Mathematical MCQ Problems: Advanced Composites Manufacturing for
Aerospace: Fiber and Matrix Properties
1. A carbon fiber has a tensile strength of 3500 MPa and a density of 1.8 g/cm³. Calculate its specific
strength in N·m/kg.
a) 1.94 × 10⁶ N·m/kg
b) 1.94 × 10⁵ N·m/kg
c) 1.94 × 10⁴ N·m/kg
d) 1.94 × 10³ N·m/kg
Answer: a) 1.94 × 10⁶ N·m/kg
2. An epoxy resin has a tensile modulus of 3.5 GPa and a Poisson's ratio of 0.35. Calculate its shear
modulus.
a) 1.20 GPa
b) 1.30 GPa
c) 1.40 GPa
d) 1.50 GPa
Answer: b) 1.30 GPa
3. A glass fiber has a diameter of 10 μm. If its cross-sectional area is increased by 21%, what is the
new diameter?
a) 10.9 μm
b) 11.0 μm
c) 11.1 μm
d) 11.2 μm
Answer: b) 11.0 μm
4. A carbon fiber tow contains 12,000 individual fibers, each with a diameter of 7 μm. Calculate the
total cross-sectional area of the tow.
a) 0.4618 mm²
b) 0.4718 mm²
c) 0.4818 mm²
d) 0.4918 mm²
Answer: a) 0.4618 mm²
5. An aramid fiber has a Young's modulus of 120 GPa and elongates by 2.5% at its breaking point.
Calculate its tensile strength.
a) 2.5 GPa
b) 3.0 GPa
c) 3.5 GPa
d) 4.0 GPa
Answer: b) 3.0 GPa
## Composite Laminate Theory
6. A unidirectional carbon fiber/epoxy lamina has a longitudinal modulus (E₁) of 140 GPa and a
transverse modulus (E₂) of 10 GPa. Calculate the modulus at 45° to the fiber direction using the
following equation: 1/E(θ) = cos⁴θ/E₁ + sin⁴θ/E₂ + (1/G₁₂ - 2ν₁₂/E₁)sin²θcos²θ, given that G₁₂ = 5 GPa
and ν₁₂ = 0.3.
a) 14.78 GPa
b) 15.78 GPa
c) 16.78 GPa
d) 17.78 GPa
Answer: b) 15.78 GPa
7. A [0/90]s laminate is made from four plies, each 0.25 mm thick. Calculate the distance from the
laminate mid-plane to the center of the outermost ply.
a) 0.25 mm
b) 0.375 mm
c) 0.5 mm
d) 0.625 mm
Answer: b) 0.375 mm
8. The compliance matrix [S] for a unidirectional lamina is given below. Calculate the value of S₆₆ if E₁
= 140 GPa, E₂ = 10 GPa, G₁₂ = 5 GPa, and ν₁₂ = 0.3.
[S] = [1/E₁ -ν₁₂/E₁ 0]
[-ν₂₁/E₂ 1/E₂ 0]
[0 0 1/G₁₂]
a) 0.1 × 10⁻⁹ Pa⁻¹
b) 0.2 × 10⁻⁹ Pa⁻¹
c) 0.3 × 10⁻⁹ Pa⁻¹
d) 0.4 × 10⁻⁹ Pa⁻¹
Answer: b) 0.2 × 10⁻⁹ Pa⁻¹
9. A [±45]s laminate is subjected to a uniaxial stress of 100 MPa. If the lamina properties are E₁ = 140
GPa, E₂ = 10 GPa, G₁₂ = 5 GPa, and ν₁₂ = 0.3, calculate the shear strain γxy in the laminate.
a) 0.005
b) 0.010
c) 0.015
d) 0.020
Answer: b) 0.010
10. The stiffness matrix [Q] for a unidirectional lamina is given by:
[Q] = [Q₁₁ Q₁₂ 0 ]
[Q₁₂ Q₂₂ 0 ]
[0 0 Q₆₆]
If E₁ = 140 GPa, E₂ = 10 GPa, G₁₂ = 5 GPa, and ν₁₂ = 0.3, calculate Q₁₂.
a) 2.14 GPa
b) 3.14 GPa
c) 4.14 GPa
d) 5.14 GPa
Answer: b) 3.14 GPa
## Fiber Volume Fraction and Density
11. A composite laminate has a fiber volume fraction of 0.6 and a total volume of 500 cm³. Calculate
the volume of fibers in the composite.
a) 250 cm³
b) 275 cm³
c) 300 cm³
d) 325 cm³
Answer: c) 300 cm³
12. A carbon fiber/epoxy composite has a fiber volume fraction of 0.55. If the density of carbon fiber
is 1.8 g/cm³ and the density of epoxy is 1.2 g/cm³, calculate the density of the composite.
a) 1.43 g/cm³
b) 1.53 g/cm³
c) 1.63 g/cm³
d) 1.73 g/cm³
Answer: b) 1.53 g/cm³
13. A composite panel weighs 2.5 kg and has dimensions of 50 cm × 50 cm × 0.5 cm. If the fiber
volume fraction is 0.6 and the fiber density is 2.6 g/cm³, calculate the matrix density.
a) 1.05 g/cm³
b) 1.15 g/cm³
c) 1.25 g/cm³
d) 1.35 g/cm³
Answer: c) 1.25 g/cm³
14. A prepreg material has a fiber areal weight of 200 g/m² and a resin content of 35% by weight. If
the fiber density is 1.8 g/cm³ and the cured ply thickness is 0.25 mm, calculate the fiber volume
fraction.
a) 0.55
b) 0.58
c) 0.61
d) 0.64
Answer: c) 0.61
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
15. A composite laminate has a fiber volume fraction of 0.5 and a void content of 2%. Calculate the
matrix volume fraction.
a) 0.46
b) 0.48
c) 0.50
d) 0.52
Answer: b) 0.48
## Manufacturing Processes
16. In a pultrusion process, a composite rod with a diameter of 10 mm is being produced at a rate of
2 m/min. Calculate the volume of material produced per hour.
a) 0.0942 m³/h
b) 0.0952 m³/h
c) 0.0962 m³/h
d) 0.0972 m³/h
Answer: a) 0.0942 m³/h
17. A filament winding machine has a mandrel with a diameter of 200 mm and a length of 1 m. If the
fiber tow has a width of 5 mm and is wound at a 45° angle, how many complete circuits are needed
to cover the mandrel surface once?
a) 56
b) 57
c) 58
d) 59
Answer: c) 58
18. In a resin transfer molding (RTM) process, the mold cavity has dimensions of 50 cm × 30 cm × 0.5
cm. If the fiber preform has a porosity of 40%, calculate the volume of resin needed to fill the mold.
a) 280 cm³
b) 290 cm³
c) 300 cm³
d) 310 cm³
Answer: c) 300 cm³
19. An autoclave cure cycle for a carbon/epoxy prepreg requires a temperature ramp rate of 2°C/min
from room temperature (20°C) to the cure temperature of 180°C. How long does it take to reach the
cure temperature?
a) 70 min
b) 75 min
c) 80 min
d) 85 min
Answer: c) 80 min
20. In a compression molding process, a force of 1000 kN is applied to a mold with a surface area of
0.5 m². Calculate the molding pressure.
a) 1 MPa
b) 2 MPa
c) 3 MPa
d) 4 MPa
Answer: b) 2 MPa
## Mechanical Testing and Properties
21. A composite tensile test specimen has a gage length of 150 mm and a cross-sectional area of 50
mm². If it elongates by 1.5 mm under a load of 15 kN, calculate its Young's modulus.
a) 20 GPa
b) 30 GPa
c) 40 GPa
d) 50 GPa
Answer: b) 30 GPa
22. In a three-point bending test, a composite beam with a span of 100 mm and a rectangular cross-
section (width = 25 mm, height = 2 mm) deflects by 5 mm under a central load of 100 N. Calculate
the flexural modulus.
a) 20 GPa
b) 25 GPa
c) 30 GPa
d) 35 GPa
Answer: b) 25 GPa
23. A composite laminate has a coefficient of thermal expansion (CTE) of 2 × 10⁻⁶ /°C in the
longitudinal direction and 25 × 10⁻⁶ /°C in the transverse direction. If the laminate is heated from
20°C to 120°C, calculate the strain in the transverse direction.
a) 0.0015
b) 0.0020
c) 0.0025
d) 0.0030
Answer: c) 0.0025
24. A unidirectional composite lamina has a longitudinal tensile strength of 2000 MPa and a
transverse tensile strength of 50 MPa. Using the maximum stress theory, calculate the tensile
strength at an angle of 30° to the fiber direction.
a) 173.2 MPa
b) 183.2 MPa
c) 193.2 MPa
d) 203.2 MPa
Answer: a) 173.2 MPa
25. In a Charpy impact test, a composite specimen with a cross-sectional area of 80 mm² absorbs 15 J
of energy. Calculate the impact strength in kJ/m².
a) 167.5 kJ/m²
b) 177.5 kJ/m²
c) 187.5 kJ/m²
d) 197.5 kJ/m²
Answer: c) 187.5 kJ/m²
## Composite Failure Theories
26. Using the Tsai-Hill failure theory, calculate the failure index for a unidirectional lamina under a
stress state of σ₁ = 500 MPa, σ₂ = 20 MPa, and τ₁₂ = 30 MPa. The lamina strengths are X = 1500 MPa, Y
= 50 MPa, and S = 70 MPa.
a) 0.1815
b) 0.2815
c) 0.3815
d) 0.4815
Answer: c) 0.3815
27. A [0/90]s laminate is subjected to a uniaxial stress of 200 MPa in the 0° direction. If the lamina
properties are E₁ = 140 GPa, E₂ = 10 GPa, ν₁₂ = 0.3, and the lamina thickness is 0.25 mm, calculate the
stress in the 90° plies.
a) 10.7 MPa
b) 11.7 MPa
c) 12.7 MPa
d) 13.7 MPa
Answer: d) 13.7 MPa
28. Using the maximum strain theory, determine if failure occurs in a unidirectional lamina under a
strain state of ε₁ = 0.010, ε₂ = 0.002, and γ₁₂ = 0.005. The lamina failure strains are ε₁ᵤ = 0.015, ε₂ᵤ =
0.006, and γ₁₂ᵤ = 0.010.
a) No failure
b) Failure in longitudinal direction
c) Failure in transverse direction
d) Failure in shear
Answer: a) No failure
29. A composite pressure vessel with a radius of 0.5 m and a wall thickness of 5 mm is subjected to
an internal pressure of 10 MPa. Using the thin-walled pressure vessel theory, calculate the hoop
stress in the composite.
a) 900 MPa
b) 950 MPa
c) 1000 MPa
d) 1050 MPa
Answer: c) 1000 MPa
30. Using the Hashin failure criterion for fiber tension, calculate the failure index for a unidirectional
lamina under a stress state of σ₁ = 1200 MPa, σ₂ = 30 MPa, and τ₁₂ = 50 MPa. The lamina strengths
are X_t = 2000 MPa and S = 100 MPa.
a) 0.3625
b) 0.3725
c) 0.3825
d) 0.3925
Answer: a) 0.3625
31. A composite aircraft wing spar has a rectangular cross-section with a height of 200 mm and a
width of 50 mm. If the allowable bending stress is 500 MPa, calculate the maximum bending
moment
