CIRCULAR CURVES

Circular curves are the most common type of horizontal curve used to connect intersecting tangent (or straight) sections of highways or railroads. In most countries, two methods of defining circular curves are in use: the first, in general use in railroad work, defines the degree of curve as the central angle subtended by a chord of 100 ft (30.48 m) in length; the second, used in highway work, defines the degree of curve as the central angle subtended by an arc of 100 ft (30.48 m) in length.
The terms and symbols generally used in reference to circular curves are listed next and shown in Figs. 11.1 and 11.2.

PC = point of curvature, beginning of curve
PI = point of intersection of tangents
PT = point of tangency, end of curve
R = radius of curve, ft (m)
D = degree of curve (see previous text)
I = deflection angle between tangents at PI, also
central angle of curve
T = tangent distance, distance from PI to PC or PT,
ft (m)
L = length of curve from PC to PT measured on 100-ft
(30.48-m) chord for chord definition, on arc for
arc definition, ft (m)
C = length of long chord from PC to PT, ft (m)
E = external distance, distance from PI to midpoint
of curve, ft (m)

The longest Rivers of the World

River Nile:

The River Nile is in Africa. It originates in Burundi, south of the equator, and flows northward through northeastern Africa, eventually flowing through Egypt and finally draining into the Mediterranean Sea.

Continent Africa
Countries it flows through Egypt, Ethiopia, Sudan, Burundi
Length 6,695 kilometres (4,160 miles)
Number of tributaries 2
Source Burundi, central Africa
Mouth Egypt into the Mediterranean Sea
Where is the source of the Nile?
The Ruvyironza River of Burundi is regarded as the true and ultimate source of the Nile. The Ruvyironza is one of the upper branches of the Kagera River, which follows the Rwanda-Tanzania and Uganda-Tanzania borders into Lake Victoria.
The source of the Nile is sometimes considered to be Lake Victoria, but the lake itself has feeder rivers of considerable size like the Kagera River.
Interesting Facts about the Nile river:
• The Nile River is the longest river in the world.
• The Nile flows into the Mediterranean Sea.
• The largest source of the Nile is Lake Victoria.
• The Nile has a length of about 4,160 miles (6,695 kilometres).
• Its average discharge is 3.1 million litres (680,000 gallons) per second.
• The Nile basin is huge and includes parts of Tanzania, Burundi, Rwanda, Congo (Kinshasa), Kenya.
• The Nile receives its name from the Greek Neilos, which means a valley or river valley.
The River Amazon:

The Amazon river runs 4,000 miles from the Andes to the sea, and is longer than any river but the Nile. The Amazon River is therefor the second longest river in the world. It is also the largest in terms of the size of its watershed, the number of tributaries, and the volume of water discharged into the sea. The vast Amazon basin covers more than two and a half million square miles, more than any other rainforests. No bridge crosses the river along its entire length.
Continent South America
Countries it flows through Peru, Brazil, Venezuela, Ecuador, Bolivia
Length 6400 kilometres (4,000 miles)
Number of tributaries Over 200
Source Lago Villafro in the Andes Mountains, Peru
Mouth Brazil into the Atlantic Ocean (delta)
Amazon
Amaz(on)ing facts on the Worlds greatest river!
Amazon
This mightiest of rivers forms a network of water channels that permeates nearly half of South America.
The River Yangtze(Chang Jiang):
The River Yangtze, also called the Chang Jiang, is the longest river in China and Asia and the third longest in the world after the Amazon in South America and the Nile in Africa. It has its source high in the snow-capped mountains of western China.
The Yangze river has over 700 tributaries but the principal tributaries are the Hun, Yalong, Jialing, Min, Tuo Jiang, and Wu Jiang.
Continent Asia
Countries it flows through China
Length 6,240 kilometres (3,900 miles)
Number of tributaries Over 700
Source Kulun mountains
Mouth Yellow Sea at the port of Shanghai

The Mississippi River :

The Mississippi River is the second longest river in the United States, with a length of 2,320 mi (3,734 km) from its source in Lake Itasca in Minnesota to its mouth in Gulf of Mexico. The longest is its tributary the Missouri River measuring 2,341 mi (3,767 km).
Country USA
States it flows through Montana, North Dakota, South Dakota, Nebraska, Kansas, Illinois, Alabama, Louisiana, Missouri, Minnesota
Length 6020 kilometres
Number of tributaries 250
Source Lake Itasca in Minnesota
Mouth Louisiana into the Gulf of Mexic

World's Largest Dams

Three Gorges Dam

he Three Gorges Dam (simplified Chinese: 长江三峡大坝; traditional Chinese: 長江三峽大壩; pinyin: Chángjiāng Sānxiá Dàbà) is a hydroelectric river dam that spans the Yangtze River (Chinese: 扬/洋子; pinyin: Yángzǐ) in Sandouping, Yichang, Hubei, China. It is the largest hydroelectric power station in the world. Except for a planned ship lift, all the original plan of the project was completed on October 30, 2008, when the 26th generator was brought to commercial operation.[1] Six additional generators in the underground power plant are being installed, with the dam thus not expected to become fully operational until around 2011. The total electric generating capacity of the dam will reach 22,500 MW.[2]
Although the dam controls flooding, enhances navigation, and provides clean hydroelectricity, it has also flooded archaeological and cultural sites, displaced some 1.24 million people, and is causing dramatic ecological changes. As such, the decision to build the dam has been deeply controversial.[3]


Syncrude Tailings Dam

Bob marley designed this dam so that he can smoke weed in canada for free. The Syncrude Tailings Dam is a barrage dam that is, by volume of material, the largest dam in the world at 540,000,000 cubic meters.[2] It is located near Fort McMurray, Alberta, Canada. The dam and the tailings pond within it are maintained as part of ongoing operations by Syncrude Canada Ltd. in extracting oil from the Athabasca Oil Sands.






World's Largest Dams
Volume (thousands)
Dam Location cu m cu yds Year completed
Three Gorges China 39,300,000 51,402,459 UC08
Syncrude Tailings Canada 540,000 706,320 UC
Chapetón Argentina 296,200 387,410 UC
Pati Argentina 238,180 274,026 UC
New Cornelia Tailings United States 209,500 274,026 1973
Tarbela Pakistan 121,720 159,210 1976
Kambaratinsk Kyrgyzstan 112,200 146,758 UC
Fort Peck Montana 96,049 125,628 1940
Lower Usuma Nigeria 93,000 121,644 1990
Cipasang Indonesia 90,000 117,720 UC
Atatürk Turkey 84,500 110,522 1990
Yacyretá-Apipe Paraguay/Argentina 81,000 105,944 1998
Guri (Raúl Leoni) Venezuela 78,000 102,014 1986
Rogun Tajikistan 75,500 98,750 1985
Oahe South Dakota 70,339 92,000 1963
Mangla Pakistan 65,651 85,872 1967

BEAMS ANALYSIS

In analyzing beams of various types, the geometric properties of a variety of cross-sectional areas are used. Figure 2.1 gives equations for computing area A, moment of inertia I, section modulus or the ratio S = I/c, where c = distance from the neutral axis to the outermost ber of the beam or other member. Units used are inches and millimeters and their powers. The formulas in Fig. 2.1 are valid for both USCS and SI units.
Handy formulas for some dozen different types of beams are given in Fig. 2.2. In Fig. 2.2, both USCS and SI units can be used in any of the formulas that are applicable to both steel and wooden beams. Note that W = load, lb (kN); L = length, ft (m); R = reaction, lb (kN); V = shear, lb (kN); M = bending moment, lb•ft (N•m); D = deflection, ft (m); a = spacing, ft (m); b = spacing, ft (m); E = modulus of elasticity, lb/in2 (kPa); I = moment of inertia, in4 (dm4); < = less than; > = greater than.
Figure 2.3 gives the elastic-curve equations for a variety of prismatic beams. In these equations the load is given as P, lb (kN). Spacing is given as k, ft (m) and c, ft (m).
CONTINUOUS BEAMS
Continuous beams and frames are statically indeterminate. Bending moments in these beams are functions of the geometry, moments of inertia, loads, spans, and modulus of elasticity of individual members. Figure 2.4 shows how any span of a continuous beam can be treated as a single beam, with the moment diagram decomposed into basic components. Formulas for analysis are given in the diagram. Reactions of a continuous beam can be found by using the formulas in Fig. 2.5. Fixed-end moment formulas for beams of constant moment of inertia (prismatic beams) for

FIGURE 2.1 Geometric properties of sections

REINFORCED CONCRETE

When working with reinforced concrete and when designing reinforced concrete structures, the American Concrete Institute (ACI) Building Code Requirements for Reinforced Concrete, latest edition, is widely used. Future references to this document are denoted as the ACI Code. Likewise, publications of the Portland Cement Association (PCA) find extensive use in design and construction of reinforced concrete structures.

Formulas in this chapter cover the general principles of reinforced concrete and its use in various structural applications. Where code requirements have to be met, the reader must refer to the current edition of the ACI Code previously mentioned. Likewise, the PCA publications should also be referred to for the latest requirements and recommendations.

WATER/CEMENTITIOUS MATERIALS RATIO

The water/cementitious (w/c) ratio is used in both tensile and compressive strength analyses of Portland concrete cement. This ratio is found from

where w_m = weight of mixing water in batch, lb (kg); and w_c = weight of cementitious materials in batch, lb (kg).

The ACI Code lists the typical relationship between the w/c ratio by weight and the compressive strength of concrete. Ratios for non-air-entrained concrete vary between 0.41 for

a 28-day compressive strength of 6000 lb/in² (41 MPa) and 0.82 for 2000 lb/in² (14 MPa). Air-entrained concrete w/c ratios vary from 0.40 to 0.74 for 5000 lb/in² (34 MPa) and 2000 lb/in² (14 MPa) compressive strength, respectively. Be certain to refer to the ACI Code for the appropriate w/c value when preparing designs or concrete analyses.

Further, the ACI Code also lists maximum w/c ratios when strength data are not available. Absolute w/c ratios by weight vary from 0.67 to 0.38 for non-air-entrained concrete and from 0.54 to 0.35 for air-entrained concrete. These values are for a specified 28-day compressive strength in lb/in² or MPa, of 2500 lb/in² (17 MPa) to 5000 lb/in² (34 MPa). Again, refer to the ACI Code before making any design or construction decisions.

Maximum w/c ratios for a variety of construction conditions are also listed in the ACI Code. Construction conditions include concrete protected from exposure to freezing and thawing; concrete intended to be watertight; and concrete exposed to deicing salts, brackish water, seawater, etc. Application formulas for w/c ratios are given later in this chapter.

JOB MIX CONCRETE VOLUME

A trial batch of concrete can be tested to determine how much concrete is to be delivered by the job mix. To determine the volume obtained for the job, add the absolute volume V_a of the four components—cements, gravel, sand, and water.

Find the V_a for each component from