Technological Institute of the Philippines Arlegui St., Quiapo, Manila College of Engineering and Architecture Civil Engineering Department Structural Theory 1: CLASSIFICATION OF STRUCTURE AND LOADS Submitted by: RANOLA, KLAUS JEWEL G. BSCE / FOURTH YEAR / 1620182 CE41FA1 Submitted to: Engr. Jovito Sarzaba DECEMBER 14, 2018 CONNECTIONS These are part of a structure that joins or links the ends of its members and are either flexible/hinged connections or rigid connections. Flexible or hinged connection are capable of transmitting forces but not moments of the members. This connection usually prevents relative translation of the members connected to it but not its rotations. In that case, these members have the same translation of axes but possible to rotate in different directions. On the other hand, rigid connection provides a more stable support by preventing the relative translation and rotations of members that are connected to it. With that being said, this connection is able to transmit forces as well as moments between connected members. Original angles between the members are also maintained by rigid connection after the structure are deformed under the application of load. There are three types of joints that are commonly used in designing a structure which are pinned, roller, and fixed joints. In pinned and roller connection, the members of structure are allowed to move in a limited direction while otherwise in fixed connection. Pinned connection is a cast steel joint that acts as a node or intersections to resolve a number of tensile forces. Fixed connection is usually the main source of building failures if the ideal or expected compressive forces are miscalculated. These connections can be used in metals, concretes, and timbers either by welding or bolting except for timber structures that use pin-connected joint to sufficiently restrain the members from rotating with respect to each other. Examples of metals and concretes that were joint together are given below. SUPPORTS Structural support is used to connect a structure to the ground thus, helping in transferring the load to the ground and providing stability to the structure supported on it. These supports tend to oppose the forces exerted by the applied load thereby, preventing the structure from moving and keeping it in an equilibrium state. Support reactions depends on the type of supporting device used in the structure as well as the type of movement it prevents. A support that prevents translation of the structure in a particular direction exerts a reaction force on the structure in that direction. Similarly, a support that prevents rotation of the structure about a particular axis exerts a reaction couple on the structure about that axis. Structural supports are mainly classified into external and internal supports. External supports are usually provided without disturbing the structural members such as fixed supports, pinned or hinged support, roller support, rocker support, link support and simple support which are defined below. A. Fixed supports These supports are also known as rigid supports because they resist any type of force or moment. In designing a structure, there should be least one of this support to have a good stability. B. Pinned or Hinged supports These supports are restrained against translation thus, preventing any movement along the vertical and horizontal axis but cannot resist rotation or moment which is limited only in one direction. C. Roller supports Roller supports move freely along the horizontal direction for it only resist perpendicular forces. These are usually placed in one end of a bridge to give an allowance for contraction or expansion of the bridge deck due to changes of temperature. D. Rocker supports These supports are quite similar to roller supports. It also allows parallel forces and moments but resist perpendicular forces. However, the horizontal movement is due to the curve surface at the bottom of these supports which makes the horizontal movement limited. E. Link supports In these supports, rotation and translation along the direction of the link is prevented and perpendicular forces and moments to the direction of the link in allowed. F. Simple supports These are resting supports and only resist vertical movement with the help of the gravity. Horizontal or lateral movements are allowed but limited and if it exceeds the allowable amount of force, the structure will lose its supports. These can usually be seen along the zones of frequent seismic activity. Internal supports separate the whole structural member into parts for they are provided internally such as internal hinge and roller described below. A. Internal hinge It also resists translation in both directions and allows any rotation like the hinge support. In structures, internal hinges can be found in axial members while middle hinges are in beam members. B. Internal rollers It has the same reactions like the rollers but provided on the middle of structural members. Usually used in tower or harbor cranes because of its horizontal movement which is helpful in shifting members from place to place. DEAD LOADS Dead loads are gravity loads of constant magnitudes and fixed positions that act permanently on the structure. Such loads consist of the weights of the structural system itself and of all other material and equipment permanently attached to the structural system. For example, the dead loads for a building structure include the weights of frames, framing and bracing systems, floors, roofs, ceilings, walls, stairways, heating and airconditioning systems, plumbing, electrical systems, and so forth. In some cases, a structural dead load can be estimated satisfactorily from simple formulas based on the weights and sizes of similar structures. Through experience one can also derive a “feeling” for the magnitude of these loadings. Ordinarily, though, once the materials and sizes of the various components of the structure are determined, their weights can be found from tables that list their densities. The densities of typical materials used in construction are listed in Table 1–2, and a portion of a table listing the weights of typical building components is given in Table 1– 3. Although calculation of dead loads based on the use of tabulated data is rather straightforward, it should be realized that in many respects these loads will have to be estimated in the initial phase of design. These estimates include nonstructural materials such as prefabricated facade panels, electrical and plumbing systems, etc. Furthermore, even if the material is specified, the unit weights of elements reported in codes may vary from those given by manufacturers, and later use of the building may include some changes in dead loading.As a result, estimates of dead loadings can be in error by 15% to 20% or more. Normally, the dead load is not large compared to the design load for simple structures such as a beam or a single-story frame; however, for multistory buildings it is important to have an accurate accounting of all the dead loads in order to properly design the columns, especially for the lower floors. MOST COMMON BUILDING STRUCTURES Girder A girder is a support beam used in construction. It is the main horizontal support of a structure which supports smaller beams. Girders often have an I-beam cross section composed of two load-bearing flanges separated by a stabilizing web, but may also have a box shape, Z shape and other forms. A girder is commonly used to build bridges. Beam A beam is a structural element that primarily resists loads applied laterally to the beam's axis. Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, that in turn induce internal stresses, strains and deflections of the beam. Beams are characterized by their manner of support, profile (shape of cross-section), length, and their material. Concrete Slab A concrete slab is a common structural element of modern buildings. Horizontal slabs of steel reinforced concrete, typically, between 4 and 20 inches (100 and 500 millimeters) thick, are most often used to construct floors and ceilings, while thinner slabs are also used for exterior paving. Sometimes these thinner slabs, ranging from 2 inches (51 mm) to 6 inches (150 mm) thick, are called mud slabs, particularly when used under the main floor slabs or in crawl spaces. Live Loads. Live Loads can vary both in their magnitude and location. They may be caused by the weights of objects temporarily placed on a structure, moving vehicles, or natural forces. The minimum live loads specified in codes are determined from studying the history of their effects on existing structures. Usually, these loads include additional protection against excessive deflection or sudden overload. Building Loads. The floors of buildings are assumed to be subjected to uniform live loads, which depend on the purpose for which the building is designed. These loadings are generally tabulated in local, state, or national codes. A representative sample of such minimum live loadings, taken from the ASCE 7-10 Standard, is shown in Table 1–4.The values are determined from a history of loading various buildings. They include some protection against the possibility of overload due to emergency situations, construction loads, and serviceability requirements due to vibration. In addition to uniform loads, some codes specify minimum concentrated live loads, caused by hand carts, automobiles, etc., which must also be applied anywhere to the floor system. For example, both uniform and concentrated live loads must be considered in the design of an automobile parking deck. SAMPLE PROBLEM: COMPUTATION OF LIVE LOADS A two-story office building shown in the photo has interior columns that are spaced 22 ft apart in two perpendicular directions. If the (flat) roof loading is 20 lb/ft2determine the reduced live load supported by a typical interior column located at ground level. Highway Bridge Loads. The primary live loads on bridge spans are those due to traffic, and the heaviest vehicle loading encountered is that caused by a series of trucks. Specifications for truck loadings on highway bridges are reported in the LRFD Bridge Design Specifications of the American Association of State and Highway Transportation Officials (AASHTO). The size of the “standard truck” and the distribution of its weight is also reported in the specifications. Although trucks are assumed to be on the road, all lanes on the bridge need not be fully loaded with a row of trucks to obtain the critical load, since such a loading would be highly improbable. Railway Bridge Loads. The loadings on railroad bridges are specified in the Specifications for Steel Railway Bridges published by the American Railroad Engineers Association (AREA). Since train loadings involve a complicated series of concentrated forces, to simplify hand calculations, tables and graphs are sometimes used in conjunction with influence lines to obtain the critical load. Also, computer programs are used for this purpose. SAMPLE PROBLEM: MOVING LOADS A truck with axle loads of 40 kN and 60 kN on a wheel base of 5 m rolls across a 10-m span. Compute the maximum bending moment and the maximum shearing force. R=40+60=100kN xR=40(5) x=200/R x=200/100 x=2m For maximum moment under 40 kN wheel: ΣMR2=0 10R1=3.5(100) R1=35kN M To the left of 40 kN =3.5R1 M To the left of 40 kN=3.5(35) M To the left of 40 kN=122.5kN⋅m For maximum moment under 60 kN wheel: ΣMR1=0 10R2=4(100) R2=40kN M To the right of 60 kN=4R2 M To the right of 60 kN=4(40) M To the right of 60 kN =160kN⋅m Thus, Mmax=160 kN⋅m answer The maximum shear will occur when the 60 kN is over a support. ΣMR1=0 10R2=100(8) R2=80kN Thus, Vmax=80kN answer SAMPLE PROBLEM: MOVING LOADS Repeat problem above using axle loads of 30 kN and 50 kN on a wheel base of 4 m crossing an 8-m span. R=30+50=80kN xR=4(30) x=120/R x=120/80 x=1.5m Maximum moment under 30 kN wheel: ΣMR2=0 8R1=2.75(80) R1=27.5kN M To the left of 30kN=2.75R1 M To the left of 30kN=2.75(27.5) M To the left of 30kN=75.625kN⋅m Maximum moment under 50 kN wheel: ΣMR1=0 8R2=3.25(80) R2=32.5kN M To the right of 50 kN=3.25R2 M To the right of 50 kN=3.25(32.5) M To the right of 50kN=105.625kN-m Thus, Mmax=105.625 kN-m answer The maximum shear will occur when the 50 kN is over a support. ΣMR1=0 8R2=6.5(80) R2=65kN Thus, Vmax= 65kN answer Tension Structures The members of tension structures are subjected to pure tension under the action of external loads. Because the tensile stress is distributed uniformly over the crosssectional areas of members, the material of such a structure is utilized in the most efficient manner. Tension structures composed of ﬂexible steel cables are frequently employed to support bridges and long-span roofs. Because of their ﬂexibility, cables have negligible bending stiffness and can develop only tension. Thus, under external loads, a cable adopts a shape that enables it to support the load by tensile forces alone . In other words, the shape of a cable changes as the loads acting on it change. This Is a familiar type of cable structure—the suspension bridge. In a suspension bridge, the roadway is suspended from two main cables by means of vertical hangers. The main cables pass over a pair of towers and are anchored into solid rock or a concrete foundation at their ends. Because suspension bridges and other cable structures lack stiffness in lateral directions, they are susceptible to wind-induced oscillations. An example of this is the Tacoma Narrows Bridge ( built in July 1,1940 and collapsed in November 7 of the same year. Bracing or stiffening systems are therefore provided to reduce such oscillations. Besides cable structures, other examples of tension structures include vertical rods used as hangers (for example, to support balconies or tanks) and membrane structures such as tents. Compression Structures Compression structures develop mainly compressive stresses under the action of external loads. Two common examples of such structures are columns and arches. Columns are straight members subjected to axially compressive loads. When a straight member is subjected to lateral loads and/or moments in addition to axial loads, it is called a beam-column. An arch is a curved structure, with a shape similar to that of an inverted cable. Such structures are frequently used to support bridges and long-span roofs and flyovers. Arches develop mainly compressive stresses when subjected to loads and are usually designed so that they will develop only compression under a major design loading. However, because arches are rigid and cannot change their shapes as can cables, in order to maintain its shape, this resulted to secondary loading involving shear and moment, which must be considered in their design. Because compression structures are susceptible to buckling or instability, the possibility of such a failure should be considered in their designs; if necessary, adequate bracing must be provided to avoid such failures. EARLY GEOLOGIST In 1669, Scientist Nicolas Steno publish the first laws of Stratigraphy. Stratigraphy is the science of interpreting the strata or layers of rock in Earth’s outer surface. Law of Superstition In 1760s, Italian geologist Giovanni Arduino classified mountains according to rock type: Primary layer - Metamorphic and Volcanic rocks Secondary layer - Sedimentary rocks Tertiary and Quaternary layer - Softer alluvial deposits (gravel, sands) In 1819, English geologist William Smith came up with the Principal of Faunal Succession. Principal of Faunal Succession is based on the observation that sedimentary rock strata contain fossilized flora and fauna, and that these fossils succeed each other vertically in a specific, reliable order that can be identified over wide horizontal distances. Geological time scale is a table showing the sequence of geological periods in the history of earth. It also shows the lengths of time different geological periods are assumed to have occupied it is measured in millions of years. It has been constructed by studying rock strata, where these have been exposed by excavations or mining or where rivers have cut deeply into the earth’s crust Major Events of Geological Time Scale: 1. Bryophytes evolved on the earth during the Silurian Period of Paleozoic era (i.e. between 395 to 430 million years ago) and are still surviving. 2. Pteridophytes evolved sometime in Silurian, dominated the earth during Carboniferous and are still surviving. 3. Gymnosperms evolved sometime at the end of Triassic Period (i.e. about 225 million years ago) Mesozoic era, dominated the earth sometime during Paleocene epoch (i.e. about 65 million years ago) and are still surviving. 4. Angiosperms evolved during Jurassic Period of Mesozoic era and are now dominating the earth in the recent epoch of Quaternary Period of Cenozoic era. A summary of geological time scale is presented in Table 25.1. Tectonic Plates are pieces of Earth's crust and uppermost mantle, together referred to as the lithosphere. Each tectonic plate boundary can interact with each other in three ways: Divergent plates pull apart from each other Convergent plates push plates together Conservative (transform) plate boundaries slide across from each other. IMPACT LOAD The load experienced by the structure when a moving body is stopped by the structure. The percentage increase of the live loads due to impact is called the impact factor (I) For highway bridges, the AASHTO specification requires that: I = 50/ L +125 (not larger than 0.3)Where L is the length or span in feet that is subjected to live load. SEISMIC LOAD Seismic load is one of the basic concepts of earthquake engineering which means application of an earthquake-generated agitation to a building structure or its model. It happens at contact surfaces of a structure either with the ground, or with adjacent structures, or with gravity waves from tsunami. V = CsW Wherein: V = Total Lateral Force Cs = Seismic response coefficient W = Dead load of the building We cannot see the deep interior of Earth, but we know from a variety of observations that it is in continuous motion. This is because the mantle convects. This fundamental planetary process has profoundly influenced the character and evolution of Earth. What is Convection? Convection is the process by which less dense material rises and more dense material sinks. The former are said to be more “buoyant” than the latter and the vertical forces due to density difference are referred to as buoyancy forces. Rocks, water, and air— indeed, most materials—expand and thus become less dense as temperature increases, so convection is typically driven by temperature differences. In Earth’s mantle hot rock rises and slightly cooler rock sinks. WIND LOAD A force or pressure that the wind exerts on a building or structure. Load placed by the wind speed and its air density onto a building. Wind Speeds Maximum sustained wind A common indicator of the intensity of the storm Represents the highest average wind over either a one-minute or ten-minute time span anywhere within the tropical cyclone. Wind speed The rate of the movement of wind in distance per unit of time. o Rate of the movement of air flow Forward speed / travelling speed It represents the pace at which it travels across the landscape. Wind gust Brief increase in speed of the wind. Reported when the peak wind speed reaches at least 8 m/s. o Duration is less than 20 seconds. WINDWARD & LEEWARD Windward - the side which is directly exposed to wind (pressure) Leeward - the side which is not exposed directly to the wind forces (suction) FORMULAS For wind load: Where: Q = dynamic pressure ( ⁄ ) = mass density of air ( ⁄ ) * 1.225 at sea level and at 15 °c V= wind speed (m/s) * = 0.613 2 Design wind pressure for structure When v is in m/s = 0.613 When v is in kph = 47.3 × 10 where: = design wind pressure in ⁄ = velocity exposure coefficient = factor that accounts for a wind increase due to hills and escarpment * For flat grounds: = 1.0 = wind speed in ⁄ or kph velocity of a 3-second gust wind measured (above the ground during a 50-year recurrence period) = Importance Factor Design force for signs Where: = design wind pressure in ⁄ = wind gust coefficient factor = a force coefficient which depends upon the ratio of the large dimension “m” to small dimension “n” = area of face of the sign * To allow for normal and oblique wind direction, the design force is assumed to act either through the geometric center of the face of the sign or from a vertical line passing through the geometric center if a distance of 0.2 times the average width of the sign. External wind pressure ℎ= Where: = design wind pressure in ⁄ = wind gust coefficient factor = height (from base to roof) over length Tables force coefficients, Roof pressure coefficients, Examples #1 The structure represents an above ground sign whose location is an open flat terrain with an importance factor of 0.87. Given the following data: (velocity exposure coefficient) = 0.85 (for flat terrain) = 1.0 (wind gust coefficient factor) = 0.85 a) Determine the resultant force of the wind acting on its face if the wind velocity is 38 m/s b) Determine the maximum “y” coordinate of where the result acts c) Determine the moment due to this force about the vertical axis 2 Determine the external wind pressure on the roof of the rigid-gabled frame of a school, the wind direction is normal to the ridge as shown. Given: = 40 m/s = 12 + 52 = 14.5 m = 0.85 = 1.15 TIMBER STRUCTURES Traditional timber framing is the method of creating framed structures of heavy timber jointed together with various joints, commonly and originally with lap jointing, and then later pegged mortise and tenon joints. Diagonal bracing is used to prevent "racking", or movement of structural vertical beams or posts. Types of TIMBER STRUCTURES There are numerous types of wood that you can use for timber frames. The most common ones used are KAMAGONG, NARRA, MOLAVE, TANGUILE and YAKAL. KAMAGONG Also known as Philippine Ebony, kamagong is a wood unique to the country. With a black heartwood (inner region) and gray sapwood, this produces really dramatic, dark timber hence the name. Ideal for: Small, decorative pieces and combat tools like arnis sticks and eskrima NARRA This very popular tropical wood has tones that range from yellow to red. The grain (texture and alignment of wood fiber) is often interlocked and wavy, which creates interesting flame and ribbon figures when quartersawn or flat sawn, which makes it a beautiful finishing material. Ideal for: furnishings, floor planks, wall panels MOLAVE One of the hardest local woods, molave has a fine texture that makes it smooth to the touch. It's available in pale yellow to pinkish-brownish tone with a lighter sapwood (outer region), and mostly straight grain. It has no distinct odor. Ideal for: window frames, shipbuilding, structural posts, railroad tracks, and other outdoor applications TANGUILE A moderately hard reddish wood, tanguile is one of the seven local woods often referred to as Philippine Mahogany. This abundant wood type boasts of fine ribbon or straight grain. It's relatively soft and easy to work on, but resilient enough for outdoor construction. Ideal for: interior finishes, cabinets, boat building YAKAL This resinous wood with yellow to golden-red tones is another local mahogany type. A high-grade timber, yakal can tolerate harsh hot and cold weathers. Ideal for: furniture, surface finishes, small weapons, and outdoor constructions BOARD FOOT Board foot is the unit of measure used in computing volume of lumber despite the introduction of the metric measures. One board foot simply mean one square foot by one inch thick or equivalent to 144 cu. inches. The width and thickness of the lumber are expressed in inches while the length are in feet of even numbers. How to determine the number of board foot Board foot is found by dividing the product of the thickness times the width and the length by 12. Formula: T = thickness W = width L = length How to determine the number of board foot in a log. Bd. Ft. volume = where: D = is the smaller diameter of log L = the length of the log 4 = slab reduction allowance COMPOSITE STEEL STRUCTURES Structural members that are made up of two or more different materials are known as composite elements. The main benefit of composite elements is that the properties of each material can be combined to form a single unit that performs better overall than its separate constituent parts. The most common form of composite element in construction is a steel-concrete composite, however, other types of composites include; steel-timber, timber-concrete, plastic-concrete. COMPOSITE SLABS are typically constructed from reinforced concrete cast on top of profiled steel decking. The decking is capable of acting as formwork and a working platform during the construction stage, as well as acting as external reinforcement at the composite stage. Decking is lifted into place in bundles and distributed across the floor area by hand. Slab depths range from 130 mm upwards. Slabs are most commonly made of concrete because of its mass and stiffness which can be used to reduce the floor's deflections and vibrations, and achieve the necessary fire protection and thermal storage. COMPOSITE BEAMS A down stand beam is connected to a composite slab by the use of through-deck welded shear studs. An upstand beam is the one in which its structural top level is raised upwards relative to the structural top level of adjoining slab. A shallow foundation is a type of building foundation that transfers building loads to the earth very near to the surface, rather than to a subsurface layer or a range of depths as does a deep foundation. PERFORATED METAL also known as perforated sheet, perforated plate, or perforated screen, is sheet metal that has been manually or mechanically stamped or punched to create a pattern of holes, slots, or decorative shapes. LACING consists of connecting the components of the column by a system of generally flat plates. (In some cases angles and channels are also used as lacings). Lacing plates may be 50 mm to 75 mm wide and 8 mm to 10 mm thick.