Lesson test: Deflection

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Deflection

1.[2p]
What does the Euler-Bernoulli beam equation $E I v'' = M$ assume about the deflected shape?

That the slope is small enough for the square of the slope to be dropped from the curvature

Correct

That the beam is statically determinate

The answer is: That the slope is small enough for the square of the slope to be dropped from the curvature

That the bending moment is constant along the span

The answer is: That the slope is small enough for the square of the slope to be dropped from the curvature

That shear deformation is the dominant contribution

The answer is: That the slope is small enough for the square of the slope to be dropped from the curvature

2.[3p]
A steel beam spans 10 m under 8 kN per metre, with $I = 3.5 \times 10^{8}$ mm⁴ and $E = 210$ GPa. What is the maximum deflection, in mm?

CorrectNot quite: 14.2

3.[3p]
A steel cantilever projects 2.5 m with 15 kN at its tip, $I = 8 \times 10^{7}$ mm⁴ and $E = 210$ GPa. What is the tip deflection, in mm?

CorrectNot quite: 4.65

4.[3p]
A propped cantilever of 6 m span carries 20 kN per metre. What is the reaction at the prop, in kN?

CorrectNot quite: 45

5.[2p]
Doubling the span of a beam under the same load per metre multiplies its maximum deflection by what factor?

Sixteen

Correct

Two

The answer is: Sixteen

Four

The answer is: Sixteen

Eight

The answer is: Sixteen

6.[3p]
Why does using a higher grade of steel often fail to reduce deflection?

Deflection is governed by Young's modulus, which is essentially the same for every steel grade

Correct

Higher grade steels are rolled into shallower sections

The answer is: Deflection is governed by Young's modulus, which is essentially the same for every steel grade

Higher grade steels creep more under load

The answer is: Deflection is governed by Young's modulus, which is essentially the same for every steel grade

Deflection depends on the yield strength squared

The answer is: Deflection is governed by Young's modulus, which is essentially the same for every steel grade

7.[2p]
In a uniform propped cantilever, the prop reaction depends on the material the beam is made of.

True

The answer is: False

False

Correct

8.[3p]
Match each standard case to its maximum deflection.

Cantilever, point load at tip
Cantilever, uniform load
Simply supported, uniform load
Simply supported, central point load

wL⁴/8EI
PL³/3EI
PL³/48EI
5wL⁴/384EI

Show the answer

Cantilever, point load at tip: PL³/3EI Cantilever, uniform load: wL⁴/8EI Simply supported, uniform load: 5wL⁴/384EI Simply supported, central point load: PL³/48EI

9.[3p]
Which effects does the elastic deflection calculation of this lesson leave out?

Select all that apply

Extra deflection from shear distortion, which matters for short deep beams

Correct

Loss of stiffness once a reinforced concrete section cracks in tension

Correct

Long term creep deflection under sustained load

Correct

The dependence of deflection on the second moment of area

The answer is: Extra deflection from shear distortion, which matters for short deep beams, Loss of stiffness once a reinforced concrete section cracks in tension, Long term creep deflection under sustained load

1.[2p] What does the Euler-Bernoulli beam equation EIv''=M assume about the deflected shape?

2.[3p] A steel beam spans 10 m under 8 kN per metre, with I=3.5×108 mm⁴ and E=210 GPa. What is the maximum deflection, in mm?

3.[3p] A steel cantilever projects 2.5 m with 15 kN at its tip, I=8×107 mm⁴ and E=210 GPa. What is the tip deflection, in mm?

4.[3p] A propped cantilever of 6 m span carries 20 kN per metre. What is the reaction at the prop, in kN?

5.[2p] Doubling the span of a beam under the same load per metre multiplies its maximum deflection by what factor?

6.[3p] Why does using a higher grade of steel often fail to reduce deflection?

7.[2p] In a uniform propped cantilever, the prop reaction depends on the material the beam is made of.

8.[3p] Match each standard case to its maximum deflection.

9.[3p] Which effects does the elastic deflection calculation of this lesson leave out?

1.[2p]
What does the Euler-Bernoulli beam equation $E I v'' = M$ assume about the deflected shape?

2.[3p]
A steel beam spans 10 m under 8 kN per metre, with $I = 3.5 \times 10^{8}$ mm⁴ and $E = 210$ GPa. What is the maximum deflection, in mm?

3.[3p]
A steel cantilever projects 2.5 m with 15 kN at its tip, $I = 8 \times 10^{7}$ mm⁴ and $E = 210$ GPa. What is the tip deflection, in mm?

4.[3p]
A propped cantilever of 6 m span carries 20 kN per metre. What is the reaction at the prop, in kN?

5.[2p]
Doubling the span of a beam under the same load per metre multiplies its maximum deflection by what factor?

6.[3p]
Why does using a higher grade of steel often fail to reduce deflection?

7.[2p]
In a uniform propped cantilever, the prop reaction depends on the material the beam is made of.

8.[3p]
Match each standard case to its maximum deflection.

9.[3p]
Which effects does the elastic deflection calculation of this lesson leave out?