Lesson test: Stress

1.[2p]
A steel bar of rectangular section 30 mm by 40 mm carries 180 kN in tension. What is the normal stress, in MPa?

CorrectNot quite: 150

2.[1p]
Why is 1 MPa the same as 1 N mm⁻²?

A megapascal is a million newtons per square metre, and a square millimetre is a millionth of a square metre

Correct

Because megapascals are defined from millimetres by convention

The answer is: A megapascal is a million newtons per square metre, and a square millimetre is a millionth of a square metre

Because structural steel happens to yield near 1 MPa

The answer is: A megapascal is a million newtons per square metre, and a square millimetre is a millionth of a square metre

It is an approximation, accurate to about one per cent

The answer is: A megapascal is a million newtons per square metre, and a square millimetre is a millionth of a square metre

3.[3p]
A thin-walled cylinder of 800 mm internal diameter and 10 mm wall carries 2 MPa of internal gauge pressure. What is the hoop stress, in MPa?

CorrectNot quite: 80

4.[1p]
In a thin-walled cylinder under internal pressure, the longitudinal stress is half the hoop stress.

True

Correct

False

The answer is: True

5.[3p]
A 24 mm diameter bolt in double shear transmits 90 kN. What is the shear stress, in MPa?

CorrectNot quite: 99.5

6.[2p]
What does Saint-Venant's principle allow?

Treating the stress as uniform away from the ends, whatever the detail of how the load was applied

Correct

Ignoring stress concentrations at holes and notches

The answer is: Treating the stress as uniform away from the ends, whatever the detail of how the load was applied

Assuming that shear stress is always half the normal stress

The answer is: Treating the stress as uniform away from the ends, whatever the detail of how the load was applied

Replacing a distributed load by its resultant when finding internal forces

The answer is: Treating the stress as uniform away from the ends, whatever the detail of how the load was applied

7.[2p]
For a small circular hole in a wide plate under uniform tension, what is the elastic stress concentration factor at the edge of the hole?

CorrectNot quite: 3

8.[3p]
Why does a stress concentration matter far more in cast iron than in mild steel under a steady load?

Mild steel yields locally and sheds the excess to its neighbours, while cast iron has no such mechanism

Correct

Cast iron has a much lower stiffness, so it deflects more at the hole

The answer is: Mild steel yields locally and sheds the excess to its neighbours, while cast iron has no such mechanism

Mild steel is stronger, so the concentration never reaches its strength

The answer is: Mild steel yields locally and sheds the excess to its neighbours, while cast iron has no such mechanism

Cast iron holes are always drilled more roughly

The answer is: Mild steel yields locally and sheds the excess to its neighbours, while cast iron has no such mechanism

9.[3p]
Which of these are true of the thin-walled pressure vessel formulas?

Select all that apply

They follow from equilibrium alone and use no material property

Correct

They predict a burst along a line parallel to the axis rather than a break across it

Correct

They assume the radius is large compared with the wall thickness

Correct

They require the material to be linearly elastic

The answer is: They follow from equilibrium alone and use no material property, They predict a burst along a line parallel to the axis rather than a break across it, They assume the radius is large compared with the wall thickness

1.[2p] A steel bar of rectangular section 30 mm by 40 mm carries 180 kN in tension. What is the normal stress, in MPa?

2.[1p] Why is 1 MPa the same as 1 N mm⁻²?

3.[3p] A thin-walled cylinder of 800 mm internal diameter and 10 mm wall carries 2 MPa of internal gauge pressure. What is the hoop stress, in MPa?

4.[1p] In a thin-walled cylinder under internal pressure, the longitudinal stress is half the hoop stress.

5.[3p] A 24 mm diameter bolt in double shear transmits 90 kN. What is the shear stress, in MPa?

6.[2p] What does Saint-Venant's principle allow?

7.[2p] For a small circular hole in a wide plate under uniform tension, what is the elastic stress concentration factor at the edge of the hole?

8.[3p] Why does a stress concentration matter far more in cast iron than in mild steel under a steady load?

9.[3p] Which of these are true of the thin-walled pressure vessel formulas?

1.[2p]
A steel bar of rectangular section 30 mm by 40 mm carries 180 kN in tension. What is the normal stress, in MPa?

2.[1p]
Why is 1 MPa the same as 1 N mm⁻²?

3.[3p]
A thin-walled cylinder of 800 mm internal diameter and 10 mm wall carries 2 MPa of internal gauge pressure. What is the hoop stress, in MPa?

4.[1p]
In a thin-walled cylinder under internal pressure, the longitudinal stress is half the hoop stress.

5.[3p]
A 24 mm diameter bolt in double shear transmits 90 kN. What is the shear stress, in MPa?

6.[2p]
What does Saint-Venant's principle allow?

7.[2p]
For a small circular hole in a wide plate under uniform tension, what is the elastic stress concentration factor at the edge of the hole?

8.[3p]
Why does a stress concentration matter far more in cast iron than in mild steel under a steady load?

9.[3p]
Which of these are true of the thin-walled pressure vessel formulas?