Topic 9 Structures

9.1 Young’s modulus—stress and strain

9.1.1 Define Young’s modulus. Young's modulus (E) is a measure of the stiffness of a material. It is also known as the Young modulus, modulus of elasticity, elastic modulus It is defined as the ratio of stress over strain in the region in which Hooke's Law is obeyed for the material. This can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material. 9.1.2 State that stress (load) is force per unit area acting on a body or system. Stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces. The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the deformation will be permanent and non-reversible. 9.1.3 State that strain is the ratio of a change in dimension to the original value of that dimension.

Strain is the deformation of materials caused by the action of stress. Strain is calculated by first assuming a change between two body states: the beginning state and the final state. Then the difference in placement of two points in this body in those two states expresses the numerical value of strain. Strain therefore expresses itself as a change in size and/or shape

9.1.4 Draw and describe a stress/strain graph and identify the elastic region, plastic flow region, yield stress and ultimate tensile strength (UTS).

For most materials the elastic region is a straight line, which changes to a curved line (plastic region). Quantitative details of specific materials are not required.

http://www.youtube.com/watch?v=VgE7TaXuUqI 9.1.5 Outline the importance of yield stress in materials. This is the stress at the yield point on the stress/ strain graph. Beyond the yield point, the material undergoes plastic deformation. 9.1.6 Explain the difference between plastic and elastic strains.

When a material behaves elastically, if the stress on the material is released before it breaks, the extension (strain) relaxes and the material returns to its original length. Beyond the yield point, the material deforms plastically and does not return to its original length or shape. Elastic Strain is a deformation that lasts only as long as the stress is applied. When the stress is removed, the object returns to its

original shape. Everyday examples include the stretching of a rubber band, vibrations through a piece of metal, and bending a fork to fling food in a food fight. Ductile or Plastic Strain is a deformation that is permanent; the object does not return to its original shape when the stress is removed. Examples of ductile strain from everyday life include the way that modeling clay holds whatever

shape you give it, or the way a fork stays bent if you pull back on it too hard. Brittle Strain or Failure occurs when an object breaks under the stresses that are applied

9.1.7 Calculate the Young’s modulus of a range of materials. Young’s modulus = stress Strain You fill a range of activities at this address: http://www.matter.org.uk/schools/Content/YoungModulus/stiffnessExercise.html 9.1.8 Explain how knowledge of the Young’s modulus of a material affects the selection of materials for particular design contexts. Young’s modulus provides quantitative data relating to the relationship of sand stiffness in structures. Let's say we're trying to decide how to make a rucksaframe. We need to choose a material this stiff, light, strong and cheap – we wtherefore need to find information abouthe Young's modulus, density, strength ancost for lots of different materials. As unlikely that the cheapest material will also be the lightest and stiffest, we are going to have to make some judgements to determine which is the ‘best’ choice. Since there are over 20,000 materials in common use, choosing the best one looks to be a daunting prospect! Clearly we need some way to rationalise all this information in ordesimplify the selection process. Fortunately, materials may be grouped in a tree-like st

trength

ck at

ill t

d it is

r to ructure:

These materials selection charts g lots

e

good compromise between high stiffness and low ractice?

st of

provide a way of rapidly assessinof different materials and choosing theones which are worth considering further. Returning to our rucksack frame example, the E-r chart abovsuggests that ceramics represent a

density. So why don’t we use ceramics in pThe answer is that we need to consider the reour requirements. If we look at a chart of strength-

cost, we can see that metals can be a lot cheaper than ceramics.

In addition, from our knowledge of strength, we know that although ceramics look as on.

From this chart it appears that od

re to teel,

In theory, if we were to choose

manufacturing issues) which determine which alloy we ng

9.2 Forces

.2.1 Describe what is meant by an external load acting on a structure.

his involves loads where physical contact is made.

.2.2 Describe what is meant by body load.

his is a load without physical contact, for example, a structure’s own

orce is a force that acts on the volume of a body and also can

.2.3 Describe the difference between weight and mass.

efer to the effect of gravity and how commonly people refer to the weight of an object

ent of

though they are stronger than metals this is only the case if we load them in compressiSo maybe metals are a better choice for a rucksack frame, but which metal? We can now‘zoom-in’ and look in more detail at the different metals.

aluminium alloys might be a gochoice: although they are a bit lessstiff than steel, they are a lot lighter. Of course we would also want to check that the strength and cost of aluminium alloys were reasonable before we wechoose them in preference to sso we would also need to zoom-in on our strength-cost chart.

aluminium alloys, we could keepzooming-in in order to determine which particular aluminium alloy touse. However, we can see from our charts, that there is not likely to be that much difference between thevarious alloys and in practice it is likely to be other factors (e.g.

will finally choose. When selectimaterials on the basis of properties, you have to use your judgement to determine at whatlevel of detail it is most sensible to stop.

9 T 9 Tweight. A body fbe defined as an external force acting throughout the mass of a body. Gravity is a body force, 9 Rwhen they should refer to its mass. What's the difference between weight and mass? As long as you stay on Earth, the difference is more philosophical than practical. Mass is a measurement of how much matter is in an object; weight is a measurem

how hard gravity is pulling on that object. Your mass is the same wherever you are--on Earth, on the moon, floating in space--because the amount of stuff you're made of doechange. But your weight depends on how much gravity is acting on you at the moment; you'd weigh less on the moon than on Earth, and in interstellar space you'd weigh almost nothing at all.

sn't

But if you stay on Earth, gravity is always the same, so it really doesn't matter whether you

Points to remember:

Mass Weight

talk about weight or mass.

Is always a constant at any place and time on gravity at the place Depends

Is measured in kilograms in SI unit Is measured in Newtons (not in kilograms as onemight think)

Is measured using balance sing scales Is measured u

Can never be zero Can also be zero

Is an intrinsic property of a body and is object which is attracting it

ich iindependent of any external factor.

Depends on 1. Mass of the 2. Force with which it is being attracted (whturn depends on the distance between the two

.2.4 State the units of weight and mass.

eight is measured in Newtons and Mass is measured in Kilograms

.2.5 Explain the relationship of external loads to internal forces and the concept of the

Internal vs. External Forces

There are a variety of ways to categorize all the types of forces. All types of forces can be

t

ity,

een ally

.

9 W 9balance of equilibrium of forces within a structure.

categorized as contact forces or as action-at-a-distance forces. Whether a force is categorized as an action-at-a-distance force was dependent upon whether or not thatype of force could exist even when the objects were not physically touching. The force of gravelectrical forces, and magnetic forces are examples of forces which could exist betwtwo objects even when they are not physictouching. The two categories of forces are referred to as internal forces and external forces

Forces can be categorized as internal forces or external forces. There are many ways of explaining and distinguishing between internal and external forces. Many of these ways

vity

Int s

are commonly discussed at great length in physics textbooks. For our purposes, we will simply say that external forces include the applied force, normal, tension force, friction force, and air resistance force. And for our purposes, the internal forces include the graforces, magnetic force, electrical force, and spring force.

ernal forces External forceGravity Applied Spring Normal Magnetic Tension Friction Air resistance

The normal force is the support force exerted t which is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is

n

d within loaded structural elgenerated within every type of element; if they were not d

pretirces within the structural members.

force is a push or pull that tends to cause an object to

he actual effect of a force on a structure depends on:

rce’s magnitude, the stronger it is and the more

e is applied

ted by an rrow. The different sized arrows tell us a little about the

cture is in equilibrium, otherwise it would ove (the forces acting upon it are equal in size and

opposite in direction).

upon an objec

exerting an upward force upon the book in order to support the weight of the book. Ooccasions, a normal force is exerted horizontally between two objects which are in contact with each other. For instance, if a person leans against a wall, the wall pushes horizontally on the person.

Internal forces are generate ements. These forces are eveloped, the structure would

und in

ng how external loads give rise to internal

change its movement or shape.

fail. These are known as Shear, Moment, and Normal Forces . The normal force is focolumns and beams with an axial load. Shear and moment are found in beams and frames. Most of the elements that will be analyzed in this course will be beams, including joists, purlins, girders, decking, planking, etc. 9.2.6 Explain how a structure “works” by interfo External and Internal Forces act on structures A Magnitude, Direction, and Location T • the magnitude, or size, of the force (the bigger the foeffect it will have on a structure) • the direction of the force • the location where the forc When drawing forces, the force is represenamagnitude, direction and location of the forces in a diagram. A static strum

9.2.7 Explain the differences between tensile and compressive forces and how they affect

quilibrium within a structure.

stretch a strompressive loads tend to compress

tamoving or an object moving with a given

If a force acts on an object then that objen additional force that exactly balances this resultant. Such a force is called the

9.2.8 Calculate a tensile or compressive stress, given values of force and area

area

.2.9 Calculate a tensile or compressive strain, given values of the original dimension and e change in dimension.

original length

rtance of forces in a de

9.3 The strength and stiffness of structures

9.3.1 Explain the rela

gree at all oints between A and B. It is at A however

e

ructure, that part will be deflected to an extent that depends on the size of the load and

e Tensile loads tend to extend or uctural member.

or shorten a structural member.

rt

ct can be brought into equilibrium by applying

CTensile and compressive forces must balance if the structure is to maintain equilibrium.

If this is not the case the object would s

velocity to speed up or slow down or change direction such that the velocity of the object changes.

aequilibrant and is equal in magnitude but opposite in direction to the original resultant force acting on the object.

Stress = force 9th Strain = change of length 9.2.10 Evaluate the impo sign context.

es.

tionship between deflection and stiffness in structur

When a force is applied to a beam the beam experiences stress to some depwhere most stress occurs, and where the beam is likely to break. We say that the greatest bending moment is at A. Bending moment is the product of the force and the differencbetween the force and the point of bending. If an external load is applied to some part of a st

the stiffness of the structure. 9.3.2 Calculate the stiffness of a structure.

ion

.3.3 Outline what is meant by bending moment in relation to structures. tion.

ntities of

,

.3.4 Outline what is meant by moment arm. e moment about the pivot. The distance

oment Arms ill probably be the most useful for you.

Here is the first example. What you see is an object of r

t, etc. Does not really matter.

http://www.youtube.com/watch?v=wV1pYkTtsxg&eurl=http://www.societyofrobots.com/m

Stiffness = load deflect 9This is the moment that a beam has to resist in bending at a particular secIn physics, the moment of force (often just moment, though there are other quathat name such as moment of inertia) represents the magnitude of force applied to a rotational system at a distance from the axis of rotation. The concept of the moment armthis characteristic distance, is key; it models the operation of the lever, pulley, gear, and most other simple machines involving a mechanical advantage. 9The load × distance from the pivot is called thbetween the load and the pivot is called the moment arm. MMoment arms wThe basic equation is moment equals force times the distance of the beam the force is being applied perpendicularly at. Moment = Force * distance

some length. It is fixed rigidly at one end. And the othehas some force being applied to it. This force can be something hanging on it, something pushing it, a hammer hitting it, a gear moving it, gravity/weigh

echanics_statics.shtml 8.3.5 Explain the need for a factor of safety in structural design.

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.3.6 Calculate the factor of safety for a structure.

load

.3.7 Apply the concept of factor of safety to other areas of design.

Structures are designed to take higher loads than those they are normalsupport. In order to make a structure that is strong enough, but it will not be too expensivdesigners have to try and calculate the forces that will act on it. Getting the balance right is very tricky. Even very skilled designers can never be absolutely sure that they have planned for all the forces that might act on a structure. Who is to say that a 100kg manot sit on a swing designed for 5 year olds, or that a jack designed to lift loads of up to 500kg won’t be used to try and lift 1000kg. Because of problems such as these structureare designed with a factor of safety. This is determined by calculation the forces a structuhas to take then multiplying them by the required number, for example 4. So, if a swing frame is being designed to take loads of 120 Newtons, using a safety factor of 4, it shouldfact be capable of supporting loads of up to 480 Newtons. 8Factor of safety = design load normal maximum 8

A factor of safety is simply the ratio of the quantitative value of a design (factor) divided by the normal maximum expected value.

So what should your factor be? Guess. I would recommend 1.2, but its really up to you. What does this number mean? Suppose your calculations say you need a motor rated at least 100Nm, then multiple that by 1.2 to get 120Nm as your minimum motor force. The factor of safety is not an exact science, obviously. If you expect to have high fatigue from shock or overuse, high friction, or bending, make the factor of safety higher.

8.3.8 Evaluate the importance of strength and stiffness in a design context.

9.4 Beams

9.4.1 Describe a beam. Beams are structural members that are subject to loads acting normally to their longitudinal axis. The loads create shear stresses and

bending moments and cause the beam to bend or flex. Beams are classified according to the way they are supported; for example, cantilever beams are rigidly supported at one end with the other end free. A beam is a structural element that is capable of withstanding load primarily by resisting bending.

The bending force induced into the material of the beam as a result of the external loads, own weight and external reactions to these loads is called a bending moment. 9.4.2 Describe how beams are designed to transfer forces and distribute loads through the beams. Beams generally carry vertical gravitational forces but can

also be used to carry horizontal loads (i.e., loads due to an earthquake or wind). The loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent

structural compression members. In Light frame construction the joists rest on the beam. Beams are characterized by their profile (the shape of their cross-section), their length, and their material. In contemporary construction, beams are typically made of steel, reinforced concrete, or wood. One of the most common types of steel beam is the I-beam or wide-flange beam (also known as a "universal beam" or, for stouter sections, a "universal column"). This is commonly used in steel-frame buildings and bridges. Other common beam profiles are the C-channel, the hollow structural section beam, the pipe, and the angle.

C Channel beamCellular beams

Wide flange 9.4.3 Describe the historical development of the materials used to manufacture beams. A beam bridge is a direct descendant of the log bridge, now more normally made from shallow steel 'I' beams, box girders, reinforced concrete, or post-tensioned concrete. It is frequently used in pedestrian bridges and for highway overpasses and flyovers. Solid wood beams—high bulk. Concrete beams with metal. Metal sectional beams reduce in the amount of material in the beam. 9.4.4 Identify a variety of shapes for sectional members of a structure. Consider rectangular, circular, L-shaped, I-shaped, castle-shaped.

9.4.5 Describe how the shape of sectional members of a structure makes the most effective and economic use of materials

9.4.6 Explain that sectional members of a structure may be manufactured in sheet material. For example, laminated veneer lumbar (LVL).

Laminated veneer lumber (LVL) is an engineered wood product that uses multiple layers of thin wood assembled with adhesives. It offers several advantages over typical milled lumber: it is stronger, straighter, and more uniform. It is much less likely than conventional lumber to warp, twist, bow, or shrink due to its composite nature. Made in a factory under controlled specifications, LVL products allow users to reduce the onsite labor. They are typically used for headers, beams, rimboard, and edge-forming material.

It is similar in appearance to plywood without crossbands. and is typically rated by the manufacturer for elastic modulus and allowable bending stress. Common elastic moduli are 1.8, 1.9, and 2.0 million psi, and common allowable bending stress values are 2800 and 3000 psi.

9.4.7 Outline the benefits of using LVL beams in the construction industry. LVL is used in place of more expensive wooden beams where the finished product is hidden by other forms of cladding.

9.4.8 Explain the importance of factor of safety in the design of beams. The safety factors can vary depending upon whose safety are we talking about. If it is the question of machine failure which may involve some cost of repair, the safety factor may be lower as compared to a situation where human safety is involved. In the design of a vertical elevator, safety factor should not only be high, but there have to be also many safety devices to reduce the probability of loss of life

Components all have a point of failure, such as a horizontal steel beam bending irreversibly from an overload. Most materials, such as steel, have an ultimate yield strength, in which collapse occurs, and have a maximum elastic strength, in which they can bend and still recover. It's standard engineering design to load such members to only 25% of the maximum elastic strength, and that is the "safety factor". For example, a bridge designed to carry 12 vehicles will be designed to be able to carry 60 (for a safety factor of 5), without permanent deformation. The bridge may very well be able to carry much more before it actually collapses into the river.

There is also a profit angle in the factor of safety which is how a businessman will think.