Mechanics unit 3 - mechanical properties of materials & structures - deck 2

Question 1

Most materials have an initial region on their stress-strain curve in which they behave both elastically and linearlly (straight line). This region extends from the origin to the proportional limit.

What law is used to describe this elastic linear behaviour?

Answer 1

Hookes law - this states that up to a certain level of stress (the proportional limit), the strain produced is proportional to the applied stress

Question 2

Define what the stiffness of a material is

Answer 2

This is a measure of how difficult it is to deform a material under loading (i.e. the strain under the action of stress)

Question 3

What is the stiffness of a material indicated by ?

Answer 3

Its youngs modulus (sometimes called the modulus of elasticity)

Question 4

Define what youngs modulus is

Answer 4

It is the ratio of stress to strain, and is an indication of the stiffness of a material

Question 5

State the equation for calculating youngs modulus and its SI units

Answer 5

SI units = N m^-2 or Pa (the same as stress and pressure - since strain has no units)

Question 6

How can youngs modulus be calculated using a stress-strain curve ?

Answer 6

By calculating the gradient of the curve (only up to the proportional limit)

Question 7

Describe what a large and small youngs modulus tells us about the stiffness of a material

Answer 7

For these definitions rearrange youngs modulus equation to calculate strain: ε = σ / E

A material with a small youngs modulus requires only a small amount of stress to produce a large strain i.e. it is flexible

M material with a large youngs modulus requires a large amount of stress to produce a small strain i.e. it is stiff

Question 8

Do SAQ 5 on pg. 11 mechanical properties unit

Answer 8

Ans in workbook

Question 9

Define what the rigidity of a bar is

Answer 9

This is an indication of its ability to resist axial deformation

Question 10

State the equation for calculating the rigidity of a material

Answer 10

Units = N (because m² cancels with the m^-2 of youngs modulus units)

Question 11

What happens to the rigidity of a bar as the cross-sectional area of the bar increases?

Answer 11

Its rigidity will increase

Question 12

Describe the difference between stiffness of a material and rigidity of a bar

Answer 12

• The stiffness of a material itself is indicated by its youngs modulus and is a measure of how difficult the material is to deform under loading
• Whereas the rigidity of a bar is an indication of the bars ability to resist axial deformation (this is different as it is dependent on the cross-sectional area and the youngs modulus i.e. how stiff the material is which is used to make the bar)

Question 13

Define what the stiffness of a bar (not just the material being considered) is

Answer 13

This is the force required to produce a unit of deflection (elongation or shortening of the bar by 1m)

Question 14

State the 2 equations which can be used to calculate stiffness of a bar

Answer 14

Units for k = N m^-1 see SAQ 6 for explanation

Question 15

What is the stiffness of a bar equal to ?

Answer 15

The rigidity of a bar per unit length

Question 16

Define what the flexibility of a bar is

Answer 16

This is the deflection under a unit load (it is therefore the inverse of stiffness)

Question 17

State the 3 equations which can be used to calculate the flexibility of a bar

Answer 17

Note that for the 1st & 2nd equation the 1 stands for length but for the 3rd the 1 stands for one as its simply the inverse of stiffness

Question 18

Using the equations that can be used to calculate the flexibility and stiffness of a bar state what will an increase in the length of the bar do to the stiffness and flexibility of it

Answer 18

It will decrease the stiffness and increase the flexibility of the bar

Question 19

Using the equations that can be used to calculate the flexibility and stiffness of a bar state what will an increase in the cross-sectional area of the bar do to the stiffness and flexibility of it ?

Answer 19

It will increase the stiffness and decrease the flexibility

Question 20

Do SAQ 6 pg. 12 mechanical properties unit 3

Answer 20

Ans in workbook

Question 21

What is the difference in what rigidity, stiffness and flexibility of a material are dependent on compared to the youngs modulus?

Answer 21

Youngs modulus is dependent soley on the material, where as the others are dependent on the material and its shape and size