Training Civil Engineering Placement Test Practice — Civil Engineering
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Placement Test Practice — Civil Engineering

25 min Civil Engineering

Placement Test Practice — Civil Engineering

These problems cover the math used in civil engineering courses: statics, structural analysis, fluid mechanics, and surveying.

Practice Test — 25 Questions

1. A simply supported beam of 8 m span has a 40 kN load at 3 m from the left support. Find the left reaction.
2. Find the bending moment at the load point in Problem 1.
3. A rectangular beam is 150 mm × 300 mm. Calculate $I$ about the strong axis.
4. Using the beam in #3 with $M = 20$ kN·m, find $\sigma_{\max}$.
5. A column carries 200 kN over an area of 0.04 m². Find the compressive stress.
6. Find the hydrostatic pressure at 15 m depth in fresh water.
7. A retaining wall holds back 6 m of water. Find the force per meter of wall width.
8. Where does the force in #7 act measured from the base?
9. A triangular truss with span 10 m, height 5 m, and a 50 kN load at the apex. Find the reactions.
10. In #9, find the force in one of the inclined members.
11. Convert a slope of 3:4 to an angle in degrees.
12. A surveyor measures a distance of 200 m at a slope of 5%. Find the vertical rise.
13. Find the section modulus $S = I/c$ for a 200 mm × 400 mm rectangle.
14. If $\sigma_{\text{allow}} = 10$ MPa, what max moment can the beam in #13 carry?
15. A simply supported beam with UDL $w$ kN/m: max moment $= wL^2/8$. Find $M$ for $w = 5$, $L = 6$ m.
16. Max deflection of a simply supported beam with UDL: $\delta = 5wL^4/(384EI)$. Find $\delta$ for $w = 5$ kN/m, $L = 6$ m, $E = 200$ GPa, $I = 5 \times 10^{-5}$ m⁴.
17. A soil sample weighs 1.8 kN and has a volume of 0.001 m³. Find the unit weight.
18. Bearing capacity factor: if $q_{\text{ult}} = cN_c$ and $c = 50$ kPa, $N_c = 5.14$, find ultimate bearing capacity.
19. Total settlement = 25 mm. If the structure tolerance is L/500 and span is 10 m, is this acceptable?
20. A circular pipe has outer diameter 300 mm and wall thickness 15 mm. Find the inner diameter and $I$.
21. Factor of safety = capacity / demand. If capacity = 450 kN and demand = 300 kN, find the FOS.
22. A 100 m tape measures a distance as 247.5 m on a 3% slope. Find the true horizontal distance.
23. A concrete mix ratio is 1:2:4 by volume. If total volume needed is 3.5 m³, find the cement volume.
24. Shear stress in a rectangular beam: $\tau_{\max} = \frac{3V}{2A}$. For $V = 40$ kN and $A = 0.06$ m², find $\tau_{\max}$.
25. A truss has 9 joints and 15 members with 3 reactions. Is it determinate, indeterminate, or unstable?
Show Answer Key

1. $R_A = 40 \times 5/8 = 25$ kN

2. $M = R_A \times 3 = 75$ kN·m

3. $I = 0.15 \times 0.3^3/12 = 3.375 \times 10^{-4}$ m⁴

4. $\sigma = 20{,}000 \times 0.15 / 3.375 \times 10^{-4} = 8.89$ MPa

5. $\sigma = 200/0.04 = 5{,}000$ kPa $= 5$ MPa

6. $P = 1{,}000 \times 9.81 \times 15 = 147.2$ kPa

7. $F = \frac{1}{2}(1{,}000)(9.81)(36)(1) = 176.6$ kN/m

8. $h/3 = 2$ m from the base

9. $R_A = R_B = 25$ kN

10. $L_{\text{member}} = \sqrt{25+25} = 7.07$ m; $\sin\alpha = 5/7.07$; $F = 25/\sin\alpha = 35.4$ kN (compression)

11. $\theta = \arctan(3/4) = 36.87°$

12. Rise $= 200 \times 0.05 = 10$ m

13. $S = (0.2 \times 0.4^2)/6 = 5.333 \times 10^{-3}$ m³

14. $M = 10 \times 10^6 \times 5.333 \times 10^{-3} = 53.3$ kN·m

15. $M = 5 \times 36 / 8 = 22.5$ kN·m

16. $\delta = 5(5{,}000)(1{,}296)/(384 \times 200 \times 10^9 \times 5 \times 10^{-5}) = 8.44 \times 10^{-3}$ m $= 8.4$ mm

17. $\gamma = 1.8/0.001 = 1{,}800$ kN/m³ $= 18$ kN/m³

18. $q_{\text{ult}} = 50 \times 5.14 = 257$ kPa

19. Tolerance $= 10{,}000/500 = 20$ mm. Settlement 25 mm > 20 mm — not acceptable.

20. $d_i = 300 - 30 = 270$ mm; $I = \pi(0.3^4 - 0.27^4)/64 = 1.37 \times 10^{-4}$ m⁴

21. FOS $= 450/300 = 1.5$

22. $d_h = 247.5 \cos(\arctan 0.03) \approx 247.39$ m

23. Cement $= 3.5 \times 1/7 = 0.5$ m³

24. $\tau = 3(40{,}000)/(2 \times 0.06) = 1{,}000$ kPa $= 1$ MPa

25. $m + r = 15 + 3 = 18 = 2j = 18$. Determinate.

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