Free Practice Quiz Question List

7 Distributed Loads and Centroids Online Quiz Questions

Use this free practice quiz with 20 questions to review 7 Distributed Loads and Centroids, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

A beam load intensity is measured in N/m and acts over a length measured in m. What are the units of its equivalent resultant, found by integrating the intensity over the length?

A
N
B
N/m
C
m
D
N·m

True or false

1 point

On a free-body diagram, you replace a distributed load with its equivalent point resultant. You should also keep all the original distributed-load arrows because both representations are needed to preserve the load's effect. True or false?

A
True
B
False

Written response

1 point

A uniform downward load of $2.5\,\text{kN/m}$ acts over a $4\,\text{m}$ beam segment. What is the magnitude of its equivalent resultant?

Choose one

1 point

A triangular load increases linearly from zero at the left end of a beam segment to its peak at the right end. Where does its equivalent resultant act, measured from the right end?

A
At the midpoint of the segment
B
One-third of the segment length from the high-intensity end
C
Two-thirds of the segment length from the high-intensity end
D
At the zero-load end

Fill in the blank

1 point

For component resultants $R_i$ acting at positions $x_i$ , the combined line of action is at , provided the total resultant is nonzero.

Choose all

1 point

Select all statements that correctly locate the centroid of the stated shape.

A
A rectangle's centroid is at the intersection of its diagonals.
B
A triangle's centroid is one-third of the altitude from the base.
C
A symmetric shape's centroid lies on each axis of symmetry.
D
A triangle's centroid is at the midpoint of its base.
E
A rectangle's centroid is at one of its vertices.

Written response

1 point

What centroid determines the location of the resultant when pressure varies over a flat surface?

Choose all

1 point

When calculating the centroid of a composite area containing a hole, select all correct statements about the method.

A
The centroid coordinate can be calculated as $\bar{x}=\frac{\sum_i A_i x_i}{\sum_i A_i}$ .
B
A hole is included as a negative area.
C
Each component area is weighted by the coordinate of its centroid.
D
A hole should be counted as a positive area so it adds material.
E
The combined centroid is always the average of the component centroid coordinates, regardless of their areas.

True or false

1 point

If the signed total of a distributed load is zero, the centroid-location formula for its resultant is undefined. True or false?

A
True
B
False

Fill in the blank

1 point

A triangular load rises from zero to $w_{\max}$ over a length $L$ . Its resultant magnitude is .

Choose one

1 point

A flat surface is subjected to uniform pressure over its entire area. Through which point does the equivalent resultant act?

A
At the point of maximum pressure
B
At a corner of the surface
C
Through the area centroid
D
At the midpoint of whichever side is longest

Open ended

1 point

A $5\,\text{m}$ beam segment carries a downward load consisting of a uniform $3\,\text{kN/m}$ component over the full length and a triangular component that rises from zero at the left end to $6\,\text{kN/m}$ at the right end. Determine the magnitude and direction of the equivalent resultant, and its position measured from the left end.

Choose one

1 point

A beam segment has a $5\,\text{kN}$ downward load resultant and a $3\,\text{kN}$ upward load resultant. What is the magnitude and direction of the net resultant?

A
8 kN downward
B
2 kN downward
C
2 kN upward
D
8 kN upward

Written response

1 point

A $4\,\text{kN}$ upward force acts at $x=0.5\,\text{m}$ , and a $4\,\text{kN}$ downward force acts at $x=2.5\,\text{m}$ . The net force is zero. What is the magnitude of the resulting pure couple?

Choose one

1 point

A beam carries a distributed load with intensity in $\text{kN/m}$ over a length measured in metres. What are the units of its resultant force?

A
$\text{kN}$
B
$\text{kN/m}$
C
$\text{kN}\cdot\text{m}$
D
$\text{m/kN}$

True or false

1 point

The centroid of a plane shape lies on every axis of symmetry that the shape has.

A
True
B
False

Choose one

1 point

A downward uniform load of $3\,\text{kN/m}$ acts over a $4\,\text{m}$ beam segment. Which equivalent resultant has the same force and moment as the distributed load?

A
$12\,\text{kN}$ , located $1\,\text{m}$ from the left end
B
$12\,\text{kN}$ , located $2\,\text{m}$ from the left end
C
$7\,\text{kN}$ , located $2\,\text{m}$ from the left end
D
$7\,\text{kN}$ , located $4\,\text{m}$ from the left end

Choose one

1 point

A downward triangular load rises linearly from zero at the left end to $9\,\text{kN/m}$ at the right end of a $6\,\text{m}$ beam segment. Which resultant force and location are equivalent to this load?

A
$27\,\text{kN}$ , located $2\,\text{m}$ from the left end
B
$54\,\text{kN}$ , located $4\,\text{m}$ from the left end
C
$27\,\text{kN}$ , located $4\,\text{m}$ from the left end
D
$18\,\text{kN}$ , located $6\,\text{m}$ from the left end

Choose one

1 point

A uniform pressure of $5\,\text{kPa}$ acts normally on a flat rectangular surface measuring $2\,\text{m}$ by $3\,\text{m}$ . Which equivalent resultant is correct?

A
$30\,\text{kN}$ , acting at a corner of the surface
B
$15\,\text{kN}$ , acting through the area centroid
C
$11\,\text{kN}$ , acting through the area centroid
D
$30\,\text{kN}$ , acting through the area centroid

Written response

1 point

For $x$ measured in metres, a distributed load has intensity $w(x)=(2\,\text{kN/m}^2)x$ on $0\le x\le3\,\text{m}$ . What is the load's moment about the left end? Enter the numerical value in kN·m.