Blog Archives

The hit-and-miss method

Posted by on 21/ 11/ 15

Referring to Fig. 6.6, a rectangular region Ш = {(x, y)a < x < b, 0 < y < c} is superimposed to enclose the area Ф = {(x, y)a < x < b, 0 < y = g(x) < c} represented by Eq. (6.49). By the hit-and-miss method, the rectangular region Ш containing the area under g(x), that is, Ф, is hung on the wall, and one is to throw n darts on it. Assume that the darts fly in a random fashion and that all n darts hit within the rectangular region. The area under g(x), then, can be estimated as the proportion of n darts hitting the target multiplied by the known area of rectangular region Ш, that is,

G = A(6.50)

where G is the estimate of the true area G under g(x), A = c(b – a) is the area of the rectangular region, and nh is the number of darts hitting the target out of a total of n trials.

The hit-a...

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SLIP BASE DESIGNS

Posted by on 21/ 11/ 15

Slip base designs for small sign supports consist of two components: (1) the anchor assembly up to the bottom of the slip base, and (2) the sign support, containing the top of the slip base on the lower end and the sign panel on the upper end. Small sign slip bases are categorized as unidirectional or multidirectional.

Slip base designs allow the use of stronger sign supports than can safely be achieved by base-bending or fracture designs. The anchor piece of slip base designs is fixed into a foundation and should remain immovable during an impact. The sign sup­port is connected to the anchor piece with bolts through a plate, which are attached to a similar plate on the anchor piece. The holes in the plates are slotted...

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PROBLEMS RELATED TO TEMPERATURE AND Laying Techniques

Posted by on 21/ 11/ 15

Thermal problems occurring during the manufacture and placement of SMA are often underestimated, and yet they can lead to significant defects in a new course and reduce its working lifetime. It has already been indicated in Section 11.6 that the placement of a cool SMA mixture may result in an excessive content of voids.

Aside from problems directly connected with the temperature of a mixture, the effects of wrongly adjusted equipment during placement may be observed. Now and again errors in laying and the effects of an unsuitable mixture temperature superim­pose onto each other. These problems may be divided as follows:

• Manufacture and transport

• Unsuitable temperature of an SMA ingredients during manufacturing and storing in a silo

• Wrong methods of transporting a mixture

• La...

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SMA SEEPAGE AND PERMEABILITY TO WATER

Posted by on 21/ 11/ 15

SMA surface seepage is directly related to excessive porosity of a compacted mixture (see Chapter 12) and the condition (watertightness) of the course situated just under the SMA. When assessing the watertightness of an SMA course, one must not forget that water permeability is determined not only by the contents of voids on the surface of a compacted course but also by the shape and interconnectedness of the inner pores. Finally, most national regulations and numerous publications recommend a [68]

image118

FIGURE 11.10 The surface of an SMA course just after spreading at too low a temperature. (Photo courtesy of Krzysztof Blazejowski.)

image119

FIGURE 11.11 Seepage of water through an SMA layer. (Photo courtesy of Bohdan Dolzycki.)

limit of 6...

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TOO POROUS SMA STRUCTURE

Posted by on 21/ 11/ 15

Just as it is possible to find an SMA course that is too closed, so too it is possible to find a course that has too high a void content. This problem may occur over very large areas, which are marked by excessive porosity. Local porosity over smaller areas, is described in Sections 11.8.2.3 through 11.8.2.9.

The issue of how open the SMA structure should be has been debated for some time. True enough, we happen to find a quite porous SMA structure every now and then. An investor or may owner sometimes agrees to leave in place an SMA that is too closed (after an antiskid treatment); unfortunately an SMA that is too open more often falls victim to a road-milling machine. An open structure (Figure 11...

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CHAMFERING A POST

Posted by on 21/ 11/ 15

Chamfering the tops of railing posts or the ends of beams is a nice finish­ing touch you can add when building a deck or a porch. A plain, square-topped post looks clunky, but in a few minutes’ time you can give the post a more dis­tinguished appearance. All you need is a Speed square and a circular saw. For best results, use a sharp, fine-toothed blade on your saw. If you haven’t tried this technique before, practice on a spare length of 4×4. Also, you may find it easier to make chamfer cuts “on the flat," with the 4×4 set on some saw­horses. It takes a little more experience with a circular saw to chamfer a post that’s already installed verti­cally. Here’s how to chamfer a post in four simple steps:

LAY OUT THE CHAMFER LINES...

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Monte Carlo Integration

Posted by on 21/ 11/ 15
Подпись: Ps = Подпись: ft (t) dt Подпись: (6.47)

In reliability analysis, computations of system and/or component reliability and other related quantities, such as mean time to failure, essentially involve inte­gration operations. A simple example is the time-to-failure analysis in which the reliability of a system within a time interval (0, t) is obtained from

where ft (t) is the failure density function. A more complex example of the reli­ability computation is by load-resistance interference in that the reliability is

Ps = P[R(Xr) > L(Xl)] = P [W(Xr, Xl) > 0] = P [W(X) > 0]

= f fx (x) dx (6.48)

JW (x)>0

where R(XR) and L(XL) are, respectively, resistance and load functions, which are dependent on some basic stochastic variables XR = (X1, X2,…, Xm) and XL = (Xm+1,Xm+2,…,XK), and W(X) is the performance function...

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Begin with the posts

Posted by on 21/ 11/ 15

The most difficult part about building any railing is making sure the posts are well secured to the deck or stairs. Remember:

People will be leaning against the railings, so make them strong. A post that extends up to the roof framing will be solid and secure.

Short posts that support only the railing are more of a concern. Railing posts should be evenly spaced across a deck or porch and no more than 6 ft. apart. A good height for a rail­ing is 36 in. to 42 in.

I like to notch railing posts to fit against the rim joist and on top of the decking (see the photo below). A notched post, installed with a couple of %-in. or l^-in.-dia. carriage bolts, makes for a strong and attractive instal­lation. For a 4×4 post, make notches I/ in...

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TOO CLOSED SMA STRUCTURE

Posted by on 21/ 11/ 15

It happens that, after the completion of an SMA course, a sight reminiscent of mas­tic asphalt may unfold before the observer’s eyes (Figure 11.8). Such a closed SMA structure means utter failure and the likely removal and replacement (possibly by recycling) of the layer. This kind of problem is directly connected to the discussion in Section 11.2 about fat spots of mastic (without segregation) but usually occurs over most or all of the layer.

Reasons for such a significant setback include the following:

• Errors of mixture design

• Too much mastic in relation to the voids’ volume among the compacted coarse aggregates

• Upward designing of a gradation curve in the filler-sand fraction

• Use of weak aggregates

• Errors of compaction—application of excessive compaction energy (t...

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Begin with the posts

Posted by on 21/ 11/ 15

The most difficult part about building any rail­ing is making sure the posts are well secured to the deck or stairs. Remember: People will be leaning against the railings, so make them strong. A post that extends up to the roof fram­ing will be solid and secure. Short posts that support only the railing are more of a concern. Railing posts should be evenly spaced across a deck or porch and no more than 6 ft. apart. A good height for a railing is 36 in. to 42 in.

I like to notch railing posts to fit against the rim joist (see the photo below). A notched post,

installed with a couple of ‘/s-in. or ‘T-in.-dia. carriage bolts, makes for a strong and attractive installation. For a 4×4 post, make notches 1/2 in...

read more