very difficult to justify for a project this size,

especially given the other alternatives. Even on land, driving piles is an expensive process and

engineers often attempt to use as few as possible. Over the water, the complications are

compounded and costs rise even higher, possibly prohibitively so. However, the other side of this

argument promises a lot of jobs for the community. Casting the concrete deck and piles creates

jobs at a concrete yard, and driving them into the bay must be done carefully with experienced

workers. This requires a lot of equipment, workers, and time, all of which cost money.

The concrete slab-on-piles bridge alternative addresses many of the needs of the project. ADA

specifications must be followed absolutely for any public work. Fortunately, the concrete slab-on-

piles bridge will stay at a constant elevation throughout its span from its initial launch point off of

the land. There should be no problems in keeping the pedestrian bridge accessible to all members

of the community.


access. The concrete slab-on-piles bridge would be a great addition to the community and to the


admire the eastern span of the SFOBB. This type of bridge can also be lower to the water than the

single-span alternatives. The continuous support underneath means that the bridge does not need

to be as deep, so the top of the deck is much closer to the underside of the bridge and the surface

of the bay. This seemingly small change can make a big difference in the feel of the bridge to the

public once they set foot over the water. Fishermen will also be able to cast lines from the floating



22

Another way to connect the park and bridge to the community is to hold events. The concrete box-





must serve the community for years to come. The concrete slab-on-piles bridge has a design life

of 75 years; what is typically expected for non-critical, non-building structures. Climate change

that results in rising sea levels poses a problem for structures near the ocean. In order to tackle this

problem, the piers will need an additional layer of concrete atop them to ensure they stay above

the king tide not only today, but in the event of sea level rise. Once the tops of the piers are

sufficiently tall, the concrete slab-on-piles can span between them and stay out of the tide’s reach.






and its history.






Alternative 6 may be have the most environmental impact on the bay. Driving piles into bay mud

could be damaging to local wildlife in more than a few ways. The process would stir up a lot of

dirt and debris, clouding the water during construction. It would also be extremely noisy, both on

land and in the water, which would certainly be disruptive to aquatic life. It is also important to

note that this almost the opposite of the State of California’s pledge to remove the piers from the

bay; rather than taking out the intrusions, more are placed instead.

2.3 Comparisons of Alternatives’ Characteristics

2.3.1. Funding

The Bay Area Transit Authority (BATA) has allocated approximately $50 million for the removal

of piers E1, E2, and E19-23. The cost of many of these alternatives is considerably less than the

cost of demolition. With the diversion of some of the funds allocated for demolition, BATA and

the state could very realistically save tens of millions of dollars with the additional benefit of

creating a point of public access to the bay.


23

2.3.2. Costs

Each design option, including the no-build alternatives, pile alternative, and no-pile alternatives,

carry different financial costs. Even among each category the costs can vary greatly. Some of the

alternatives are almost prohibitively expensive while others have a much more reasonable price

tag.

The concrete slab-on-pile bridge would be very costly, since hundreds of new foundation piles

would have to be driven in the bay. Driving piles is already expensive on land, but to do so in the

San Francisco Bay, which has countless regulations and complications, would be an unreasonable

expense. Another expensive option is to remove the piers in the bay as originally agreed upon by

the State of California and the BCDC. The controlled demolition that was used for pier E3 was a

very expensive operation. Although it was the biggest pier in the deepest water, removing four

smaller piers would be comparatively exorbitant.

The remaining options are much more financially attractive. Clearly, the no-build alternative that

leaves the piers in the water would have literally zero construction costs. However, leaving the

piers in the water without suitably repurposing them violates the original removal agreement and

Caltrans could face legal action if the piers remain in the water without a suitable purpose. This is

of course highly undesirable for all stakeholders including the state and government agencies.

The other no-pile alternatives are relatively inexpensive. Each option has different costs based on

the complication of design, installation, and overall construction. The precast box girder bridge is

the most expensive of the three since it needs custom formwork for each segment of the box, which

can only be built by skilled carpenters. Then the boxes must be floated on a barge to the job site

and then lifted into place using two cranes operated by experienced workers and supported by

another barge. The pieces are carefully set into place and fixed by crews on the piers. Each step in

this process requires significant manpower and precision.

The concrete I-girder bridge has a comparable construction procedure as the box girder bridge, but

costs a bit less. The transportation and assembly processes are similar to before, with the barges

carrying the girders and the cranes. However, casting the I-girders in the yard is a simpler process.

I-girders are very common and the design requires less detail. Casting yards have molds that can

be endlessly reused to create the necessary-sized I-girder without much trouble. Costs are cut in

the pouring stage because the molds don’t need to be custom built by skilled carpenters.

The most cost-effective alternative is the floating concrete bridge. Although each concrete bridge

is unique and must be carefully sized, most everything else is simple and inexpensive. Materially,

the floating concrete bridge is very economical. The majority of the volume of the bridge is

composed of Styrofoam, much less expensive than structural concrete, in order to create enough

buoyancy in the water. The Styrofoam is of course surrounded by reinforced concrete and has

reinforced diaphragms in the interior, but overall it uses much less structural material since it is

continuously supported by the buoyant force. Additionally, the transportation and assembly is


24

much easier than the girder bridges which span the distance between the piers. Since the concrete

bridge floats by itself, the barge is unnecessary. The pieces can simply be affixed to a tugboat and

pulled to the construction site. Once they have arrived, it is a simple matter of floating them into

place and then fixing them to the piers. No barges, cranes, or other complicated procedures are

needed for the floating concrete bridge.

2.3.3. Constructability & Schedule

All alternatives listed are viable construction alternatives, but some are more practical than others.

The no-build option that leaves the piers in the San Francisco Bay needs no action, and is

essentially already accomplished. However, this option fails to satisfy the regulations governed by

the BCDC and fails to follow through on the promise made by the State of California to restore

the Bay to its former state. The other no-build alternative, removing the piers, certainly requires

more work, as shown during the removal of pier E3, but it follows through on the state’s promise

and is therefore more desirable of the two.

The build alternatives are obviously the more challenging options. The slab-on-piles alternative

requires extensive preparation before any work even begins. Since the slab needs to be supported

by hundreds of piles, this goes completely against the original end-goal of dismantling the old

SFOBB, which is removing man-made obstructions from the bay. Instead of demolishing the old

piers, they not only remain, but even more concrete is inserted into the bay mud. This option carries

significant environmental risk essentially kills it as a viable alternative, since it would basically

never be approved. Aside from the regulatory challenge, it would be quite challenging and time

consuming to drive the hundreds of new piles into the bay.

The no-pile bridge alternatives are more practically constructible because they have minimal

contact with the Bay water and floor. The majority of the work for all three of these options is

done off-site at a concrete yard during the casting of the bridge segments. The piers themselves

need a deeper slab of concrete, must be refinished, and need connections installed where the bridge

will attach, but these processes are well-controlled and should have very little interaction with the

Bay. Assembly should also be fairly quick since the pieces for all three alternatives must only be

set in place—the girder bridges are more challenging but should not cause any greater harm to the

environment than the floating bridge. Each of these designs is practical in their constructability,

but they also intrinsically fail the state’s promise to remove the piers from the bay. The overall

positive impact must be deemed superior to the environmental and political impacts of leaving the

piers in the bay.

2.3.4. Public Access

Both of the no-build alternatives are the least attractive alternatives for the public. Neither option

provides the community with a new location to come together; there is no positive impact for the

public. The no-build alternatives may be economically viable, but they don’t provide any public

access and are more communal blight than boon.


25

Each build alternative will provide a new level of public access to the Bay for the community. The

slab-on-piles bridge and both girder bridges offer essentially the same level of public access. All

of these designs grant the community a new public location to walk out over the water and admire

the San Francisco Bay’s natural beauty. These alternatives also provide an excellent site for

fishermen to settle for an afternoon to try their luck, which has been sorely missing from the East

Bay since the closure of the Berkeley Pier. The space available on these bridge alternatives would

allow the public to hold events out over the water, fostering a growing sense of community for the

area.

The floating concrete bridge rises above all other alternatives in terms of public access. It has all

the features of the out-of-water bridges with some very notable additions. Connecting the

community to the bay is of primary importance to this project. The floating bridge brings members

of the community physically closer to the bay than any other alternative. The underside of the

bridge is obviously in contact with the water and its top barely rises over the surface of the water.

Park patrons could reach over the edge and actually touch the bay water! Additionally, since the

bridge is mostly in the water, waves and tides will move the walking surface. Measures will be

taken to ensure that the bridge does not move too violently, but a gentle rocking will allow

pedestrians to feel the bay’s motion beneath their feet. The proximity to the water also allows water

sport enthusiasts an easy access point to explore the bay as a whole. Since the bridge surface is so

close to that of the water, kayakers, windsurfers, and their ilk could launch right off the bridge. A

simple gate or a removable section of barrier is all that is needed to create an aquatic activity hub.

For all these reasons, the floating concrete bridge alternative clearly provides the greatest public

access.

2.3.5. History

The San Francisco Bay Area is rich with history and importance that influenced not only

California, but also the United States its connection with the rest of the Pacific Rim. The old

SFOBB was envisioned during California’s formulation during the Gold Rush but would not be

built until the 1930s. The SFOBB represents the economic and political growth of the Bay Area

and California as a whole and the attitude and stick-to-itiveness of the people who lived and died

in this wonderful land. Preserving a piece of the old SFOBB would serve as an educational and

cultural landmark to the hard work and perseverance of our state and residents.

The no-build alternatives both do very little to pay homage to our history. By destroying these four

piers, the last of the SFOBB would be permanently removed from the bay without a visible trace

and leaving the piers in the water without access is almost as dismissive. Providing pedestrian

access out to the piers is a better way to honor and preserve the past.

Each of the build alternatives can be an equally effective monument to the old SFOBB. Atop each

pier currently stand two pedestals that supported the superstructure of the bridge. All of these

alternatives will leave the pedestals intact and thicken the floor slab surrounding them. There is


26

plenty of room on the piers to mount plaques bearing information about the history of the region

and the motivation for building the original bridge. These pedestals could also educate the public

on basic engineering principles. By allowing people to come in contact with these pedestals, they

can appreciate the enormous scale of infrastructure that they often take for granted. It could also

provide perspective on the challenges that the constructing workers and engineers faced almost

one hundred years ago when designing and building such an ambitious structure. As the Bay Area

continues to develop, it is important to have a window into the past to as a reminder of our

challenges faced and our ability to overcome them.

2.3.6. Climate Change & Sea Level Rise

One of the most significant challenges facing coastal development is the threat of climate change

and future sea-level rise. Oceans are predicted to rise by as much as 55 inches in by the end of the

21st century (BCDC 2015). Any coastal structures with lifetimes comparable to this time frame

must come equipped to deal with rising sea-levels. The alternatives outlined here have varying

capability of dealing with climate change and rising tides.

The floating concrete bridge is clearly the most capable of dealing with changes in sea level. The

bridge is already designed to not be permanently affixed to the supporting piers and to rise and fall

with the tides. Among the very few measures needed is to increase the height of the piers to

outreach the future sea-level height increase. The slab on top of these piers must already be

heightened since the bay waters rise a few inches above the top during king tides. By adding an

additional five feet to the top of the piers, the walking surface will remain above water not only

during today’s king tides, but also for those predicted by the end of the century. The other

important measure is increasing vertical size of the shear key holding the floating bridge in place.

This is a simple measure that prevents rising oceans from pushing the floating bridge up over the

shear keys, which would cause it to float off into the bay. Increasing the pier height by five feet

instead of a few inches and building larger sheer keys requires more labor and construction

materials, but lengthens the pedestrian-accessible service life of the piers approximately to the year

2100.

The precast box-girder bridge and I-girder bridge do not have the same natural adaptive advantage

as the floating bridge, but similar measures can be taken to protect them from sea-level rise.

Compared to the floating bridge, the piers need an additional height increase to keep the tops above

future high tides, but must be even higher if the bottoms of the girders are to remain above the sea-

level. Then, the precast sections can be lain, spanning between the piers, several feet above the

current water level. As long as the initial height is sufficient, the precast bridges should be well-

equipped to deal with sea-level rise.

The concrete slab-on-piles bridge requires additional efforts on top of those for the precast bridges.

The pier must be raised to account for rising sea-level, high enough to keep the bottom of the slab

out of the water. Additionally, each individual pile has to rise that far out of the water. The

increased heights of all these piles results in a significant increase in material and financial cost

for this alternative. On top of these costs, the bridge would rise over five feet out of the water at


27

the time of construction. This would give it an awkward, stilt-like appearance. Next to the beautiful

new SFOBB, it would be a complete eyesore.

Finally, there are the two no-build alternatives. Sea-level rise is entirely irrelevant for the pier-

removal option, but could be problematic if the piers remain. Since the piers currently get

covered by a few inches of water during king tide, if they were to remain as oceans rise, the tops

would become constantly covered. This would eliminate the unpleasant sight of them, but would

be extremely hazardous to boats, kayaks, and other bay activities as invisible, barely submerged

obstacles.

2.3.7. Environmental Impact/Advantages

Every construction project has, at the very least, an effect on the local environment. For

construction over water, these effects typically carry even greater impact. Many of the build

alternatives use as many precast elements as possible in order to minimize concrete poured on site

and shift some of the impact to a concrete casting yard instead of the bay waters.

Conversely, several of these alternatives have the option to create one or two small bird sanctuaries

on the piers. Each pier that is left in the water that does not have pedestrian access could be

specially engineered to serve as a bird nesting habitat. Far from the shore, these piers are isolated

from the land and are model nesting sites, protected from terrestrial ovivorous (egg-eating)

animals. The opportunity for inexpensive bird sanctuaries left on the piers offsets some of the

potential environmental harm resulting from leaving the piers or construction over the bay.

Of the build alternatives, the slab-on-piles bridge would be most detrimental to the environment.

Even though the slab and piles would be cast off-site, this alternative disrupts the bay more than

any other. The slab-on-piles bridge needs hundreds of piles driven into the bay mud, which would

greatly disturb aquatic life by churning up dirt and debris and with the deafening clatter of a pile

driver. This alternative also completely goes against the state’s original pledge to remove the man-

made remnant piers of the old bridge and instead adds more piles.

The remaining build alternatives each have roughly the same environmental impact. The floating

concrete bridge, the concrete box-girder bridge, and the concrete I-girder bridge have very similar

building requirements. They each need the piers to be raised several feet, which will require a

construction crew to pour concrete directly on the piers. This process carries risk of pouring

concrete into the bay water due to its immediate proximity. Each of these alternatives also needs a

way to hold the bridge in place, be it a shear key for the floating concrete bridge or a seat-type

abutment for the girder bridges. These pieces would likely be cast off-site and carefully affixed to

the augmented piers. The shear key will need to be set in place and bonded to the pier using

cementitious material, again carrying the risk of spillage into the bay.

The no-build, do nothing alternative that leaves the piers in the bay still has a significant impact

on the environment. Despite this option not requiring any construction or demolition, it is in direct

violation of the state’s pledge to remove the remnants of the old bridge from the bay. Even though


28

nothing new is added in this option, the piers are still man-made, foreign objects in an

environmentally protected area. Additionally, the remaining piers protruding from the water could

be a bit of a blight on the otherwise beautify bay.

The no-build alternative that removes the existing piers from the bay does the most to restore the

bay to its original state. This alternative also follows through on the state’s original commitment

to clear all the piers from the bay after the completion of the new eastern span. This is the only

alternative that purely works towards returning the bay to its virginal, unspoiled state.

2.3.8. Economic Stimulus/Jobs

A project’s effect on the local economy can be one of the most important avenues to its approval.

Local jobs and local spending are very attractive to communities and to their local politicians who

can espouse the advantages and success of the project. The best projects are both competitively

priced and large employers to the local community.

Each of the build alternatives would stimulate the local economy and provide jobs for the

community. The vast majority of the concrete work can be done off-site in a casting yard. Some

of these yards employ up to hundreds of skilled laborers working on various projects throughout

the community. The floating bridge and the box girder bridges all require great amounts of

materials and many workers to complete the job in an adequate time frame. These three alternatives

have many similar economic advantages to each other and should be quite attractive to politicians

and local workers.

The no-build, pier removal option also provides work to the community. Although it does not

require any construction or new materials, the task of removing the piers is complicated,

dangerous, and requires highly-skilled, highly-trained workers. Pier E3 was carefully removed

using a controlled implosion set into motion by several divers who fixed carefully placed

explosives along the pier’s submerged surface. This delicate operation does not employ as many

people as construction would, but still provides jobs to the community and injects money into the

local economy.

The no-build, do nothing alternative clearly falls short of all other alternatives from an economic

perspective. No money moves to material suppliers or construction employers when there is no

work to be done. There is really political or economic advantage to the do nothing alternative.

2.4 Selecting a Preferred Alternative

After weighing many factors, including financial costs, funding, constructability, erection time,

ability to address the purpose and need of the project, and environmental impact, the floating

concrete bridge (Alternative 3) was selected as the Preferred Alternative. Table 2.1 illustrates how

the strengths and weaknesses of each alternative was weighed and quantified.


29

Alternatives

No build Pile

alternatives No pile alternatives

Leave

piers

Remove

piers per

original EIR

Slab-on-

piles

concrete

bridge

Precast I-

girder

bridge

Precast

box girder

bridge

Floating

concrete

bridge

Public Access -1 -1 2 2 2 3

Historic Preservation -1 -1 2 2 2 2

Climate change/rising

ocean preparedness N/A N/A 1 1 1 2

Financial Cost 2 -2 -2 2 1 3

Completing original EIR

commitment -2 2 -2 -1 -1 -1

Schedule -2 1 -2 -1 -1 -1

Risk -1 1 -2 0 0 0

Architecture/Communit

y experience -1 1 -1 1 1 2

Fill in the Bay -1 2 -2 -1 -1 -1

Bird habitat/ sanctuary 1 -1 1 1 1 1

Jobs -1 1 2 2 2 2

Total -7 3 -3 8 7 12

Table 2.1


30

2.5 Construction Process of the Preferred Alternative

The floating concrete bridge alternative has many steps in the construction process. Here is a broad

overview of the construction plan:

Prepare the tops of existing piers for heightening and resurfacing

Pour the new, raised surface of the piers

Begin offsite casting of concrete shear keys to hold spans

Prepare piers for shear key installation (bores in the sides of the piers for shear key

attachment)

Begin offsite casting of floating concrete spans

Bring half of the shear keys to jobsite, fit them to the piers, and attach using cement paste

Float the bridge from the casting yard down to the jobsite and slide into place

Attach the other half of the shear keys, locking the floating bridge in place

Install ADA compliant ramp connecting the piers to the bridge decks

Install railings and apply aesthetic touches

Building substructure of the bridge

Traffic closures and diversion during erection of temporary framework

Pour concrete for superstructure of bridge and apply prestressing

Traffic closures and diversion during removal of temporary framework

Each stage must be carefully coordinated and timed to ensure the least amount of downtime as

possible. Transporting structural elements from the concrete yard via tug boat may require

arrangements with the coast guard or tariffs paid to the local regulatory agency. Construction over

the bay must follow all BCDC regulations, restrictions, and requirements unless otherwise

exempted.

Full Construction Staging of Preferred Alternative

Alternative 3 is an unconventional design for a bridge, but it has some similarities to floating

concrete docks used in marinas. The bridge is made of reinforced concrete encasing a foam

interior, which causes it to float. This design is on a much larger scale compared to floating docks

and has two interior “girders” which increase the flexural rigidity of the bridge. With these

uncommon design considerations, the instructions in this design must be carefully followed to

ensure that the bridge remains safe and strong. The following are the longer, more detailed steps

in constructing the floating concrete bridge:

1. Prepare the tops of piers for the increase in height by scouring off the exposed concrete that has

been worn by weather effects. Bore vertical holes in the concrete that will serve as splice points for

the new pier tops.

2. Place rebar in the newly bored holes on top of the pier and pour the new surface of the piers, five

feet higher than the old surface. The rebar in the bores should splice the old and new concrete

together. Leave horizontal holes on the sides of the pier where the shear keys will splice in.


31

3. In a casting yard, construct wood formwork for shear keys that will restrain lateral movement of

the bridge but allow for vertical movement.

4. Place rebar in the shear key formwork and pour the concrete Allow concrete to cure up to strength.

5. Prepare the piers for shear key attachment. Bore horizontal holes in the portion of the pier where

the shear keys will splice in. Build formwork that keeps water off of the area that will receive the

shear key.

6. In a casting yard, begin construction of the floating concrete bridge. Shape the interior foam into

three pieces, each 248 feet long, 104 inches wide, and 66 inches tall.

7. Place structural reinforcing bars around and between the foam in the T-shape that the concrete will

take. Reinforcing bars should also be in the “girders” between the foam blocks and outside the foam

blocks; each foam block should have reinforcement surrounding it on all sides except for the

bottom. (Figure 2.1)

Figure 2.1


32

8. Build formwork for the floating concrete bridge around the existing foam and rebar (Figure 2.2)

Figure 2.2

9. Cast lightweight concrete around the foam blocks, over the rebar and finish the surface. (Figure

2.3)

Figure 2.3


33

10. Steam cure the concrete bridge under cover to expedite strengthening process. (Figure 2.4)

Figure 2.4

11. Once the shear keys have cured, transport them to the job site.

12. Attach shear keys on one side using the splice holes in the pier and fill them with cementitious

material.

13. After the concrete bridge has cured, apply rubber or wood padding around the top edges to reduce

impact between the bridge and the piers

14. Using a crate, hoist the floating concrete bridges into the water or onto a barge. (Figure 2.5)

Figure 2.5


34

15. Tug concrete bridges down to the job site, and float them into place.

16. Attach the other half of the shear keys, locking the bridge in place.

17. Attach railings to the sides of the bridge deck and to the sides of the piers

18. Attach the rotating ramps to the piers and allow them to run onto the bridge decks.

19. Apply finishing architectural touches to the piers and bridges.

20. Install lights and other electrical features on the piers.

21. Install any bench seating, binoculars, and or/plaques.

22. Clean up the job site and open up for the public!

2.6 Bridge or Barge?

One may ask if the floating concrete bridge is actually a bridge. After all, it floats on the water

rather than spanning the distance. Some might say it is more barge or dock than bridge, and it is

therefore important to refute this notion immediately. The floating concrete bridge is a very real

structure that meets bridge design codes. It is not a cheap dock that will fall apart in a few years.

This bridge has a 75 year design life and is capable of supporting thousands of pedestrians and a

15 ton trick simultaneously. All strength and loading calculations for the bridge include factors

of safety to ensure that the bridge can handle anything thrown at it. A barge tied between two

piers would rust quickly, drift significantly, and be very unsafe. A barge has no structural design

requirements and could not endure nearly the magnitude and frequency of loading that the bridge

can.

Chapter 3: Loading Demands

35

CHAPTER 3: LOADING DEMANDS

3.1 Vertical Loads

The floating concrete bridge is designed as a pedestrian walkway out over the bay. It should be

capable of supporting large numbers of pedestrians and the occasional maintenance truck.

AASHTO prescribes a pedestrian loading of 85psf over the area where people are allowed to walk.

This bridge has been designed with additional capacity in mind at 100psf in case of accidental

overloading during special events or even crises. The maintenance truck used in design is an H-15

truck weighing 24 kips on the rear axle and 6 kips on the front axle. To prevent disaster, these

loads are applied in a variety of configurations and orientations in an attempt to create a “worst-

case scenario” that loads the bridge as severely as possible. These loading scenarios could all be

run simultaneously and analyzed with a three-dimensional model or projected into two dimensions

and run in two two-dimensional models. This bridge was analyzed using the latter method with a

longitudinal model and a lateral model.

3.1.1 Load Paths

It is very important to understand the load path of a structure during design. The engineer must

know how the forces move through the structure in order to effectively size and link structural

components. A typical deck-on-girders bridge designed to carry vehicular traffic has a simple load

path that generally progress down the structure. The begins in a vehicle, goes through the tires,

loads the deck, then loads the girders, then that is passed to an abutment or bent, then down to the

foundation and piles, which finally transfers it to the ground. A simple diagram numbering the

steps is shown below in Figure 3.1.

Figure 3.1


36

The floating concrete bridge has a different load path that is slightly shorter. The loads begin the

same, starting with the truck, then to the tires, then onto the deck. The load path begins to diverge

here by sending the forces into the girders and the foam between the girders alike, and then the

load goes into the water where the bridge is held up by the buoyant force. The numbered load path

is shown below in Figure 3.2. The way the loads are distributed into the girders and the foam

together greatly reduce the moments and shears in the girders. The buoyant force acts along the

entire underside of the bridge exactly matching the downward loads.

Figure 3.2

3.1.2. Longitudinal Loading Configurations

There are eight different loading configurations for the longitudinal model. Some include only

pedestrian loads and some include both the pedestrian and truck loads. Trucks and pedestrians are

placed in an attempt to create the worst possible loading conditions for the bridge. In a few of these

load cases, the trucks are on the very far edges of the bridge in an attempt to create the largest

moment for a continuously supported beam. Also, some of these loading situations will actually

not be permitted in reality, like a truck load superimposed over the pedestrian load. These cases

are included mostly as a thought experiment, but can also be realized in the event that people

decide to ignore the temporary barriers set up during maintenance and walk too close to the

maintenance truck. Below are the eight loading configurations analyzed in the longitudinal model.


37

Figure 3.3


38

3.1.3. Transverse Loading Configurations

There are six different loading configurations for the transverse model. Some include only

pedestrian loads and some include both the pedestrian and truck loads. Some of these loading

configurations are designed to induce moments of opposite signs over the transverse length of the

deck to ensure the deck can deflect in both vertical directions. Included are load cases that have

with pedestrians all the way to the edge of the deck, and some stop just over the outermost girder.

The transverse model analyzes a segment of deck that is 16 feet deep, which is wide enough to fit

the entire H-15 truck which has axles 14 feet apart. Below are the six loading configurations

analyzed in the transverse model.

Figure 3.4


39

3.2 Lateral Loading Considerations

3.2.1. Seismic Loading

The floating concrete bridge has a very different seismic response than the other bridge alternatives

outlined previously. All of the other alternatives were supported entirely by the piers or supported

by the piers in conjunction with interior piles. The floating bridge, however, is different in that it

is continuously supported by the water. For the case of the floating bridge, the piers’ only job is to

keep the bridge from floating off into the bay; they only restrain motion in the horizontal directions,

not in the vertical direction. Essentially, there is no real fixity between the floating bridge and the

piers. The bridge basically just slides into place and is kept in the proper location with concrete

shear keys covered with a layer of wood or rubber to reduce collision impact forces. This type of

“connection” is very helpful when considering the seismic response of the structure.

Since the bridge is continuously supported by water and basically detached from the piers, the

seismic loading on the bridge can be ignored. Without a rigid connection, there is no load path for

the earthquake forces to reach the floating concrete bridge. During an earthquake, many different

types of waves are produced and propagate either through the interior of the Earth (body waves)

or along the surface of the Earth (surface waves). There are two types of body waves, the Primary

wave, or P-wave, which travels more quickly, and the Secondary wave, or S-wave, which is a

transverse shear wave that is slower and more destructive. The two basic types of surface waves

are Rayleigh waves, or “ground roll,” which cause solids to roll and ripple like the surface of a

fluid, and Love waves, which are a horizontal shear wave. What is most important to note, is that

the only type of seismic wave that the bridge can feel is the least destructive of them all, the P-

wave. Rayleigh waves can be extremely damaging, but cannot effectively propagate through

fluids. S-waves and Love waves can also be very destructive, but these are both types of shear

waves, and water, of course, cannot sustain or transmit and shear force at all.

The fundamental feature of the floating concrete bridge perfectly shields it from the most

destructive aspects of earthquakes. Floating in a fluid protects the bridge from all of the most

destructive seismic waves, the roll action and shear action. Therefore, there is no need to run a

seismic analysis on the floating concrete bridge.

Conversely, the piers do feel seismic forces because their foundations are fixed deep in the mud,

sand, gravel, clay, and rock beneath the bay floor. The piers will shake and deflect under

earthquake loads, but there is no need to worry about them. The remaining substructure was

previously designed to hold the weight of the superstructure, ten traffic lanes full of cars, and a

train load. Since the mass of the structure is so severely reduced, the ground accelerations will not

produce nearly the same force that they would have previously. Therefore, the piers are

considerably overdesigned for the magnitude of forces that they would likely receive during the

next design life. Due to these advantages, seismic forces do not control the design on the piers.


40

3.2.2. Wave Loading

The main lateral load on the floating concrete bridge will come from the ebb and flow of tidal

currents and waves crashing against the side. For an initial calculation, the drag equation

determines the magnitude of the lateral forces acting on the bridge.

Equation 3.1

Here FD is the drag force, ρ is the mass density of the fluid, A is the area of the face over which

the fluid flows, CD is the drag coefficient of the face the fluid flows over and is based on the

geometry and orientation, and v is the velocity of the fluid flow. Using a fluid velocity of 3 knots,

very high for the bay, especially so close to the shore, and considering two surfaces, the underside

of the bridge and the “front” face where the incoming water is orthogonally incident (which would

create the largest loads), the total drag force on the entire body is calculated at about 55.5 kips.

Then that load can be divided along the length of the bridge to get a continuous distributed load of

about 0.226 kip/ft. From here, the bridge can be modeled as a simply supported beam with a

distributed load. What is “vertical” here is really the “lateral” load coming from the waves. This

load is very minor compared to the vertical loads and the existing reinforcement is more than

sufficient to keep lateral deflections and cracks under control.

Figure 3.5


41

Using only this drag force equation is a huge simplification. In reality, there could be many more

factors adding greater stresses on the bridge. One of the spans comes out from the shore, so there

is very little water flowing beneath the underside, at least on one side. This situation may result in

a quasi-damming behavior that accumulates more water on the side from which the water, resulting

in hydrostatic forces on one side of the bridge. Additionally, the span closer to the shore may even

bottom out in the shallow water during low tides. This would send all the water flow around to

where the floor is deeper, creating unpredictable flows. These could be major concerns, but it is

impossible to say without more information. Before any designs are made final and any

construction takes place, further on-site studies may be necessary and additional lab sensitivity

studies would also be prudent.

Chapter 4: Design and Calculations

42

CHAPTER 4: DESIGN AND CALCULATIONS

4.1 Design

The floating concrete box pedestrian bridge is modeled in SAP2000 using two models—a

transverse model and a longitudinal model. Together, these models tell the full, three-dimensional

story of the bridge and accurately analyze the structure. The effects of the dead load uniformly

sink the bridge into the water, while the various live loads induce greater stresses and deflections.

The following design successfully satisfies the strength requirements of the bridge based on the

vertical dead and live loads and the lateral wave loads. Several architectural renderings of the

design can be found in the appendix.

The materials used in the bridge are common and readily available. All the concrete in the bridge

is sand-lightweight 5000 psi concrete to keep the section as buoyant as possible. All steel

reinforcement will be epoxy-coated 60 ksi steel to provide sufficient strength and corrosion

resistance. The expanded polystyrene (EPS) will be EPS29, a common, sturdy, lightweight plastic

material manufactured to meet ASTM D6817, “Standard Specification for Rigid, Cellular

Polystyrene Geofoam.” EPS29 has a compressive resistance of about 10.9 psi and a modulus of

elasticity of 1090 psi. These physical properties should not come into play, however, since the

entirety of the load is carried by the steel and concrete.

4.1.1. Floating Box Design - Longitudinal

Piers E23, E22, and E21 are all equally spaced at 292 feet apart center-to-center and are 44 feet

wide. The full job requires two identical bridges, each 248 feet long with a 30 foot wide top deck

that is 6 inches deep. The deck of the bridge has an overhang that extends 16 inches over the

outside of the girders, making the width of the foam and girder section a total of 27 feet 4 inches.

There are three 4-inch girders in the bridge 108 inches apart center-to-center, each 4 inches thick,

extending 66 deep. The bridge uses #8, #6, and #4 bars for different steel reinforcement. The

longitudinal reinforcement in the deck are #8 bars and have a clear cover of 2.5 inches from the

top and are spaced 8 inches apart. The girders contain #6 bars and #8 bars with different spacing.

The bottom 33 inches of the girder have #8 bars spaced 4 inches apart with 2 inch cover on all

sides. The top 33 inches contain #6 bars spaced 6 inches apart with 2 inch cover on the sides. The

space between the girders is filled with expanded polystyrene geofoam to displace water and create

a buoyant force that keeps the deck above water. The foam is entirely enclosed by the girders on

the sides and by a thin layer of cementitious material over fiberglass mesh to keep water out.

The bridge will be constructed off-site in a concrete yard with access to water that connects to the

bay. Each 248 foot span will be constructed as one piece so that no on-site assembly is required to


43

finish the bridge. Once cast in the yard, the bridge can float all the way to the site and simply slide

into place.

Figure 4.1

4.1.2. Floating Box Design – Transverse

The transverse reinforcement in the deck must support an H-15 truck load and pedestrian load in

almost any combination. There are two sets of transverse #4 bars in the deck to handle both

negative and positive moments. They have a clear cover of 2 inches from the top of the deck and

2 inches from the bottom of the deck and are both spaced 8 inches apart. For shear reinforcement

in the girders, alternating lower level of deck bars bend down from the deck into the outer edge

of the exterior girders making a U-shape. Since every other bar in the bottom transverse

reinforcement goes into the girders, the spacing is 16 inches. The interior girders will have

vertical #4 bars as well, but these ones are simply tied into the transverse reinforcement, not

continuous, bent bars. The #4 bars run down to the bottom layer of #8 bars in the girders as

shown in the figure below.


44

Figure 4.2

4.1.3. New Pier Caps Design

Currently, the tops of the piers barely stand above the water during the typical high tide, and are

even covered by water during king tide. To prepare for future rising sea levels, the piers need to

be heightened. BCDC predicts that oceans will rise approximately 55 inches by the end of the

century. To pre-emptively combat rising sea level, a 2-2.5 foot tall cap will be added to the tops of

the existing piers. In a few decades, another cap can be added on top as water approaches the new

top of the pier

The exterior walls of the pier will be extended upward with the same thickness and reinforcement

as the original design, but with newer, modern materials. The walls around the perimeter of the

pier and around the pylons are 4 feet thick with #6 bars spaced 18 inches from each in both the

vertical and horizontal directions. The slab spanning between the vertical walls will be 20 inches

deep with #8 reinforcing bars with 6 inch spacing at a depth of 18 inches in both horizontal

directions. This design is sufficiently strong to resist both the H15 truck load and the full 100 psf

pedestrian live loads. The old piers will need rebar inserted into vertically bored holes staggered

between the 18 inch spacing in the vertical reinforcement in the walls to act as a splice with the

new caps. The rebar will extend into both sections and will be secured using cement paste.

4.1.4. ADA Ramp

The new structure is of course required to follow requirements outlined in the American with

Disabilities Act. This includes providing a wheelchair ramp with slope no greater than 1:12 for

persons with disabilities. According to the United States Access Board, ADA ramps that connect

to aquatic structures must be constructed with the prescribed slope, but can exceed also that slope

due to water level changes such as tidal flow (USAB 2003). This regulation applies to many public

places, like boating facilities in reservoirs, where the water may rise and fall dramatically based

on recent rainfall. The USAB also allows ramps connecting to aquatic structures to exceed to

typical 30 foot maximum length. This is very important, since after the new pier cap heightened

by 2.5 feet is installed, a ramp would need to be at least 30 feet long during any time other than

high tide to maintain 1:12 slope. These two allowances for ramps connecting to aquatic structures

allow for some forgiveness in fulfilling what would otherwise be very challenging legal

requirements.

The ramp must be large enough, about 10-12 feet wide, and made of a sufficiently strong material,

like steel, to carry the weight of several pedestrians or the occasional maintenance vehicle. To

increase the moment capacity, small T-shaped sections could be welded to the underside of the

ramp, increasing its moment of inertia (Figure 4.3). The ramp will have a pinned connection to the

pier cap will run down to the bridge deck where it will be supported by rolling wheels (Figure 4.4).

This will allow the ramp to move along the bridge deck surface as it rises and falls with the tides.


45

Figure 4.3

Figure 4.4


46

4.2 Hand Calculations

There are many ways for bridges to fail and each must be carefully considered and checked. The

most important and fundamental requirements are shear and moment capacities of the bridge in

the longitudinal and transverse directions. Also, the new slab placed atop the piers must satisfy

similar shear and moment requirements. Additionally, the bridge deck must be able to support a

maintenance truck, so punching shear requirements are calculated. The presence of salt water all

around the bridge is extremely important, so crack widths on the deck and the underside of the

girders are calculated and minimized.

4.2.1. Positive Longitudinal Moment Capacity

Longitudinal bending moment capacity is probably the most fundamental aspect of a bridge’s

strength. The bridge deck and girders behave like T-section beams and are analyzed as such. The

differing geometry of the exterior girders and interior girders is considered, but it turns out that the

analysis is the same for each. The first step in the moment capacity calculation is the determination

of the “effective width” of the flange. Interior and exterior girders have different equations, but

they yield the same result in this case.

Interior girder Exterior girder

𝑏𝑒 = 𝑙𝑒𝑎𝑠𝑡 𝑜𝑓 {

𝐿4⁄

𝑏𝑤 + 6𝑡𝑏𝑤 + 2𝑏𝑜

𝑏𝑒 = 𝑙𝑒𝑎𝑠𝑡 𝑜𝑓 {𝑏𝑤 +

𝐿12⁄

𝑏𝑤 + 6𝑡𝑏𝑤 + 𝑏𝑜

Equation 4.1 Equation 4.2

In this case, the first options are basically meaningless since the span length, L, is essentially zero

since the bridge is continuously supported by the buoyant force. Therefore, the second option

controls for both the exterior and interior girders and gives an effective width of 40 inches.

Then, as with any reinforced concrete beam calculation, assume steel is reaching or exceeding its

yield strain. Calculate the tension force in the equation based on the cross-sectional area of the

reinforcing steel, 𝐴𝑠 , multiplied by its yield strength, 𝑓𝑦.

𝑇 = 𝐴𝑠𝑓𝑦

Equation 4.3

Next, enforce equilibrium between the tension in the steel and compression in the concrete and

work towards sizing Whitney stress block and then the overall size of the compression zone.

Fortunately, the depth of the compression zone is considerably less than the 6 inch depth of the

deck. Here 𝑓′𝑐 is the compressive strength of the concrete.


47

𝑎 = 𝐴𝑠𝑓𝑦

0.85𝑓′𝑐𝑏𝑒

Equation 4.4

Then it is time to check the size of the actual compression zone. The intensity of the compression

is approximated as a parabola with maximum width c. The 𝛽 factor is based on the strength of the

concrete. Both c and 𝛽 are defined as follows:

𝑐 = 𝑎

𝛽 𝛽 = 1.05 − 5 ∗ 10−5𝑓′𝑐


Now it is time to verify that the steel strain is beyond yielding. Here 𝜀𝑠 is the strain in the steel, 𝜀𝑐

is the maximum compressive strain in concrete (0.003), 𝜀𝑦 is the yield strain of steel, 0.00207, and

d is the depth from the top of the deck to the centroid of the reinforcing steel.

𝜀𝑠 = 𝜀𝑐 (𝑑 − 𝑐

𝑐) ≥ 𝜀𝑦

Equation 4.7

Fortunately, the steel is indeed yielding and it is possible to calculate the moment capacity of each

girder as follows.

𝑀𝑛 = 𝐴𝑠𝑓𝑦 (𝑑 − 𝑎

2)

Equation 4.8

Each T-beam has a moment capacity of approximately 20812 kip in (1734.4 kip ft). The strength

reduction factor for bending moment is ∅=0.9 so the strength becomes 18731 kip in (1560.9 kip

ft). Therefore, the factored flexural strength of the entire deck is approximately 74924 kip in

(6243.7 kip ft). This comes from simply multiplying the strength by four, the number of girders.

In reality, the bridge will share the load better than four individual girders would because they are

actually one structure. Some size effects may reduce the strength from this value, but the effect

should be mitigated by already using the effective width of the flange instead of the entire span

length between girders.

4.2.2. Negative Longitudinal Moment Capacity

The calculations above were for positive bending moment. It is also important to analyze the

negative bending moment capacity for the structure since it will likely experience negative flexure


48

as well. The negative moment calculation is done in a very similar manner to that of the positive

moment capacity, but a bit simpler. For the negative moment case, the top flange is instead in

tension and the bottom of the web carries the compression. The width of the section is clearly

defined, so there is no need to calculate and “effective width” as before. The T-section can be

treated as a rectangular beam since the compression zone is now in the web. The calculation begins

with Equation 2 and proceeds in the same manner. The negative flexural capacity for each

individual “girder” (including the strength reduction factor of 0.9) is approximately 17990 kip in

(1500 kip ft) making the total negative flexural capacity about 71960 kip in (6000 kip ft).

4.2.3. Transverse Moment Capacity

The transverse capacity is calculated basically as a slab, since the longitudinal girders add very,

very little to the transverse moment capacity. For the slab, there is no need to find an effective

width since the geometry is uniform. Instead of taking the entire 248 feet, this calculation uses 16

foot widths as discretizations of the slab. This width is large enough to fit an entire H15 truck

inside it, allowing for basically all possible loading conditions. The “length” of the bridge in the

transverse calculation is 30 foot width of the bridge.

Beginning from Equation 2, follow the same steps as the longitudinal moment capacity. The

transverse moment capacity for a 16-foot wide section of the bridge is 957.17 kip in (79.76 kip ft).

After applying the strength reduction factor, the moment capacity is 861.45 kip in (71.79 kip ft).

This is both the positive and negative moment capacity for the section. Because the slab section is

symmetrical about the neutral axis, it has identical behavior for positive and negative flexure.

4.2.3. Longitudinal Shear Capacity

The shear capacity of any beam-like structure is incredibly important to its integrity. Shear checks

have many penalties placed upon them throughout building codes due to the potentially

catastrophic nature of its failure; sudden and often explosive. Fortunately, the continuous support

under the bridge from the buoyant force of the water the shear forces acting on the bridge and

helps to mitigate the dangers of sudden shear failure. Regardless, it is necessary to verify the shear

strength of the structure.

Reinforced concrete beams provide shear resistance from both of its constitutive materials; the

concrete and the steel. The nominal resistance is given by this simple equation adding the two

together.

𝑉𝑛 = 𝑉𝑐 + 𝑉𝑠

Equation 4.9


49

There are several equations that give the shear strength of the concrete in a beam. Some equations

contain variables that change along the span length, which naturally complicate the calculation.

For this case, a simpler, more conservative equation is used where 𝜆 is 0.85 for sand-lightweight

concrete, 𝑓′𝑐 is the compressive strength of the concrete, and A is the area of the entire cross-

section.

𝑉𝑐 = 2𝜆√𝑓′𝑐𝐴

Equation 4.10

Then, the shear resistance of the steel must also be measured. The following equation uses stirrup

spacing, s, to help determine how much steel crosses over the potential shear cracks. Although this

structure does not have “stirrups” per-se, the vertical reinforcing steel in each girder fulfills the

same purpose, so that spacing is used instead. 𝐴𝑣 is the area of the cross-section of the shear steel

(the stirrups). This calculation breaks the bridge into each individual girder, so the steel shear

capacity here is ¼ of the steel shear capacity of the entire bridge

𝑉𝑠 = 𝐴𝑣𝑓𝑦𝑑

𝑠

Equation 4.11

Finally, calculate the steel shear capacity of the entire bridge and add it with the shear capacity of

the concrete, apply a reduction factor ∅=0.75 and compare to the largest shears found in each

load case, 𝑉𝑢.

𝑉𝑢 = ∅𝑉𝑛

Equation 4.12

The nominal shear capacity of the bridge in the longitudinal direction is 818.59 kip. Applying the

strength reduction factor of 0.75 requires that the maximum shear of the bridge stay 451.9 kip.

4.2.4. Transverse Shear Capacity

The transverse shear capacity is calculated in the same way as before. The deck behaves

basically as a slab, so the beam calculations used for the longitudinal shear will also work here.

The transverse section does not have any stirrups, so the shear is carried entirely in the concrete

and the transverse steel. The factored shear strength of a 16-foot wide transverse section of the

bridge comes out to 117.36 kip.

4.2.4. Punching Shear Strength

Punching shear is typically a concern for structures in which a column is supported by a slab and

the entire axial force of the column must be resisted in shear. Although there are no column-slab


50

interfaces in the bridge, the weight of an H15 truck passing through its tire into the deck behaves

quite similarly. ACI 318-08 11.11 explains the required punching shear calculations.

The first step is to determine the punching stress exerted by the truck tire.

Equation 4.13

Where Vu is the magnitude of the shear force and is taken to be 12 kips, the weight on one tire on

the heavier rear axle, A is the area of the critical section, Mu is the unbalanced column moment

(which is zero in the case of the tire on the bridge deck), and therefore γ, I, and c, the ratio of

moment transferred by shear, the moment of inertia of the critical section, and the distance from

the point of interest to the center of the critical section respectively, are irrelevant.

There are different areas for different locations of loading. Since the truck can move around and

park most anywhere on the bridge, the worst case, what is referred to as “corner column” was

selected.

Equation 4.14

Where b1 and b2 are the dimensions of the critical section (contact area) and d is the average depth.

AASHTO 3.30 states that tire contact area is 10 inches by 20 inches and the designed depth of the

bridge is 6 inches, giving a shear area of 180 square inches. Therefore, going back to Equation 13,

the punching stress is 66.67 psi.

Next, the allowable stress must be determined and the code has several different stress states and

equations. Since the truck can move around it may be closer to the edge of the deck than four times

the deck thickness, 24 inches. Therefore, the following equations determine the allowable shear

stress.

𝑣𝑐 = 𝑙𝑒𝑎𝑠𝑡 𝑜𝑓

{

(2 +

4

𝛽) 𝜆√𝑓′𝑐

(2 + 𝛼𝑠 𝑑

𝑢) 𝜆√𝑓′𝑐

4𝜆√𝑓′𝑐

Equation 4.15


51

Where 𝛽 is the ratio of the larger side of the critical section to the smaller side (2, in this case) and

𝛼𝑠 has a value of 20 for corner columns. In this case, the first equation is the smallest and with

sand-lightweight concrete yields a 𝑣𝑐 of 180.5 psi.

Finally, it is a simple check to make sure the reduced allowable stress is greater than the existing

punching stress.

𝑉𝑢 < ∅𝑉𝑐

Equation 4.16

With the shear reduction factor of ∅=0.75, the reduced capacity is 135.3 psi and is still twice

as large as the punching stress. The concrete alone provides more than sufficient strength

and the rebar in the deck will only further strengthen the section.

4.2.5. Crack Width and Crack Control

Cracking in structural concrete becomes a very real concern when the structure is exposed to water,

especially salt water. Corrosion from salt water attack could potentially eat away at the steel

reinforcement, basically removing it from the structure. In order to prevent this, ACI 244 has

guidelines on maximum crack size and crack calculations.

ACI 244 specifies maximum allowable crack widths for structures with a variety of purposes and

is shown in Table 4.1


52

Obviously, the floating concrete bridge falls into the seawater and seawater spray category and

crack widths must be restricted to 0.006 inches or less.

There are two expressions outlined in the code that dictate maximum crack width along the tension

face of a beam, that developed by Gergely & Lutz and that developed by Frosch. Both equations

are suitable since the reinforcing steel is still less than 2.5 inches from the tension face (Frosch).

The more recent equation developed by Frosch in 1999 is used here.

𝑤 = 2𝑓𝑠

𝐸𝑠𝛽𝑑∗ 𝑑∗ = 𝑙𝑒𝑠𝑠𝑒𝑟 𝑜𝑓 {

√𝑑𝑐2 + (𝑠

2)2

√𝑑𝑐2 + 𝑑𝑠2


Where w is the crack width, fs is the stress in the steel when the crack is being determined, 𝛽, is

the ratio of the neutral axis measured from the tension face to the distance from the neutral axis to

the centroid of the reinforcing steel, dc is the concrete cover from the tension face to the closest

steel bar, s is the spacing between the bars, and ds is cover distance from a bar to the side of the

concrete beam. Based on the current design, the maximum crack width comes to approximately

0.0095 inches and unfortunately is larger than the code prescribed 0.006 inches for seawater

structures. For the final design, this calculation will need to be revised or be further in-depth.

The current 𝛽 calculation is based on the centroid of the reinforcing steel, which is useful when

the steel is concentrated in one section of the beam. This design, however has the steel distributed

up the girder, so the centroid is pulled much, much higher than the bottom steel, 14 inches higher

than the centroid of the bottom steel, in fact. This distribution of steel over such a long distance

will result in different bars having different stresses, which have differing effects on the cracks.

Although this is unrealistic, if the centroid of the steel is taken to be at the very bottom piece of

steel, the crack width goes down to 0.0071 inches, much closer to the allowable limit. This is an

odd situation. Additional steel bars above the bottom layer should not cause increased cracking as

the ACI equations dictate.

As the design currently stands, cracks will form at the bottom off the girder large enough for salt

water to seep in. Eventually, the water will corrode the rebar, no matter how well it is coated. Once

the bottom layer of rebar is entirely corroded in all four girders, the positive moment capacity

drops to about 61000 kip in (5080 kip ft). This is still quite a large moment capacity, but it is loses

about 14000 kip in.

It is also important to note that all rebar used in the bridge will be epoxy-coated to prevent

corrosion. The use of epoxy rebar does not change any building requirements with regards to crack

width, of course, but it is an additional safeguard against corrosion and salt water attack.

Chapter 5: Model and Results

53

CHAPTER 5: MODEL AND RESULTS

5.1 Model Setup

The floating concrete bridge is continuously supported by the buoyant force of the water it

displaces. As more force is added to the bridge, it sinks further into the water and an equal force

pushes back. This is basically the behavior of a spring and should behave like a beam on an

elastic foundation. An approximation of this behavior was modeled in SAP2000 version 17.

Unfortunately, SAP2000 is not readily able simulate continuous support and so it is necessary to

break up the supports into small, discrete springs.

5.1.1 Longitudinal Model

The longitudinal model is 248 feet long and discretized into 1-foot sections to create a total of 249

springs. Each spring has a spring constant of 1.7054 kip/ft (0.1421kip/in). This value comes from

calculating the self-weight of the bridge and setting that equal to the specific weight of water

multiplied by the volume of the displaced water. Knowing the length and width of the bridge, the

depth of water displaced is found. Then, the spring constant of the entire body is found using

Hooke’s Law:

Equation 5.1

To get the spring constant of each discrete spring, simply divide by the 249 springs in the model.

5.1.2. Transverse Model

The transverse model is 30 feet wide and discretized into 6-inch sections. Unlike the longitudinal

model, not every node in the transverse model has a spring supporting it. Recall that the deck

extends out over the edge of the outer girder. The springs in the transverse model therefore start

18 inches in from each side, corresponding to the centerline of the outer girders. There are a total

of 55 springs in the transverse model, each with a spring constant of 7.6898 kip/ft (0.6408 kip/in).

This value was derived in a manner analogous to that used for the longitudinal model.

5.1.3. Verifying Model Validity

Before any meaningful analysis can be conducted, it is important to verify the validity of the model.

The goal is for the model to behave like a beam on an elastic foundation. The springs should push

up to resist the downward force, but never pull down in the event that one side lifts up out of the

water. Fortunately, the behavior of beams on elastic foundations is well-understood and well-

documented. To verify its validity, the model is tasked with analyzing a previously solved beam


54

on elastic foundation problem. Below are various results from the SAP model and the results of

two solved beam on elastic foundation problems, one using a concentrated moment at the center

and one using two concentrated point loads (Sun). Differences between the two should be expected

since there is nothing pulling uplifted pieces of the bridge back down in the model, but the general

behavior should be similar and recognizable.

Figure 5.1

Figure 5.2 Deflected shape of bridge with concentrated unit moment at the center

Figure 5.3 Moment diagram of bridge with concentrated unit moment at the center


55

Figure 5.4 Shear diagram of bridge with concentrated unit moment at the center

Figure 5.5

Figure 5.6 Deformed shape of bridge with two concentrated unit point loads


56

Figure 5.7 Moment diagram of bridge with two concentrated unit point loads

Obviously, these responses are not identical, but the behavior is indeed very similar. It is

reasonable to say that the model is accurately representing realistic behavior of the bridge.

5.2 Results of Analysis

The SAP2000 model ran analysis for the eight longitudinal and six transverse loading

configuration. Each loading configuration was applied with the ASCE 7-05 load factors in the

Strength I case of 1.2 DL + 1.6LL. The results of the analysis yielded a deflected shape, moment

diagram, and shear diagram. The images are pulled directly from SAP2000 and are annotated with

the largest deflections and the positive and negative moments and shears with the greatest

magnitudes. The deflected shape is measured in inches, and the only real concern is in the U3

direction, i.e. the vertical direction. It should be noted that SAP2000 uses the opposite moment

convention and plots positive moment on the tension side, whereas the American convention plots

positive moment on the compression side. Therefore, the numbers listed next to the images follow

the American sign convention and are the opposite of the values listed in SAP2000 and the moment

diagrams should be flipped. The loading conditions are shown again here for the reader’s ease.

Moment diagrams and the deflected shapes of the bridge for each load combination can be found

in the appendix.


57


58


59

5.2.1. Longitudinal Model – Structural Analysis Results

The maximum values are gathered from the eight longitudinal load combinations. The greatest

positive moment is 68480.44 kip in (5706.70 kip ft) in combination 6. The greatest negative

moment is 66079.59 kip in (5506.53 kip ft) in combination 8. The largest deflection is 68.88 inches

downward in the impossible combination 4 that superimposes the truck load on top of the

pedestrian load. The largest deflection from a possible load combination is 60.41 inches downward

in combination 5.

The results of longitudinal model come in below the strength analysis conducted earlier. The

positive and negative moment capacities are 74924 kip in (6243.7 kip ft) and 71960 kip in (6000

kip ft), respectively, a comfortable amount larger than the worst-case scenarios. Even in the

impossible loading case, combination 4, the top of the deck remains above the bay surface, a

promising show of stability and safety.

It should also be noted that the moment capacity of the bridge after salt water has corroded the

entire bottom layer of steel in all four girders falls to 61000 kip in (5080 kip ft). This value is only

exceeded by load combinations 6 and 7, which are indeed unusual cases. In order for the bridge to

fail, there must be hundreds of pedestrians concentrated in the middle-third of the bridge and the

entire bottom layer of steel must be entirely corroded. Obviously, this does not excuse large crack

widths in a structure submerged in salt water, but it shows the strength of the design.

The continuously supported nature of the bridge certainly helps reduce shear forces felt by the

structure. Although there is no shear analysis here, it is easy to reason that the bridge has plenty of

shear strength. Consider a simply supported beam 248 feet long and 30 feet wide, fully loaded

with the 100psf pedestrian load over entirety of the bridge deck and the 30 kip H-15 truck load

superimposed directly over one of the supports. The shear felt by the beam at the support under

the truck would be half of the entire pedestrian load (due to symmetry) and the entire 15 kip load

of the truck, totaling 387 kips. This is the largest possible shear that the simply supported beam

could feel using these two load combinations in this thought experiment. Clearly, the continuously

support of the floating concrete bridge eases the maximum possible shear, so the real-world

scenario will have even less shear than the 387 kips. Even considering this unrealistic case, bridge

feels a shear significantly less than its longitudinal shear capacity of 451.9 kips. Basically, the

bridge is capable of resisting shear in a much worse scenario than is present in the bridge.

5.2.2. Transverse Model

The maximum values are gathered from the six transverse load combinations. The greatest positive

moment is 659.359 kip in (54.576 kip ft) in combination 1. The greatest negative moment is

403.821 kip in (32.386 kip ft) in combination 4. The largest deflection is 5.75 inches downward in

load combination 3.


60

The results of the transverse model also come in below the strength of the section. The positive

and negative moment capacities a 16-foot portion of the transverse deck is 861.45 kip in (71.79

kip ft), 30% higher than the greatest positive moment and 100% higher than the greatest negative

moment. The maximum deflection of the deck, which stayed under 6 inchers, is certainly well

within acceptable deformation limits. Pedestrians would be able to see the deflection, but would

probably be unable to even feel its effects.

The transverse model also lacks shear analysis, but a worse-case scenario can be similarly

reasoned. The very edges of the transverse have a short cantilever of 18 inches on the outer edges

that are not supported by springs. Therefore, the transverse model will be compared to a cantilever

beam rather than a simply supported beam. Just as before, the deck will be fully loaded with

pedestrians and an H-15 truck will be superimposed on top. The transverse segment in the model

is a 16-foot element of bridge deck with the full 30 foot width. Based on the size of the deck and

the magnitude of the loads, if this was a cantilevered beam, the total shear would be 63 kips. Again,

this value is well below the shear strength of the 16-foot transverse section, which is 117.36 kips.

Even without any steel reinforcement, the concrete provides sufficient shear resistance to a case

much worse than could ever be present in a continuously supported bridge.

Chapter 6: Looking forward

61

CHAPTER 6: LOOKING FORWARD

Based on the report above and the analysis shown, it is reasonable to say that constructing a

pedestrian walkway into the bay waters is not only feasible, but quite plausible. This report

contains a design based largely on the reasonable prescribed vertical loads, namely the pedestrians

that will use the bridge and the maintenance truck that will keep it operational. The mandatory

environmental constraints and regulations, along with supposed needs of the public helped dictate

that the floating concrete bridge would be the structure best-suited for the setting.

In order to emulate the continuous buoyant support from water, the floating concrete bridge was

modeled using 249 discrete springs spaced one foot apart. Under SAP2000 analysis, the bridge

behaved very similarly to the known behavior of a beam on an elastic foundation. This similarity

lent credence to the model’s behavior during actual loading situations.

The cost of the bridge is an important factor to consider. Based on the current design materials and

quantities, a rough cost is developed. Each of the two bridges contains roughly 620 cubic yards of

sand-lightweight 5000 psi concrete, 2,700 cubic yards of expanded polystyrene geofoam, 150,000

lb of #8 bars, 28,800 lb of #6 bars, and 36,000lb of #4 bars, all coated with epoxy. Based on

common material costs, concrete is roughly $75,000 and the epoxy coated rebar is roughly

$80,000. The cost of the EPS geofoam is more difficult to estimate since the shape is quite unusual

and estimates range from about $75,000 to $225,000. These values are each estimates for one

bridge, so the total material cost would be roughly twice that, but probably slightly less since the

formwork and design are identical, amounting to somewhere between $460,000 to $760,000.

Labor costs vary from place to place, but a typical cost for the rebar would be about $25,000, a

cost for pouring concrete could be another $20,000-$30,000 for each bridge. Therefore, the labor

cost of assembling the bridge in the yard would fall within about $45,000-$55,000. Moving the

bridges into place will require renting a tug boat, which can range from about $3,500-$8,000 per

tug. Based on these costs, with a 50% contingency added due to the unusual nature of this job, the

cost comes to about $2,500,000 for both bridges. This is a very large contingency, but this does

not include the installation costs, which are difficult to estimate since the project is unique.

Although rough, this is a good initial cost estimate and an excellent starting place to assess cost

viability.

This design is successful in many ways, but still needs refinement. The design has provides

sufficient moment and shear resistance in the longitudinal and transverse directions, but it has a

problem with cracking. The current design iteration does not pass the stringent crack width

requirements for structures wetted by sea water. This is an extremely important issue since salt

water is highly corrosive to steel. It should be noted, however, that the ACI codes requirements

and equations are intended to calculate crack widths in typical beam sections. The exceptionally

deep and thin web of this beam and the single column of longitudinal steel (no side-by-side

reinforcing bars in any individual girder) are quite unusual and may exhibit different behavior from

what is expected in a typical reinforced concrete girder. In order to gain a better understanding of

the actual cracking in an unusual structure like this, further research may be required, including

laboratory crack tests of the girders.


62

There are a few design changes that could help reduce crack width. One of the best ways to

minimize cracks is to use more, smaller bars in place of fewer, larger bars. This reduces the

concrete area in tension around each individual bar. Unfortunately, using smaller bars reduces the

moment capacity of the section, which, as it currently stands, is pretty close to the existing

moments in some cases. Using more small bars may also necessitate increased web width in order

to supply sufficient concrete cover, which would then increase the area in tension around each bar.

This is a delicate balancing act that can be refined in a more advanced design. Another common

crack control measure is prestressing the concrete, which puts the entirety of a structure in

compression and greatly reduces deflections which cause cracks. Prestressed concrete is also an

expensive process that requires skilled workers to install. Prestressing is very helpful, but it may

not be worth the added cost for a project like this.

The main structural focus of this project was on vertical loads and their combinations and although

these loads are undeniably important to analyze and will control many strength requirements, but

they are certainly not all that is required. This project briefly touched on lateral loading faced by

the bridge, but only in the form of drag force induced by wave and tidal action. Firstly, the tidal

action must be more thoroughly verified. The drag force was calculated using the highest typical

wave speed in the bay. This is a great start, but the bay covers a vast area and wave and tidal speeds

are likely highly variable. The calculation used before also assumes that the velocity is constant

through the depth of the bridge which is fortunately a conservative estimate, since water velocities

are usually highest on the surface. However, the topography of the bay floor and the depth of the

bridge may cause unexpected disruptions in the local water flow. The combination low tides and

large loads could cause the bridge to bottom out near the shore, creating a quasi-damming effect

on the water. If this occurred, concentrated pressures could build and apply unforeseen lateral

forces to the bridge and would be cause for concern, especially if bridge motion became obstructed

by the bay floor. On-site studies would be prudent to predict the possibility of such behaviors and

to more fully understand the tidal flow of the region. Additional lab sensitivity studies attempting

to replicate the environment and its effects on the bridge may also be sensible based on site

conditions. It is important to address these potential issues if design and erection are to progress.

Before any construction begins or further design iterations are made, many of the decisions and

assumptions in this report must be verified. Weighing the construction alternatives was a largely

subjective process. Some considerations, like the financial cost and climate change preparedness,

are more quantitative in nature and are ranked accordingly. Other aspects of the project, like

architecture and community experience, will elicit a wide variety of responses and emotions from

the public based on personal experiences and preferences. In order to gain a better understanding

of the subjective needs, these options should be presented to the community in an unbiased manner

that clearly illustrates their objective strengths and weakness. In doing so, those planning the

project will gain a more holistic understanding of the community’s desires for the structure. It is

entirely possible that the public desires an alternative other than the floating concrete bridge

because they value a certain experience or architectural element over the strengths of the floating

concrete bridge. If that is the case, then the project must surely be amended to fit the community’s

desires, because serving the community is truly the essence of a public works project like this.


63

64

APPENDIX

A.1 Longitudinal Load Combinations

Figure A.1

Load Combination

Moment Diagram

Max positive moment: 1739.132 kip in (144.925 kip ft)

Deflected Shape

Appendix

65

Figure A.2

Load Combination

Moment Diagram


Max negative moment: -12293.97 kip in (-1025.37 kip ft)

Deflected Shape

Appendix

66

Figure A.3

Load Combination

Moment Diagram


Deflected Shape

Appendix

67

Figure A.4

Load Combination

Moment Diagram


Deflected Shape

Appendix

68

Figure A.5

Load Combination

Moment Diagram



Deflected Shape

Appendix

69

Figure A.6

Load Combination

Moment Diagram


Deflected Shape

Appendix

70

Figure A.7

Load Combination

Moment Diagram



Deflected Shape

Appendix

71

Figure A.8

Load Combination

Moment Diagram


Deflected Shape

Appendix

72

A.2 Transverse Loading Combinations

Figure A.9

Load Combination

Moment Diagram


Deflected Shape

Appendix

73

Figure A.10

Load Combination

Moment Diagram


Max negative moment: 327.743 kip in (26.522 kip ft)

Deflected Shape

Appendix

74

Figure A.11

Load Combination

Moment Diagram


Deflected Shape

Appendix

75

Figure A.12

Load Combination

Moment Diagram


Max negative moment: 403.821 kip in (32.386 kip ft)

Deflected Shape

Appendix

76

Figure A.13

Load Combination

Moment Diagram


Deflected Shape

Appendix

77

Figure A.14

Load Combination

Moment Diagram


Deflected Shape

Appendix

78

A.3 Plan Sheets

Appendix

79

Appendix

80

Appendix

81

A.4 Architectural Renderings

Figure A.15 – Aerial View

Figure A.16 – View from E21 looking in

Appendix

82

Figure A.17 – Standing on E22

Figure A.18 – View from E23 ramp looking out

Figure A.19 – Elevation View

Appendix

83

Figure A.19 – Plan View

Works cited

84

WORKS CITED

ACI Committee 318-08. (January 2008) Building Code Requirements for Structural Concrete

(ACI 318-08) and Commentary. Farmington Hills, Mich: American Concrete Institute.

American Association of State Highway and Transportation Officials. (2002). AASHTO LRFD

Bridge Design Specifications, 17th Edition. Washington, D.C: American Association of State

Highway and Transportation Officials.

Americans with Disabilities Act of 1990, Pub. L. No. 101‐336, § 2, 104 Stat 328 (1991)

Barth, Florian & Frosch, Robert J., ACI Committee 224 (May 2001) Control of Cracking in

Concrete Structures (ACI 224R-01). American Concrete Institute.

"CostSection FrameSet." CostSection FrameSet. N.p., n.d. Web. http://www.get-a-

quote.net/QuoteEngine/costbook.asp?WCI=CostSectionFrameSet&SectionId=5639867

Frosch, R. J., 1999, “Another Look at Cracking and Crack Control in Reinforced Concrete,” ACI

Structural Journal, V. 96, No. 3

San Francisco Bay Conservation & Development Commission (2015). San Francisco Bay Plan.

http://www.bcdc.ca.gov/plans/sfbay_plan#9

Sun, Qing-Ping. Chapter Four: Elastic Foundations [PowerPoint slides]. Retrieved from

http://www.me.ust.hk/~meqpsun/Notes/CHAPTER4.pdf

United States of America. United States Access Board Accessible Boating Facilities: A Summary

of Accessibility Guidelines for Recreation Facilities. 1331 F Street, NW, Suite 1000,

Washington, DC 20004-1111: June 2003

http://www.get-a-quote.net/QuoteEngine/costbook.asp?WCI=CostSectionFrameSet&SectionId=5639867

http://www.get-a-quote.net/QuoteEngine/costbook.asp?WCI=CostSectionFrameSet&SectionId=5639867

http://www.bcdc.ca.gov/plans/sfbay_plan#9

http://www.me.ust.hk/~meqpsun/Notes/CHAPTER4.pdf

master's project writeup 9-29

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