A beam, in Structural Engineering terms, is a member that can be comprised of a number of materials (including steel, wood aluminum) to withstand loads – typically applied laterally to the beam axis. Beams can also be referred to members, elements, rafters, shafts or purling.
A beam can exist within a frame, a truss or on its own as its own structure. SkyCiv also has some write ups of each of the different types of beams, including cantilever beam, or continuous beam.
Beams can come in a wide range of shapes that have different applications and strength purposes. Some common shapes are i beams (as shown in the 3D renderer above), T-beams, channel sections, rectangular, hollow rectangular and pipes. Regardless of the shape, they are all considered beams. In analysis and design, they are often picked up from different manufacturer libraries and databases so that the industry is all modeling structures based on the same shapes and dimensions.
Types of Beams
Support Configuration
The most common way that structural engineers classify beams is by their support configuration, there are many possible configurations however, these are the 4 most common types:
Simply supported beams are defined as having two supports at either end – one pinned and one roller. This is generally considered as being the most simple type of beam. This is a very common type of beam and is determinate because there are three equilibrium equations and only 3 unknown reactions. 2 from the pinned support and 1 from the roller support.
Cantilever Beams are supported from one end, using a Fixed Support. This is the only type of support that can be used in this scenario as it offers the moment resistance required for the beam to remain stable. If a pinned or roller support was used, it would not offer the moment restraint that the beam would need. A good example of a cantilever beam is a shop awning – where the beam is bolted directly into the wall. This is also a determinate beam because there are only 3 unknown reactions which, is equal to the number of equilibrium equations available.
Continuous beams are multi-spanned beams that have multiple supports across the length of the beam. An example of a continuous beam would be a single beam that is supported by a number of columns along its length. This beam is indeterminate since there are more unknown reactions (6) than equilibrium equations available (3). This is then called a level 3 indeterminate beam.
Fixed Beams have fixed supports at either end – offering moment resistance at either end. This type of beam may be used when the designer wants to control the deflection at the mid-span because the two fixed supports prevent rotation. This beam is also indeterminate as the unknown reactions (6) are greater than the equations available (3). This is also a level 3 indeterminate beam.
Overhanging beams are those with two supports, but unlike simply supported beams, one of the supports is not at the end of the member. A typical example of this is a balcony which is being extended from a frame structure. The frame offers the two supports, yet no support exists at the end of the member – allowing it to ‘overhang’ as the name suggests. This too is an indeterminate beam as the number of unknown reactions (4) is greater than equilibrium equations (3). This is a level 1 indeterminate beam.
It is the Basic Components Of A Building You Should Know of a building situated underneath the surrounding ground.
2- SUPERSTRUCTURE
The portion which is situated above the ground level is called superstructure. The components of a building can be further classified as under
1- FOUNDATION
Foundation is the lowest part of a structure below the ground level which transfers all the loads (dead load, live load etc) to the soil.
2- PLINTH
The Portion of a building between the ground surrounding the building and the top floor just above the ground is termed as plinth. Plinth is provided to prevent the surface water from entering the building.
building.
3- DPC
DPC or damp proof course is a layer of waterproofing materials like asphalt, bitumen, waterproof cement etc on which the walls are constructed.
4- WALLS
Walls are the vertical members on which the roof finally rests. Walls are provided to divide the floor space in the desired pattern. Walls provide privacy, security, and protects from the sun, rain wind, cold etc.
5- COLUMN
Columns are the isolated load bearing member which carry the axial compressive load of a structure.
6- FLOORS
Floors can be defined as flat supporting elements dividing a building into different levels ( e.g first floor, second floor etc) to create more accommodation on a given land. They provide a firm and dry platform for people and other items like furniture, equipment, stores etc.
7- DOORS, WINDOWS, AND VENTILATION
Doors are provided as a barrier secured in an opening left in a wall to access the building, room or passage. A window may be defined as an opening left in a wall for the purpose of providing daylight, vision, natural air, and ventilation.
8- STAIRS
Stairs can be defined as a structure comprising a number of steps arranged in a series connecting one floor to another. Stairs are used to access various floors of the building.
9- ROOF
A roof is the topmost part of a building which covers the space below and protects from rain, direct sunlight, snow, the wind etc.
10- BUILDING FINISHES
Building finishes include items like plastering, pointing, washing, varnishing, painting, dis-tempering etc.
1- BUILDING SERVICES
Building services include services like water supply, drainage, lighting, sanitation, electricity, acoustics, ventilation, heating, air conditioning, fire detection, and control etc.
Geodetic surveys involve such extensive areas that allowance must be made for the Earth’s curvature. Baseline measurements for classical triangulation (the basic survey method that consists of accurately measuring a base line and computing other locations by angle measurement) are therefore reduced to sea-level length to start computations, and corrections are made for spherical excess in the angular determinations. Geodetic operations are classified into four “orders,” according to accuracy, the first-order surveys having the smallest permissible error. Primary triangulation is performed under rigid specifications to assure first-order accuracy.
Efforts are now under way to extend and tie together existing continental networks by satellite triangulation so as to facilitate the adjustment of all major geodetic surveys into a single world datum and determine the size and shape of the Earth spheroid with much greater accuracy than heretofore obtained. At the same time, current national networks will be strengthened, while the remaining amount of work to be done may be somewhat reduced. Satellite triangulation became operational in the United States in 1963 with observations by Rebound A-13, launched that year, and some prior work using the Echo 1 and Echo 2 passive reflecting satellites. The first satellite specifically designed for geodetic work, Pageos 1, was launched in 1966.
A first requirement for topographic mapping of a given area is an adequate pattern of horizontal and vertical control points, and an initial step is the assembly of all such existing information. This consists of descriptions of points for which positions (in terms of latitude and longitude) and elevations above mean sea level have been determined. They are occasionally located at some distance from the immediate project, in which case it is necessary to expand from the existing work. This is usually done on second- or third-order standards, depending upon the length of circuits involved.
The accuracy of survey measurements can be improved almost indefinitely but only at increased cost. Accordingly, control surveys are used; these consist of a comparatively few accurate measurements that cover the area of the project and from which short, less accurate measurements are made to the objects to be located. The simplest form of horizontal control is the traverse, which consists of a series of marked stations connected by measured courses and the measured angles between them. When such a series of distances and angles returns to its point of beginning or begins and ends at stations of superior (more accurate) control, it can be checked and the small errors of measurement adjusted for mathematical consistency. By assuming or measuring a direction of one of the courses and rectangular coordinates of one of the stations, the rectangular coordinates of all the stations can be computed.
A system of triangles usually affords superior horizontal control. All of the angles and at least one side (the base) of the triangulation system are measured. Though several arrangements can be used, one of the best is the quadrangle or a chain of quadrangles. Each quadrangle, with its four sides and two diagonals, provides eight angles that are measured. To be geometrically consistent, the angles must satisfy three so-called angle equations and one side equation. That is to say the three angles of each triangle, which add to 180°, must be of such sizes that computation through any set of adjacent triangles within the quadrangles will give the same values for any side. Ideally, the quadrangles should be parallelograms. If the system is connected with previously determined stations, the new system must fit the established measurements.
When the survey encompasses an area large enough for the Earth’s curvature to be a factor, an imaginary mathematical representation of the Earth must be employed as a reference surface. A level surface at mean sea level is considered to represent the Earth’s size and shape, and this is called the geoid. Because of gravity anomalies, the geoid is irregular; however, it is very nearly the surface generated by an ellipse rotating on its minor axis—i.e., an ellipsoid slightly flattened at the ends, or oblate. Such a figure is called a spheroid. Several have been computed by various authorities; the one usually used as a reference surface by English-speaking nations is (Alexander Ross) Clarke’s Spheroid of 1866. This oblate spheroid has a polar diameter about 27 miles (43 kilometres) less than its diameter at the Equator.
Because the directions of gravity converge toward the geoid, a length of the Earth’s surface measured above the geoid must be reduced to its sea-level equivalent—i.e., to that of the geoid. These lengths are assumed to be the distances, measured on the spheroid, between the extended lines of gravity down to the spheroid from the ends of the measured lengths on the actual surface of the Earth. The positions of the survey stations on the Earth’s surface are given in spherical coordinates.
Bench marks, or marked points on the Earth’s surface, connected by precise leveling constitute the vertical controls of surveying. The elevations of bench marks are given in terms of their heights above a selected level surface called a datum. In large-level surveys the usual datum is the geoid. The elevation taken as zero for the reference datum is the height of mean sea level determined by a series of observations at various points along the seashore taken continuously for a period of 19 years or more. Because mean sea level is not quite the same as the geoid, probably because of ocean currents, in adjusting the level grid for the United States and Canada all heights determined for mean sea level have been held at zero elevation.
Because the level surfaces, determined by leveling, are distorted slightly in the area toward the Earth’s poles (because of the reduction in centrifugal force and the increase in the force of gravity at higher latitudes), the distances between the surfaces and the geoid do not exactly represent the surfaces’ heights from the geoid. To correct these distortions, orthometric corrections must be applied to long lines of levels at high altitudes that have a north–south trend.
Trigonometric leveling often is necessary where accurate elevations are not available or when the elevations of inaccessible points must be determined. From two points of known position and elevation, the horizontal position of the unknown point is found by triangulation, and the vertical angles from the known points are measured. The differences in elevation from each of the known points to the unknown point can be computed trigonometrically.
The National Ocean Service in recent years has hoped to increase the density of horizontal control to the extent that no location in the United States will be farther than 50 miles (80 kilometres) from a primary point, and advances anticipated in analytic phototriangulation suggest that the envisioned density of control may soon suffice insofar as topographic mapping is concerned. Existing densities of control in Britain and much of western Europe are already adequate for mapping and cadastral surveys.
Surveying, a means of making relatively large-scale, accurate measurements of the Earth’s surfaces. It includes the determination of the measurement data, the reduction and interpretation of the data to usable form, and, conversely, the establishment of relative position and size according to given measurement requirements. Thus, surveying has two similar but opposite functions: (1) the determination of existing relative horizontal and vertical position, such as that used for the process of mapping, and (2) the establishment of marks to control construction or to indicate land boundaries.
Surveying has been an essential element in the development of the human environment for so many centuries that its importance is often forgotten. It is an imperative requirement in the planning and execution of nearly every form of construction. Surveying was essential at the dawn of history, and some of the most significant scientific discoveries could never have been implemented were it not for the contribution of surveying. Its principal modern uses are in the fields of transportation, building, apportionment of land, and communications.
Except for minor details of technique and the use of one or two minor hand-held instruments, surveying is much the same throughout the world. The methods are a reflection of the instruments, manufactured chiefly in Switzerland, Austria, Great Britain, the United States, Japan, and Germany. Instruments made in Japan are similar to those made in the West.
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History
It is quite probable that surveying had its origin in ancient Egypt. The Great Pyramid of Khufu at Giza was built about 2700 BCE, 755 feet (230 metres) long and 481 feet (147 metres) high. Its nearly perfect squareness and north–south orientation affirm the ancient Egyptians’ command of surveying.
Evidence of some form of boundary surveying as early as 1400 BCE has been found in the fertile valleys and plains of the Tigris, Euphrates, and Nile rivers. Clay tablets of the Sumerians show records of land measurement and plans of cities and nearby agricultural areas. Boundary stones marking land plots have been preserved. There is a representation of land measurement on the wall of a tomb at Thebes (1400 BCE) showing head and rear chainmen measuring a grainfield with what appears to be a rope with knots or marks at uniform intervals. Other persons are shown. Two are of high estate, according to their clothing, probably a land overseer and an inspector of boundary stones.
There is some evidence that, in addition to a marked cord, wooden rods were used by the Egyptians for distance measurement. There is no record of any angle-measuring instruments of that time, but there was a level consisting of a vertical wooden A-frame with a plumb bob supported at the peak of the A so that its cord hung past an indicator, or index, on the horizontal bar. The index could be properly placed by standing the device on two supports at approximately the same elevation, marking the position of the cord, reversing the A, and making a similar mark. Halfway between the two marks would be the correct place for the index. Thus, with their simple devices, the ancient Egyptians were able to measure land areas, replace property corners lost when the Nile covered the markers with silt during floods, and build the huge pyramids to exact dimensions.
The Greeks used a form of log line for recording the distances run from point to point along the coast while making their slow voyages from the Indus to the Persian Gulf about 325 BCE. The magnetic compass was brought to the West by Arab traders in the 12th century CE. The astrolabe was introduced by the Greeks in the 2nd century BCE. An instrument for measuring the altitudes of stars, or their angle of elevation above the horizon, took the form of a graduated arc suspended from a hand-held cord. A pivoted pointer that moved over the graduations was pointed at the star. The instrument was not used for nautical surveying for several centuries, remaining a scientific aid only.
The Greeks also possibly originated the use of the groma, a device used to establish right angles, but Roman surveyors made it a standard tool. It was made of a horizontal wooden cross pivoted at the middle and supported from above. From the end of each of the four arms hung a plumb bob. By sighting along each pair of plumb bob cords in turn, the right angle could be established. The device could be adjusted to a precise right angle by observing the same angle after turning the device approximately 90°. By shifting one of the cords to take up half the error, a perfect right angle would result.
About 15 BCE the Roman architect and engineer Vitruvius mounted a large wheel of known circumference in a small frame, in much the same fashion as the wheel is mounted on a wheelbarrow; when it was pushed along the ground by hand it automatically dropped a pebble into a container at each revolution, giving a measure of the distance traveled. It was, in effect, the first odometer.
The water level consisted of either a trough or a tube turned upward at the ends and filled with water. At each end there was a sight made of crossed horizontal and vertical slits. When these were lined up just above the water level, the sights determined a level line accurate enough to establish the grades of the Roman aqueducts. In laying out their great road system, the Romans are said to have used the plane table. It consists of a drawing board mounted on a tripod or other stable support and of a straightedge—usually with sights for accurate aim (the alidade) to the objects to be mapped—along which lines are drawn. It was the first device capable of recording or establishing angles. Later adaptations of the plane table had magnetic compasses attached.
Plane tables were in use in Europe in the 16th century, and the principle of graphic triangulation and intersection was practiced by surveyors. In 1615 Willebrord Snell, a Dutch mathematician, measured an arc of meridian by instrumental triangulation. In 1620 the English mathematician Edmund Gunter developed a surveying chain, which was superseded only by the steel tape beginning in the late 19th century.
The study of astronomy resulted in the development of angle-reading devices that were based on arcs of large radii, making such instruments too large for field use. With the publication of logarithmic tables in 1620, portable angle-measuring instruments came into use. They were called topographic instruments, or theodolites. They included pivoted arms for sighting and could be used for measuring both horizontal and vertical angles. Magnetic compasses may have been included on some.
The vernier, an auxiliary scale permitting more accurate readings (1631), the micrometer microscope (1638), telescopic sights (1669), and spirit levels (about 1700) were all incorporated in theodolites by about 1720. Stadia hairs were first applied by James Watt in 1771. The development of the circle-dividing engine about 1775, a device for dividing a circle into degrees with great accuracy, brought one of the greatest advances in surveying methods, as it enabled angle measurements to be made with portable instruments far more accurately than had previously been possible.
Modern surveying can be said to have begun by the late 18th century. One of the most notable early feats of surveyors was the measurement in the 1790s of the meridian from Barcelona, Spain, to Dunkirk, France, by two French engineers, Jean Delambre and Pierre Méchain, to establish the basic unit for the metric system of measurement.
Many improvements and refinements have been incorporated in all the basic surveying instruments. These have resulted in increased accuracy and speed of operations and opened up possibilities for improved methods in the field. In addition to modification of existing instruments, two revolutionary mapping and surveying changes were
introduced: photogrammetry, or mapping from aerial photographs (about 1920), and electronic distance measurement, including the adoption of the laser for this purpose as well as for alignment (in the 1960s). Important technological developments starting in the late 20th century include the use of satellites as reference points for geodetic surveys and electronic computers to speed the processing and recording of survey data.
An example of a 
A 3D Rendering of an I-Beam
Source: SkyCiv Beam
Source: Cantilever Beam Calculator
Source: SkyCiv Beam
Source: SkyCiv Beam
Source: SkyCiv Beam
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