Pushing the Mathematical Envelope

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Pushing the Mathematical Envelope
Case Studies in Solving Modern Civil and Structural Engineering Calculations Challenges

Like engineers in every major discipline, civil and structural engineers are facing an expanded array
of mathematical challenges. Now more than ever, societies are placing a greater emphasis on:
• Environmental issues – protecting and preserving natural resources
• Sustainability – as the global population grows and the human footprint expands
• Socially supportive, intelligent infrastructure – as societies become more sophisticated and
demand greater efficiency and real-time results
For civil and structural engineers, accurate and intelligent system models – and the complex mathematics that they require – are at the core of meeting these sophisticated, modern challenges.
The need to accurately model infrastructure and utilities, environmental systems, urban planning
and large architectural projects has never been more critical – and difficult. Engineers are facing
unprecedented pressure to get it right the first time under increased regulatory oversight.
The engineering calculations that can solve these
issues are complex and difficult to manage. It is no
longer sufficient to have these calculations, an organization’s intellectual property, locked away in spreadsheets and traditional engineering notebooks.
The good news is that mathematical technology has
evolved to give engineers solutions that, if used properly, can be very effective. Design and calculation
software gives civil and structural engineers the tools
to solve today’s most pressing and complex problems,
and innovate like never before.
This article will discuss modern civil and structural
engineering projects where complex engineering
mathematics has been at the heart of overcoming
these new challenges. Specifically, we will look at
engineers who are:
• Designing sustainable buildings like the Shanghai
Tower that can withstand a broad range of environmental conditions and disasters
• Protecting water resources in Virginia
• Working with the Australian Aid program to construct infrastructure that can meet the demands of
aging populations and increased urbanization
Page 1 of 5 | Pushing the Mathematical Envelope

At 662 meters tall, the Shanghai Tower, shown under construction on the left, will become the second tallest building on earth
upon completion in 2014..

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The Shanghai Tower: A Case Study in
Sustainable Design
Economic and political factors are putting pressure on
engineers and designers to make decisions today that
will minimize environmental impacts on future generations. Sustainable design is especially important
for large structures, where the challenge is to design
buildings that can withstands these environmental
disasters while minimizing energy consumption and
materials.
At 662 meters tall, the Shanghai Tower will become
the second tallest building on earth upon completion
in 2014. Lead designer, Peter Weingarten, knows full
well that it took years for engineers just to figure out
how to get super-tall buildings to stand at all. “Once
you get above 80 stories, most private brokers will tell
you that the economics of the building don’t pan out,
because you have so many structural considerations
because of the lateral load,” he says in an interview
with CleanTechies.
But today, using advanced problem-solving techniques and engineering calculation software, vertical cities like the Shanghai Tower aren’t only possible,
they’re at the forefront of the green building revolution.
The structure sets a new standard in sustainability by
including the following features:

tions need to account for curvature and other properties of the aerodynamic structure, which requires more
advanced and comprehensive calculations.

Overcoming Civil and Structural
Engineering Challenges Requires
Sophisticated Calculations
Advances in math calculation software ensure
accuracy and mitigate risk.

Challenge

Design sustainable
buildings that
can withstand
environmental
factors and natural
disasters

• A twisted shape design that reduces structural
steel by more than 20 percent
Weingarten admits that one of the biggest challenges
his team faced was the wind force near the top of the
building. A unique, curved shape not only solved the
problem, but also cut steel costs by nearly a quarter.
“We were able to save 25 percent of the ton steel tonnage
by not presenting a broad face to the wind,” Weingarten
reveals. “By allowing the wind to flow aerodynamically
we mitigate direct lateral pressures. We also made use
of the Diagrid System, which allows the wind to flow in
a natural way instead of orthogonally like with classic
designs.” Traditional lateral load and force calcula-


• Lateral load
• Maximal lateral
impulse force
• Equivalent static
analysis
• Response spectrum
analysis
• Linear dynamic
analysis
• Non-linear static
analysis
• Non-linear dynamic
analysis

• Wind turbines that can generate up to 350,000 kWh
of electricity per year
• A rainwater recycling system

Calculations
Required

Conduct watershed
studies to protect
water resources

• Fluid mechanics and
hydrology
• Computational fluid
dynamics
• Fluid structure
interactions

Examine impact of
population growth
on infrastructure
and resources

• Rate of natural
increase
• Demographic transition
modeling
• Carrying capacity

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In addition to its special, aerodynamic shape, the
Shanghai Tower incorporates what’s called an outrigger truss every 14 floors for greater support. Each
outrigger truss “acts like your shoulder” to broaden the
base of the building, according to Weingarten. Structures that involve reinforced support systems, such as
outrigger trusses, typically require intensive linear and
nonlinear static and dynamic analysis of the complete
structure and its components. Using an engineering
software package is essential to getting this right.
Because the building will be sturdier, the designers
were able to engineer additional sustainability features, such as a double skin. According to Gensler’s
Dan Winey, while the double skin is “an ode to the city’s
historic open courtyards,” the design has definite
sustainability benefits: “The continuous glass skin will
admit the maximum amount of daylight into the atriums,
reducing the need for artificial lighting,” Winey says.
“The glass also has a spectrally selective low-E coating
that will help reduce heating and cooling loads.”

At the Center for Watershed Studies at the Virginia
Polytechnic Institute and State University (Virginia
Tech) , biological systems engineers are using a geographic information system (GIS) to help the State of
Virginia correct the way it calculates sediment volume
in rivers and streams in an effort to reduce erosion.
Up until now, the state has directed its efforts toward
reducing erosion from agricultural and urban lands,
while ignoring another major source of sediment –
stream bank erosion. Due to complexity and a lack of
physically based algorithms to describe the process,
the quantification of stream bank erosion has been
significantly underestimated.

As Weingarten explains:
“We built a space between the inner skin and what’s
really the facade of the building to create a series of
vertical parks that act as a thermal buffer between
the face of the building and the outside world. Instead
of having a completely opaque building you have a
clear one. Most skyscrapers are essentially opaque
to the outside because of the high reflectivity of their
windows, a necessity to limit solar heat gain.”

Channel Erosion Quantification: A Case Study in
Watershed Protection
While some engineers focus on the sustainability of
man-made constructions, others are working hard to
maintain the sustainability of natural structures like
watersheds. Unhealthy watersheds can have a negative impact on drinking water supplies, recreational
opportunities, and the food chain, so it’s important to
come up with ways to minimize pollution, erosion and
other threats to the world’s freshwater ecosystems.


Researchers at the Center for Watershed Studies at the Virginia
Polytechnic Institute and State University (Virginia Tech) are
working to ensure that stream bank erosion is accurately calculated in erosion models.

The engineering researchers at Virginia Tech are
working to develop new models and statistical calculations to more accurately estimate sediment loading
from stream channel degradation. This will require
study of fluid structure interactions, mathematical equations of fluid mechanics and hydrology, and
computational fluid dynamics modeling. They intend to
incorporate their results into a long-term plan to help
ensure that stream bank erosion is accurately calculated into the erosion model.

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AusAID: A Case Study in Sustainable Infrastructure
The quality of life in the world’s cities is dependent on
the health and sustainability of urban infrastructure.
To ensure infrastructure success, modern engineers
are implementing technologies that fall under the
umbrella of “intelligent infrastructure.” According to a
report by the Organisation for Economic Co-Operation
and Development (OECD), civil and structural engineers will be called upon to explore:
• Decision support models and automation in the
electricity sector, which can help optimize generation capacity, transmission lines and the grid. Distribution losses could be reduced, peak consumption better handled, reliability enhanced and the
environment better protected
• Intelligent system modeling technologies in the
water sector, which can provide a greater ability to
monitor and control the water cycle in real time. At
the local or end-user level, the virtual closing of
the water cycle can also be monitored with sensors,
embedded software and artificial intelligence
• Integrating multiple alternative wireless technologies (AWT) into a single multi-service platform in
telecommunications systems, which can lead to
a highly simplified infrastructure including selfhealing and self-organizing networks. Such integration could, for example, facilitate the creation of
integrated health care systems, or “smart house”
concepts for the elderly

In Papua, New Guinea, transport infrastructure improvements are
essential for the efficient flow of produce to markets and for the
provision of goods and services to rural and urban communities.


• Intelligent highway systems and advanced vehicle
technologies in land transportation, which could
bring substantial benefits to network management,
accident response, driver information and road/rail
capacity
Mathematical models will play a key role in meeting
these objectives. Computationally understanding fundamental factors such as carrying capacity, demographic transition, and rate of natural increase will
be critical pieces necessary to measure progress and
assess where the gaps are.
The Australian Aid program (AusAID), a governmentrun agency, is using infrastructure investments to
lift economic growth and support social objectives
in neighboring countries in East Asia and the Pacific,
with an expanding effort in South Asia and sub Saharan Africa. AusAID’s approach to infrastructure
improvement centers on four pillars:
1. Delivering sustainable transport infrastructure
2. Facilitating increased access to basic water and
sanitation services
3. Creating reliable energy services and supporting
information and communication technologies
4. Supporting urban infrastructure planning and
development
Through the Economic Infrastructure Initiative
approved in 2009/10, AusAID provides funding for high
priority infrastructure, strengthening the capacity of
partner governments’ agencies to respond to rapid
urbanization, and promoting conditions for increased
infrastructure financing. AusAID is also putting an
increased focus on sub-national governments, in
recognition of the decentralization of infrastructure
planning and delivery taking place throughout the
developing world.
In Indonesia, AusAID is supporting a major national
roads program. In Papua, New Guinea, the organization is helping to improve processes for the planning
and delivery of transport infrastructure. And in the
Greater Mekong, AusAID is looking to support infrastructure programs that promote regional integration.

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Conclusion

Sources

The extent to which today’s civil and structural engineers can overcome major design and environmental
challenges will have a tremendous impact on human
societies for generations to come.

Arlein, Jacob (2010). “The Shanghai Tower: The Beginnings
of a Green Revolution in China,” CleanTechies, March 25,
2010. Retrieved March 2012 from: http://www.matternetwork.com/2010/3/shanghai-tower-beginnings-green-revolution.cfm

Designing sustainable structures, preserving natural resources and meeting the infrastructure needs
of changing populations – all within budgets acceptable to governments and private citizens alike – will
require extraordinary effort and ingenuity.
Engineers will also continue to rely on technological
advances to help them meet current and future challenges. Enhanced computer power and design software will increase performance, and sophisticated
calculation software will help ensure accuracy and
mitigate risk.

NOTE: The timing of any product release, including any features or functionality,
is subject to change at PTC’s discretion.
© 2012, PTC. All rights reserved. Information described herein is furnished for
informational use only, is subject to change without notice, and should not be construed as a guarantee, commitment, condition or offer by PTC. PTC, the PTC Logo,
PTC Creo Elements/Pro, and all PTC product names and logos are trademarks
or registered trademarks of PTC and/or its subsidiaries in the United States and
in other countries. All other product or company names are property of their
respective owners. The timing of any product release, including any features or
functionality, is subject to change at PTC’s discretion.

“Developing Strategies for Urban Channel Erosion Quantification in Upland Coastal Zone Streams,” Center for Watershed Studies at Virginia Tech, 2010. Retrieved March 2012
from: http://www.cws.bse.vt.edu/index.php/research/
project/developing_strategies_for_urban_channel_erosion_quantification_in_upla
Infrastructure to 2030: Telecom, Land Transport, Water and
Electricity, OECD Publishing, 2006.
“Sustainable Economic Development: Infrastructure Thematic Strategy,” AusAID, 2011. Retrieved May 2012 from:
http://www.ausaid.gov.au/aidissues/infrastructure/Pages/
home.aspx
Winey, Dan (2011). “Shanghai Tower: Sustainable Strategies in a Super Tall Building,” GenslerOnCities, July 18, 2011.
Retrieved May 2012 from: http://www.gensleron.com/cities/2011/7/18/shanghai-tower-sustainable-strategies-in-asuper-tall-buildi.html

J0767-MC-Pushing-Envelope-WP–EN–0912


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Pushing the Mathematical Envelope

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