360R-06 Design of Slabs-on-Ground
R-30 ACI COMMITTEE REPORT
tải về 2.35 Mb. Chế độ xem pdf
|
| 360R-30 ACI COMMITTEE REPORT
In an analysis that considers the reaction of the subgrade, and that considers the load to be applied over a contact area of radius a ( Fig. 6.1 ), Westergaard derives the expression for critical tension at the top of the slab, occurring at a distance 2 from the corner of the slab (6-2) where f t = concrete tensile stress, psi (Pa); a = radius of load contact area, in. (m); P = load on the slab-on-ground, lb (N); h = slab thickness, in. (m); and in which L is the radius of relative stiffness [in. (m)], equal to (6-3) where E = elastic modulus of concrete, psi (Pa); μ = Poisson’s ratio for concrete—approximately 0.15; and k = modulus of subgrade reaction, lb/in. 3 (N/m 3 ). The value of L reflects the relative stiffness of the slab and the subgrade. It will be large for a stiff slab on a soft base, and small for a flexible slab on a stiff base. Case 2: Wheel load considerable distance from edges of slab—When the load is applied some distance from the edges of the slab, the critical stress in the concrete will be in tension at the bottom surface. This tension is greatest directly under the center of the loaded area, and is given by the expression ] (6-4) Case 3: Wheel load at edge of slab, but removed consid- erable distance from corner—When the load is applied at a point along an edge of the slab, the critical tensile stress is at the bottom of the concrete, directly under the load, and is equal to ] (6-5) For Eq. (6-4) and (6-5), use P in pounds (lb), h in inches (in.), and k in pounds per cubic inch (lb/in. 3 ), then f b will be in pounds per square inch (lb/in. 3 ). log is base 10 log. In the event that the flexural tensile stress in the slab, as given by the previous equations, exceeds the allowable flexural tensile stress on the concrete, it is necessary to increase the thickness of the slab, increase the concrete flexural strength, or provide reinforcement. Such reinforcement is usually designed to provide for all the tension indicated by the analysis of the assumed homogeneous, elastic slab. Its centroid should be no closer to the neutral axis than that of the tension concrete that it replaces. Loads distributed over partial areas—In addition to concentrated loads, it may be that uniform loads distributed over partial areas of slabs will produce the critical design condition. Again, in warehouses, heavy loads alternate with clear aisles. With such a loading pattern, cracking is likely to occur along the centerline of the aisles. In an analysis based on such loading, Rice (1957) derived an expression for the critical negative moment in the slab M c that occurs at the center of the aisle (6-6) where M c = slab moment center of the aisle, in.-lb/in. (m-N/m); λ = , in. –1 (m –1 ); E = elastic modulus of concrete, psi (Pa); I = moment of inertia, in. 4 (m 4 ); a = half-aisle width, in. (m); k = modulus of subgrade reaction, lb/in. 3 (N/m 3 ); w = uniform load, psi (N/m 2 ); and e = base of natural logarithms. Recognizing that the width of the aisle cannot always be predicted exactly, Rice suggested that a “critical aisle width” be used. This width is such as to maximize the above for bending moment (Westergaard 1926). Generally accepted thickness design methods for unre- inforced slabs-on-ground are: • PCA method (Section 6.2.1); • WRI method ( Section 6.2.2 ); and • COE method ( Section 6.2.3 ). Each of these methods, the evolution of which is described in Chapter 1 and previously, seek to avoid live load-induced cracks through the provision of adequate slab cross section by using an adequate safety factor against rupture. The PCA and WRI methods only address live loads imposed on the slab’s interior, while the COE method only considers live loads imposed on the slab’s edges or joints. All three methods assume that the slab remains in full contact with the ground at all locations. Curl-induced stresses are not considered. ACI 117 does provide tolerances for slabs-on- ground, and both the slab designer and the contractor should consider these tolerances. Specifying a minimum thickness may be appropriate. Design examples in Appendixes l , 2 , and 3 show how to use all three methods. 6.2.1 PCA design method—The PCA method is based on Pickett’s analysis (Ringo 1986). The variables used are flexural strength, working stress, wheel contact area, spacing, and the subgrade modulus. Assumed values are Poisson’s ratio (0.15) and the concrete modulus of elasticity (4,000,000 psi [28,000 MPa]). The PCA method is for interior loadings only; that is, loadings are on the surface of the slab, but are not adjacent to free edges. tải về 2.35 Mb. Chia sẻ với bạn bè của bạn:
|