Lesson test: Bending

1.[3p]
Why does the neutral axis of a beam in pure bending pass through the centroid of the section?

Zero net axial force forces the first moment of area about that axis to vanish, which defines the centroid

Correct

Because the centroid is where the material is densest

The answer is: Zero net axial force forces the first moment of area about that axis to vanish, which defines the centroid

Because the section is always symmetric about it

The answer is: Zero net axial force forces the first moment of area about that axis to vanish, which defines the centroid

Because the bending moment is applied at the centroid

The answer is: Zero net axial force forces the first moment of area about that axis to vanish, which defines the centroid

2.[2p]
A rectangular section is 100 mm wide and 300 mm deep. What is its second moment of area about the horizontal centroidal axis, in mm⁴?

CorrectNot quite: 225000000

3.[3p]
The same 100 mm by 300 mm section carries a bending moment of 90 kN m. What is the maximum bending stress, in MPa?

CorrectNot quite: 60

4.[3p]
A beam must carry a design moment of 180 kN m at a stress of 275 MPa. What elastic section modulus is required, in mm³?

CorrectNot quite: 654545

5.[3p]
A rectangular joist is turned from lying flat to standing on edge, so its depth and width swap. Its depth was four times its width. What happens to its bending strength?

It becomes four times greater, since the section modulus scales with the ratio of depth to width

Correct

It is unchanged, since the area is the same

The answer is: It becomes four times greater, since the section modulus scales with the ratio of depth to width

It becomes sixteen times greater

The answer is: It becomes four times greater, since the section modulus scales with the ratio of depth to width

It becomes twice as great

The answer is: It becomes four times greater, since the section modulus scales with the ratio of depth to width

6.[2p]
The parallel axis theorem adds $A h^{2}$ because the cross term in the expansion vanishes when $y$ is measured from the centroid.

True

Correct

False

The answer is: True

7.[2p]
Why is steel rolled into an I shape rather than a square bar of the same area?

The second moment of area weights material by the square of its distance from the neutral axis, so flanges far out are worth far more than a solid core

Correct

Rolling an I shape uses less energy than rolling a square

The answer is: The second moment of area weights material by the square of its distance from the neutral axis, so flanges far out are worth far more than a solid core

An I section resists torsion better than a square

The answer is: The second moment of area weights material by the square of its distance from the neutral axis, so flanges far out are worth far more than a solid core

The web carries the bending and needs to be thin

The answer is: The second moment of area weights material by the square of its distance from the neutral axis, so flanges far out are worth far more than a solid core

8.[3p]
Which assumptions underlie the flexure formula $M / I = σ / y$ ?

Select all that apply

Cross sections remain plane and perpendicular to the bent axis

Correct

The material is still linear and elastic

Correct

The beam is slender, so the span is large compared with the depth

Correct

The section is symmetric about the neutral axis

The answer is: Cross sections remain plane and perpendicular to the bent axis, The material is still linear and elastic, The beam is slender, so the span is large compared with the depth

9.[2p]
For a rectangular section, the plastic section modulus is $b d^{2} / 4$ and the elastic one is $b d^{2} / 6$ . What is the ratio of the two?

CorrectNot quite: 1.5

1.[3p] Why does the neutral axis of a beam in pure bending pass through the centroid of the section?

2.[2p] A rectangular section is 100 mm wide and 300 mm deep. What is its second moment of area about the horizontal centroidal axis, in mm⁴?

3.[3p] The same 100 mm by 300 mm section carries a bending moment of 90 kN m. What is the maximum bending stress, in MPa?

4.[3p] A beam must carry a design moment of 180 kN m at a stress of 275 MPa. What elastic section modulus is required, in mm³?

5.[3p] A rectangular joist is turned from lying flat to standing on edge, so its depth and width swap. Its depth was four times its width. What happens to its bending strength?

6.[2p] The parallel axis theorem adds Ah2 because the cross term in the expansion vanishes when y is measured from the centroid.

7.[2p] Why is steel rolled into an I shape rather than a square bar of the same area?

8.[3p] Which assumptions underlie the flexure formula M/I=σ/y?

9.[2p] For a rectangular section, the plastic section modulus is bd2/4 and the elastic one is bd2/6. What is the ratio of the two?

1.[3p]
Why does the neutral axis of a beam in pure bending pass through the centroid of the section?

2.[2p]
A rectangular section is 100 mm wide and 300 mm deep. What is its second moment of area about the horizontal centroidal axis, in mm⁴?

3.[3p]
The same 100 mm by 300 mm section carries a bending moment of 90 kN m. What is the maximum bending stress, in MPa?

4.[3p]
A beam must carry a design moment of 180 kN m at a stress of 275 MPa. What elastic section modulus is required, in mm³?

5.[3p]
A rectangular joist is turned from lying flat to standing on edge, so its depth and width swap. Its depth was four times its width. What happens to its bending strength?

6.[2p]
The parallel axis theorem adds $A h^{2}$ because the cross term in the expansion vanishes when $y$ is measured from the centroid.

7.[2p]
Why is steel rolled into an I shape rather than a square bar of the same area?

8.[3p]
Which assumptions underlie the flexure formula $M / I = σ / y$ ?

9.[2p]
For a rectangular section, the plastic section modulus is $b d^{2} / 4$ and the elastic one is $b d^{2} / 6$ . What is the ratio of the two?