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10 FE practice problems: material properties and concrete mix, with solutions

By Dr. Mohamed Elansary, PhD Environmental EngineeringUpdated

These ten original problems practice material properties and concrete mix, a topic from the FE Civil exam specification, using the Mechanics of Materials, Uniaxial Loading and Deformation part of the FE Reference Handbook 10.6. Each problem gives the situation and the values with units. Work it with the handbook PDF open and commit to an answer before you open the solution. Every solution shows the handbook page, the equation, the substitution with units, a size check, and the mistake behind each wrong option, so a wrong pick tells you exactly what to fix.

How to use these problems

Give each problem an honest attempt before you open the solution: write the given values with units, find the equation in the FE Reference Handbook PDF, and commit to an answer. Then compare line by line. If you picked a wrong option, read the note for that option; each one names the mistake that produces it.

The problems

Problem 1 · FE Civil, Material properties and concrete mix

In a tension test on a metal specimen with a diameter of 0.505 in. and a gauge length of 2 in., a load of 4 kips (within the elastic range) stretches the gauge length by 0.00399 in. The modulus of elasticity is most nearly:

  • A 10,000 ksi
  • B 7,860 ksi
  • C 2,500 ksi
  • D 40,000 ksi

Handbook: Mechanics of Materials, Uniaxial Loading and Deformation, FE Reference Handbook 10.6

Show the worked solution
Answer
A (10,000 ksi)
Given
d = 0.505 in., L0 = 2 in., P = 4 kips, dL = 0.00399 in., si =
Find
modulus of elasticity E (ksi)
Handbook
Mechanics of Materials, Uniaxial Loading and Deformation (σ = P/A, ε = δ/L, σ = Eε), page 131
Equation
σ = P/A, ε = δ/L, E = σ/ε (Hooke's law)
Substitute
  1. σ = P/A = 4 kips/[π(0.505 in.)²/4] = 19.97 ksi
  2. ε = ΔL/L0 = 0.00399 in./2 in. = 0.001995
  3. E = σ/ε = 10,000 ksi
Result
10,000 ksi, 3 significant figures
Check
10,000 ksi is in the range of common structural metals; strain is a pure ratio.
Why the others are wrong
  • B: used d² for the area, leaving out π/4
  • C: used πd² for the area (the diameter as if it were the radius)
  • D: put the radius into πd²/4

Problem 2 · FE Civil, Material properties and concrete mix

A concrete batch uses 340 kg of cement, 155 kg of added water, and 640 kg of sand that carries 1.6% free water (by mass of sand, beyond saturated surface dry). The water-cement ratio is most nearly:

  • A 0.169
  • B 0.486
  • C 0.456
  • D 0.426

Handbook: Materials Science/Structure of Matter, Concrete, FE Reference Handbook 10.6

Show the worked solution
Answer
B (0.486)
Given
cement = 340 kg, water = 155 kg, sand = 640 kg, free = 1.6%
Find
water-cement ratio (by mass)
Handbook
Materials Science/Structure of Matter, Concrete (water-cement ratio), page 126
Equation
w/c = total mixing water/cement (by mass)
Substitute
  1. Free water from the sand = 640 kg × 1.6% = 10.24 kg
  2. Total water = 155 + 10.24 = 165.2 kg
  3. w/c = 165.2/340 = 0.486
Result
0.486, 3 significant figures
Check
a lower w/c gives higher strength (handbook figure); free water in the aggregate counts as mixing water.
Why the others are wrong
  • A: divided by cement plus sand
  • C: left out the free water carried in by the sand
  • D: subtracted the free water instead of adding it

Problem 3 · FE Civil, Material properties and concrete mix

In a tension test on a metal specimen with a diameter of 12.5 mm and a gauge length of 50 mm, a load of 11 kN (within the elastic range) stretches the gauge length by 0.0219 mm. The modulus of elasticity is most nearly:

  • A 102 GPa
  • B 51.2 GPa
  • C 161 GPa
  • D 205 GPa

Handbook: Mechanics of Materials, Uniaxial Loading and Deformation, FE Reference Handbook 10.6

Show the worked solution
Answer
D (205 GPa)
Given
d = 12.5 mm, L0 = 50 mm, P = 11 kN, dL = 0.0219 mm, si =
Find
modulus of elasticity E (GPa)
Handbook
Mechanics of Materials, Uniaxial Loading and Deformation (σ = P/A, ε = δ/L, σ = Eε), page 131
Equation
σ = P/A, ε = δ/L, E = σ/ε (Hooke's law)
Substitute
  1. σ = P/A = 11 kN/[π(12.5 mm)²/4] = 89.64 MPa
  2. ε = ΔL/L0 = 0.0219 mm/50 mm = 0.0004380
  3. E = σ/ε = 205 GPa
Result
205 GPa, 3 significant figures
Check
205 GPa is in the range of common structural metals; strain is a pure ratio.
Why the others are wrong
  • A: used twice the gauge length in the strain
  • B: used πd² for the area (the diameter as if it were the radius)
  • C: used d² for the area, leaving out π/4

Problem 4 · FE Civil, Material properties and concrete mix

A concrete batch uses 355 kg of cement, 110 kg of added water, and 660 kg of sand that carries 5.0% free water (by mass of sand, beyond saturated surface dry). The water-cement ratio is most nearly:

  • A 0.961
  • B 0.310
  • C 0.217
  • D 0.403

Handbook: Materials Science/Structure of Matter, Concrete, FE Reference Handbook 10.6

Show the worked solution
Answer
D (0.403)
Given
cement = 355 kg, water = 110 kg, sand = 660 kg, free = 5.0%
Find
water-cement ratio (by mass)
Handbook
Materials Science/Structure of Matter, Concrete (water-cement ratio), page 126
Equation
w/c = total mixing water/cement (by mass)
Substitute
  1. Free water from the sand = 660 kg × 5.0% = 33.00 kg
  2. Total water = 110 + 33.00 = 143.0 kg
  3. w/c = 143.0/355 = 0.403
Result
0.403, 3 significant figures
Check
a lower w/c gives higher strength (handbook figure); free water in the aggregate counts as mixing water.
Why the others are wrong
  • A: used the free-water percentage as a fraction ten times too large
  • B: left out the free water carried in by the sand
  • C: subtracted the free water instead of adding it

Problem 5 · FE Civil, Material properties and concrete mix

A steel tension specimen has gauge marks 50 mm apart. After fracture, the pieces are fitted together and the marks are 58.51 mm apart. The percent elongation is most nearly:

  • A 17.0%
  • B 117%
  • C 15.7%
  • D 14.5%

Handbook: Mechanics of Materials, Uniaxial Stress-Strain, FE Reference Handbook 10.6

Show the worked solution
Answer
A (17.0%)
Given
L0 = 50 mm, Lf = 58.51 mm
Find
percent elongation (%)
Handbook
Mechanics of Materials, Uniaxial Stress-Strain (Percent Elongation), page 130
Equation
% Elongation = (ΔL/L0) × 100
Substitute
  1. % Elongation = (ΔL/L0) × 100 = (58.51 mm - 50 mm)/50 mm × 100 = 17.0%
Result
17.0%, 3 significant figures
Check
percent elongation measures ductility; it uses the original gauge length.
Why the others are wrong
  • B: is the ratio of the lengths, not the change
  • C: computed the true (logarithmic) strain instead of the engineering elongation
  • D: divided by the final length instead of the original gauge length

Problem 6 · FE Civil, Material properties and concrete mix

In a tension test on a metal specimen with a diameter of 20 mm and a gauge length of 50 mm, a load of 36 kN (within the elastic range) stretches the gauge length by 0.0819 mm. The modulus of elasticity is most nearly:

  • A 17.5 GPa
  • B 70.0 GPa
  • C 35.0 GPa
  • D 280 GPa

Handbook: Mechanics of Materials, Uniaxial Loading and Deformation, FE Reference Handbook 10.6

Show the worked solution
Answer
B (70.0 GPa)
Given
d = 20 mm, L0 = 50 mm, P = 36 kN, dL = 0.0819 mm, si =
Find
modulus of elasticity E (GPa)
Handbook
Mechanics of Materials, Uniaxial Loading and Deformation (σ = P/A, ε = δ/L, σ = Eε), page 131
Equation
σ = P/A, ε = δ/L, E = σ/ε (Hooke's law)
Substitute
  1. σ = P/A = 36 kN/[π(20 mm)²/4] = 114.6 MPa
  2. ε = ΔL/L0 = 0.0819 mm/50 mm = 0.001638
  3. E = σ/ε = 70.0 GPa
Result
70.0 GPa, 3 significant figures
Check
70.0 GPa is in the range of common structural metals; strain is a pure ratio.
Why the others are wrong
  • A: used πd² for the area (the diameter as if it were the radius)
  • C: used twice the gauge length in the strain
  • D: put the radius into πd²/4

Problem 7 · FE Civil, Material properties and concrete mix

In a tension test on a metal specimen with a diameter of 12.5 mm and a gauge length of 50 mm, a load of 29 kN (within the elastic range) stretches the gauge length by 0.1027 mm. The modulus of elasticity is most nearly:

  • A 115 GPa
  • B 57.5 GPa
  • C 90.4 GPa
  • D 460 GPa

Handbook: Mechanics of Materials, Uniaxial Loading and Deformation, FE Reference Handbook 10.6

Show the worked solution
Answer
A (115 GPa)
Given
d = 12.5 mm, L0 = 50 mm, P = 29 kN, dL = 0.1027 mm, si =
Find
modulus of elasticity E (GPa)
Handbook
Mechanics of Materials, Uniaxial Loading and Deformation (σ = P/A, ε = δ/L, σ = Eε), page 131
Equation
σ = P/A, ε = δ/L, E = σ/ε (Hooke's law)
Substitute
  1. σ = P/A = 29 kN/[π(12.5 mm)²/4] = 236.3 MPa
  2. ε = ΔL/L0 = 0.1027 mm/50 mm = 0.002054
  3. E = σ/ε = 115 GPa
Result
115 GPa, 3 significant figures
Check
115 GPa is in the range of common structural metals; strain is a pure ratio.
Why the others are wrong
  • B: used twice the gauge length in the strain
  • C: used d² for the area, leaving out π/4
  • D: put the radius into πd²/4

Problem 8 · FE Civil, Material properties and concrete mix

A concrete batch uses 755 lb of cement, 325 lb of added water, and 1,290 lb of sand that carries 3.7% free water (by mass of sand, beyond saturated surface dry). The water-cement ratio is most nearly:

  • A 0.494
  • B 0.430
  • C 0.182
  • D 0.675

Handbook: Materials Science/Structure of Matter, Concrete, FE Reference Handbook 10.6

Show the worked solution
Answer
A (0.494)
Given
cement = 755 lb, water = 325 lb, sand = 1,290 lb, free = 3.7%
Find
water-cement ratio (by mass)
Handbook
Materials Science/Structure of Matter, Concrete (water-cement ratio), page 126
Equation
w/c = total mixing water/cement (by mass)
Substitute
  1. Free water from the sand = 1,290 lb × 3.7% = 47.73 lb
  2. Total water = 325 + 47.73 = 372.7 lb
  3. w/c = 372.7/755 = 0.494
Result
0.494, 3 significant figures
Check
a lower w/c gives higher strength (handbook figure); free water in the aggregate counts as mixing water.
Why the others are wrong
  • B: left out the free water carried in by the sand
  • C: divided by cement plus sand
  • D: used the free-water percentage as a fraction ten times too large

Problem 9 · FE Civil, Material properties and concrete mix

A steel tension specimen has gauge marks 2 in. apart. After fracture, the pieces are fitted together and the marks are 2.542 in. apart. The percent elongation is most nearly:

  • A 127%
  • B 21.3%
  • C 24.0%
  • D 27.1%

Handbook: Mechanics of Materials, Uniaxial Stress-Strain, FE Reference Handbook 10.6

Show the worked solution
Answer
D (27.1%)
Given
L0 = 2 in., Lf = 2.542 in.
Find
percent elongation (%)
Handbook
Mechanics of Materials, Uniaxial Stress-Strain (Percent Elongation), page 130
Equation
% Elongation = (ΔL/L0) × 100
Substitute
  1. % Elongation = (ΔL/L0) × 100 = (2.542 in. - 2 in.)/2 in. × 100 = 27.1%
Result
27.1%, 3 significant figures
Check
percent elongation measures ductility; it uses the original gauge length.
Why the others are wrong
  • A: is the ratio of the lengths, not the change
  • B: divided by the final length instead of the original gauge length
  • C: computed the true (logarithmic) strain instead of the engineering elongation

Problem 10 · FE Civil, Material properties and concrete mix

A steel tension specimen has gauge marks 2 in. apart. After fracture, the pieces are fitted together and the marks are 2.198 in. apart. The percent elongation is most nearly:

  • A 9.90%
  • B 9.44%
  • C 110%
  • D 9.01%

Handbook: Mechanics of Materials, Uniaxial Stress-Strain, FE Reference Handbook 10.6

Show the worked solution
Answer
A (9.90%)
Given
L0 = 2 in., Lf = 2.198 in.
Find
percent elongation (%)
Handbook
Mechanics of Materials, Uniaxial Stress-Strain (Percent Elongation), page 130
Equation
% Elongation = (ΔL/L0) × 100
Substitute
  1. % Elongation = (ΔL/L0) × 100 = (2.198 in. - 2 in.)/2 in. × 100 = 9.90%
Result
9.90%, 3 significant figures
Check
percent elongation measures ductility; it uses the original gauge length.
Why the others are wrong
  • B: computed the true (logarithmic) strain instead of the engineering elongation
  • C: is the ratio of the lengths, not the change
  • D: divided by the final length instead of the original gauge length

A new problem posts every day inside the lab, with the full worked solution the same evening.

Frequently asked questions

Where is material properties and concrete mix in the FE Reference Handbook?

Look in the Mechanics of Materials, Uniaxial Loading and Deformation part of FE Reference Handbook 10.6. Each solution gives the exact page, so you can practice finding it in the PDF the way you will on exam day.

Are these real FE exam questions?

No. They are original problems generated from the handbook formulas and checked by code. Real exam questions are confidential, and sharing them breaks the NCEES agreement every examinee accepts.

How do I check my answer before opening the solution?

Check the units of your result and whether its size makes sense for the situation. Each solution ends with the same kind of check, so you can compare your habit with ours.

Sources

  1. NCEES FE Civil CBT exam specifications (PDF). Retrieved October 3, 2026.
  2. NCEES FE Reference Handbook 10.6 (free PDF in MyNCEES). Retrieved October 3, 2026.