8.6 Concrete :
In the making of concrete, the proportions of the sand, gravel, and Portland or similar cement are carefully measured. The strength of the concrete is partly determined by the amount of cement in the mixture. More cement would give a stronger, more durable mix, but would be more expensive. It is important not to use too much water as this will make the concrete weak. On the other hand, the concrete must be packed densely in the moulds, which cannot be done if the mixture is too dry. Producing concrete of good quality is therefore a skilled business. Nowadays mechanical vibrators are used to make strong compact concrete from fairly dry mixes.
The size of reinforced concrete beams can be reduced if the reinforcement is stretched before the concrete is poured into position and the pull maintained until the concrete is hard and strong. The stretching force is then removed and, as a result, the beam is compressed. This type of concrete usually has reinforcement in the form of wires and is known as prestressed concrete. Sometimes separate blocks of concrete are made with holes through them. Cables of wire are threaded through these holes so that the concrete blocks are like beads on a string. The cables are fetched, wedges are placed in the holes of the end block, and the cables are then released. The effect is to compress the row of blocks so that they form a beam or girder.
Concrete is strong in its resistance to loads trying to crush it (compression), but much weaker in resisting forces that tend to pull it apart (tension). It is not therefore suitable by itself for making beams or other parts liable to be bent or pulled. To overcome this weakness, steel rods may be embedded in the mixture, thus forming reinforced concrete. Reinforced concrete was first developed in France by Joseph L. Lambot in 1849. To make reinforced concrete the steel rods are held in position and the concrete poured round them.
The concrete bonds to the steel reinforcement. Any forces tending to pull the reinforced concrete apart will be resisted by the great strength of the steel rods, or bars. Nearly all concrete used for buildings and structures is reinforced.
Concrete is a kind of artificial rock made from hydraulic cement, crushed stone or gravel, and sand. It has the great advantage that it can be made in whatever shape is needed. For this reason concrete is preferred to natural rock, which is difficult to extract from the ground and which has to be worked to the required shape.
Pre-cast concrete is concrete already made into building sections for later use in housing, bridges, and other structures. They are taken to the site, lifted by cranes, and fixed together with concrete.
By means of concrete it is possible to form such parts of buildings as walls, floors, beams or columns, bridge supports and girders, dams, roads and airfield runways, or blocks of stone of any desired shape. Concrete may be delivered ready-mixed, but it is one of the few building materials that can be made on the building site.
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Lightweight concrete can be made by including processed clinker or air in the mix. Concrete can be made in different colours or painted with special paint. Different patterns can be made on the surface by using different types of shuttering. Sometimes the cement layer on the surface is removed after the concrete has set to expose the stones. This is called exposed aggregate. Concrete can be used for thin roofs called shells over large spaces such as gymnasiums or aircraft hangars. The thin slab is strengthened by curving.
8.7 , :
1. Concrete has the great advantage because
a) it is made from hydraulic cement, crushed stone or gravel, and sand.
b) it is made in any shape.
c) it has to be worked to the required shape.
2. Concrete is the building material that
a) can be made on the building site.
b) cant be delivered ready-mixed to the building site.
c) can support walls, floors, beams, columns, girders.
3. The strength of concrete is determined by the quantity of
a) sand and gravel.
b) water.
c) cement.
4. To make concrete stronger
a) it should be put under loads.
b) steel rods should be embedded.
c) it should be put under compression or tension.
5. The reinforced concrete beam is compressed because
a) it is stretched.
b) the stretching force is removed.
c) holes are made through it.
6. Lightweight concrete can be made by using
a) processed clinker or air.
b) different types of shuttering.
c) exposing the stones.
8.8 Bricks:
Good bricks are the most lasting of man-made building materials. They are not much affected by the weather and, if a building catches fire, brickwork resists the effects of fire longer than most other forms of construction. Bricks are fairly small and light and therefore easy to handle, but when they are bonded together with mortar they make extremely strong structures. Good brickwork needs very little maintenance, lasts for a long time, and looks attractive.
Brick is formed in three ways: the soft-mud, stiff-clay, and pressed brick processes. In the soft-mud process, clay is mixed with water to form a stiff paste which is then thrown by hand or forced by machine into wooden or metal box-like moulds of the size of a brick. Sand or water is sprinkled on the inside of the moulds tokeep the clay from sticking. The sand or water also gives the brick a pleasant finish. Such bricks are called sand-struck or water- struck bricks. The soft, wet bricks are removed from the moulds for drying.
In the stiff-clay process, the ground clay is mixed with water in a long trough containing a revolving shaft with blades. The blades mix the clay with water as they revolve and at the same time push it forward into an extrusion machine. This forces it through a rectangular opening. It is extruded in a long bar of the length and width of a brick. A moving belt carries the clay bar to a cutter, which is a metal frame with a number of wires stretched across it. The wires are brought down on the bar to cut it into bricks, which are then dried. Bricks formed in this way are known as extruded wire-cut bricks.
In the pressed brick system, the clay is semi-dry, and is pressed by a heavy machine into metal moulds under such high pressure that the clay particles hold together. Because pressed brick has very little water, it needs little drying.
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After being formed, bricks are loaded on rail trucks and pushed into driers, and then into kilns to be fired. Drying takes two to three days and then the bricks are ready for firing.
Clay is the material most often associated with bricks, but since the late 19th century other materials have been used. For example, calcium silicate bricks, sometimes known as sand lime bricks, are made by pressing a mixture of moist sand and lime into brick shape by machine.
The bricks are then steamed under high pressure in an autoclave. This process produces bricks of an attractive light sandy colour which can be textured and pigmented in a variety of ways.
Not all bricks are completely solid. Some have frogs in them. They make it easier to press and fire the bricks and reduce the weight. Lighter bricks are easier to handle and cheaper to transport. Nowadays many machine-made bricks have holes in them for similar reasons. These are called perforated bricks. Specials as the name suggests, are bricks made for a specific purpose. They are usually shaped to fit angles and curves or to produce a decorative effect.
The colour of clay bricks depends on several factors. The type of clay used, chemicals in the clay, the supply of oxygen while the bricks are being fired, and the temperature the bricks reach during firing. The colours vary from dark purple to light yellow. Facing bricks to be used in the outer walls of buildings can be given a rough or textured surface, or they may be glazed to add to their attractiveness.
Sand-lime bricks are naturally white, off-white, or pink, depending on the sand used to make them. By adding pigments, any colours from pale pastels to dark tones can be produced.
Blocks are essentially oversize bricks commonly about the size of six bricks. They may be made of clay or concrete. Clay blocks are hollow; concrete blocks may be solid or hollow. The advantage of blocks over bricks is that building can be carried out faster with them.
8.9 :
1. Why are bricks considered to be the most lasting of man-made building materials?
2. What ways are bricks made in?
3. What is the soft-mud process characterized by?
4. What does the stiff-clay process consist in?
5. What is specific of the pressed brick process?
6. When are bricks ready for firing?
7. What process produces the bricks of light sandy colour?
8. What advantages do lighter bricks have?
9. What factors does the colour of clay bricks depend on?
10. What are oversize bricks called?
| THE QUESTIONS |
A. .
, yes no:
Do you like ice-cream? Yes, I do.
Can you speak English? Yes, I can.
Are you a schoolboy? No, I am not.
Have you bought a text book? Yes, I have.
.
Ø (, -) ,
Ø ( ),
Ø ( ).
Ø .
- :
What is your name? My name is Peter.
Where do you live? I live in Rostov.
: who () where () whom () why () what () how long ( ) which () how many () whose () how much () when () how ()
:
1. (what, where, who, when, how . .),
2. (, -) ,
3. ,
4. ,
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5. ,
6. (, , ..).
, Present Past Indefinite, to do (did) :
Who wants to go to the cinema?
Whose pen is it?
Who lives here?
B. .
:
Do you like coffee or tea? ?
C. , or .
D.
. ( ), , , , ? ?
You are an engineer, arent you? , ?
You arent an engineer, are you? , ?
, , . to be to have, .
is reading, isnt he? , ? ( .)
can read, cant he? , ? ( .)
is a good specialist, isnt he? , ? ( to be.)
has a book, hasnt he? , ? ( to have, .)
, .
, , , :
is there, isnt he? , ?
isnt there, is he? , ?
8.A :
1. Concrete is a composite building material comprised of aggregate and a binder.
Is concrete a composite building material comprised of aggregate and a binder?
Yes, it is. / No, it isnt.
Concrete is a composite building material comprised of aggregate and a binder, isnt it?
2. The wire bends easily.
Does the wire bend easily?
Yes, it does. / No, it doesnt.
3. Compared with other wall materials, cinder bricks have excellent properties and a low price.
Compared with other wall materials, have cinder bricks excellent properties and a low price?
Yes, they have. / No, they havent.
4. His success was entirely due to hard work.
Was his success entirely due to hard work?
Yes, it was. / No, it wasnt.
5. He wrote to me concerning our construction business.
Did he write to me concerning our construction business?
Yes, he did. / No, he didnt.
6. You can forme clay bricks in a moulding.
Can you forme clay bricks in a moulding?
Yes, you can. / No, you cant.
7. In some localities water will be available in unlimited quantities.
Will in some localities water be available in unlimited quantities?
Yes, it will be. / No, it wont be.
8.B :
:
1. They got the lumber to build a house. 2. Apart from civil engineering, my interest is mathematics. 3. The joints are filled with mortar made of cement and sand.
:
4. The construction of the cottage lasted two years. 5. Low-cost bricks include cinder block made mostly with concrete. 6. The maximum size of the aggregate should not greater than one quarter of the minimum thickness of the finished concrete.
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7. They strengthened the wall with metal supports. 8. Reinforced concrete was used in these structural elements. 9. The system for housing provision relied on the centralized production of building materials.
8.C :
1. The soil was removed down to the natural clay. 2. The information is being processed by the computer. 3. A new internal wall surface is created using a very strong, very versatile, high density polyethylene. 4. While the steel frame is being erected, the wall planks are fixed. 5. Wood can be flexible under loading, keeping strength while bending. 6. A molten substance, such as metal, or a plastic substance is poured or forced into a mould and allowed to harden. 7. The maximum size of the aggregate should not greater than one quarter of the minimum thickness of the finished concrete. 8. The purpose of reinforcing is to provide a material with a high tensile strength. 9. Many new building materials are environmental hazards, which have become a big concern to all.
| MODULE9 | BUILDING SCIENCE |
9.1 : tensile, failure, compressive strength, tension, shear stress, yield strength, tensile stress, compressive failure, fatigue strength, impact strength, brittle failure.
1. the condition of being stretched
2. the ability of a material to resist shock loading
3. the resistance of a material to a force tending to tear it apart
4. the ability of a metal to tolerate gradual progressive force without permanent deformation
5. collapse caused by compression
6. the form of stress in a material that tends to produce cutting rather than stretching or bending
7. the strength of a substance under tension
8. a complete fracture of the specimen in a direction perpendicular to the direction of loading
9. the maximum stress a material can endure for a given number of cycles without failure
10. the ability of a material to resist forces attempting to crush it
9.2 :
| 1. fulfil | 2. decrease | A. | B. , |
| 3. assess | 4.ductile failure | C. | D. , |
| 5. dimension | 6. failure | E. , | F. , |
| 7. deflection | 8. capability | G. , | H. |
| 9. displacement | 10. enable | I. , | J. , |
| 11. implement | 12. withstand | K. , | L. , |
| 13. prevent | 14. bear | M. | N. , |
| 15. strength of materials | O. , |
9.3 :
1. a. A limiting strain defines the failure of reinforcement.
b. A strain limit of 1% should be applied.
c. If the stress is small, the material may strain a little.
2. a. The strength properties of this type of steel may increase.
b. No increase in the construction charges will be made.
c. Residential construction is on the increase.
3. a. Storm caused a lot of damage to the house.
b. The flood damage prevention measures should be taken.
c. Earthquakes can damage unreinforced masonry buildings.
4. a. A load bearing wall carries the parts of the house upon it.
b. The columns bearing the load must be properly located.
c. A steel beam bearing was installed on concrete masonry.
5. a. The material was subjected to the applied load.
b. They subjected the beam to various tests.
c. They tested the structures subjected to wind forces.
9.4 STRENGTH OF MATERIALS:
Building science is the collection of scientific knowledge that focuses on the analysis and control of the physical phenomena affecting buildings. This includes the detailed analysis of building materials and building envelope systems. The practical purpose of building science is to provide predictive capability to optimize building performance and understand or prevent building failures.
One of the fields of building science is the strength of materials. Its purpose is to determine the dimensions of the constructions in order to resist to strains which they have to withstand, or to check if a specific construction is able to withstand certain strains. The strength of materials also gives the value of the bearing reactions of the hyperstatic structures. It enables to ensure the good performance of the beams under the permanent and service loads. Furthermore, this science studies the mechanical properties of materials used in the construction industry. The strength of materials is also the study of dimensions and choice of materials to Amaterialloadedin implement in a construction. To design a
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a) compression, mechanical part, a structure, it is initially
b) tension, to imagine the forms and geometrical
c) shear skeleton which fulfil the specific functions
then, it is to determine the quantities of matter necessary and sufficient to achieve these forms and to ensure a resistance without damage to the object with all the strains it will be subjected to during its service. This dimensioning calls upon calculations that forecast the performance of the object whose design must combine the best conditions of security, economy, and esthetics.
In general, when an external force is applied to a body, a deformation takes place; this is called the strain. This deformation causes forces to be set up in the internal structure of the material, and the material is then said to be in a state of stress. The strain increases until the resulting stresses are sufficient to neutralize the applied force when the body is again in a condition of equilibrium. Deformation of the material is the change in geometry when stress is applied in the form of force loading, gravitational field, thermal expansion, etc. Deformation is expressed by the displacement field of the material. Strain or reduced deformation is a mathematical term to express the trend of the deformation change among the material field. For uniaxial loading displacements of a specimen (for example, a bar element) it is expressed as the quotient of the displacement and the length of the specimen. Deflection is a term to describe the magnitude to which a structural element bends under a load.
There are three kinds of stresses: compressive, tensile and shear. Compressive stress is the stress state caused by an applied load that acts to reduce the length of the material in the axis of the applied load, in other words the stress state caused by squeezing the material. Compressive strength for materials is generally higher than that of tensile stress. Tensile stress is the stress state caused by an applied load that tends to elongate the material in the axis of the applied load, in other words the stress caused by pulling the material. The strength of structures of equal cross sectional area loaded in tension is independent of cross section geometry. Shear stress is the stress state caused by opposing force acting along parallel lines of action through the material.
There are some strength terms in the strength of materials. Yield strength is the lowest stress that gives permanent deformation in a material. Compressive strength is a limit state of compressive stress that leads to compressive failure in the manner of ductile failure or in the manner of brittle failure. Tensile strength is a limit state of tensile stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of failure, some hardening in the second stage and break after a possible neck formation) or in the manner of brittle failure (sudden breaking in some pieces with a low stress state). Fatigue strength is a measure of the strength of a material or a component under cyclic loading, and is usually more difficult to assess than the static strength measures. Impact strength is the capability of the material in withstanding by the suddenly applied loads.
9.5 :
1. The strength of materials is one of the fields of building science.
2. The strength of materials only studies bearing reactions of structural systems.
3. The strength of materials does not cover dimensions and choice of materials.
4. A deformation takes place when the material is in a state of stress.
5. Strain expresses the deformation change.
6. Compressive stress elongates the material in the axis of the applied load.
7. Tensile stress reduces the length of the material in the axis of the applied load.
8. Shear stress causes opposing forces to act along parallel lines of action.
9. Yield strength, compressive strength, tensile strength, fatigue strength, and impact strength are not the terms in the strength of materials.
9.6 :
1. Its purpose is to determine the dimensions of the constructions in order to resist to strains which they have to withstand
What does the pronoun its refer to?
2. It enables to ensure the good performance of the beams under the permanent and service loads.
What does the pronoun it refer to?
3. this science studies the mechanical properties of materials used in the construction industry.
What does the demonstrative adjective this refer to?
4. it is to determine the quantities of matter necessary and sufficient to achieve these forms
What does the demonstrative adjective these refer to?
5. this is called the strain.
What does the pronoun this refer to?
6. it is expressed as the quotient of the displacement and the length of the specimen.
What does the pronoun it refer to?
7. Compressive strength for materials is generally higher than that of tensile stress.
What does the pronoun that refer to?
9.7 , STRESS-STRAIN RELATIONS :
1. Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are:
2. Elasticity is the ability of a material to return to its previous shape after stress is released. In many materials, the relation between applied stress and the resulting strain is directly proportional to a certain limit, and a graph representing those two quantities is a straight line. The slope of this line is known as Youngs modulus, or the modulus of elasticity. The modulus of elasticity is the mathematical description of an object or substance tendency to be deformed elastically (i.e. non-permanently) when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region:
3. Youngs modulus describes tensile elasticity or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus.
4. The shear modulus or modulus of rigidity describes the tendency of an object to shear when acted upon by opposing forces; it is defined as shear stress over shear strain. The shear modulus is part of the derivation of viscosity.
5. Where lambda is the elastic modulus; stress is the force causing the deformation divided by the area to which the force is applied; and strain is the ratio of the change caused by the stress to the original state of the object. An alternative definition is that the elastic modulus is the stress required to cause a sample of the material to double in length. This is not realistic for most materials as the value is greater than the yield stress of the material or the point where elongation becomes nonlinear, but some may find this definition more intuitive.
6. Plasticity or plastic deformation is the opposite of elastic deformation and is accepted as unrecoverable strain. Plastic deformation is retained even after the relaxation of the applied stress. Most materials in the linear-elastic category are usually capable of plastic deformation. Brittle materials, like ceramics, do not experience any plastic deformation and will fracture under relatively low stress. Materials such as metals usually experience a small amount of plastic deformation before failure while soft or ductile polymers will plastically deform much more.
7. The bulk modulus describes volumetric elasticity, or the tendency of an object to deform in all directions when uniformly loaded in all directions; it is defined as volumetric stress over volumetric strain, and is the inverse of compressibility. The bulk modulus is an extension of Youngs modulus to three dimensions.
9.8 :
1. What is elasticity?
2. What is the type of the line representing applied stress and the resulting strain?
3. What are the definitions of modulus of elasticity?
4. What do Youngs modulus, the shear modulus and the bulk modulus describe?
5. What is plastic deformation?
6. What materials experience plastic deformation?
9.9 , Nanotechnology and Construction :
1. It is rather an extension of the sciences and technologies that have already been in development for many years and it is the logical progression of the work that has been done to examine the nature of our world at an ever smaller scale.
2. This is achieved both prior to the construction process by a reduction in pollution during the production of materials (e.g. cement) and also in service through efficient use of energy due to advancements in insulation.
3. The size of the particles is very important because at the length scale of the nanometre, 10-9 m, the properties of the material actually become affected.
4. However, construction also tends to be a fragmented, low research oriented and conservative endeavour and this plays against its adoption of new technologies, especially ones that appear so far removed from its core business.
5. The sheer size and scope of the construction industry means that the accompanying economic impact will be huge. In order to capitalize on the effects of nanotechnology on the business, however, much more funding for construction related research, increased interdisciplinary working between researchers and communication between those researchers and industry is needed.
6. The former is being used for its ability to break down dirt or pollution and then allow it to be washed off by rain water on everything from concrete to glass and the latter is being used to strengthen and monitor concrete.
Nanotechnology is the use of very small particles of material either by themselves or by their manipulation to create new large scale materials. _. The precise size at which these changes are manifested varies between materials, but is usually in the order of 100 nm or less.
Nanotechnology is not a new science and it is not a new technology. _. A nanometre is a billionth of a metre. The recent developments in the study and manipulation of materials and processes at the nanoscale offer the tantalizing prospect of producing new macro materials, properties and products.
The construction business will inevitably be a beneficiary of this nanotechnology; in fact it is already in the fields of concrete, steel and glass. Concrete is stronger, more durable and more easily placed, steel tougher and glass self-cleaning. Increased strength and durability are also a part of the drive to reduce the environmental footprint of the built environment by the efficient use of resources. _.
Two nano-sized particles that stand out in their application to construction materials are titanium dioxide (Ti02) and carbon nanotubes (CNTs). _. CNTs have many more properties, apart from exceptional strength, that are being researched in computing, aerospace and other areas and the construction industry will benefit directly or indirectly from those advancements as well.
Cost and the relatively small number of practical applications for now hold back much of the prospects for nanotechnology. _. Materials are construction core business and the prospects for more changes are significant in the not too distant future. In fact, the researchers surveyed and predicted that many advances would arrive within five years. _.
9.10 :
1. What is nanotechnology?
2. Why is the size of particles so important in nanotechnology?
3. Is nanotechnology a new science?
4. What prospects does nanotechnology offer?
5. What will construction benefit from nanotechnology?
6. What nano-sized participles are applied to building materials?
7. What holds back the development of nanotechnology?
8. When will the advances in the use of nanotechnology arrive?
| THE NUMERIALS |
.
, ?, , ?.
13 19 -teen .
, , -ty. (first, second, third) -th -eth . .
| 10 ten | the tenth | ||
| ? | ? | 11eleven | the eleventh |
| 1one | the first | 12 twelve | the twelfth |
| 2two | the second | 13 thirteen | the thirteenth the twentieth |
| 3 three | the third | 14 fourteen | the fourteenth |
| 4 four | the fourth | 15 fifteen | the fifteenth |
| 5 five | the fifth | 16 sixteen | the sixteenth |
| 6 six | the sixth | 17 seventeen | the seventeenth |
| 7 seven | the seventh | 18 eighteen | the eighteenth |
| 8 eight | the eighth | 19 nineteen | the nineteenth |
| 9 nine | the ninth | 20 twenty | twentieth |
:
20 twenty the twentieth 30 thirty the thirtieth 40 forty the fortieth 50 fifty the fiftieth 60 sixty the sixtieth 70 seventy-the seventieth 80 eighty the eightieth 90 ninety - the ninetieth
:
twenty-one the twenty-first twenty-two the twenty-second thirty-three - the thirty-third forty-four the forty-fourth fifty-five the fifty-fifth sixty-six the sixty-sixth
100 : 100 a (one) hundred 101 - a (one) hundred and one 200 - two hundred 1000 - (one) thousand 1001 a (one) thousand and one 5,550 five thousand five hundred and fifty 5,000,000 - five million 1500 - fifteen hundred
100th the hundredth 101st - the one hundred and first 200th the two hundredth 1000th - the thousandth
hundred, thousand, million -s, . , -s, of.
hundreds of books two hundred books
thousands of books five thousand books
millions of people 2 million people
, , , , , . : page 15, house 40, flat 13, bus 72.
?
, , , . 1900 nineteen hundred, in (the year) nineteen hundred
2000 two thousand, in (the year) two thousand 1905 nineteen five, in (the year) nineteen five : April 12, 2001, on the twelfth of April, two thousand one, on April the twelfth, two thousand one
?
1/2 - a (one) half; 0.1-0 [ou] point one
1/4 a (one) quarter 2.45 - two point four five
2/3 two thirds 35.25 three five ( thirty- five) point two five
1.5 one and a half
9.A :
:
A) A (one) half B) two thirds C) a (one) quarter D) three fourths E) two and a (one) half F) five and one sixth H) a (one) fifth.
:
A) Zero (nought/ou) point two B) two point four five C) four point five D) three four (thirty four) point one zero two E) nought point nought one F) six point three five G) fifty eight point three nought five.
:
- past:
Its ten past eleven. 10 .
Its a quarter past eleven. .
Its half past eleven. .
, to:
Its ten to twelve. .
Its a quarter to twelve. .
Its twenty minutes to twelve. .
It is eleven sharp. .
a.m. ( . ante meridiem), . ( . post meridiem).
: 10 a.m. . 6 p.m. .
( on):
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
( in):
January
February
March
April
May
June
July
August
September
October
November
December
( in): spring summer autumn winter
:
a watch (, )
a clock (, )
My watch is five minutes fast. 5 .
My watch is five minutes slow. - 5 .
What day is it today? ()?
What date is it today? ?
What time is it now? ?
What is the time? ?
, :
yesterday
the day before yesterday
today
tonight
tomorrow
the day after tomorrow
a fortnight
from 10 till 12 10 12
half an hour
10 days ago 10
Its time to... ( -)
in an hours time
in time ( ; , )
on time ( )
in the middle of...
this week (month, year) ( , )
next week last week
9.B :
isosceles triangle
rectangular triangle (right- angled triangle)
base
side
equilateral triangle
altitude
radius (. radii, radiuses)
parallelogram
circle
1. Find the area of an isosceles triangle if its base is 4 cm and its altitude is 5 cm (centimeters).
2. Find the area of an equilateral triangle if its base is 6 cm and its altitude is 5 cm.
3. Find the area of a rectangular triangle if its base is 4 cm and its altitude is 5 cm.
4. Find the area of a square if its side is 4 cm.
5. Find the area of a parallelogram if its base is 8 cm and its altitude is 5 cm.
6. Find the area of a circle if its radius is 10 cm.
:
(x) multiply, times (:) divide, divided by (+) add, sum up, plus (-) subtract, minus (=) equals, is equal, makes 22 two in the second power
addition 12 + 15 = 27 Twelve plus fifteen is (makes, equals) twenty seven.
addend
sum
subtraction 41 24 = 17 Forty-one minus twenty-four is (equals) seventeen.
minuend
subtrahend
remainder, difference
to do subtraction
multiplication 6 x 4 = 28 Seven times four is twenty-eight (seven multiplied by four is twenty-eight) multiplicand
multiplier (factor)
product
multiplication table
division 60: 10 = 6 Sixty divided by ten is six.
dividend
divisor
quotient
division with remainder
without remainder
9.C :
1. -7 + 9 =
2. 0,02 x 1,8 =
3. ½ + 3/8 =
4. 30 x 0,55 =
5. -12: 6 =
6. 32: 0,11x 4 = 17
7. 20x + 1/4 8 = 12x
8. 22 x = 83
9. 102x + 16 = 85x: 3
10. 17 + 32/5 -10x = 52
9.D :
1. Convert 5/12 to a decimal.
2. Express 0,28 as a fraction.
3. What is 67.469 to 3 significant figures.
4. Find 16% of 8.
9.E :
percentage ; dealer ; mark-up .
1. Find 21 as a percentage of 193.
2. The price of an item including the dealers 15% mark-up is $28. What did it cost before the mark-up?
3. If it costs 8$ to drive x kilometres, then what is the cost of driving 2 kilometres?
9.F :
1. Faceplates priced at x pence per dozen are repacked in boxes of 100. What will the cost of such a box be, in pounds?
2. There are x female workers and y male workers in a factory. Write down an algebraic expression to show that the total work force must be less than 150.
3. Where does the graph of s = 3t + 5 cross the x -axis?
| MODULE10 | STRUCTURAL ENGINEERING AND INTERESTING CONSTRUCTIONS |
10.1 THE ELASTIC THEORY OF STRUCTURES:
A significant achievement of the first industrial age was the emergence of building science, particularly the elastic theory of structures. With it, mathematical models could be used to predict structural performance with considerable accuracy, provided there was adequate quality control of the materials used. Although some elements of the elastic theory, such as the Swiss mathematician Leonhard Eulers theory of column buckling (1757), were worked out earlier, the real development began with the English scientist Thomas Youngs modern definition of the modulus of elasticity in 1807. Louis Navier published the elastic theory of beams in 1826, and three methods of analyzing forces in trusses were devised by Squire Whipple, A. Ritter, and James Clerk Maxwell between 1847 and 1864. The concept of a statically determinate structure that is, a structure whose forces could be determined from Newtons laws of motion alone was set forth by Otto Mohr in 1874, after having been used intuitively for perhaps 40 years. Most 19th-century structures were purposely designed and fabricated with pin joints to be statically determinate; it was not until the 20th century that statically indeterminate structures became readily solvable. The elastic theory formed the basis of structural analysis until World War II, when bomb-damaged buildings were observed to behave in unpredicted ways and the underlying assumptions of the theory were found to require modification.
10.2 :
1. What was a significant achievement of the first industrial age?
2. What was it used for?
3. What contributions did L. Euler, Th. Young, L. Navier, S. Whipple, A Ritter, J.C. Maxwell, and O. Mohr make to the elastic theory of structures?
4. What were the structures of the 19th century designed and fabricated with?
5. Why did the elastic theory form the basis of the structural analysis until World War II?
10.3 NANOTECHNOLOGY'S FOR REAL IN THE BUILDING INDUSTRY:
Nanotechnology is sometimes seen as all hype, with little real-world application. But nanomaterials are already all around us. Take the buildings that we live and work in, for instance. You will find nanotechnology used to create stronger steel, self-cleaning glass, solar-collecting fabrics, and even smog-eating concrete. And not only are these nanomaterials present in our buildings, they are making them better places to live and work.
Self-cleaning glass has a nanoparticle coating dirt cant stick to, eliminating the need for expensive and dangerous manual window washing on tall buildings. Solar-collecting fabric is the first of a new wave of building components that convert solar radiation into electricity. That means no more applying unattractive solar panels to the roof, but instead integrating energy production into building facades. Nanocomposite steel is more corrosion resistant than conventional steel, and can reduce installation costs by up to 50%. And the quantity required to make a building may be up to 40% less than conventional steel. Smog-eating concrete is produced by applying a nanolayer of titanium dioxide to concrete, which triggers a catalytic reaction that destroys many pollutants in contact with the surface. At the very least, these materials reduce building maintenance costs, leaving more money for other improvements, and they can help clean up the environment. They can reduce energy costs as well. And for every nanomaterial available today, there are approximately seventy more in research and development, meaning that building construction and architecture are in for some big changes thanks to small technology.
10.4 :
1. Nanotechnology is sometimes _ as all _,
with little real-world _.
2. Take the _ that we live and _ in, for instance.
3. You will find _ used to create stronger steel,
_ glass, solar-collecting fabrics, and even _ concrete.
4. Solar-collecting _ is the first of a new wave of building components that _ solar radiation into _.
5. _ steel is more corrosion_ than conventional steel, and can reduce _ costs by up to 50%.
6. Smog-eating concrete is produced by _ a nanolayer of titanium dioxide to _, which triggers a catalytic reaction that _ many pollutants in contact with the _.
7. At the very least, these materials _ building
_ costs, leaving more money for other _, and they
can help clean up the_.
8. And for every nanomaterial _ today, there are
_ seventy more in _ and development, meaning
that building _ and architecture are in for some big thanks to small technology.
10.5 A HORIZONTAL SUPPORT:
A beam is a structural component mainly working in bending through the agency of vertical forces and that transmits to the bearing points the loads that are applied to it. A beam is a lengthened and horizontal support made of metal, wood, reinforced or prestressed concrete and whose section has been studied for a good bending strength. Beams are mainly subjected to bending moments and shearing forces. Simple beams are made up of only one piece, of a section calculated to withstand the strains that aim at making them bending. When the strains become too strong, reinforced beams or compound beams are then used. Beams rest:
Ø either on a bearing with restraint (cantilever) or are restrained at both ends (exceptional);
Ø either on a cantilever and are then presented as continuous beams to which have been added a number of extra articulations in order to free oneself of the consequences of the difference in level of the supports;
Ø either on two free bearings, free and restrained; they are independent or isostatic beams. These beams work on the positive bending moment in the middle of span and with simple shearing force on bearing;
Ø either on several bearings (beam in continuity); they are continuous or hyperstatic beams. This type of beam bears on one hand a positive bending moment much weaker than an independent beam; but, on the other hand, when on bearing, it bears an important negative bending moment as well as the shearing force.
10.6 :
1. What is a beam?
2. What materials can beams be made of?
3. What forces are beams usually subjected to?
4. What conditions are reinforced beams used under?
5. What elements can beams rest on?
10.7 ROOF:
The roof of a building often reflects the climate of the place in which the building is located since it protects the people in it from rain and sun. In dry countries the roof is flat and can be used as an outdoor room when the sun is not too hot. Where it often rains the roof usually slopes so that the wet can run off it, and where there are snowfalls, the roof slopes steeply so that the snow will slide off and not build up into a thick layer. A roof that slopes is called a pitched roof.
After a time people found it inconvenient to live in a house with sloping sides, so they built upright walls and laid big beams called tie-beams across the top at regular distances from each other. Then they put up the triangular frameworks resting on the tie-beams. These triangles of beams are called trusses. A ridge-piece, purlins, and rafters were used to complete the skeleton of the roof.
In the Middle Ages the wooden frame of the roof was not hidden by a ceiling on the inside and was often richly decorated. To increase the effect of height and space the hammer-beam roof was designed. This had no tie-beams, but instead there were short beams sticking out from both walls, and to these beams other timbers called struts were fixed to support the main rafters.
The waterproof covering of a pitched roof is usually of tiles, slates, or shingles. Tiles are thin slabs of baked clay, generally red or brown in colour. Strips of wood called battens are fixed to the outside of the rafters, usually over sheets of weatherproof roofing-felt which help to keep out draughts and wind-blown snow. The tiles, shingles, or slates are then hung on by projecting pieces called nibs, or nailed or clipped to the battens in regular horizontal rows or courses. Flat roofs usually consist of boards covered with overlapping sheets of roofing felt coated with bitumen. When a roof has to cover a large space, steel trusses are used instead of wood. Large flat roofs may be made of reinforced concrete with a waterproof covering.
10.8 :
1. The roof design depends on the climate of the place in which a building is located.
2. The roof of a building protects people from rain and sun.
3. Where it often rains, the roof slopes steeply.
4. It is convenient to live in a house with sloping sides.
5. Triangular frameworks are called trusses.
6. In the Middle Ages the wooden frame of the roof was hidden by a ceiling.
7. The hammer-beam roof increased the effect of height and space.
8. The waterproof covering of a pitched roof is made of thick slabs of baked clay.
9. Sheets of weatherproof roofing-felt help to keep out rains.
10. When a roof covers a large space, wood trusses are used.
10.9 STRUCTURAL BUILDING ENGINEERING:
Structural building engineering includes all structural engineering related to the design of buildings. It is the branch of structural engineering that is close to architecture. Structural building engineering is primarily driven by the creative manipulation of materials and forms and the underlying mathematical and scientific ideas to achieve an end which fulfills its functional requirements and is structurally safe when subjected to all the loads it could reasonably be expected to experience. This is subtly different from architectural design, which is driven by the creative manipulation of materials and forms, mass, space, texture and light to achieve an end which is aesthetic, functional and often artistic.
The structural design for a building must ensure that the building is able to stand up safely, able to function without deflections or movements which may cause fatigue of structural elements, cracking or failure of fixtures, fittings or partitions, or discomfort for occupants. It must account for movements and forces due to temperature, creep, cracking and imposed loads. It must also ensure that the design is practically buildable within acceptable manufacturing tolerances of the materials. It must allow the architecture to work, and the building services to fit within the building and function (air conditioning, ventilation, electrics, etc). The structural design of a modem building can be extremely complex, and often requires a large team to complete.
10.10 :
1. What does structural building engineering include?
2. What is structural building engineering driven by?
3. Does structural building engineering differ from architectural design?
4. What must the structural design ensure?
5. Why does the structural design require a team of experts to complete a project?
| WORLDBUILDING |
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