Mechanics unit 3 - mechanical properties of materials & structures - deck 1

Question 1

Describe the difference between a structure and a structural material

Answer 1

• A structure is an arrangement of one or more materials in a way that is designed to sustain loads.
• Whereas a structural material is any material that may be used to construct a structure

Question 2

What can the basic mechanical behaviours of materials be described by?

Answer 2

Their mechanical properties

Question 3

Are the mechanical properties of a material independent of a materials size and shape (its structure) ?

Answer 3

Yes

Question 4

State the symbols used to represent the following:

1. Stress
2. Strain
3. The coefficient of viscosity

Answer 4

1. Stress = σ
2. Strain = ε
3. The coefficient of viscosity = η

Question 5

Describe what the branch of mechanics called solid mechanics or deformable body mechanics is

Answer 5

• This is the branch of mechanics that looks at deformable bodies (i.e. ‘‘real world materials’’) by examining how their shape and size are changed under loading.
• This is different from what previous has been covered in flashcards which looks are dynamic problems where we assume the bodies under investigation were rigid (i.e. did not deform)

Question 6

Define what deformation is

Answer 6

This is the change in shape or size of a structure or any part of it

Question 7

Everything deforms to some extent when a load is applied to it - T or F?

Answer 7

True - a butterfly landing on the top of a mountain squashes the mountain ever so slightly

Question 8

What is the study of deformable bodies important for ?

Answer 8

When designing a piece of equipment, a structure or a device, once the force analysis has been perfomed it is important to calculate the stresses it will need to withstand under the expected working conditions.

Question 9

What must the material chosen to build a structure be able to withstand and not do?

Answer 9

The expected stresses and not deform excessively

Question 10

What does the deformation of a material depend on ?

Answer 10

The deformation will depend upon the magnitude of the applied forces, the structure and the mechanical properties of the material.

Question 11

What does the mechanical properties of a material allow us to predict ?

Answer 11

What will happen to a body when it is loaded

Question 12

Define what stress is

Answer 12

It is the force per cross-sectional area

Question 13

Consider two bars made of the same material and with the same length but one has twice the cross-sectional area (A1 and A2), if you subjected both bars to an increasing stretching force or load until they broke what would you find ?

Answer 13

You would find that the bar with the cross-sectional area twice the size of the other bar would require twice the force to break it.

Question 14

What is the breaking force of a material dependent on?

Answer 14

The material and the cross-sectional area of the bar

Question 15

Consider two bars made of the same material and with the same length but with different cross-sectional areas (A1 and A2) - when the two bars break the stress within the bars will be the same regardless of the cross-sectional area - T or F?

Answer 15

True - this is because the breaking stress of a material is dependent on the material alone and not on its structure.

Think about the equation for stress = force / cross-sectional area. As the force required to break the two bars will be different so will the cross-sectional area, the force and cross-sectional area balance each other out in both situations and produce the same stress

Question 16

Stress is independent of the shape and size (structure) of a material, it is only dependent on the material itself. The stress in bars of the same material will be equal when they break despite the fact that the forces required to break them will be different, therefore is stress a useful indication of ? and what can it be used to predict?

Answer 16

• It is a useful indication of the strength of a material.
• It can be used to predict the breaking force for a material with any shape

Question 17

State the equation for calculating stress and the SI units of stress

Answer 17

σ = F / A

• σ = stress
• F = applied force
• A = cross-sectional area

SI units = N m^-2 or the dervied unit Pa (the same as for pressure)

Question 18

Do worked example and SAQ 1 pg. 4 mechanical properties unit

Answer 18

Ans in workbook

Question 19

Define what strain is

Answer 19

This is equal to the change in length divided by the original length in the direction of change

Question 20

What is the amount of elongation (change in length) of a body e.g. a bar dependent on ?

Answer 20

On the length of the bar, the amount of elongation is proportional to the length of the bar/ body i.e. the longer the bar the greater the elongation

Question 21

Consider two bars of the same material and of the same cross-sectional area but of different lengths (one is twice the length of the other), if you applied the same stretching force to both bars then they would both elongate - describe the difference in the elongation seen in the shorter bar compared to the longer bar

Answer 21

The elongation of the longer bar will be twice that of the shorter bar as the amount of elongation is proportional to the length of the bar

Question 22

State the equation used to calculate strain

Answer 22

ε = ∆I / I or = I₁ - I / I

• ε = strain
• I₁ = original length
• I = the changed length
• ∆I = the change in length

Question 23

What are the units of strain ?

Answer 23

Strain does not have any units

Question 24

Do worked example pg. 5 mechanical properties unit

Answer 24

Ans in workbook

Question 25

Do SAQ 2 pg. 6 mechanical properties unit

Answer 25

Ans in workbook

Question 26

Define tensile and compressive forces or loads

Answer 26

• Tensile forces which when applied stretch a bar/ body
• Compressive forces/ loads are those which when applied shorten a bar/ body

Question 27

Define what axial loads are

Answer 27

They are both tensile and compressive loads applied along a geometric axis of a structure producing pure tension or compression (as opposed to bending or twisting)

Question 28

Do SAQ 3 pg. 6 mechanical properties unit

Answer 28

Ans in workbook

Question 29

Are stress and strain independent of each other?

Answer 29

No - if a stess is applied to a material then there will be a resulting strain

Question 30

What is a useful tool for conveying the mechanical properties and behaviour of a material ?

Answer 30

A stress-stain curve

Question 31

In this unit I will be discussing the stress-strain curves of materials which are loaded in what way?

Answer 31

Axially

Question 32

What does a stress-strain curve show?

Answer 32

• It shows the stress of a material against its strain as it deforms as it is loaded
• Therefore they provide a useful way of comparing different materials to see there behaviours which is relavitvely more or less stiff, tough, ductile &/ or brittle (all materials show these behaviours but may predominately show one of them)

Question 33

Describe where the proportional limit lies on a stress-strain curve and the relationship between stress and strain in this part of the graph

Answer 33

The proportional limit lies between the origin (O) and the proportional limit (P)

Between these two points this is the linear region of the stress-strain curve where the stress is directly proportional to strain (==> as stress doubles, strain also doubles)

Question 34

Define what is meant when a material is said to exhibit elastic behaviour

Answer 34

This is a material which deforms instantaneously on loading and returns immediately to its original shape and size when the load is removed e.g. rubber

Question 35

Define what is meant when a material is said to exhibit plastic behaviour

Answer 35

This is a material which will deform instantaneously under an applied load, but then retains its new size and shape once the load is removed e.g. putty

Question 36

State what the elastic limit (E) on a typical stress-strain curve is

Answer 36

This is the greatest stress that may be applied to the material without causing any permanent deformation (greatest point the material will still display elastic behaviour)

Question 37

What happens when a material is loaded beyond its elastic limit (E) ?

Answer 37

The material will not return to its original size and shape (display plastic behaviour), it may partially recover its shape but not completely and there will remain a residual or permanent strain (extension or compression)

Question 38

Where does the elastic region lie between in a typical stress-strain curve?

Answer 38

Between the origin (O) and the elastic limit (E)

Question 39

In the elastic region how does the curve produced by unloading of the material compare to when it is loaded? and then when loaded past the elastic region how does it compare?

Answer 39

• In the elastic region the material will follow the same stress-strain curve when it is unloaded as it did when loaded
• When the material is loaded beyond the lastic limit it will follow a new curve on unloading, the material may partially recover its original shape but not completely, and there will remain a residual or permanent strain

Question 40

Why is it important that a structural material is not stressed beyond its elastic limit?

Answer 40

Because a material that has become plastic is no longer of use since it will deform greatly under only a small increase in load (the plastic region points E to H)

Question 41

What happens once the yield point (Y) on a typical stress-strain curve is passed and what behaviour is displayed here?

Answer 41

• The material will undergo considerable elongation (yielding) without a corresponding increase in stress. (indicated by the flatness of the region following the yield point)
• In this region the material exhibits perfectly plastic bahviour (no elastic recovery)

Question 42

What is the stress at the yield point called?

Answer 42

The yield strength of the material

Question 43

After undergoing the large strain that can occur during yielding what happens and why ?

Answer 43

Strain hardening occurs where the material undergoes changes in atomic and crystalline structure resulting in an increased resistance to further deformation

(this region lies from points H to V)

Question 44

What is the ultimate strength point (U) of a material in a typical stress-strain curve and what is the stress at this point called?

Answer 44

• This is the highest point of the stress-strain curve
• The stress at this point is called the ultimate strength

Question 45

Describe what happens in the region after the ultimate strength point (U) on a typical stress-strain curve and why

Answer 45

Stretching (increase in strain) occurs with an actual reduction in the stress on the material. This is because of necking or waisting in the material, whereby the cross-sectional area of the material is reduced.

Question 46

Define what necking of a material is

Answer 46

This is the phenomenon whereby a materials cross-sectional area is reduced during loading such that the material appears to reduce in strength

Question 47

What is it important to remember is the cause for the reduction in stress the bar can withstand after the ultimate strength is due to ?

Answer 47

It is due to the reduction in the cross-sectional area of the bar not due to ant loss of material strength. If the cross-sectional area of the narrowest part of the neck is used to calculate the stress then the true stress-strain curve is obtained. (fig shows this)

Question 48

What is the rupture point (R) on a typical stress-strain curve defined as and what is the stress at this point known as?

Answer 48

• This is the point at which the material breaks
• The stress at this point is known as the rupture strength

Question 49

Describe what is meant when a material is described as brittle

Answer 49

This is when a material can only withstand a small amount of strain before breaking e.g. glass

Question 50

Describe what is meant when a material is described as ductile

Answer 50

This is a material which can deform considerably (plastically) before breaking e.g. copper

Question 51

Do SAQ 4 pg. 9 mechanical properties unit

Answer 51

Ans in workbook