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Groveland is a Town in Essex County, Massachusetts. It is 34 miles away from Boston in the north. Groveland is a small residential community with a suburban setting. The town started to develop greatly afterthe 1960s and keep on improving ever since.
According to the US Census Bureau, the total area of Groveland is 9.4 square miles of which about 5% is water. It is located along the Merrimack River, and there are severalother streams and brooks flowing through the town.
Route 97 and 113 enter the town, but there are no interstates passing through it. A single mass transit route leads through the town, operated by the Merrimack Valley Regional Transit authority. TheMBTA Commuter railway terminates from Haverhill, near Groveland.
The first settlers came to the area of Groveland in 1639. Reverend Ezekiel left Rowley, in Yorkshire England with 20 families, because they thought that the Puritan church was at stake there. They aimed the New World, and finally landed in Salem. They could not manage to create an own settlement until the next spring.
Their settlement later became part of Bradford, it was called Rowley on the Merrimack. They got separated in 1672; Bradford, in turn, was annexed by Haverhill. Groveland officially got incorporated on September 9, 1850. Residents of Groveland celebrate the anniversary of this day.
There were 6,459 residents living in Groveland in 2010. This number included 2,346 households and 1,812 families. The population density was 724.8 people per square mile. In 2010, the average household size was 2.75, and the average family size was 3.25.
The age distribution of the town was 24.7% under the age of 18, 6.9% between the ages 18 and 24, 21.3% between the ages 25 and 44, 32.1% between the ages 45 and 64, and 15.1 % who were 65 years or older.
The median household income was $84,232, and the median family income was $95,451. The per capita incomefor the town was $34,254. Approximately 4% of the population was below the poverty line on 2010.
The violent crime rate of Groveland was 0.331 per a thousand people in 2010.
Groveland uses an open town meeting form of government. The registered voters of the town meeting represent the legislative branch of the government, however, any citizen can attend the meetings. The executive branch is represented by the five-member board of selectmen, who serve in their positions for 3 years and are elected by the town’s legislative body. The board of selectmen meets bi-weekly to deal with operational affairs of the town. They work together with the Finance Director, the Town Accountant, and the Finance Committee to create the annual budget.
Groveland belongs to the Pentucket Regional School district, which also includes West Newbury and Merrimac. The district runs the Pentucket regional Middle Schooland the Pentucket Regional Hight School. These schools are located in West Newbury. Groveland also has an own educational institution, the Bagnall Elementary School, that also runs the popular Groveland Summer Recreation Program.
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Shearing Stresses in Reinforced Concrete Beams
The variation of shear in a rectangular reinforced concrete beam may be ascertained by considering a small portion of such a beam between any two sections a small distance, ds, apart, as shown in Fig. 26a, the breadth of the beam being taken as b inches. The forces acting on this bit of beam consist of the normal stresses (C and T) Fm 26 and the shear (V), it being assumed that the moment at BB' is larger than that at AA', and that the sections are so close together that the two shears May be considered equal. These forces are in equilibrium and applying the condition MM = 0. The tendency of the small portion of the, beam cdBA to be pulled to the right is resisted by the horizontal shear on the cd plane which may be expressed as the intensity of shear on that plane (v), assumed to be uniform, multiplied by the area bds. As the concrete is assumed to take no tension, the shear intensity is constant between the neutral plane and the steel while above that plane it varies as in a homogeneous rectangular beam. Accordingly Equation (1) gives the maximum intensity of horizontal, and likewise of vertical, shear (as explained in Art. 50) at any section of a rectangular reinforced concrete beam.
This demonstration applies equally well in essential details to a rectangular concrete beam reinforced for both tension and compression and to a reinforced concrete tee beam. Tests confirm the conclusion that in the matter of shear a tee beam may be considered as equivalent to a rectangular beam of the same depth, with a width equal to that of the stem of the tee beam. The standard notation for this tee beam stem width is b and so for tee beams the formula is written. The value of j does not vary greatly for a wide range of conditions and an average value of 0.86 is usually taken for all shear computations. Since all computations in which the value of the shear is used are highly approximate greater precision than that obtained by the average value is unnecessary.
52. Diagonal Tension in Reinforced Concrete Beams. The concrete in a reinforced beam is no stronger in itself than when unreinforced and it cracks in any loaded beam when the tensile limit is exceeded, the line of cracking being indicated in a general way in Fig. 10, sloping more steeply toward the ends of the beam, tending to lie at right angles to the inclined web stress. The function of the reinforcement is not to prevent cracking, that being impossible, but to keep any one crack from opening up widely, thus compelling the formation of many minute cracks in place of a single large one which would cause failure. It is plain that so long as the cracks are vertical the horizontal bars are effective reinforcement, but where they are inclined horizontal bars are very ineffective, there being nothing but concrete to carry the vertical component of the inclined tension. When a beam is reinforced for normal stress only, failure occurs under small load somewhat as pictured in Fig. 27a, the part of the beam toward the center dropping below the end portion. To be accurate the sketch should show only gradual curves in the steel. There is insufficient strength in the concrete below the rods to the left of the rupture to resist the pressure brought upon it, and it spalls off in such a failure.
A beam is made secure against diagonal tension failure by supplying it with a sufficient amount of reinforcement, so placed as to cross a sufficient number of the inclined lines of potential failure. The more nearly perpendicular to the cracks the more effective are the rods. In practice use is made of stirrups (Fig. 27b) generally vertical, looped about the main steel, and of main longitudinal rods bent up at an angle across the region of diagonal tension stress in those portions of the beam where they are no longer needed to resist the normal tension. In order to proportion such reinforcement knowledge must be had of the amount of the diagonal tension. Unfortunately this cannot be computed accurately in a reinforced concrete beam since the concrete cracks irregularly and just how much tension is taken by the steel it is impossible to say. If there were no normal tension on any section below the neutral axis the maximum diagonal tension would act at 45 degrees and have intensity equal to that of the shear at the section. This is always the assumption made in design. In all discussions of diagonal tension these words from the 1916 Report of the. Joint Committee should be kept in mind: "In designing, resource is hard to the use of calculated vertical shearing stresses as a means of comparing or measuring the diagonal tension stresses developed, it being understood that the vertical shearing stress is not the numerical equivalent of the diagonal tensile stress, and that there is not even a constant ratio between them. It does not seem feasible to make a complete analysis of the action of web reinforcement and more or less empirical methods of calculation are therefore employed. Study of tests indicate that the concrete is effective in resisting small amounts of diagonal tension and may be counted on with safety to perform this duty unaided when the shearing stress is less than about 2 per cent of the ultimate compressive strength of the concrete, about 40 pounds per square inch for ordinary 1-24 mixes. When the shearing stress exceeds this limit, the concrete is ordinarily still counted on as carrying a portion of the diagonal tension.
The use of the shear as a measure of the diagonal tension accounts for the fact that diagonal tension failure and diagonal tension reinforcement are very commonly, and erroneously, spoken of as shear failure and shear reinforcement. It is hardly worth S while to quarrel with this usage so long as it is held clearly in exactly what the terms refer to.
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