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Structural Mechanics

For those just starting to learn about structures, this section is a must to read before looking at the Structural Analysis section.  I found it on the internet several years ago and thought it was good.  Unfortunately I did not make a note of the author, but I would like to thank them for all the hard work they put into this, whoever they may be.

Introduction 

There are many different types of structures all around us. Each structure has a specific purpose or function. Some structures are simple, while others are complex, however there are two basic principles that structures must meet if they are to perform as designed.  

These principles are:

It should be noted that Stonehenge and the Leaning Tower of Pisa violate at least one of the principles just mentioned. Can you say why? 

Many people only consider buildings, bridges and other such frames as structures. However there are many simple objects which can be classed as structures such as a motor bike or even the humble college chair, to mention but a few.  

Use of structures 

Structures have been designed to resist the loads and forces that they are
subjected too.  There are many examples of structures all around us, but these are usually taken for granted because they work without problems most of the time.  In fact there is one structure that we use all of the time without even thinking about it, our skeleton.  In simple terms our skeleton supports the mass of our body as a static or dynamic load, depending on whether we are stationary or moving.

The skeleton is very resilient and only usually fails when there is an accident

Structural forms

Frame: A frame consists of bars joined together to from a framework, much in the same way as the legs of your college chair.  Framed structures are used extensively throughout the construction industry.  Sometimes the frame is always visible such as in a bridge, while at other times the frame may only be visible during construction.

Shell: usually assembled from panels to form a protective structure, an example would be the plastic seats of a chair or the body of a vehicle. 

Can you say whether the structures in these photos are frames, shells or possibly a combination of the two?

Plastic road sign

 Motorbike

 Telephone box

Plastic wall mounted rubbish bin.

Wheelbarrow.

Cycle shelter                     

Can you think of some frame and shell structures that may be around your home?

Structural failure

At times structures may fail by collapsing or they may not perform as they were intended to.  The main reasons for failure in a structure include improper construction, poor design, material failure or from applying loads which are too large for the structure.

The leaning tower of Pisa is a good example of a structure that has failed.
The ground under the tower is unable to properly support the structure and as a
result the tower is leaning to one side.

    (Click on picture to enlarge it)

  The tower of Pisa, an example of a structure that has failed.

Closer to home there are many simple structures which can fail.  If you have a bookshelf at home and you place too many books on it, then it may fail.  The book shelf behaves as a beam and as you place more and more books on the shelf it begins to bend until a point is reached when it can no longer support the load.  At this point it will begin to crack on the under side, and may eventually break in two as indicated below.

Another structure that you are familiar with is your own body.  When your body is subjected to a force or load that is too great for it then it is likely to break.  Falling down the steps and banging you leg could result in breaking a bone in your leg.  This can be viewed as a structural failure, even though you may not usually think of your body as being a structure.

Summary 

Structures have been designed to resist the loads and forces that they are subjected too.

You have learned that there are two main types of structure, these are:

Examples of these structures can be seen all around the home, in college, in fact almost anywhere.

Structures may fail by collapsing or they may not perform as they were intended to. 

The main reasons for failure in a structure is usually as a result of one or more of the following: 

Framed structures

If you were to look at various structures that are around us, such as an electricity pylon or tower crane you will see some similarities between these types of structure.

Can you say what these are?

On both of these structures there are many members that cross each other to form a brace.  This section will deal with the concept of strengthening structures and examples of how engineers strengthen structures will be given.

Here are some more examples of structures that have been strengthened.
Notice the use of cross-bracing or stiffened corners.

Add a third member to the structure as indicated to split the square into two triangles. Apply the pushing force as before and observe what happens.

 You should have noticed that in the first case the square was not rigid and when the force was applied it went out of shape.  When the bracing member was added and the force applied the frame remained rigid.  This is because the bracing member prevented the corners 'a' and 'c' from moving apart as they did in the first case.

If you add gusset plates to the structure as indicated.  The gusset plates strengthen the corners of the frame.  Apply the pushing force as before and observe what happens.

 You should have noticed that in the first case the square was not rigid and that when the force was applied it went out of shape.  When the gusset plate was added, and the force was applied the frame remained rigid.  This is because the gusset plates prevented the corners 'a' and 'c' from moving.

Refer back to the climbing frame.

How Engineers do it! 

Many buildings that are designed by engineers consist of some sort of rigid frame that is covered by a protective shell known as cladding.  The cladding could consist of bricks, stone, glass, wood or other similar materials and it is designed to keep the weather out and make the structure habitable.

The photo below is an example of such a structure.  In this case though there is also a rigid frame on the outside of the building.  This frame is made from steel and is bolted or welded together at the joints.  Notice the arrangement of the members, they form rigid triangles.  This framework has been erected to help support the building while it is being modernised.

The framework above is an example of the kind of internal structure that is used inside many types buildings.  The frame consists of a series of beams and columns that are bolted of welded together. 

The frame can also be constructed using reinforced concrete.
Regardless of the materials that are used to construct the frame, the principles are the same.  The frames are arranged in such a way so that they are as strong as possible.  The strengthening of the frame can be achieved by adding bracing as previously explained, or by stiffening joints by using gusset plates or special connectors.  If a structure were not strengthened in this way it would deform excessively or even collapse.

The concept behind strengthening structures is to help the structure withstand the loads that they are subjected to without unnecessarily losing their shape or form.

Which of these structures is rigid and which is non-rigid?

What about these??

Summary 

You have learned that framed structures sometimes need strengthening to make them rigid.  There are two common methods adopted to make structures rigid, these are:

Many framed structures can be seen all around us, which use one of the above methods to make the structure rigid.

Many large buildings and other similar structures adopt similar methods as described above to make them rigid. 

However, due to the external cladding of bricks, stone, glass, wood or other similar materials it is not always possible to see how these structures have been strengthened. 

Stability 

A structure is said to be stable when it will not topple over easily when acted upon by a force.  Stability is an important concept not only for civil and structural engineering but also for life in general.  There are many structures around the home that depend on the principles of stability.  Consider what would happen in the home if simple household products were designed without considering stability.  You would have cupboards falling over, chairs would be unstable, pans and pots in the kitchen would be constantly tipping over.  You would have a pretty rough time! This section will describe the basic principles of structures and show how engineers take account of stability.

    Pushing Force       

The concept of stability

If a force is applied to the triangle it will tip up as shown.  When the force is released, the triangle falls back down to its original position.  The behaviour of this structure is said to be stable.

 When the process is repeated on the structure below it will tilt over then topple.  The behaviour of this structure is said to be unstable.

The concept of stability

If a force is applied to the triangle it will tip up as shown.  When the force is released, the triangle falls back down to its original position.  The behaviour of this structure is said to be stable. 

When the process is repeated on the structure below it will tilt over then topple.  The behaviour of this structure is said to be unstable.

The concept of stability

If a force is applied to the triangle it will tip up as shown.  When the force is released, the triangle falls back down to its original position.  The behaviour of this structure is said to be stable. 

When the process is repeated on the structure below it will tilt over then topple.  The behaviour of this structure is said to be unstable.

Pushing Force

To fully understand stability, you must first have an understanding of the principles of Centre of gravity 

Centre of gravity 

Balance a ruler on your finger as shown below with more of the ruler on one side of your finger than the other.

You will observe that it topples off your finger. This is because there is more material to the left of your finger than to the right.  Gravity has an effect on the material at each side of your finger, and since there is not an equal amount on either side the ruler is unbalanced and thus topples over.

The pull of gravity acting on the ruler is what gives it its weight and causes the ruler to tilt.

In order to balance the ruler on your finger, you must position it so that the point at which the pull of gravity acting to the right and left of your finger is equal.  When you position the ruler on your finger so that it is perfectly balanced, then you have found the centre of gravity. 

You can apply this principle to any shaped object. Once the object is perfectly balanced you have found the centre of gravity. 

Can you determine the centre of gravity of these objects?

Accurately determining the centre of gravity.

The method that was previously explained for finding the centre of gravity of an object is by trial and error, and therefore is only an approximation.  For a more accurate approach try this exercise. 

Use a piece of thick card and cut out an irregular shape as shown opposite. Hang the string and a plumb line from a pin as shown. Mark the position of the plumb line with a pencil.

Repeats the process again, but this time place the pin at a different location, and mark the position of the plumb line string.  Where the two pencil lines cross is the centre of gravity of the shape.

This method of determining the centre of gravity of an object is very accurate, and will work with any irregular shaped object.

The stability of a structure is related to the position of the centre of gravity for that structure.  As indicated in the diagram below, as the structure is tilted, its centre of gravity rises.  It is rotated about point b, caused by the pulling force.

If the structure is stable, on release of the pulling force the structure will return to its original position

However, it must be noted that this will only be the case if the centre of gravity remains inside the base of the structure.  When the structure is tilted to such a degree that its centre of gravity is outside its base, then the structure will become unstable as gravity acts on it and causes it to topple over.

If an unstable object is rotated as shown below, when the pulling force is removed the structure will continue to rotate and will eventually topple over.

Why do Engineers build structures that are fat at the bottom and thin at the top? 

It is more difficult to make an object with a low centre of gravity topple than a structure with a high centre of gravity.

The bus opposite has a low centre of gravity      
since there is a large weight in the lower section of the bus.  This means that the force of gravity will act through the base of the bus to keep it on the road.

The bus opposite has a high centre of gravity
since there is a large weight in the top section
of the bus.  Due to the high centre of gravity
this bus is unstable because the centre of gravity
is acting outside the base of the bus.
In reality buses are designed to take account of
this problem, so they are very unlikely to turn
over very easily.

You have learnt some of the basic concepts
relating to stability.  It must be pointed out
though, that in reality stability of structures
in civil engineering are much more complex
than triangles or other simple shapes that
have been previously illustrated.

It is not always possible to design or build
structures that are wide at the base and thin
at the top, or structures that have the greater
part of their weight in their lower half.
You will recall that these types of structures are
stable. The picture opposite shows an
access platform on the outside of a tower block.
This is a long thin structure, which ordinarily would
be very unstable.

However, to make the structures stable it is necessary to physically fix the access platform to the building.  If this were not done, as soon as a load was carried up in the platform it would topple over as indicated in the picture opposite.

There are many types of structures in reality that to some extent are unstable, and it is thus necessary to provide some type of support.

Making structures stable

You have previously learned about stability, and you know that in order to make a structure stable it is usual to concentrate most of the weight at a low level in the
structure, or to ensure that the base of the structure is wide.  In reality this is not always possible for engineers.  Consider a tower crane used in the construction industry.

The tower crane is a long slender structure with a very thin base, and a very wide top. It has a large load to carry at the top at one end of the arm as indicated in the previous picture.

So why does a tower crane not fall over?

 A counter weight is placed on
the opposite side of the crane arm to that of the load, as indicated in the picture opposite. This system works by balancing the load with that of the counter weight.

It works in much the same way as a person carrying a heavy bag in one hand.  It is quite difficult to balance properly. However if there were a bag of similar weight in each hand the person would be much more stable.

The counter weight alone will not make the crane stable, it must also be securely fixed down to the ground to make it stable. 

It is not always possible to ensure that a structure will remain stable. Sometimes the very nature of the structure may make it unstable and therefore special precautions must be taken to stabilise the structure.

Summary

You have learned that a structure is said to be stable when it will not topple over easily when acted upon by a force.

You have also learned that the centre of gravity is very important when considering stability; this was illustrated by considering a ruler balanced on the finger.
 

Some rules for stability:

 It is not always possible to design structures that comply with these rules, and sometimes special measures should be taken to make a structure stable.

Forces in structures 

In order for a structure to perform as it was designed to, it must be able to withstand all the forces that it is subjected to when loaded.  In order to understand how a structure will behave when loaded it is important to investigate the forces acting on the external surface of the structure, and those acting internally.  This section will deal with the forces found in structures and the effect they have on the structure.
Before you can understand how a structure will behave when loaded you must first have a knowledge of the different types of forces that may be present in a structure. 

There are five main types of force, these are :

Tension: a force which causes an object to stretch when it is applied is called a Tension force.

The member above is subject to a tension force when it is pulled as shown.

Compression: a force which causes an object to be squashed or to buckle when it is applied is called a Compression force.

The member opposite is subject
to a compression force when it
is pushed together as shown.

Bending: a force which causes an object to bend when it is applied at an angle to that object is called a Bending force.

The member opposite is subjected to a bending force when the load is
applied as shown.

 Shear: a force which acts across a object in a way that causes one part of the structure to slide over an other when it is applied is called a Shear force.

A teapot maybe subjected to a shear force
between the handle and the body when the teapot is full of water.  The reaction on the handle is upwards, while the load is downwards, this will cause a shear force between the body and the handle.

Torsion: a turning force which causes an object to twist when it is applied is called a torsional force.

The member opposite is subjected to a torsional force when it is twisted as shown.

 All structures will have some force or a combination of forces acting on them when they are loaded.  If the resultant forces cause the structure to act as it was designed to do, then the structure is suitable for its purpose. However, when excessive loads are applied to a structure it may fail.  The failure could result in the structure cracking, or may cause it to deform excessively.  A much more potentially dangerous failure could result in the total collapse of the structure.

You may initially find it difficult to determine the type of forces acting on a structure.
It may help you to remember the simple rule shown below.

 A structure will change its shape when a force is applied to it.

As an example of this consider what happens to a plastic ruler when a force is applied at the centre.  The deflection of the ruler will clearly be seen, however with engineering structures the deflection is not always so obvious. 

When a load is applied, and the member deflects, then it may be stretched, compressed or affected by other types of external force.  As a result of this, internal forces are set up which push back against the external forces produced by the load.

When assessing members for shear, torsion and bending, it is usually quite easy to
visually determine what type of force is acting.  The table below summarises these types of force. 

For members subjected to a tensional force, wires, cables and flat sections are generally used.  However such sections are poor in compression.  In many structures thin members or cables are used to resist tension, an example of this are the ropes or chains used on a children's swing in the park.

The ropes or chains used on a swing in the park are subjected to tensional forces when children are swinging on them.

The rope or chains of the swing are clearly
good in tension as indicated opposite.
Thicker members could be used to support the
load of the girl, however using such members
would not be an efficient use of materials since
thin members or chains are more than
satisfactory for the purpose.

When a member is subjected to a compressive force, thick sections or special shaped sections such as H-sections (Universal Columns) are used.

These sections are good in both tension and compression.  It is important to choose the right section type for a particular structure, since the structure will have to resist the applied loads.

The inspection platform which is used in many garages allows the mechanic to inspect the under-side of a vehicle. This platform is supported by a hydraulic ram.  This ram is a thick metal member which is strong enough to be able to support the weight of the truck above.  The weight of the vehicle on the platform acts on the ram causing it to be subjected to a compressive force.

If the hydraulic ram was made out of a section that was too thin it would not be able to support the weight of the truck and may break or buckle as indicated in the picture below.

What type of force would the chair's legs be subjected to if someone sat on this chair?

If the force was too large what might happen to the chair ?

There are five different types of force that a structure a can be subjected to, theses are listed below:
 

Remember this

Wires, cables and thin (slender) sections are used for members in a structure that are subjected to tension.

Thick, stocky or special sections are used for members in a structure that are
subjected to compression.

Civil and structural engineers commonly have to design structures that are very complex and subjected to a combination of different types of forces.  Due to the complex nature of many structures extensive calculations have to be carried out when analysing these structures.  Sometimes it is necessary to use a computer to carry out the analysis because it is so complex and long.

Bending Members
 

The floor of the foot bridge which links these
two buildings together consists of a series
of beams.  The load acting on the bridge
would be due to the weight of pedestrians
walking across the bridge.

When a beam is loaded it is able to resist the bending to a certain degree.  This resistance is known as stiffness.  The stiffness of a beam is dependent on two main factors, which are : 

Beams are commonly used throughout the construction industry.  Sometimes they may be visible, while at other times they are hidden by the cladding of the structure. There are many simple structures all around us that use beams.  The seesaw in a children's playground is a good example of a beam, as is a shelf at home which is loaded with books.  Beams are used extensively as spanning members.

Remember this 

The stronger the material, the stiffer the beam. 

Suppose that you were in the countryside and there was a small stream that you had to cross.  There were three beams spanning the river, 

1 steel
1 balsa wood
1 plastic

If all of the beams were of the same dimensions, which one would bend the least if it were walked on? 

Which beam is the stiffest and why?

It is all to do with Young's Modulus of Elasticity.  (E)

The material with the highest value of E will be the stiffest.

Remember this

The deeper the section for a given material, the stiffer the beam. The mathematical relationship for stiffness is :
 

Stiffness = breadth x depth³ = BD³

The stiffness of a beam is important because it governs how well the beam can resist the deflection induced as a result of the applied load.  If a beam is not stiff enough and it deflects excessively then it will not be fit for its intended purpose.

So you can see that the material of the beam affects stiffness as does the section dimensions. 

Beam behaviour
When a load is applied to a beam as indicated below, forces are set-up or induced in the beam.  The top section of the beam is compressed and thus becomes shorter, while the bottom section is in tension and hence stretches.

The picture opposite shows a beam spanning a stream which is subjected to a load.  Deflection of the beam is as shown, and the forces at the top and bottom of
the beam can be seen.

C = Compression
T = Tension
N.A = Neutral Axis

From the previous picture it can be seen that the forces in a beam change from compression at the top of the beam to tension at the bottom.  However at mid depth of the beam the compressive and tensile forces cancel out.  This point in the beam is known as the Neutral Axis (N.A), the resultant force at this point is zero.

How do Engineers use the neutral axis to their own advantage?

Originally, many beams were solid and of rectangular construction.  This made beams heavy and expensive because of the amount of material used.  However, you have learned that the forces in a beam are compressive at the top, decreasing to zero in the middle, then becoming tensile.  The maximum forces are at the top and bottom of the beam, while in the middle, the forces are smaller and reduce to zero at the Neutral Axis.  In order to reduce costs and weight, beams can be made up of special sections such as a steel I-beam (Universal Beam).
For a beam to resist the applied loads, most of the material of the beam must be placed where the forces are greatest.  It is for this reason that I-beams have a thin web where the forces are small, and thick wide flanges where the forces are the greatest.

How engineers use beams.
Beams are used by engineers in many different types of structure, ranging from bridges, to floor beams in buildings.  The most common types of materials used for beams in large structures are steel, timber and concrete.

Unlike steel or timber beams, concrete beams have a special problem that has to be overcome.  It relates to the fact that concrete is weak in tension.  The diagram below indicates what can happen to a concrete beam when it is loaded.

As previously mentioned, concrete is weak in tension, but you have learned that when a beam is loaded the bottom section of the beam is the part in tension.  If a concrete beam were loaded as shown in the previous drawing it would fail at a relatively small load.  As the beam deflects due to the load, tension cracks would form at the bottom side of the beam.  Initially these cracks will be small, but as the load increases the cracks would grow larger until the beam eventually fails.

Remember this

The tension in the beam is pulling the concrete apart causing the cracks to appear

Can you determine how the problem of the concrete cracking can be overcome?

Engineers solve this problem by reinforcing
the concrete with steel bars where it is most
vulnerable to cracking.

When the concrete beam is being made, steel bars are positioned as shown in the drawing above.  You have already learned that steel is good in tension.  This is why the reinforcing steel is placed in the concrete beam where it is susceptible to large tensional forces.  So, instead of the concrete trying to resist the tensional forces, the steel resists these forces.  There are many different shapes of section used for reinforced concrete beams.

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