Axial load ratio

The next edition of ASCE 41 - ASCE/SEI 41-13 (ASCE 2014) - has just been published and expands the remit of ASCE 41 to include the multitiered seismic assessment approach previously found in ASCE/SEI 31-03 (ASCE 2003). The nonlinear response history analysis procedures have been expanded somewhat, reflecting significantly increased application of this method and the availability of research efforts such as Deierlein et al. 2010 NEHRP Consultants Joint Venture 2010, since the publication of ASCE/SEI 41-06. Nonlinear behavior of force-controlled actions is now permitted to allow explicit modeled of post-failure redistribution following brittle failure. Finally, and importantly for this entry, the unreinforced masonry (URM) wall provisions have been updated major changes are that bed-joint sliding is now considered a deformation-controlled action, while the pier rocking mechanism is now limited to lower axial load ratios and for piers at least 6" in thickness. 

There are two well-accepted models for stress transfer. In the Cox model [94] the composite is considered as a pair of concentric cylinders (Fig. 19). The central cylinder represents the fiber and the outer region as the matrix. The ratio of diameters r/R) is adjusted to the required Vf. Both fiber and matrix are assumed to be elastic and the cylindrical bond between them is considered to be perfect. It is also assumed that there is no stress transfer across the ends of the fiber. If the fiber is much stiffer than the matrix, an axial load applied to the system will tend to induce more strain in the matrix than in the fiber and leads to the development of shear stresses along the cylindrical interface. Cox used the following expression for the tensile stress in the fiber (cT/ ) and shear stress at the interface (t) ... 

For most practical purposes, the onset of plastic deformation constitutes failure. In an axially loaded part, the yield point is known from testing (see Tables 2-15 through 2-18), and failure prediction is no problem. However, it is often necessary to use uniaxial tensile data to predict yielding due to a multidimensional state of stress. Many failure theories have been developed for this purpose. For elastoplastic materials (steel, aluminum, brass, etc.), the maximum distortion energy theory or von Mises theory is in general application. With this theory the components of stress are combined into a single effective stress, denoted as uniaxial yielding. Tlie ratio of the measure yield stress to the effective stress is known as the factor of safety. 

Because there is a large literature, we restrict ourselves to an interesting example, useful for understanding the axial support of thin mirrors. Consider a thin circular plate of radius a and thickness h, with elastic constant E and Poissons ratio v. Let this plate be axially loaded by gravity and assume we will support this plate against this load by N supports. This is shown in Fig. 2. 

Poisson s ratio-ratio of lateral strain to axial strain in an axial loaded specimen. It is a constant that relates the modulus of rigidity to Young s modulus. 

Elasticity of solids determines their strain response to stress. Small elastic changes produce proportional, recoverable strains. The coefficient of proportionality is the modulus of elasticity, which varies with the mode of deformation. In axial tension, E is Young s modulus for changes in shape, G is the shear modulus for changes in volume, B is the bulk modulus. For isotropic solids, the three moduli are interrelated by Poisson s ratio, the ratio of traverse to longitudinal strain under axial load. 

FIGURE 49.2 Ratio of total contact area to joint area in the (a) anterior/middle facet and (b) posterior fecet of the subtalar joint as a function of applied axial load for three different positions of the foot. (From Wagner U.A., Sangeorzan B.J., Harrington R.M., and Tencer A.F. 1992. /. Orthop. Res. 10 535. With permission.)... 

Poisson s ratio (v or )i) is the ratio of transverse strain to longitudinal strain in an axial loaded specimen. 

The traffic volume is expressed in equivalent standard (80 kN) axles. The process of converting axial loads into typical axles uses equivalency factors, determined from the equivalence law to the power of 4. The strength of all layers is expressed by their elastic moduli and Poisson ratios. The method also considered environmental temperatures, that is, monthly average air temperatures converted to weighted layer temperature, since they directly affect the stiffness of the asphalt considered in the design. 

Undoubtedly, as the axial loads pass over the rigid slab, stresses are developed. The severity of stresses that developed depends on the position of the wheels (loading point) with respect to the slab. In addition, axle configuration, frequency of loading (intensity of traffic), quality/strength of sub-base and subgrade and Poisson s ratio should also be considered. 

Poisson s ratio Ratio of lateral strain to axial strain in axially loaded specimen. 

Fig. 2. An example of the stress distribution in an axially loaded butt joint (after Adams et al.y (ao = applied average axial stress a = 2.5 GPa Eg = 69 GPa aspect ratio = 20)...

If the slenderness ratio exceeds the above specified limits, the effects can be approximated by the use of moment magnification factor. If the slenderness ratio KLJr exceeds 100, however, a more detailed second-order nonlinear analysis will be required. Any detailed analysis should consider the influence of axial loads and variable moment of inertia on member stiffness and forces and the effects of the duration of the loads. 

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