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bài giảng về móng bè bằng tiếng AnhMat-Foundation.
Lecture #10The Design of Mat Foundations- Compensated mats- Rigid mats- Semi-rigid mats A mat foundation is primarily shallow foundation. In essence, it is an expanded continuous footing and is usually analyzed in the same way.Mat foundations are sometimes referred to as raft foundations.Mat foundations are selected when:1. The area covered by the individual footings exceeds 50% of the structural plan area. This is usually the case for buildings higher than 10-stories, and/or on relatively weak soils where q < 3 ksf = 150 kPa;2. The building requires a deep basement, below the phreatic surface. For example, to build several levels of parking, for mechanical systems, access to subway stations, etc;3. The Engineer wishes to minimize the differential settlement in variable (that is, heterogeneous) soils, or if pockets of extremely weak soils are known to be present;4. The Engineer wishes to take full advantage of the soil’s increasing bearing capacity with depth by excavating basements, and thereby seek a fully or a partially compensated foundation. Problem Soils That May Necessitate the Use of Mat Foundations.1. Compressible soils, occur in highly organic soils including some glacial deposits and certain flood plain areas. Highly plastic clays in some glacial deposits and in coastal plains and offshore areas there can be significant amounts of compressible soils. Problems involved are excessive settlements, low bearing capacity, and low shear strength.2. Collapsing soils, settlement in loose sands and silts primarily. Densification occurs by the movement of grains to reduce the volume. Typically includes shallow subsidence. May occur in sandy coastal plain area, sandy glacial deposits, and alluvial deposits of intermountain regions of the western United States.3. Expansive soils, containing swelling clays, mainly Montmorillite, which increase in volume when absorbing water and shrink when loosing it. Climate is closely related to the severity of the problem. Semi-arid and semi-humid areas with swelling clays are the most severe because the soil moisture active zone has the greatest thickness under such conditions. Foundation supports should be placed below the active soil zone. Expansive soils are most prevalent on the Atlantic and Gulf coastal plain and in some areas of the central and western United States. Photograph of the construction of the mat foundation for the new Century Hotel in San Francisco (1999). Having had 25 feet of dredge spoils and excavated soil stored on its construction site may have saved Harvest States Cooperative up to a half million dollars in construction costs on its new Amber Milling facility in Houston, Texas. For about 20 years, the dredged material from nearby waterways and excavated soil from a neighboring project sat on the mill site. The material acted as a surcharge which compacted the soil to the point of allowing for mat foundations and shallow footings instead of more traditional pile foundations. Without the need for 60- to 80- foot piles, the shallow foundations also allowed construction without disturbing contaminated soils below. Most mat foundations employ a constant thickness ‘T’. This type of constant thickness is called a flat plate mat.A AA - A In most tall and large buildings, the mat thickness T varies with the load. Therefore, the Engineer may desire to separate the various sections of the structure.Mats have been used for centuries:Assyrians joined ceramic blocks with asphalt.Chinese joined large stones with keys of molten lead.Romans joined stones with hydraulic cements.Today, we exclusively use reinforced concrete. Many buildings are designed for multi-purposes, such as the one shown above, where a light structure is required for offices, versus heavier structural frames are required for the ware-house. The dilatation joint between them helps isolate the structures, but not the soil reactions. Therefore, a mat foundation may be a solution to minimize the coupled actions. When large column loads must be designed to prevent shear, other thickening designs are common. Below are some typical flat plates with thickening under the columns. Slab with basement walls acting as stiffness for the mat grillages. [...]... Example 4. Design the steel lying in the East-West direction of the mat shown below with external dimensions of 42 feet by 74 feet. The columns are all 15”by 15”, the LF = 1.6, f c ’ = 3 ksi f y = 50 ksi, and q all = 1.0 ksf. B G F H Cy x A D 85k 110k 97k 330k 330k 250k 330k 330k 250k 85k 110k 90k 1’ 74’ 1’ 15” 15” 1ft D/2 D/2 Edge of the mat Q = 330 kips Step 3. Determine the mat thickness T. The maximum... effective depth d of the mat by checking for diagonal tension shear at the columns (ACI 318 11.12.2.1c); 7) From the all the moment diagrams of all the strips in one direction, choose the maximum positive and negative moments per unit of width; and 8) Determine the areas of steel per unit width for the positive and the negative reinforcement in both directions. y x xy Mx My Q q AII =±± For the critical... Solution. Step 1. Find the total columnar load upon the mat. The area of the mat A = BL = (16.5 m)(21.5 m) = 355 m 2 . I x = BL 3 /12 = (16.5 m)(21.5 m) 3 /12 = 13,700 m 4 I y = LB 3 /12 = (21.5 m)(16.5 m) 3 /12 = 8,050 m 4 SQ = 350 + 2(400) + 450 + 2(500) + 2(1200) + 4(1500) = 11,000 kN Step 2. Find the soil pressures at the mat invert. Find the centroid of the column loads (location of the resultant R)... Analysis and Design Procedure for Rigid Mats. 1) Calculate total column load, Q = Q 1 + Q 2 + Q 3 … ; 2) Determine the pressure on the soil q, at the mat s invert, 3) Compare the resulting soil pressures with the allowable soil pressure; 4) Divide the mat into several strips in the x and y directions; 5) Draw the shear V and the moment M diagrams for each strip in both directions; 6) Determine the effective... found by using the x-y coordinate system off the mat foundation. Determine the average soil reaction. (92.34(78.8)69.8) 79 6 avg qpsf ++ ∆== Therefore, the average pressure increase in the clay layer is, The pressure p o at the center of the clay layer is, p o = γ sand h sand + γ’ sand h’ sand + γ’ clay h’ clay = (100)(4) + (100–62.4)(16) + (125-62.4)(8 ft/2) = 1,252 psf Finally, determine the settlement... d/2d/2 24+d 24+d d/2 d/2 Once the stress distribution is known for a rigid mat, the shears V and moment M can be found, V = S Qi – ∫ σ dx M = S (Qi xi) – ∫ σ x dx The loads Qi do not usually include the mat weight, but should be in the final iteration. The assumption of linear distribution is conservative for rigid mats, and yields satisfactory results. Many buildings are designed for multi-purposes, such as the one... 3,800) = 0.931 Example 1. A mat foundation is being designed for a small office building with a total live load of 250 kips and dead load of 500 kips. Find: (a) the depth D f for a fully compensated foundation, (b) the depth D f if a soft clay with γ = 120 pcf, c u = 100 psf and q all = 1 ksf with FS = 3, and (c) the settlement under mid -mat for the partially compensated mat shown if D f = 2 ft. A 60' 40' Plan 2' 2' 16' 8' Sand Sand Clay Sand 60'... structure is required for offices, versus heavier structural frames are required for the ware- house. The dilatation joint between them helps isolate the structures, but not the soil reactions. Therefore, a mat foundation may be a solution to minimize the coupled actions. ABMN BCDKLM DEFIJK FGHJ q aver = 1.147 kip/ft 2 1.18 1.22 1.253 Strip width 14 ft 24 ft 24 ft 14 ft Mat width 96 ft 96 ft 96 ft... diagrams. Example 2. Using the Independent Strip Method, analyze and design the 16.5 m by 21.5 m mat shown in the figure on the next slide. Given that f’ c = 20.7 MN/m 2 , f y = 413.7 MN/m 2 , with a load factor = 1/7. Solution. Divide the mat into 3 strips AGHF, GIJH, and ICDJ, where Strip AGHF, B 1 = 4.25 m, Strip GIJH, B 2 = 8 m, and Strip ICDJ, B 3 = 4.25 m. Determination of the load eccentricities... Climate is closely related to the severity of the problem. Semi-arid and semi-humid areas with swelling clays are the most severe because the soil moisture active zone has the greatest thickness under such conditions. Foundation supports should be placed below the active soil zone. Expansive soils are most prevalent on the Atlantic and Gulf coastal plain and in some areas of the central and western United . Lecture #1 0The Design of Mat Foundations- Compensated mats- Rigid mats- Semi-rigid mats A mat foundation is primarily shallow. analyzed in the same way .Mat foundations are sometimes referred to as raft foundations .Mat foundations are selected when:1. The area covered by the individual