Lesson test: Shear in beams

1.[3p]
Why must horizontal shear stress exist inside a beam?

The bending moment varies along the span, so the bending stresses on the two faces of a slice do not balance

Correct

Because the supports push upwards on the beam

The answer is: The bending moment varies along the span, so the bending stresses on the two faces of a slice do not balance

Because the beam deflects, and deflection implies sliding

The answer is: The bending moment varies along the span, so the bending stresses on the two faces of a slice do not balance

Because the material is not perfectly elastic

The answer is: The bending moment varies along the span, so the bending stresses on the two faces of a slice do not balance

2.[3p]
A rectangular beam 150 mm wide and 300 mm deep carries a shear force of 45 kN. What is the maximum shear stress, in MPa?

CorrectNot quite: 1.5

3.[2p]
For a rectangular section, what is the ratio of the maximum shear stress to the average shear stress $V / A$ ?

CorrectNot quite: 1.5

4.[2p]
Where in a rectangular beam section is the shear stress largest?

At the neutral axis, where the first moment of the area above the cut is greatest

Correct

At the top and bottom faces, where the bending stress is greatest

The answer is: At the neutral axis, where the first moment of the area above the cut is greatest

Uniformly across the whole depth

The answer is: At the neutral axis, where the first moment of the area above the cut is greatest

One quarter of the depth from the top

The answer is: At the neutral axis, where the first moment of the area above the cut is greatest

5.[2p]
In an I-beam, the flanges carry most of the bending stress and the web carries most of the shear.

True

Correct

False

The answer is: True

6.[3p]
Why does the shear stress jump sharply at the junction between an I-beam's web and its flange?

$Q$ is continuous there but the width $t$ changes abruptly, and $t$ is in the denominator

Correct

The bending stress reaches its maximum at that level

The answer is: $Q$ is continuous there but the width $t$ changes abruptly, and $t$ is in the denominator

The weld between web and flange concentrates the stress

The answer is: $Q$ is continuous there but the width $t$ changes abruptly, and $t$ is in the denominator

The neutral axis lies at that level

The answer is: $Q$ is continuous there but the width $t$ changes abruptly, and $t$ is in the denominator

7.[3p]
A built-up beam has $I = 1.135 \times 10^{8}$ mm⁴ and a flange whose first moment about the neutral axis is $Q = 625000$ mm³. Under a shear force of 4 kN, what is the shear flow at the joint, in N per mm?

CorrectNot quite: 22

8.[2p]
For which beam is shear most likely to govern rather than bending?

A short deep beam, such as a lintel over a doorway

Correct

A long slender beam carrying a uniform load

The answer is: A short deep beam, such as a lintel over a doorway

A cantilever with a load at its tip

The answer is: A short deep beam, such as a lintel over a doorway

A beam of any span made from steel rather than timber

The answer is: A short deep beam, such as a lintel over a doorway

9.[3p]
Which of these does the formula $τ = V Q / I t$ fail to describe?

Select all that apply

Diagonal buckling of a slender web under shear

Correct

Local crushing of the web under a concentrated load

Correct

The variation of shear stress across the width of a wide flange

Correct

The shear stress at the neutral axis of a narrow rectangular section

The answer is: Diagonal buckling of a slender web under shear, Local crushing of the web under a concentrated load, The variation of shear stress across the width of a wide flange

1.[3p] Why must horizontal shear stress exist inside a beam?

2.[3p] A rectangular beam 150 mm wide and 300 mm deep carries a shear force of 45 kN. What is the maximum shear stress, in MPa?

3.[2p] For a rectangular section, what is the ratio of the maximum shear stress to the average shear stress V/A?

4.[2p] Where in a rectangular beam section is the shear stress largest?

5.[2p] In an I-beam, the flanges carry most of the bending stress and the web carries most of the shear.

6.[3p] Why does the shear stress jump sharply at the junction between an I-beam's web and its flange?

7.[3p] A built-up beam has I=1.135×108 mm⁴ and a flange whose first moment about the neutral axis is Q=625000 mm³. Under a shear force of 4 kN, what is the shear flow at the joint, in N per mm?

8.[2p] For which beam is shear most likely to govern rather than bending?

9.[3p] Which of these does the formula τ=VQ/It fail to describe?

1.[3p]
Why must horizontal shear stress exist inside a beam?

2.[3p]
A rectangular beam 150 mm wide and 300 mm deep carries a shear force of 45 kN. What is the maximum shear stress, in MPa?

3.[2p]
For a rectangular section, what is the ratio of the maximum shear stress to the average shear stress $V / A$ ?

4.[2p]
Where in a rectangular beam section is the shear stress largest?

5.[2p]
In an I-beam, the flanges carry most of the bending stress and the web carries most of the shear.

6.[3p]
Why does the shear stress jump sharply at the junction between an I-beam's web and its flange?

7.[3p]
A built-up beam has $I = 1.135 \times 10^{8}$ mm⁴ and a flange whose first moment about the neutral axis is $Q = 625000$ mm³. Under a shear force of 4 kN, what is the shear flow at the joint, in N per mm?

8.[2p]
For which beam is shear most likely to govern rather than bending?

9.[3p]
Which of these does the formula $τ = V Q / I t$ fail to describe?