PrepFE™

We've selected 10 diverse practice problems from our question bank that you can use to review for the Civil engineering FE exam and give you an idea about some of the content we provide.

1) A level circuit was run from Station 1+00 to Station 2+00 and back. Partial leveling notes were taken as shown on the table below. What is most nearly the elevation at Station 2+00? $$ \begin <|c|c|c|>\text & \text& \text& \text & \text\\ \hline \ 1+00 & 8.12' & \text &\text&450.21' \\ \ 2+00 & 7.11' & &5.92'& \\ \end $$

2) Evaluate the following expression: $\int_1^2 5x^2dx$

3) What is the angle of rotation needed to get the stress element to the maximum principal stress state?

4) A table has been set up to aid in the drawing of an influence line. What is most nearly the internal force in member AF when the influence line point load is placed at joint B? Assume the moving point load is equal to 1kN. $$ \begin \text & F_ \\ \hline \text & 0\si \\ \text & \\ \text & 0\si \\ \end $$

5) A 20-acre suburban commercial lot has stores and parking lots. The corresponding NRCS curve number is 97. What is most nearly the amount of runoff created after a 2.75" rain event over the course of 24 hours?

6) A vertical curve connects a 3% downslope with a 2.5% upslope. What is most nearly the minimum curve length required to meet AASHTO's standard headlight sight distance requirements? Assume the sight distance is 750 ft.

7) Select all that apply. Which of the following is part of an activated sludge system when treating wastewater?

8) What is most nearly the bending moment in the beam when shear equals zero?

9) A geotechnical investigation at a proposed road construction site spotted a 7 ft thick weak clay layer, 10 feet below the ground surface. On top of the weak clay layer, there is 10 feet of fill material. A sample was obtained from the drilling investigation and was subsequently sent to a lab for testing. The lab results for the weak clay layer and the fill material layer can be seen below. Assume building a road on top of the soil profile will increase vertical stress by 100 psf at the midpoint of the weak clay layer and the clay layer is a normally consolidated clay. What is most nearly the primary consolidation of the weak clay layer?

10) What is most nearly the area moment of inertia about the x-axis of the composite shape shown below?

Solutions

1) A level circuit was run from Station 1+00 to Station 2+00 and back. Partial leveling notes were taken as shown on the table below. What is most nearly the elevation at Station 2+00? $$ \begin <|c|c|c|>\text & \text& \text& \text & \text\\ \hline \ 1+00 & 8.12' & \text &\text&450.21' \\ \ 2+00 & 7.11' & &5.92'& \\ \end $$

Explanation:

The easiest way to solve leveling problems during the FE exam is by sketching them out. The sketch always looks like this, a survey instrument in the middle with a measuring rod to the left and to the right of the survey instrument. Refer to the explanation image in this problem.

HI = Elevation of the surveying instrument from datum
BS = Backsight reading
FS = Foresight reading
Elev. = Station elevation from datum

Ultimately, we must solve for the elevation at station 2+00. By looking at the figure, we can infer that $$ \text_\text=\text_\text-\text_\text $$ First, find $\text_\text$. By looking at the figure, we can infer that $$ \text_\text=\text_\text+\text_\text $$ $$ \text_\text=450.21'+8.12'=458.33' $$ Now, go back and solve for the elevation at station 2+00 $$ \text_\text=458.33'-5.92'=452.41' $$ $$ \begin <|c|c|c|>\text & \text& \text& \text & \text\\ \hline \ 1+00 & 8.12' & \text &\text&450.21' \\ \ 2+00 & 7.11' &458.33' &5.92'&452.41' \\ \end $$ During the actual FE, you will have to quickly sketch out the figure above in order to come up with a solution. Just remember what HI, BS, and FS mean and you'll be prepared for this question.

2) Evaluate the following expression: $\int_1^2 5x^2dx$

Explanation:

Refer to the Indefinite Integrals section in the Calculus chapter of the FE Reference Handbook. There, you will find a long list of typical integrals.

According to this list, the integral of $x^mdx$ is $\frac>$

So if we take the integral rule stated above and apply it to $\int5x^2$, then we get: $$ \int5x^2dx \\ =(5)\int\ x^2dx \\ =(5)\frac> \\ =\frac $$ Now, evaluate the integral [1,2] via substitution. $$ \frac-\frac \\ =11.7 $$

Alternatively, you could solve this entire problem using the integration feature in your TI-36X Pro calculator .

3) What is the angle of rotation needed to get the stress element to the maximum principal stress state?

Explanation:

Refer to the Mohr's Circle section in the Mechanics of Materials chapter of the FE Reference Handbook.

Ultimately, we must determine the angle rotation needed to get the stress element to a principal stress state.

Steps to determine the angle of rotation needed:
1. Draw a quick Mohr's circle based on what's shown in the stress element.
2. Draw a right triangle from the center of the Mohr's circle to a known point along the circle. Determine the Mohr's circle's angle between the known point and the sigma axis (x-axis), which is where the principal stress occurs. That will be the Mohr's circle rotation angle needed to get to a principal stress state.
3. Convert the Mohr's circle's rotation angle needed to get to a principal stress state to the stress element's angle needed to get to a principal stress state.

Step 1. Draw a quick Mohr's circle based on what's shown in the stress element - Identify all points on the Mohr's circle.

Refer to the stress element shown in the FE Reference Handbook to understand its sign notation as well as this problem's explanation image. Play close attention to the sign notation as it's often the number one mistake when drawing Mohr's circles. Normal stresses ($\sigma_x,\sigma_y)$ in tension (going away from the stress element) are positive and normal stresses in compression (going into the stress element) are negative.

For shear stresses ($\tau_$), look at the shear arrow for the X face of the stress element and for the Y face of the stress element. If a shear arrow causes clockwise rotation to the stress element, then the shear for that stress element face (x or y face) is positive. If a shear arrow causes counterclockwise rotation to the stress element, then the shear for that stress element face (x or y face) is negative. Therefore, two points along the circle can be plotted as: $$ \text= (\sigma_x,\tau_)=(+400\si,+530\si) \\ \text= (\sigma_y,\tau_)=(-550\si,-530\si) $$ Determine the center of the Mohr's circle. $$ C=\frac=\frac=-75\si $$ Refer to the explanation image to see the final result. Plot the center of the Mohr's circle as well as the X face and Y face of the stress element.

Step 2. Plot a right triangle from the center of the Mohr's circle to the known point along the circumference of the circle.

Use Pythagoras Theorem to solve for the hypotenuse of the triangle, which is also the radius of the circle. $$ a^2+b^2=hypotenuse^2 \\ (+530)^2+(400-(-75))^2=hypotenuse^2 \\ hypotenuse=radius=711.7\si $$ The angle, 2$\theta$, is the Mohr's circle's angle to get to a principal stress state. The rotation angle needed to get the stress element to a principal stress state is $\theta$. This problem asks for the angle to get the stress element to a principal stress state.

Calculate the Mohr's circle's angle to a principal stress state. Use soh-cah-toa. $$ \sin<\left[\frac\right]>^=angle \\ \sin<\left[\frac<530>\right]>^=48^\circ $$ Step 3. Convert the Mohr's circle's rotation angle needed to get to a principal stress state to the stress element's angle needed to get to a principal stress state.

$$ \text=2\theta=48^\circ $$ Stress element's rotation angle to a principal stress state $\theta=24^\circ$ clockwise. Refer to blue arrow in the explanation image to understand why the rotation is clockwise to get to a max principal stress point.