For our participation in establishing a workplace for our EMAT 4450/6450 class to visit, Roy Jones and I have contacted a diverse firm comprised of engineers, architects, as well as construction managers. Armentrout Roebuck Matheny Consulting Group, P.C. is located here in Athens, GA and provides the local, the national and the international communities with several types of services. These services range from architectural design and project cost analysis to site development and project management. With approximately 25 employees, ARMCG has completed projects here on the UGA campus, locally throughout the state of Georgia and internationally in countries like Granada and Venezuela.
On Wednesday February 16, 2005, we met with Mr. Bret Thurmond, the firm's project manager in charge of international business development. He described the roles of his colleagues in the design world and we discussed the many ways in which they use mathematics to fulfill their professional duties. During our visit, Mr. Thurmond offered some great examples of real life math problems that they face every day.
Architectural and Structural
ARMCG provides a wide range of architectural, structural, and engineering services. They have designed industrial facilities, schools, office buildings, hospitals and government buildings. Their services include complete design, adaptive re-use of historic buildings, and modifying existing structures. All of these processes involve a variety of mathematical problems, concepts and processes.
While in the design phase of a project, ARMCG must be familiar with national, state, and local building codes. Building codes describe particular standards for design and construction, and it is often the responsibility of the architect to ensure these requirements are met. For example, the national building code describes how many exits are necessary in the building, based on the building's type and total area in square footage. ARMCG must compute the total area, and then find the corresponding amount of required exits. Even the size and placements of the exits must be designed according to code, so the architect must constantly refer to different code requirements and compute whatever values are necessary. ARMCG will need to know the area of the proposed design, the area of the surrounding site, and even an estimate of the project's occupant load, in order to compute many values required by building codes. The ADA Accessibility Guidelines also must be followed by law. Designed to protect building occupants with disabilities, ADA specifically describes such things as the slopes of ramps, or even the minimum length and width of a bathroom stall. These guidelines must be strictly followed and the designers must understand the mathematical terms that are used, such as the maximum slope of a ramp. This must be a ratio of 1:12, which means for every 1'-0" of rise, there must also be 12'-0" of run.
Percentages of areas become especially important when initially developing a design. For example, the client could specify that their budget is only large enough for a specific size of building. Usually, this size is expressed as an area in square feet. The client can then communicate with the architect in terms of percentages, such as 15%-20% of the floor plan must be reserved for the stock room and other service areas. It is important for the architect to understand ratios and percentages, in order to successfully design the building for the client. So ARMCG, as with any design firm, regularly communicates with their clients to ensure the design requirements are being met.
While designing a building, an addition, or a renovation, ARMCG uses computer programs, such as AutoCAD, to make their information and drawings electronic. During an addition or renovation, ARMCG must first measure the existing building in the field so it can be drawn on the computer. To do this, they may use a standard tape measure or a laser device for longer distances. It is important that these measurements be taken accurately to make sure that the new design will fit with the existing building properly. These quantities of lengths and areas are usually kept in terms of inches and feet, so it is important for the employees to understand the mathematical operations associated with these quantities. For example, any particular length could be represented not only as a decimal in terms of feet, but also as a fraction or in terms of inches (1.25ft = 1 1/4ft = 15 in). So there are different ways to compute these quantities depending on the type of units that are chosen. These lengths are then represented by lines electronically in AutoCAD.
Within AutoCAD, there are many mathematical operations available to the designer such as computation of areas, lengths, volumes, and ratios. Drawing and designing electronically not only saves time, but also it allows the computer program to help with these necessary math calculations. While drawing in AutoCAD, the designer is able to immediately translate lines a certain distance along the x or y-axes. Also throughout the drawing process, the designer must continually compute the proper printing scale for the drawings, to make his drawings print at a certain size depending on the size. This size will be dependent on the size of the paper that is used. Typically, standard full size drawings are on 24" x 36" paper. A series of mathematical conversions are necessary to ensure the printed drawing is not too large, or too small, for the size paper being used.
Scaling is particularly important for ARMCG in their industry. They are drawing plans, sections, elevations, and details for construction. These drawings are going to be used by the clients, contractors, and other professionals in order to understand and construct the layout of the building. It is mostly through drawings that these different professions communicate. It is very important that the scales of these drawings stay consistent and can be measured by those in the field who are assembling the structure. For example, a plan drawing may be drawn at 1/8" for every 1'-0", while details may be drawn at 3" for every 1'-0". Professionals in this industry have special rulers they uses as tools to measure these drawings. The architectural or engineering scale is a six-sided ruler that contains common conversions typically used in this industry. One side of the architectural scale is divided into 1/8" segments that each represents 1'-0". This is helpful for measuring a drawing that has been drawn in that scale. Without understanding the standard scaling of drawings, the drawing would be mostly unreadable and useless to those trying to design the drawing, or to construct from it. These quantities of lengths and scaling are represented directly on the drawings.
Another part of ARMCG responsibilities is cost
estimating and bidding. They must consult different materials
manuals and manufacturers to estimate a total cost for the project.
These calculations require total area assessment, counting specific
materials (windows, for example), and pricing of different services.
Ideally, the cost will be kept to a minimum in order to competitively
bid a project. Design projects are usually awarded to the firm
that is most cost effective, and so ARMCG must work hard to compute
accurate estimates.
Environmental and Site Planning
In addition to architectural and structural services, ARMCG also offers assistance in storm water and wetlands permitting. When dealing with these types of projects, the environmental engineer must again be familiar with local codes and zoning ordinances. For example, an engineer will have to figure the most efficient way to drain water from a site, depending on the topography. There are many types of calculations associated with site area, volume, and the percentage of slope of the land. Another important feature to maximize site design is a process of cut and fill. For an uneven site, ARMCG is required to calculate the amount of land that must be cut from the high side, and then filled in on the low side, to make the site level. Removing too much land would be costly to replace, and removing too little land would be ineffective. There are many mathematical computations involving land volume for site design.
Along with site development, ARMCG must be
familiar with local ordinances for specific requirements. Local
ordinances contain information such as what percentage of the
land has to be "green" (i.e. trees, bushes, etc.), and
what percentage of the land the building can rest on. There are
specific laws that dictate how far a building is required to be
set back from the road or drainage areas. It is important for
an environmental engineer, or any design professional, to understand
these restrictions and plan accordingly. Without full compliance,
the client as well as the firm could suffer costly setbacks and
be denied the necessary permits to construct the building.
Construction Management
During the construction management phase of
any project, ARMCG is involved in monitoring construction activities
for compliance with quality standards. They are also required
to manage the cash flow as compared to the project's overall budget.
This kind of process involves compiling spreadsheets and utilizing
other computational based software. Invoices are prepared as a
way to continually keep track of all the money involved with the
project.
Office
Management
Managing an office of this size also requires
the daily use of mathematics. From employee payroll, to the ordering
of new equipment and materials, the ARMCG managers must continually
review their daily budgets and expenses. As with any professional
office, money they make on each project has to be allotted to
paying their employees, office overhead expenses, and improving
their business.
With any design firm, it is important for employees
to keep track of their billable hours per project. Billable hours
are defined as hours spent on a project that can be directly billed
to the client. For example, time spent meeting with the client
would be considered billable, where as time spent for a general
office meeting would not be. Since clients are usually billed
based on number of hours spent working for them, ARMCG has specific
computer software to compute the total hours for the type of services
that have been provided. For example, if 40 hours in one week
is spent on the same project, it is important to note if only
10 of those hours were on the design development phase, where
as the remaining 30 were spent on drawing construction documents.
If the client is not charged a fixed fee for the project but is
charged based on the types of services provided, it is important
to show the client the breakdown in hours and bill them accordingly,
since some services are more costly. As an effort to minimize
the overall cost it is very important to accurately keep track
of hours and correctly bill the client.
Conclusion
Our class field trip to Armentrout Roebuck
Matheny Consulting Group is scheduled for April 06, 2005 at 2:30pm.
The presentation will include various examples of the mathematics
required for ARMCG to complete their professional duties, and
will include quite a few visual materials such as scaled drawings,
spreadsheets, and different building codes. After the presentation,
we will take a quick tour of their office space. With the wide
variety of professional services that are offered by ARMCG, and
the extensive mathematics that are involved for ARMCG to fulfill
their obligations, we feel that this class trip will be very enlightening
to us as future teachers of secondary mathematics.
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