Lesson test: Choosing a material

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Choosing a material

1.[2p]
What is the free variable in a typical material selection problem?

A section dimension, adjusted so the constraint is just satisfied

Correct

The material, which is what is being chosen

The answer is: A section dimension, adjusted so the constraint is just satisfied

The load the component has to carry

The answer is: A section dimension, adjusted so the constraint is just satisfied

The length of the component, fixed by the design

The answer is: A section dimension, adjusted so the constraint is just satisfied

2.[3p]
Match each design case to the material index that should be maximised.

Light tie of given stiffness
Light tie of given strength
Light beam of given stiffness
Light beam of given strength

sqrt(E)/rho
sigma/rho
sigma^(2/3)/rho
E/rho

Show the answer

Light tie of given stiffness: E/rho Light tie of given strength: sigma/rho Light beam of given stiffness: sqrt(E)/rho Light beam of given strength: sigma^(2/3)/rho

3.[3p]
Softwood along the grain has $E = 10$ GPa and $ρ = 0.45$ Mg m⁻³. What is its light stiff beam index $E^{1 / 2} / ρ$ , with $E$ in GPa?

CorrectNot quite: 7.03

4.[3p]
Structural steel, aluminium alloy and titanium alloy all have a specific stiffness $E / ρ$ near 26. Why?

Within metals, both $E$ and $ρ$ scale with the strength of the interatomic bonding, so their ratio barely moves

Correct

It is a coincidence of the particular alloys chosen

The answer is: Within metals, both $E$ and $\rho$ scale with the strength of the interatomic bonding, so their ratio barely moves

All three are alloyed with iron

The answer is: Within metals, both $E$ and $\rho$ scale with the strength of the interatomic bonding, so their ratio barely moves

Specific stiffness is defined so that metals come out equal

The answer is: Within metals, both $E$ and $\rho$ scale with the strength of the interatomic bonding, so their ratio barely moves

5.[3p]
Why does a square root appear in the light stiff beam index but not in the light stiff tie index?

The free section dimension enters $I$ with a higher power than it enters the area, so a light material may be bulky and still win

Correct

Beams are always loaded in two directions at once

The answer is: The free section dimension enters $I$ with a higher power than it enters the area, so a light material may be bulky and still win

Deflection depends on the square root of the load

The answer is: The free section dimension enters $I$ with a higher power than it enters the area, so a light material may be bulky and still win

Beams are analysed with a different definition of stiffness

The answer is: The free section dimension enters $I$ with a higher power than it enters the area, so a light material may be bulky and still win

6.[2p]
For a light stiff beam, softwood along the grain outperforms structural steel.

True

Correct

False

The answer is: True

7.[3p]
Changing the objective from mass to cost replaces $ρ$ in every index by $C_{m} ρ$ . If steel scores 1.85 at 1 unit per kg and a laminate scores 7.13 at 50 units per kg, by what factor does steel then beat the laminate?

CorrectNot quite: 13

8.[3p]
Which of these does a material index built on yield strength and density fail to account for?

Select all that apply

Fatigue strength at a welded detail, which can be under a third of yield

Correct

The loss of strength in a laminate after an impact that leaves no visible mark

Correct

The variability of timber strength between pieces of the same grade

Correct

The dependence of mass on the density of the material

The answer is: Fatigue strength at a welded detail, which can be under a third of yield, The loss of strength in a laminate after an impact that leaves no visible mark, The variability of timber strength between pieces of the same grade

9.[3p]
Why is a bicycle frame made from a different material than a bridge girder, when both are loaded mainly in bending?

The objective differs: the frame is sized to minimise mass, the girder to minimise cost

Correct

The girder carries bending and the frame does not

The answer is: The objective differs: the frame is sized to minimise mass, the girder to minimise cost

Bicycle frames are not designed by these methods

The answer is: The objective differs: the frame is sized to minimise mass, the girder to minimise cost

The frame is loaded dynamically, so no index applies

The answer is: The objective differs: the frame is sized to minimise mass, the girder to minimise cost

1.[2p] What is the free variable in a typical material selection problem?

2.[3p] Match each design case to the material index that should be maximised.

3.[3p] Softwood along the grain has E=10 GPa and ρ=0.45 Mg m⁻³. What is its light stiff beam index E1/2/ρ, with E in GPa?

4.[3p] Structural steel, aluminium alloy and titanium alloy all have a specific stiffness E/ρ near 26. Why?

5.[3p] Why does a square root appear in the light stiff beam index but not in the light stiff tie index?

6.[2p] For a light stiff beam, softwood along the grain outperforms structural steel.

7.[3p] Changing the objective from mass to cost replaces ρ in every index by Cmρ. If steel scores 1.85 at 1 unit per kg and a laminate scores 7.13 at 50 units per kg, by what factor does steel then beat the laminate?

8.[3p] Which of these does a material index built on yield strength and density fail to account for?

9.[3p] Why is a bicycle frame made from a different material than a bridge girder, when both are loaded mainly in bending?

1.[2p]
What is the free variable in a typical material selection problem?

2.[3p]
Match each design case to the material index that should be maximised.

3.[3p]
Softwood along the grain has $E = 10$ GPa and $ρ = 0.45$ Mg m⁻³. What is its light stiff beam index $E^{1 / 2} / ρ$ , with $E$ in GPa?

4.[3p]
Structural steel, aluminium alloy and titanium alloy all have a specific stiffness $E / ρ$ near 26. Why?

5.[3p]
Why does a square root appear in the light stiff beam index but not in the light stiff tie index?

6.[2p]
For a light stiff beam, softwood along the grain outperforms structural steel.

7.[3p]
Changing the objective from mass to cost replaces $ρ$ in every index by $C_{m} ρ$ . If steel scores 1.85 at 1 unit per kg and a laminate scores 7.13 at 50 units per kg, by what factor does steel then beat the laminate?

8.[3p]
Which of these does a material index built on yield strength and density fail to account for?

9.[3p]
Why is a bicycle frame made from a different material than a bridge girder, when both are loaded mainly in bending?