STRUCTURAL ANALYSIS ENGR. ATIQ UR REHMAN AWAN Types of Structures & Loads-Page 1 of 21 Department of Engineering & Technology, The University of Lahore Types of Structures & Loads 1 Introduction A structure refers to a system of connected parts used to support a load. Important examples related to civil engineering include buildings, bridges, and towers; and in other branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical systems, and electrical supporting structures are important. When designing a structure to serve a specified function for public use, the engineer must account for its safety, esthetics, and serviceability, while taking into consideration economic and environmental constraints. Once a preliminary design of a structure is proposed, the structure must then be analyzed to ensure that it has its required stiffness and strength. To analyze a structure properly, certain idealizations must be made as to how the members are supported and connected together. The loadings are determined from codes and local specifications, and the forces in the members and their displacements are found using the theory of structural analysis, which is the subject matter of this text. The results of this analysis then can be used to redesign the structure, accounting for a more accurate determination of the weight of the members and their size. Structural design, therefore, follows a series of successive approximations in which every cycle requires a structural analysis. Classification of structures It is important for a structural engineer to recognize the various types of elements composing a structure and to be able to classify structures as to their form and function. Types of Structures The combination of structural elements and the materials from which they are composed is referred to as a structural system. Each system is constructed of one or more of four basic types of structures. Trusses: When the span of a structure is required to be large and its depth is not an important criterion for design, a truss may be selected. Trusses consist of slender elements, usually arranged in triangular fashion. Planar trusses are composed of members that lie in the same plane and are frequently used for bridge and roof support, whereas space trusses have members extending in three dimensions and are suitable for towers. Types of Structures & Loads-Page 2 of 21 Due to the geometric arrangement of its members, loads that cause the entire truss to bend are converted into tensile or compressive forces in the members. Because of this, one of the primary advantages of a truss, compared to a beam, is that it uses less material to support a given load. Also, a truss is constructed from long and slender elements, which can be arranged in various ways to support a load. Most often it is economically feasible to use a truss to cover spans ranging from 30 ft (9 m) to 400 ft (122 m), although trusses have been used on occasion for spans of greater lengths. Cables and Arches: Two other forms of structures used to span long distances are the cable and the arch. Cables are usually flexible and carry their loads in tension. They are commonly used to support bridges, and building roofs. When used for these purposes, the cable has an advantage over the beam and the truss, especially for spans that are greater than 150 ft (46 m). Because they are always in tension, cables will not become unstable and suddenly collapse, as may happen with beams or trusses. Furthermore, the truss will require added costs for construction and increased depth as the span increases. Use of cables, on the other hand, is limited only by their sag, weight, and methods of anchorage. The arch achieves its strength in compression, since it has a reverse curvature to that of the cable. The arch must be rigid, however, in order to maintain its shape, and this results in secondary loadings involving shear and moment, which must be considered in its design. Arches are frequently used in bridge structures, dome roofs, and for openings in masonry walls. Types of Structures & Loads-Page 3 of 21 Frames: Frames are often used in buildings and are composed of beams and columns that are either pin or fixed connected. Like trusses, frames extend in two or three dimensions. The loading on a frame causes bending of its members, and if it has rigid joint connections, this structure is generally “indeterminate” from a standpoint of analysis. The strength of such a frame is derived from the moment interactions between the beams and the columns at the rigid joints. Structural Elements Some of the more common elements from which structures are composed are as follows. Tie Rods: Structural members subjected to a tensile force are referred to as tie rods or bracing struts. Due to the nature of this load, these members are rather slender, and are often chosen from rods, bars, angles, or channels. Slab: A slab is a broad, flat plate, with top and bottom surfaces parallel and supported by beams, by masonry or reinforced concrete walls, by structural steel members, directly by columns. According to the way loads are transferred to supporting beams and columns, slabs are classified into two types; one-way and two-way. One way slab is define as the slab who’s longer to shorter span ratio Ly/Lx ≥ 2. A one-way slab needs moment resisting reinforcement only in its short-direction because the moment along long axes is so small that it can be neglected. A slab who’s longer to shorter span ratio Ly/Lx< 2 is called two-way slab. Two-way slabs have tension reinforcing spanning in both directions. Types of Structures & Loads-Page 4 of 21 Beams: Beams are usually straight horizontal members used primarily to carry vertical loads. Based on the types of support beam is classified as simply supported, Cantilever, overhang, continuous and fixed beam. Based on the types of material used beams may be made from concrete, steel or from wood. Concrete beams generally have rectangular cross sections, since it is easy to construct this form directly in the field. Because concrete is rather weak in resisting tension, steel “reinforcing rods” are cast into the beam within regions of the cross section subjected to tension. Based on cross-sectional shape beams are rectangular, T, I, L in shape. Precast concrete beams or girders are fabricated at a shop or yard in the same manner and then transported to the job site. Based on geometry beam may be straight, curved and tapered in crosssection. Columns: Members that are generally vertical and resist axial compressive loads are referred to as columns. Tubes and wide-flange cross sections are often used for metal columns, and circular and square cross sections with reinforcing rods are used for those made of concrete. Occasionally, columns are subjected to both an axial load and a bending moment as shown in the figure. These members are referred to as beam columns. Foundation: A structural element who takes the load from super structure and then transfer to soil is known as footing. Foundation is that part of the structure which is in direct contact with soil. Here, the part of the structure above ground level is called as the superstructure. E.g. Slab, beam and column etc. where the part of the structure below the ground level is called as the substructure. E.g. footing. Foundations are generally divided into two categories: 1. Shallow foundation A shallow foundation is a type of foundation which transfers building loads to the earth very near the surface, Shallow Foundations are provided when adequate SBC is available at relatively short depth below ground level. In shallow foundation the ratio of Df /B < 1, where Df is the depth of footing and B is the width of footing. Types of Structures & Loads-Page 5 of 21 Types of shallow foundation: Isolated Footing These are independent footings which are provided when SBC (Soil Bearing Capacity) is generally high Columns are far apart Loads on footings are less The isolated footings can have different cross section. Some of the popular shapes of footings are; Square Rectangular Combined footing These are common footings which support the loads from are provided when: SBC is generally less Columns are closely spaced Footings are heavily loaded When exterior column came closer to property line in such cases footings cannot be extended on one side. Here, the footings of exterior and interior columns are connected by the combined footing. Combined footings essentially consist of a common slab for the columns it is supporting. These slabs are generally rectangular in plan. Sometimes they can also be trapezoidal in plan. Types of Structures & Loads-Page 6 of 21 Strap Footing An alternate way of providing combined footing located close to property line is the strap footing strap footing, independent slabs below columns are provided which are then connected by a strap beam. The strap beam does not remain in contact with the soil and does not transfer any pressure to the soil. Strip Footing Strip footing is a continuous footing provided under columns or walls. Strip footing is provided when more than 2 column comes in same line and their centre to centre spacing is small. Mat/Raft Foundation Mat foundation covers the whole plan area of structure. The detailing is similar to two way reinforced solid floor slabs or flat slabs. It is a combined footing that covers the entire area beneath a structure and supports all the walls and columns. It is normally provided when 1. Soil pressure is low 2. Loads are very heavy 3. Spread footings cover > 50% area Types of Structures & Loads-Page 7 of 21 2. Deep foundation Deep Foundations are provided when adequate SBC is available at large depth below ground level. In shallow foundation the ratio of Df/B ≥ 1, where Df is the depth of footing and B is the width of footing. Some of the common types are listed below. 1. Pile Foundation 2. Pier Foundation 3. Well Foundation Types of Structures & Loads-Page 8 of 21 Loads Once the dimensional requirements for a structure have been defined, it becomes necessary to determine the loads the structure must support. Once the structural form has been determined, the actual design begins with those elements that are subjected to the primary loads the structure is intended to carry, and proceeds in sequence to the various supporting members until the foundation Load is reached. Thus, a building floor slab would be designed Roof Surface first, followed by the supporting beams, columns, and last, the foundation footings. In order to design a structure, it is therefore necessary to first specify the Roof slab loads that act on it. The design loading for a structure is often specified in codes. In general, the structural Beams engineer works with two types of codes: general building codes and design codes. General building codes specify Column the requirements of governmental bodies for minimum design loads on structures and minimum standards for Foundation construction. Design codes provide detailed technical standards and are used to establish the requirements for Soil the actual structural design. Since a structure is generally subjected to several types of loads, a brief discussion of these loadings will now be presented to illustrate how one must consider their effects in practice. Dead Loads: Dead load is defined as the load which does not change its magnitude and position. Dead loads consist of the weights of the various structural members and the weights of any objects that are permanently attached to the structure. Hence, for a building, the dead loads include the weights of the columns, beams, and girders, the floor slab, roofing, walls, windows, plumbing, electrical fixtures, and other miscellaneous attachments. 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. Types of Structures & Loads-Page 9 of 21 Minimum Densities for Design Loads from Materials Material 𝐥𝐛/𝐟𝐭 𝟑 Aluminum Copper Iron Lead Steel, Rolled Limestone, Marble Sand stone Shale or slate Oil Water Ice Brick Cement, Portland, set Cement, Portland, loose Earth, dry, packed Concrete, plain cinder Concrete, plain stone Concrete, reinforced cinder Concrete, reinforced stone Clay, dry Clay, damp Masonry, lightweight solid concrete Masonry, normal weight Plywood Steel, cold-drawn Wood, Douglas Fir Wood, Southern Pine Wood, spruce 170 556 450 710 490 165 147 175 58 62.4 56 120 183 90 95 108 144 111 150 63 110 105 135 36 492 34 37 29 𝐊𝐍/𝐦𝟑 26.7 87.4 70.8 111.6 77 25.9 23.1 27.5 9.12 9.81 8.8 18.9 28.7 14 14.9 17 22.6 17.4 23.6 9.9 17.3 16.5 21.2 5.7 77.3 5.3 5.8 4.5 Frame Partitions & Walls Psf KN/m2 Exterior stud walls with brick veneer Windows, glass, frame and sash Wood studs 2×4 in.(51×102mm) unplastered Wood studs 2×4 in.(51×102mm) plastered one side Wood studs 2×4 in.(51×102mm) plastered two sides 48 8 4 12 20 2.30 0.38 0.19 0.57 0.96 9 8 12 0.017 0.015 0.023 Floor Fills Cinder concrete, per inch (mm) Lightweight concrete, plain, per inch (mm) Stone concrete, per inch (mm) Types of Structures & Loads-Page 10 of 21 Ceilings Acoustical fiberboard Plaster on tile or concrete Suspended metal lath and gypsum plaster Asphalt shingles Fiberboard 1/2in, (13 mm) 1 5 10 2 0.75 0.05 0.24 0.48 0.10 0.04 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. Various types of live loads can be found from table listed below. Sr. No Live Load Occupancy/Use 2 2 2 Kgs/m N/m Lb/ft 200 1900 40 250 to 425 2400 to 4000 50 to 85 1 Private apartment, schools class room 2 Office 3 Fixed-seats, assembly halls, library reading rooms 300 2900 60 4 Corridors in public buildings 400 3800 80 5 Moveable seats assembly halls 500 4800 100 6 Wholesales, light storage, warehouses 610 6000 125 7 Library Stack room 730 7200 150 8 Heavy manufacturing. Heavy storage warehouses, sidewalks and drive ways subjected to trucking 1200 12000 250 9 Stairs, generals 500 4800 100 10 Stairs up to two-family residences, 50% more than specifications 300 2900 60 Snow Loads: In some parts of the country, roof loading due to snow can be quite severe, and therefore protection against possible failure is of primary concern. Design loadings typically depend on the building’s general shape and roof geometry, wind exposure, location, its importance, and whether or not it is heated. Like wind, snow loads in the ASCE 7-10 Standard are generally determined from a zone map reporting 50-year recurrence intervals of an extreme snow depth. Specifications for snow loads are covered in the ASCE 7-10 Standard. If a roof is flat, defined as having a slope of less than 5%, then the pressure loading on the roof can be obtained the following empirical formula: 𝑃𝑓 = 0.7𝐶𝑒 𝐶𝑡 𝐼𝑠 𝑝𝑔 Types of Structures & Loads-Page 11 of 21 Where: 𝐶𝑒 = an exposure factor which depends upon the terrain. For example, for a fully exposed roof in an unobstructed area, 𝐶𝑒 =0.8 Whereas if the roof is sheltered and located in the center of a large city, then 𝐶𝑒 =1.2 𝐶𝑡 = a thermal factor which refers to the average temperature within the building. For unheated structures kept below freezing 𝐶𝑡 = 1.2 Whereas if the roof is supporting a normally heated structure, then 𝐶𝑡 = 1 𝐼𝑠 = the importance factor as it relates to occupancy. For example, for agriculture and storage facilities 𝐼𝑠 = 0.8, and for schools and hospitals 𝐼𝑠 =1.2 If 𝑃𝑔 ≤ 20𝑙𝑏/𝑓𝑡 2 (0.96 KN/𝑚2 ) then use the largest value for 𝑃𝑓 either computed from the above equation or from 𝑃𝑓 = 𝐼𝑠 𝑝𝑔 .If 𝑃𝑔 > 20𝑙𝑏/𝑓𝑡 2 ((0.96 KN/𝑚2 ) then use pf =𝐼𝑠 20𝑙𝑏/𝑓𝑡 2 Wind Loads: When structures block the flow of wind, the wind’s kinetic energy is converted into potential energy of pressure, which causes a wind loading. The effect of wind on a structure depends upon the density and velocity of the air, the angle of incidence of the wind, the shape and stiffness of the structure, and the roughness of its surface. 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). For twoaxle trucks, these loads are designated with an H, followed by the weight of the truck in tons and another number which gives the year of the specifications in which the load was reported. H-series truck weights vary from 10 to 20 tons. However, bridges located on major highways, which carry a great deal of traffic, are often designed for two-axle trucks plus a one-axle semitrailer as in Fig. These are designated as HS loadings. In general, a truck loading selected for design depends upon the type of bridge, its location, and the type of traffic anticipated. 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. Types of Structures & Loads-Page 12 of 21 Impact Loads: Moving vehicles may bounce or side-sway as they move over a bridge, and therefore they impart an impact to the deck. The percentage increase of the live loads due to impact is called the impact factor, I. This factor is generally obtained from formulas developed from experimental evidence. For example, for highway bridges the AASHTO specifications require that: 50 I= 𝐿+125 𝑏𝑢𝑡 𝑛𝑜𝑡 𝑙𝑎𝑟𝑔𝑒𝑟 𝑡ℎ𝑎𝑛 0.3 Where L is the length of the span in feet that is subjected to the live load. In some cases provisions for impact loading on the structure of a building must also be taken into account. For example, the ASCE 7-10 Standard requires the weight of elevator machinery to be increased by 100%, and the loads on any hangers used to support floors and balconies to be increased by 33%. Design Codes Building Code Requirements for Reinforced Concrete, American. Conc. Inst. (ACI) Manual of Steel Construction, American Institute of Steel Construction (AISC) Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials (AASHTO) National Design Specification for Wood Construction, American Forest and Paper Association (AFPA) Manual for Railway Engineering, American Railway Engineering Association (AREA) Types of Structures & Loads-Page 13 of 21 Exercise Example 1.1: The floor of a heavy storage warehouse building is made of 6in.-thick concrete. The floor is a slab having a length of 10 ft and width of 8 ft. Determine the total factored concentrated load. Solution: 6" Dead Load = 150 𝑙𝑏/𝑓𝑡 3 × {( ) × (8𝑓𝑡) × (10𝑓𝑡)} 12 =6000lb =6 kips Live Load=250 𝑙𝑏/𝑓𝑡 2 × (8𝑓𝑡) × (10𝑓𝑡) =20000 lb=20 ki Factored Load =1.2(6) + 1.6(20) = 39.2 kips Example 1.2: The “New Jersey” barrier is commonly used during highway construction. Determine its weight per foot of length if it is made from plain stone concrete. Solution: sin 55 sin 35 = ⇒ 𝑥 = 8.4𝑖𝑛 12 𝑥 sin 75 1.6 = ⇒ 𝑥 = 5.97𝑖𝑛 𝑥 sin 15 Cross-sectional Area 1 = (6×24)+(7.2×12) +2( ×8.4×12) 2 1 +(4×5.97)+ 2( ×1.6×5.97)=364.63 in2=2.53ft2 2 Load per unit length= 2.53×144=364.32 lb/ft Types of Structures & Loads-Page 14 of 21 Example 1.3: The floor beam is used to support the 6-ft width of a lightweight plain concrete slab having a thickness of 4 in. The slab serves as a portion of the ceiling for the floor below, and therefore its bottom is coated with plaster. Furthermore, an 8-ft-high, 12-in.-thick lightweight solid concrete block wall is directly over the top flange of the beam. Determine the dead load on the beam measured per foot of length of the beam. Solution: Dead load of lightweight plain Concrete Slab = 8𝑙𝑏 𝑓𝑡 2 .𝑖𝑛 × 4𝑖𝑛 × 6𝑓𝑡 =192lb/ft Dead load of Plaster Ceiling = 5𝑙𝑏 𝑓𝑡 2 × 6𝑓𝑡 =30lb/ft Lightweight Concrete Block Wall = 105𝑙𝑏 𝑓𝑡 3 × 8𝑓𝑡 × 1𝑓𝑡=840lb/ft Total dead Load on Beam= 192+30+840=1062 lb/ft Example 1.4: The unheated storage facility as shown is located on flat open terrain in Murree, where the specified ground snow load is 15lb/ft2. Determine the design snow load on the roof which has a slope of 40. Solution: Since the roof slope is < 50, So Ce =0.8 due to the open area, Ct = 1.2 and Is = 0.8.Thus, 𝑃𝑓 = 0.7𝐶𝑒 𝐶𝑡 𝐼𝑠 𝑝𝑔 =0.7(0.8)(1.2)(0.8)(15lb/ft2)= 8.06 lb/ft2 Since 𝑝𝑔 =15lb/ft2<20lb/ft2, then also 𝑃𝑓 = Is 𝑝𝑔 =1.2(15lb/ft2) =18lb/ft2 By comparison choose 𝑃𝑓 =18lb/ft2 Types of Structures & Loads-Page 15 of 21 Example 1.5: An unheated horse stall has a flat roof with a slop of 80mm/m. it is located in open field where the ground snow load is 0.72 KN/m2. Determine the snow load that is requires to design the roof of the stall. Solution: 𝜃 = tan−1 ( 80 1000 ) = 4.57° < 5° Ce =0.8 Ct = 1.2 Is = 1.2 𝑃𝑓 = 𝐶𝑒 𝐶𝑡 𝐼𝑠 𝑝𝑔 =0.7(0.8)(1.2)(1.2)(0.72 KN/m2) =0.81KN/m2 Since 𝑝𝑔 =0.72 KN/m2<0.96 KN/m2, Then also 𝑃𝑓 = Is 𝑝𝑔 =1.2(0.72 KN/m2) = 0.576 KN/m2 By comparison choose 𝑃𝑓 =0.81 KN/m2 Types of Structures & Loads-Page 16 of 21 Example 1.6: The slab of a library room is supported by beams AB, CD and DE as shown. Each beam is 15ft long and are spaced 7ft on centers. The slab is made from normal weight reinforced concrete that is 6in thick. Calculate the factored dead load per ft of length on edge and center beams. A 3.5 3.5ftft 15ft 15ft 15ft B 7 ft 77ftft C D 3.5 ft 7 ft E F Solution: The dead load on the floor is due to the weight of the concrete slab. Since 𝐿𝑦 𝐿𝑥 = 15 7 = 2.14 it is a one way slab and it delivers its load to the supporting members by one-way action). Factored dead load on edge beam= 1.2(150×3.5ft×0.5ft) =262.5 lb/ft Factored dead load on center beam= 1.2(150×7ft×0.5ft) =525 lb/ft 262.5 lb/ft 525 lb/ft C D Center Beam A B Edge Beam Types of Structures & Loads-Page 17 of 21 Example 1.7: The floor of a classroom is to be supported by the bar joists shown in Fig. Each joist is 15ft long and they are spaced 2.5ft on centers. The floor itself is to be made from lightweight concrete that is 4 in. thick. Neglect the weight of the joists and the corrugated metal deck, and determine the load that acts along each joist. Solution: The dead load on the floor is due to the weight of the concrete slab. Since Ly/Lx >2 the concrete slab is treated as a one-way slab. Load due to light weight concrete slab= 8𝑙𝑏 𝑓𝑡 2 .𝑖𝑛 × 4𝑖𝑛 × 2.5𝑓𝑡 =80lb/ft The live load for a classroom is 40 lb/ft2 Live load acting on the joist=40 lb/ft2× 2.5𝑓𝑡=100 lb/ft Therefore the uniform load along on joist=w=80+100=180 lb/ft Types of Structures & Loads-Page 18 of 21 Example 1.8: Consider the framing system in which a reinforced concrete slab having a thickness of 6in is placed on the beams AB, CD, and EF and these beams are rest on the girders AE and BF as shown. The length of the beam is 10ft and these are placed 5ft center to center. Determine the load per ft of length on beams and concentrated load on each column A, B, E and F. Solution: Since Ly/Lx ≥2 the concrete slab is treated as a one-way slab. Density of the concrete=150 lb/ft3 Load on the beam AB and EF= 150× 2.5 × Load on the beam CD= 150× 5 × 6 12 6 12 =187.5 lb/ft =375 lb/ft 187.5 lb/ft 375 lb/ft C D A 10ft 10ft 1875 lb B 1875 937.5 Load on the girder AE and BF from beam AB= (187.5×10)/2=937.5lb Load on the girder AE and BF from beam EF= (187.5×10)/2=937.5lb Load on the girder AE and BF from beam CD= (375×10)/2=1875lb Types of Structures & Loads-Page 19 of 21 937.5 1875lb 937.5lb 937.5lb A 1875lb 1875lb E 5ft 5ft 1875lb Load on the column=937.5+(1875/2)=1875lb Example 1.9: A concrete slab is supported by four 10-ft-long edge beams, AB, BD, DC, and CA as shown in fig. if the thickness of the slab is 8in then calculate the load per ft length on the beam AB. Solution: Since Ly/Lx <2 the concrete slab is treated as a two-way slab. Due to twoway slab action, the assumed tributary area for beam AB is determined by constructing diagonal 45° lines. Density of the concrete=150 lb/ft3. Load on the beam AB= 150× 5 × 8 12 =500 lb/ft Types of Structures & Loads-Page 20 of 21 Example 1.10: A slab of length 15ft and width 10ft is supported by four edge beams, AB, BD, DC, and CA as shown in fig. If the slab is made from reinforced concrete having a thickness of 8in then calculate the load per ft length on the beam AB and AC. Solution: As Ly/Lx <2 the concrete slab is treated as a two-way slab. Density of the concrete=150 lb/ft3 Load on the beam AB= 150× 5 × Load on the beam AC= 150× 5 × 8 12 8 12 =500 lb/ft =500 lb/ft Example 1.11: The flat roof of the steel-frame building shown in the photo is intended to support a total load of 2KN/m2 over its surface. Determine the roof load that is transmitted to beam BC. Solution: In this case Lx=4m and Ly=5m. Since Ly/Lx=1.25<2 we have two-way slab action. Load on surface of the slab= 2KN/m2 Load on the beam BC = (2KN/m × 2)+(2KN/m × 2) =8KN/m 2 2 Types of Structures & Loads-Page 21 of 21 8KN/m