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Franklin is a city in Norfolk, Massachusetts, located approximately 35 miles away from Boston in the southwest. Although it has been granted the city title, the city continued using ‘town’ in its official name. Franklin is the home of the USA’s first library, where the first books were donated by Benjamin Franklin.
According to the US Census Bureau, the total area of the city is 27 square miles, of which 1% is water. Most of the marshland around Franklin are protected lands by the Natural Valley Storage Project, created by the US Army Corps of Engineers. Beaver Pond is a popular municipal recreational area, which includes an artificial turf playing, a playground, and different sports fields.
The area of Franklin was first settled in 1660 and it got officially incorporated during the American Revolution of Independence, in 1778. Its name was to be Exeter, however, the citizens chose to name it after one of the founding fathers of the United States, Benjamin Franklin. With this act, Franklin Massachusetts became the first settlement that was named after Benjamin Franklin.
The citizens hoped that Benjamin Franklin would donate a new city bell for them, but instead, he decided to donate 116 books for the city. There was a debate over these books, who should get access to them. Then in 1790, at the end, it was decided that these books would be lent to the residents of the city, so the books were put in the city’s library, which is in service ever since.
As of the census of 2000, there were 32,852 residents in Franklin. Out of this number, there were 10,866 households and 7,877 families. The population density of Franklin was 1,105.4 people per square mile. The average size of a household was 2.8, and the average size of a family was 3.29.
The population was built up with 28.5% under the age of 18,6.5% between 18 and 24, 35.1% between 25 and 44, 19.9% between 46 and 64, and 9.4% of 65 years or older.
The median income in 2000 was $92,066 per household and $81,826 per family. The percapita income for Franklin was $27,849. 3.6% of the city’s population was under the poverty line at the time of the census.
Franklin uses the Council-manager form of government. The elected council responsible for the legislative functions of the city, such as creating policies, or passing ordinances. In this type of government, the role of the mayor is rather ceremonial, as they don’t have any executive functions.
The executive branch is represented by the city manager, whose task is to provide professional management to the board of directors.
Franklin has its own educational system, under the Franklin Public Schools. This system includes six elementary schools, three middle schools, and one high-school. Franklin also has a regional Vocational school and a charter school.
The Dean College is also situated in Franklin, which is a private residential college, opened in 1865. The college grants associate degrees and offers bachelor’s program as well.
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Since the concrete of the original beam carries no tension its outline is shown by dotted lines below the neutral axis, where it serves simply to transmit shearing stresses. Knowing the value of x the rest of the problem follows directly. Although no formulas have been written, all the means are now at hand for the design and investigation of reinforced concrete beams of any shape provided the section is symmetrical about the plane of bending. It is much easier to solve problems by the simple methods that follow logically and simply from the outline just given than it is to use formulas, unless plots and tables are at hand to use with the formulas.
Rectangular Concrete Beams with Tension Reinforcement.
Three problems arise regarding rectangular concrete beams reinforced in tension only:
The problem of design is by far the most common in practice. The beam here shown (Fig. 12a) carries a bending moment of 40,000 ft.-lbs.; E =30,000,000 lbs./sq. in.; E = 2,000,000 lbs./sq. in. What are the maximum fiber stresses? Following the argument of the last article the transformed section is that here given (Fig. 12b) The neutral axis is located by noting that the statically moment of the compression area about that axis (which passes through the center of gravity) equals the statically moment of the tension concrete area about the same axis, giving the expression (10x) = 30(20 —x) 2+6x= 120 Example 6.
What is the maximum moment that can be carried by the beam of Example 5, the limiting fiber stresses being = 16,000 lbs./sq. in. and f, = 650 Ibs./sq. in.? n = 15.2 As before, transform the section (Fig. 12b), locate the neutral axis and determine the arm of the resisting couple, a = 17.2 in. If f, has its maximum value of 650 Ibs./sq. in., C equals X 650 X 10 X 8.4 = 27,300 lbs.; if f5 has its maximum value T equals 16,000 X 2 = 32,000 lbs. If this last value is attained C also equals 32,000 lbs. and f exceeds the limit of 650 lbs./sq. in. It is necessary to limit C and T to 27,300 lbs. each, thus using the steel at a lower stress than the permissible, and the limiting moment accordingly is 27,300 X 17.2 x= 39,100 ft.-lbs. Another, but slightly longer, method of carrying through this problem is to complete the stress diagram by assuming either unit stress as realized. This method of solving a quadratic equation is logical and easily remembered, while solving by use of a memorized formula is a dangerous and foolish strain on that useful mental function, the memory. The standard notation uses the letter n to designate the ratio of the module and it will be employed for that purpose henceforth tripling the actual steel area by a larger value of the ratio of module. Tests show that the use of this higher value is proper and also that the common theory of design gives conservative results. It should be kept in mind that, since the modulus of elasticity for the concrete has been assumed constant, it is not possible to compute the breaking strength or the effect of loads that cause high concrete stresses by the methods outlined here. For such problems it becomes necessary to consider the actual shape of the stress-strain curve for concrete.
Cutting and/or enlarging door, window and bulkhead openings in concrete foundations.
Cutting 1" to 24" diameter perfectly round core holes for electrical, plumbing or vents in concrete floors and foundations.
Cutting and dicing concrete floors, concrete walkways, concrete patios or concrete pool decks for easy removal and/or neat patching.
Cutting trenches in concrete floors for plumbing, electrical, sump pumps, French drains or other utilities.
We cut and remove concrete, stone or masonry walls, floors, walkways, patios and stairs.
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