Lesson test: Equilibrium

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Equilibrium

1.[2p]
Why may moments be taken about any point when a body is in equilibrium?

Because the correction term between two points is the position offset crossed with the total force, which is zero

Correct

Because moments are scalars and so do not depend on position

The answer is: Because the correction term between two points is the position offset crossed with the total force, which is zero

Because only the centre of mass gives a valid moment equation, and every other point reduces to it

The answer is: Because the correction term between two points is the position offset crossed with the total force, which is zero

Because the moment of a force is always measured from the point where it acts

The answer is: Because the correction term between two points is the position offset crossed with the total force, which is zero

2.[2p]
A beam spans 9 m between a pin at A and a roller at B, carrying a point load of 45 kN at 6 m from A. What is the reaction at A, in kN?

CorrectNot quite: 15

3.[2p]
A cantilever 4 m long is built into a wall and carries a uniformly distributed load of 6 kN per metre over its whole length. What is the fixing moment at the wall, in kN m?

CorrectNot quite: 48

4.[2p]
Match each idealised support to the number of unknown reaction components it contributes in a plane.

Roller
Pin
Fixed end
Cable

Show the answer

Roller: 1 Pin: 2 Fixed end: 3 Cable: 1

5.[3p]
Which of these belong on a correct free body diagram of a whole beam?

Select all that apply

The reactions supplied by the supports

Correct

The self-weight of the beam itself

Correct

The applied loads, each at its own point of application

Correct

The forces the left half of the beam exerts on the right half

The answer is: The reactions supplied by the supports, The self-weight of the beam itself, The applied loads, each at its own point of application

6.[1p]
A beam with a pin at one end and rollers at two other points is statically determinate.

True

The answer is: False

False

Correct

7.[2p]
Three restraints act on a rigid body in a plane, and all three lines of action pass through a single point. What is true?

The count says determinate, but the body can still rotate about that point

Correct

The body is fully restrained, since three unknowns match three equations

The answer is: The count says determinate, but the body can still rotate about that point

The body is a mechanism because three restraints are never enough

The answer is: The count says determinate, but the body can still rotate about that point

The arrangement is indeterminate to the first degree

The answer is: The count says determinate, but the body can still rotate about that point

8.[2p]
Why are indeterminate structures built on purpose rather than avoided?

The extra restraint gives a second load path, so losing one support need not mean collapse

Correct

They are cheaper, because indeterminate members carry no force

The answer is: The extra restraint gives a second load path, so losing one support need not mean collapse

Equilibrium is easier to apply when there are more unknowns

The answer is: The extra restraint gives a second load path, so losing one support need not mean collapse

They deflect less because the material is stiffer

The answer is: The extra restraint gives a second load path, so losing one support need not mean collapse

9.[1p]
How many independent scalar equilibrium equations does a single rigid body provide in three dimensions?

CorrectNot quite: 6

1.[2p] Why may moments be taken about any point when a body is in equilibrium?

2.[2p] A beam spans 9 m between a pin at A and a roller at B, carrying a point load of 45 kN at 6 m from A. What is the reaction at A, in kN?

3.[2p] A cantilever 4 m long is built into a wall and carries a uniformly distributed load of 6 kN per metre over its whole length. What is the fixing moment at the wall, in kN m?

4.[2p] Match each idealised support to the number of unknown reaction components it contributes in a plane.

5.[3p] Which of these belong on a correct free body diagram of a whole beam?

6.[1p] A beam with a pin at one end and rollers at two other points is statically determinate.

7.[2p] Three restraints act on a rigid body in a plane, and all three lines of action pass through a single point. What is true?

8.[2p] Why are indeterminate structures built on purpose rather than avoided?

9.[1p] How many independent scalar equilibrium equations does a single rigid body provide in three dimensions?

1.[2p]
Why may moments be taken about any point when a body is in equilibrium?

2.[2p]
A beam spans 9 m between a pin at A and a roller at B, carrying a point load of 45 kN at 6 m from A. What is the reaction at A, in kN?

3.[2p]
A cantilever 4 m long is built into a wall and carries a uniformly distributed load of 6 kN per metre over its whole length. What is the fixing moment at the wall, in kN m?

4.[2p]
Match each idealised support to the number of unknown reaction components it contributes in a plane.

5.[3p]
Which of these belong on a correct free body diagram of a whole beam?

6.[1p]
A beam with a pin at one end and rollers at two other points is statically determinate.

7.[2p]
Three restraints act on a rigid body in a plane, and all three lines of action pass through a single point. What is true?

8.[2p]
Why are indeterminate structures built on purpose rather than avoided?

9.[1p]
How many independent scalar equilibrium equations does a single rigid body provide in three dimensions?