FE Other Disciplines (NCEES Fundamentals of Engineering) — All Questions

The modulus of elasticity (Young's modulus) of structural steel is approximately what value?

• a.20 GPa
• b.1,000 GPa
• c.70 GPa
• d.200 GPa✓

Structural steel has a Young's modulus of about 200 GPa (29,000 ksi). Aluminum, by contrast, is near 70 GPa. Modulus measures stiffness (stress-to-strain ratio in the elastic region), not strength.

A 10 m steel bar (coefficient of thermal expansion 12x10^-6 /degC) is heated by 50 degC. How much does it expand?

• a.60 mm
• b.1.2 mm
• c.6 mm✓
• d.0.6 mm

Thermal expansion delta = alpha·L·(delta T) = 12x10^-6 x 10 x 50 = 0.006 m = 6 mm. If the bar were restrained instead of free to expand, this would generate thermal stress.

What is the atomic packing factor (APF) of a face-centered cubic (FCC) crystal structure?

• a.0.74✓
• b.0.52
• c.0.90
• d.0.68

FCC and HCP both achieve the densest packing of equal spheres, APF = 0.74. Body-centered cubic (BCC) is 0.68 and simple cubic is 0.52. APF is the fraction of unit-cell volume filled by atoms.

How many nearest-neighbor atoms surround each atom in a body-centered cubic (BCC) structure (its coordination number)?

• a.6
• b.8✓
• c.12
• d.4

In BCC the central atom touches the 8 corner atoms, so the coordination number is 8. FCC and HCP have 12; simple cubic has 6. Coordination number counts touching nearest neighbors.

How many atoms are contained in one face-centered cubic (FCC) unit cell?

• a.6
• b.2
• c.4✓
• d.8

8 corners x 1/8 + 6 faces x 1/2 = 1 + 3 = 4 atoms per FCC unit cell. A BCC cell contains 2. Corner atoms are shared by 8 cells and face atoms by 2.

A two-phase alloy at 40 wt% B lies between an alpha phase at 20 wt% B and a liquid at 60 wt% B. Using the lever rule, what mass fraction is liquid?

• a.0.50✓
• b.0.40
• c.0.60
• d.0.20

Fraction liquid = (C - C_alpha)/(C_liquid - C_alpha) = (40 - 20)/(60 - 20) = 20/40 = 0.50. The lever rule uses the opposite tie-line arm to weight each phase fraction.

In a binary phase diagram, a eutectic reaction on cooling is best described as:

• a.One liquid transforming into two solid phases at a fixed temperature✓
• b.Two different solid phases combining to form a single liquid upon heating
• c.A liquid slowly freezing over a wide temperature range
• d.One solid transforming into two liquids

The eutectic reaction is L -> alpha + beta at a single invariant temperature and composition, producing a characteristic fine two-phase microstructure.

Iron-carbon alloys are generally classified as cast irons rather than steels when the carbon content exceeds approximately:

• a.4.3%
• b.0.02%
• c.2.0%✓
• d.0.8%

Steels contain up to about 2.0 wt% carbon; above roughly 2.0% the alloy is a cast iron. The 0.8% point is the eutectoid and 4.3% is the eutectic composition.

Rapidly quenching austenitized steel in water produces which hard, brittle microstructure?

• a.Spheroidite
• b.Ferrite
• c.Martensite✓
• d.Pearlite

Rapid quenching suppresses carbon diffusion and forms martensite, a hard, brittle, supersaturated structure. Tempering afterward restores toughness; slow cooling instead yields pearlite.

The primary purpose of annealing a cold-worked metal is to:

• a.Add carbon to its surface
• b.Soften it and relieve internal stresses by recrystallization✓
• c.Create an extremely hard and brittle martensitic structure throughout
• d.Increase its hardness and strength

Annealing heats the metal enough for recrystallization and grain growth, lowering strength and hardness, restoring ductility, and relieving residual stress left by cold work.

A metal bar with Poisson's ratio 0.30 is stretched to an axial strain of 0.004. What is the magnitude of the resulting transverse (lateral) strain?

• a.0.0004
• b.0.0133
• c.0.0012✓
• d.0.004

Poisson's ratio v = -(lateral strain)/(axial strain), so lateral strain = 0.30 x 0.004 = 0.0012 (a contraction). Most metals have v near 0.3.

For many steels, the 'endurance limit' on an S-N (stress vs. cycles) diagram represents:

• a.The maximum stress reached in a tensile test
• b.A stress below which the material endures essentially infinite cycles✓
• c.The stress at which creep begins
• d.The stress causing fracture in a single load cycle

The endurance (fatigue) limit is a stress amplitude below which steel can sustain effectively unlimited cycles without fatigue failure. Many nonferrous metals lack a true endurance limit.

When zinc and steel are electrically coupled in a moist environment (galvanic corrosion), which metal corrodes preferentially?

• a.Zinc, because it is more anodic (active)✓
• b.Steel, because it is stronger
• c.Neither corrodes
• d.Both corrode equally

The more active (anodic) metal in the galvanic series corrodes and protects the cathode. Zinc is anodic to steel, which is why galvanizing sacrificially protects steel.

A magnesium block bolted to a buried steel pipeline to keep the pipe from rusting is an example of:

• a.Anodizing
• b.Case hardening
• c.Sacrificial-anode cathodic protection✓
• d.Passivation by an oxide film

The magnesium acts as a sacrificial anode, corroding in place of the steel and forcing the pipe to behave as a cathode. This is sacrificial-anode cathodic protection.

Which statement correctly distinguishes a thermoplastic from a thermosetting polymer?

• a.Thermoplastics are permanently cross-linked during curing and therefore, like all thermosets, cannot be remelted or reshaped once formed
• b.Thermoplastics soften on heating and can be remolded, while thermosets are cross-linked and degrade rather than melt✓
• c.Both behave identically when heated
• d.Thermosets can be repeatedly melted and reshaped

Thermoplastics have linear or branched chains that soften and can be reshaped when heated; thermosets form permanent cross-links during curing and cannot be remelted.

Compared with metals, engineering ceramics are generally:

• a.Excellent electrical conductors
• b.Hard and strong in compression but brittle in tension✓
• c.Low in melting temperature
• d.Ductile and strong in tension

Strong ionic and covalent bonds give ceramics high hardness, compressive strength, and melting points, but little plasticity, so they are brittle and weak in tension.

According to the Hall-Petch relationship, decreasing the grain size of a polycrystalline metal will:

• a.Decrease its yield strength
• b.Turn it into a ceramic
• c.Increase its yield strength✓
• d.Have no effect on strength

Grain boundaries impede dislocation motion, so smaller grains (more boundary area) raise yield strength per sigma_y = sigma_0 + k*d^(-1/2).

Cold working (strain hardening) a ductile metal generally:

• a.Increases ductility and toughness while lowering strength and hardness
• b.Lowers both strength and hardness
• c.Increases strength and hardness but reduces ductility✓
• d.Has no effect on mechanical properties

Plastic deformation multiplies and entangles dislocations, raising strength and hardness while reducing ductility. This strain-hardening trade-off is reversed by annealing.

The modulus of resilience of a material is defined as the:

• a.Stress at fracture
• b.Strain energy absorbed per unit volume up to the elastic (yield) limit✓
• c.The total area under the entire engineering stress-strain curve up to fracture
• d.Slope of the elastic region

Resilience is the elastic strain energy stored per unit volume, equal to the area under the stress-strain curve up to yield (about sigma_y^2/2E). The total area to fracture is toughness.

Material toughness, measured by the total area under a stress-strain curve, represents:

• a.The hardness of the surface
• b.Resistance to elastic deflection only
• c.The coefficient of thermal expansion
• d.The total energy absorbed per unit volume before fracture✓

Toughness is the energy per unit volume a material absorbs up to fracture, combining strength and ductility. It differs from stiffness (modulus) and from surface hardness.

Which tensile-test quantity is most commonly used to express a metal's ductility?

• a.Ultimate tensile strength
• b.Young's modulus
• c.Hardness number
• d.Percent elongation at fracture✓

Ductility is typically reported as percent elongation (or percent reduction in area) at fracture, the amount of plastic strain the material sustains before breaking.

A Brinell or Rockwell hardness test primarily measures a material's:

• a.Electrical resistivity
• b.Resistance to localized plastic (indentation) deformation✓
• c.Melting temperature
• d.Fatigue life under repeated fully reversed cyclic loading conditions

Hardness tests press a defined indenter into the surface; hardness is the resistance to localized plastic indentation and correlates roughly with tensile strength in steels.

The linear coefficient of thermal expansion of aluminum is approximately:

• a.0.5 x 10^-6 /degC
• b.23 x 10^-6 /degC✓
• c.200 x 10^-6 /degC
• d.1 x 10^-6 /degC

Aluminum expands about 23 x 10^-6 /degC, roughly twice steel's 12 x 10^-6 /degC. This mismatch drives thermal stresses in bimetallic and composite assemblies.

For an isotropic material with E = 200 GPa and Poisson's ratio 0.30, what is the shear modulus G, where G = E / [2(1 + v)]?

• a.76.9 GPa✓
• b.153.8 GPa
• c.260 GPa
• d.100 GPa

G = E/[2(1 + v)] = 200/[2(1.30)] = 200/2.6 = 76.9 GPa. Only two of E, G, and v are independent for an isotropic elastic solid.