Parts of a roof truss

A roof truss is an engineered panel made up of triangular parts. Set out below are the main structural components and fixing points in a standard 'A' type truss.

1. Apex
2. Apex plate
3. Top chord
4. Heel plate
5. 1/3 point plate
6. Bottom chord
7. Slice plate
8. Heel
9. 1/4 point plate
10. Web
11. Nominal span
12. Overhang

Top chord

The top chord performs the job of a rafter in a conventional roof. It carries the tile battens or sheet roofing battens, and is set at the pitch or angle of the roof. In the example above, there are two top chords which meet at the apex.

Bottom chord

The bottom chord is connected at each end to the top chords using heel plates. It main structural function is to stop the top chords from spreading apart when they are under a load. It also serves as aceiling joist, allowing the ceiling lining to be fixed to the underside.

Webs

The webs are the internal members that run between the top and bottom chords. They help to give the truss its strength and rigidity by transferring the stresses in the chords throughout the structure. This is what enables a truss to span the full width of a building using small cross-sectional members.

Joints

The chords and webs are joined at the panel points by nail plates. The plates are galvanised steel sheets that have spikes protruding on one side. When they are pressed into the timber, with one plate on each side of the join, they form a solid fixing that is very strong when the truss is in an upright position.

Negative Effects of Computers and the Internet on Society

Computers and the Internet have touched almost all aspects of life. It is rare to come across a business or household that does not experience routine use of a computer in some shape or form.

Technology has allowed people to have higher levels of convenience and proficiency. Many people today would find it very difficult to go back to an age where computers were not in existence.

In addition, society has become accustomed to on-demand answers or solutions to requests or services and the Internet is the platform which fulfills this need. These are some of the positive effects of technology on society.

While there have been many positive effects of computers on society, there have also been some drawbacks too. Issues such as security and complacency have increased in addition to society's ever growing dependence on computers.

Let's take a look at some of the positive and negative effects of computers and the Internet on society:Computers and the Internet have touched almost all aspects of life. It is rare to come across a business or household that does not experience routine use of a computer in some shape or form.

Technology has allowed people to have higher levels of convenience and proficiency. Many people today would find it very difficult to go back to an age where computers were not in existence.

In addition, society has become accustomed to on-demand answers or solutions to requests or services and the Internet is the platform which fulfills this need. These are some of the positive effects of technology on society.

While there have been many positive effects of computers on society, there have also been some drawbacks too. Issues such as security and complacency have increased in addition to society's ever growing dependence on computers.

Let's take a look at some of the positive and negative effects of computers and the Internet on society:

♦Negative Effects

Unfortunately despite all the positives associated with computers and the Internet, there are some drawbacks too. These are issues society has to contend with in order to achieve the benefits and often trade-offs have to be made.

Security is one of the most prominent negative effects which emerges with the use of technology. The criminal element in society has found many ways to exploit and harm others by using computers and the Internet as a weapon instead of the tool it was designed to be.

Crimes such as identity theft, hacking, embezzlement, and other kinds of monetary theft have increased the risks of doing business online, and these have to be mitigated through using software and being vigilant. These concerns should not deter people from using the Internet, but it is a real concern which must be dealt with.

Complacency is another negative effect. While computers and the Internet have enhanced quality of life, sometimes the question begs asking of whether or not society has become too dependent on computers instead of thinking for one's self. Many people operate on the assumption the computer is always right, and this can be a dangerous notion.

While computers themselves don't make mistakes, the human design behind the software can and do make mistakes, nothing is 100% infallible.

Programmers, while in most cases are pretty accurate, do have typos or software can contain glitches. Since technology is essentially tied to everything from banking, parking meters, health insurance, and medical care, it is important to be vigilant and if something seems off to always question it.

This complacency leads to dependence. Are computers doing too much "thinking" for people? Today many people have no idea of how to manually do transactions or activities that computers routinely take care of these days.

AVERAGE TOTAL COST CURVE:

A curve that graphically represents the relation between average total cost incurred by a firm in the short-run product of a good or service and the quantity produced. The average total cost curve is constructed to capture the relation between average total cost and the level of output, holding other variables, like technology and resource prices, constant. The average total cost curve is one of three average curves. The other two are average variable cost curve and average fixed cost curve. A related curve is the marginal cost curve.

The average total cost curve is U-shaped. Average total cost is relatively high for small quantities of output, then as production increases, it declines, reaches a minimum value, then rises.

Because average total cost is a combination of average variable cost andaverage fixed cost, the U-shape of the average total cost curve is a result of both underlying averages. At small production quantities, both average fixed cost and average variable cost decline, resulting in a negatively-sloped average total cost curve.

However, because of the law of diminishing marginal returns, average variable cost eventually increases, which overwhelms the continuing decline of average fixed cost and results in a positively-sloped average total cost curve.

Average Total Cost Curve

The graph to the right is the average total cost curve for theshort-run production of Wacky Willy Stuffed Amigos (those cute and cuddly armadillos and tarantulas). The quantity of Stuffed Amigos production, measured on the horizontal axis, ranges from 0 to 10 and the average total cost incurred in the production of Stuffed Amigos, measured on the vertical axis, ranges from about $3 to over $8.

As noted above, the average total cost curve is U-shaped. For the first 6 Stuffed Amigos, average total cost declines from over $8 to a low of $3. However, for the production beyond 7 Stuffed Amigos, average total cost increases.

While it would be easy to attribute the U-shape of the average total cost curve to increasing, then decreasing marginal returns (and the law of diminishing marginal returns), such is not completely true. While the law of diminishing marginal returns is indirectly responsible for the positively-sloped portion of the average total cost curve, the negatively-sloped portion is attributable to increasing marginal returns, and perhaps more importantly to declining average fixed cost.

The average total cost curve is most important to the analysis of a firm's short-run production when compared to the price. If price is greater than average total cost, then a firm receives economic profit on each unit of the output produced and sold. If price is less than average total cost, then a firm incurs a loss on each unit produced and sold. However, whether or not the loss is great enough to force the firm to shut down production depends on a comparison between price and average variable cost.

potential benefits from monopoly

The debate about monopoly will never be settled! 

The consensus seems to be that the economic case for and against monopoly needs to be judged on a case by case basis  - particularly when assessing the impact on economic welfare.

The standard economic case against monopoly is that, with the same cost structure, a monopoly supplier will produce at a lower output and charge a higher price than a competitive industry. This leads to a net loss of economic welfare and efficiency because price is driven above marginal cost - leading to allocative inefficiency.

The diagram below shows how price and output differ between a competitive and a monopolistic industry. We have assumed that the cost structure for both the competitive firm and the monopoly is the same - indeed we have assumed that output can be supplied at a constant marginal and average cost.

Assuming that the monopolist seeks to maximise profits and that they take the whole of the market demand curve, then the price under monopoly will be higher and the output lower than the competitive market equilibrium.

This leads to a deadweight loss of consumer surplus and therefore a loss of static economic efficiency.

CAN MONOPOLY BE DEFENDED?

Monopoly and Economies of Scale

Because monopoly producers are often supplying goods and services on a very large scale, they may be better placed to take advantage of economies of scale - leading to a fall in the average total costs of production. These reductions in costs will lead to an increase in monopoly profits but some of the gains in productive efficiency might be passed onto consumers in the form of lower prices. The effect of economies of scale is shown in the diagram above.

Economies of scale provide potential gains in economic welfare for both producers and consumers.

Regulation of monopoly

Because of the potential economic welfare loss arising from the exploitation of monopoly power, the Government regulates some monopolies. Regulators can control annual price increases and introduce fresh competition into particular industries

Monopoly and Innovation

 (Research and Development)

How are the supernormal profits of monopoly used?

 

Is consumer surplus of equal value to producer surplus?

Are large-scale firms required to create a comparative advantage in global markets? Some economists argue that large-scale firms are required to be competitive in international markets.

 

 

However some of the supernormal profits might be used to invest in research and development programmes that have the potential to bring dynamic efficiency gains to consumers in the markets. There is a continuing debate about whether competitive or monopolistic markets provide the best environment for high levels of research spending.

Price Discrimination

Are there potential welfare improvements from price discrimination? Some forms of price discrimination benefit certain consumers.

Domestic monopoly but international competition

A firm may have substantial domestic monopoly power but face intensive competition from overseas producers. This limits their market power and helps keep prices down for consumers. A good example to use here would be the domestic steel industry. Corus produces most of the steel manufactured inside the UK but faces intensive competition from overseas steel producers.

Contestable markets!

Contestable market theory predicts that monopolists may still be competitive even if they enjoy a dominant position in their market. Their price and output decisions will be affected by the threat of "hit and run entry" from other firms if they allow their costs to rise and inefficiencies to develop. 

Organic Compounds

The chemical compounds of living things are known as organic compounds because of their association with organisms. Organic compounds, which are the compounds associated with life processes, are the subject matter of organic chemistry. Among the numerous types of organic compounds, four major categories are found in all living things: carbohydrates, lipids, protein, and nucleic acids.

Carbohydrates

Almost all organisms use carbohydrates as sources of energy. In addition, some carbohydrates serve as structural materials. Carbohydrates are molecules composed of carbon, hydrogen, and oxygen; the ratio of hydrogen atoms to oxygen atoms is 2:1.

Simple carbohydrates, commonly referred to as sugars, can be monosaccharides if they are composed of single molecules, or disaccharides if they are composed of two molecules. The most important monosaccharide is glucose, a carbohydrate with the molecular formula C₆H₁₂O₆. Glucose is the basic form of fuel in living things. It is soluble and is transported by body fluids to all cells, where it is metabolized to release its energy. Glucose is the starting material for cellular respiration, and it is the main product of photosynthesis.

1 shows that in the synthesis of sucrose, a water molecule is produced. The process is therefore called a dehydration. The reversal of the process is hydrolysis, a process in which the molecule is split and the elements of water are added.) Lactose is composed of glucose and galactose units. 

Figure 1

Glucose and fructose molecules combine to form the disaccharide sucrose.

Complex carbohydrates are known as polysaccharides. Polysaccharides are formed by linking innumerable monosaccharides. Among the most important polysaccharides are the starches, which are composed of hundreds or thousands of glucose units linked to one another. Starches serve as a storage form for carbohydrates. Much of the world's human population satisfies its energy needs with the starches of rice, wheat, corn, and potatoes.

Two other important polysaccharides are glycogen and cellulose. Glycogen is also composed of thousands of glucose units, but the units are bonded in a different pattern than in starches. Glycogen is the form in which glucose is stored in the human liver. Cellulose is used primarily as a structural carbohydrate. It is also composed of glucose units, but the units cannot be released from one another except by a few species of organisms. Wood is composed chiefly of cellulose, as are plant cell walls. Cotton fabric and paper are commercial cellulose products.

Lipids

Lipids are organic molecules composed of carbon, hydrogen, and oxygen atoms. The ratio of hydrogen atoms to oxygen atoms is much higher in lipids than in carbohydrates. Lipids include steroids (the material of which many hormones are composed), waxes, and fats.

2 ). A glycerol molecule contains three hydroxyl (—OH) groups. A fatty acid is a long chain of carbon atoms (from 4 to 24) with a carboxyl (—COOH) group at one end. The fatty acids in a fat may be all alike or they may all be different. They are bound to the glycerol molecule by a process that involves the removal of water. 

Arithmetic Operations and Functions

Operations

In FORTRAN, addition and subtraction are denoted by the usual plus (+) and minus (-) signs. Multiplication is denoted by an asterisk (*). This symbol must be used to denote every multiplication; thus to multiply N by 2, we must use 2 * N or N * 2not 2N. Division is denoted by a slash (/), and exponentiation is denoted by a pair of asterisks (**).

Operator	Operation
+	addition, unary plus
-	subtraction, unary minus
*	multiplication
/	division
**	exponentiation

Real Arithmetic

Providing all variables and constants in the expression are real, real arithmetic will be carried out as expected, with no decimal places being truncated.

Integer Arithmetic

Providing the expression has all integers, subtraction, addition, multiplication and exponentiation will prove no problem. However integer division is somewhat different than normal division with real values. Integer division ignores the fractional part. Any decimal places are truncated.

Example

5 / 2 gives the result 2 instead of 2.5

3 / 4 gives the result 0 instead of 0.75

Mixed Mode Arithmetic

Mixed mode arithmetic is when an expression contains both reals and integers. If ANY of the operands are real then result of the operation will be real. However, mixed mode arithmetic should be used with extreme care. You may think you have a real operand when in reality you have two integer operands.

Example

5 / 2 * 3.0	is 6.0 Incorrect because the order of operation is left to right. 5/2 = 2 then 2 * 3.0 = 6.0
3.0 * 5 / 2	is 7.5 Correct because of mixed mode arithmetic 3.0 * 5 = 15.0 then 15.0/2 = 7.5

Mixed Mode Variable Assignments

If the variable to which an expression is assigned has been declared as a real variable, any decimal places resulting from the evaluation of the expression will be preserved.

Example

real variable 5 * 2.1 will have a value of 10.5.

However, if the variable to which an expression is assigned has been declared as an integer variable, any decimal places resulting from the evaluation of the expression will be lost.

Example

integer variable 5 * 2.1 will have a value of 10

Priority Rules.

Arithmetic expressions are evaluated in accordance with the following priority rules:

• All exponentiations are performed first; consecutive exponentiations are performed from right to left.
• All multiplication and divisions are performed next, in the order in which they appear from left to right.
• The additions and subtractions are performed last, in the order in which they appear from left to right.

Functions

FORTRAN provides several intrinsic functions to carry out calculations on am number of values or arguments and return as result. Commonly used functions are shown in the table below. To use a function we simply give the function name followed by the argument(s) enclosed in parenthesis.

funtionname (name1, name2,.......)

Some FORTRAN Functions

Function	Description	Type of Argument(s)*	Type of Value
ABS (x)	Absolute value of x	I, R, DP	Same as argument
COS (x)	Cosine of x radians	R, DP	Same as argument
DBLE(x)	Conversion of x to double precision form	I, R	DP
DPROD(x,y)	Double precision product of x and y	R	DP
EXP(x)	Exponential function	R, DP	Same as argument
INT(x)	Integer part of x	R, DP	I
LOG(x)	Natural logarithm of x	R, DP	Same as argument
MAX(xl, . . . , Xn)	Maximum of xl, . . .,xn	I, R, DP	Same as argument
MIN(xl, . . . , xn)	Minimum of xl, . . ., xn	I, R, DP	Same as argument
MOD(x,y)	x (mod y); x - INT(x/y) * y	I, R, DP	Same as argument
NINT(x)	x rounded to nearest integer	R, DP	I
REAL(x)	Conversion of x to real type	I, DP	R
SIN(x)	Sine of x radians	R, DP	Same as argument

Angle of repose

The angle of repose or the critical angle of repose,of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. At this angle, the material on the slope face is on the verge of sliding. The angle of repose can range from 0° to 90°. Smooth, rounded sand grains cannot be piled as steeply as can rough, interlocking sands. If a small amount of water is able to bridge the gaps between particles, electrostatic attraction of the water to mineral surfaces will increase soil strength.

When bulk granular materials are poured onto a horizontal surface, a conical pile will form. The internal angle between the surface of the pile and the horizontal surface is known as the angle of repose and is related to the density, surface area and shapes of the particles, and the coefficient of friction of the material. However, a 2011 study shows that the angle of repose is also gravity-dependent. Material with a low angle of repose forms flatter piles than material with a high angle of repose.  

Contents

• 1 Applications of theory
• 2 Measurement
• 3 Exploitation by antlion and wormlion (Vermileonidae) larvae
• 4 Methods in determining the angle of repose
  • 4.1 Tilting box method
  • 4.2 Fixed funnel method
  • 4.3 Revolving cylinder method 
• 5 Angle of repose of various materials

  Applications of theory 

• 
  
  
• The angle of repose is sometimes used in the design of equipment for the processing of particulate solids. For example, it may be used to design an appropriate hopper or silo to store the material, or to size a conveyor belt for transporting the material. It can also be used in determining whether or not a slope (of a stockpile, or uncompacted gravel bank, for example) will likely collapse; thetalus slope is derived from angle of repose and represents the steepest slope a pile of granular material will take. This angle of repose is also crucial in correctly calculating stability in vessels.
  It is also commonly used by mountaineers as a factor in analysing avalanchedanger in mountainous areas.

  Measurement

  There are numerous methods for measuring angle of repose and each produces slightly different results. Results are also sensitive to the exact methodology of the experimenter. As a result, data from different labs are not always comparable. One method is the triaxial shear test, another is the direct shear test.
  If the coefficient of static friction is known of a material, then a good approximation of the angle of repose can be made with the following function. This function is somewhat accurate for piles where individual objects in the pile are minuscule and piled in random order.

  

  where, μ_s is the coefficient of static friction, and θ is the angle of repose. 

  Exploitation by antlion and wormlion (Vermileonidae) larvae  

  
  
  

• 

• The larvae of the antlions and the unrelated wormlions Vermileonidae trap small insects such as ants by digging conical pits in loose sand, such that the slope of the walls is effectively at the critical angle of repose for the sand. They achieve this by flinging the loose sand out of the pit and permitting the sand to settle at its critical angle of repose as it falls back. Thus, when a small insect, commonly an ant, blunders into the pit, its weight causes the sand to collapse below it, drawing the victim toward the center where the predator that dug the pit lies in wait under a thin layer of loose sand. The larva assists this process by vigorously flicking sand out from the center of the pit when it detects a disturbance. This undermines the pit walls and causes them to collapse toward the center. The sand that the larva flings also pelts the prey with so much loose, rolling material as to prevent it from getting any foothold on the easier slopes that the initial collapse of the slope has presented. The combined effect is to bring the prey down to within grasp of the larva, which then can inject venom and digestive fluids.