100+ Free PE Mechanical Machine Design Practice Questions

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Question 1

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A round bar is loaded in pure tension with a force F = 50 kN. The bar diameter is 25 mm. What is the normal stress in the bar?

64 MPa

102 MPa

128 MPa

204 MPa

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Key Facts: PE Mechanical Machine Design Exam

Exam Questions

NCEES

8 hrs

Test Time

NCEES

$400

Exam Fee

NCEES

9 hrs

Total Appointment

NCEES

CBT

Format

Pearson VUE

100

Practice Questions

OpenExamPrep

PE Mechanical Machine Design is one of three NCEES PE Mechanical sub-disciplines. The 80-question CBT runs in a 9-hour appointment and costs $400. The exam emphasizes machine elements (gears, bearings, shafts, springs, fasteners), failure theories (von Mises, Tresca, Goodman, Soderberg, Gerber), fatigue analysis with Marin factors, and codes (ASME Y14.5 GD&T, AGMA gear standards, ASTM, AWS D1.1, ASME BPVC). NCEES provides the PE Mechanical Reference Handbook as searchable PDF during the exam.

Sample PE Mechanical Machine Design Practice Questions

Try these sample questions to test your PE Mechanical Machine Design exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A round bar is loaded in pure tension with a force F = 50 kN. The bar diameter is 25 mm. What is the normal stress in the bar?

A.64 MPa

B.102 MPa

C.128 MPa

D.204 MPa

Explanation: Cross-sectional area A = pi*d^2/4 = pi*(0.025)^2/4 = 4.909e-4 m^2. Normal stress sigma = F/A = 50,000 / 4.909e-4 = 1.018e8 Pa, approximately 102 MPa. This is the basic axial stress equation used as the entry point for nearly all stress analysis.

2A 2D stress element has sigma_x = 80 MPa, sigma_y = -40 MPa, and tau_xy = 30 MPa. What is the maximum principal stress?

A.20 MPa

B.67 MPa

C.87 MPa

D.120 MPa

Explanation: Average stress sigma_avg = (80 + (-40))/2 = 20 MPa. Radius R = sqrt(((80 - (-40))/2)^2 + 30^2) = sqrt(60^2 + 30^2) = sqrt(4500) = 67.1 MPa. sigma_1 = 20 + 67.1 = 87.1 MPa. This is direct application of Mohr's circle for plane stress.

3For the same stress state (sigma_x = 80 MPa, sigma_y = -40 MPa, tau_xy = 30 MPa), what is the maximum in-plane shear stress?

A.30 MPa

B.60 MPa

C.67 MPa

D.87 MPa

Explanation: Maximum in-plane shear equals the radius of Mohr's circle: tau_max = sqrt(((sigma_x - sigma_y)/2)^2 + tau_xy^2) = sqrt(60^2 + 30^2) = 67.1 MPa. The radius of Mohr's circle is exactly the in-plane maximum shear stress.

4A ductile steel has yield strength Sy = 350 MPa. A part experiences principal stresses sigma_1 = 200 MPa, sigma_2 = 100 MPa, sigma_3 = 0. Using the distortion-energy (von Mises) criterion, what is the factor of safety against yielding?

A.1.5

B.1.75

C.2.0

D.2.5

Explanation: von Mises stress sigma' = sqrt(0.5*[(sigma_1 - sigma_2)^2 + (sigma_2 - sigma_3)^2 + (sigma_3 - sigma_1)^2]) = sqrt(0.5*[100^2 + 100^2 + 200^2]) = sqrt(0.5*60000) = sqrt(30000) = 173.2 MPa. Factor of safety n = Sy/sigma' = 350/173.2 = 2.02, approximately 2.0.

5Using the maximum-shear-stress (Tresca) criterion with the same principal stresses (sigma_1 = 200, sigma_2 = 100, sigma_3 = 0 MPa) and Sy = 350 MPa, what is the factor of safety?

A.1.50

B.1.75

C.2.00

D.3.50

Explanation: Tresca uses tau_max = (sigma_1 - sigma_3)/2 = (200 - 0)/2 = 100 MPa. The criterion compares 2*tau_max to Sy: n = Sy / (sigma_1 - sigma_3) = 350/200 = 1.75. Tresca is always more conservative than von Mises (yields a smaller FoS for the same load).

6Which failure theory is generally MOST appropriate for ductile materials under static loading?

A.Maximum normal stress (Rankine)

B.Distortion energy (von Mises)

C.Mohr-Coulomb (brittle)

D.Modified Mohr

Explanation: The distortion-energy (von Mises) criterion best matches experimental yield data for ductile metals because it accounts for shear distortion energy. Maximum-shear (Tresca) is also acceptable for ductile materials but is more conservative. Maximum-normal-stress and Mohr-based theories are intended for brittle materials.

7A simply-supported beam, 4 m span, carries a uniformly distributed load w = 10 kN/m. What is the maximum bending moment?

A.10 kN-m

B.20 kN-m

C.40 kN-m

D.80 kN-m

Explanation: For a simply-supported beam under UDL, M_max = w*L^2/8 = (10)*(4)^2/8 = 160/8 = 20 kN-m. This standard formula is foundational; memorize the M_max formulas for SS-UDL, SS-point-center, cantilever-end-point, and cantilever-UDL.

8A solid circular shaft of diameter 40 mm transmits a torque of 600 N-m. What is the maximum shear stress?

A.23.9 MPa

B.47.7 MPa

C.71.6 MPa

D.95.5 MPa

Explanation: For a solid circular shaft, tau_max = 16T/(pi*d^3) = 16*(600)/(pi*(0.040)^3) = 9600/(pi*6.4e-5) = 9600/(2.011e-4) = 4.77e7 Pa = 47.7 MPa. The 16T/(pi*d^3) form is the fastest exam shortcut.

9A hollow shaft has outer diameter Do = 50 mm and inner diameter Di = 40 mm. The polar moment of inertia J is approximately:

A.1.78e5 mm^4

B.3.61e5 mm^4

C.5.21e5 mm^4

D.6.13e5 mm^4

Explanation: J = (pi/32)*(Do^4 - Di^4) = (pi/32)*(50^4 - 40^4) = (pi/32)*(6,250,000 - 2,560,000) = (pi/32)*3,690,000 = 0.0982*3,690,000 = 362,265 mm^4, approximately 3.61e5 mm^4. Hollow shafts have nearly the J of solid shafts but much less weight.

10Steel has E = 200 GPa and Poisson's ratio nu = 0.30. What is the shear modulus G?

A.50 GPa

B.67 GPa

C.77 GPa

D.100 GPa

Explanation: For an isotropic material, G = E / (2*(1+nu)) = 200 / (2*1.3) = 200 / 2.6 = 76.9 GPa, approximately 77 GPa. This relation between E, G, and nu always holds for isotropic linear-elastic materials.

About the PE Mechanical Machine Design Exam

The NCEES PE Mechanical: Machine Design and Materials exam is one of three sub-disciplines under the PE Mechanical umbrella (alongside HVAC & Refrigeration and Thermal & Fluid Systems). The 80-question computer-based test focuses on mechanical components, design analysis, and materials selection for machinery. Major content areas include Principles (statics, mechanics of materials, dynamics, vibrations, basic heat transfer, basic fluids), Applications (machine design, fatigue, fracture, gears, bearings, shafts, fasteners, springs, brakes, clutches, manufacturing), Codes & Standards (ASME Y14.5 GD&T, AGMA, ASTM, ASME BPVC, ANSI/RIA), and Professional Practice (engineering economics and ethics).

Questions

80 scored questions

Time Limit

8 hours

Passing Score

Approximately 70% (scaled, NCEES does not publish a fixed cut)

Exam Fee

$400 (NCEES (Pearson VUE))

PE Mechanical Machine Design Exam Content Outline

~38%

Principles

Statics, mechanics of materials, dynamics, vibrations, mechanical principles of materials, fluid mechanics fundamentals, and basic heat transfer applied to machine components.

~37%

Applications

Machine design analysis: fatigue (S-N, Goodman, Soderberg), fracture mechanics, shafts, gears (AGMA), bearings (L10), fasteners, springs, brakes, clutches, vibration isolation, manufacturing, and materials selection (Ashby).

~15%

Codes & Standards

ASME Y14.5 GD&T tolerance stack-up, AGMA gear quality, ASTM material specifications, ASME BPVC pressure vessels, AWS D1.1 welding, ANSI/RIA robot safety.

~10%

Professional Practice

Engineering economics (present worth, annual worth, capital recovery), NSPE Code of Ethics, licensure law, and professional responsibility.

How to Pass the PE Mechanical Machine Design Exam

What You Need to Know

Passing score: Approximately 70% (scaled, NCEES does not publish a fixed cut)
Exam length: 80 questions
Time limit: 8 hours
Exam fee: $400

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

PE Mechanical Machine Design Study Tips from Top Performers

1Master the NCEES PE Mechanical Reference Handbook layout — know exactly where Marin factors, Goodman criteria, and AGMA gear equations appear

2Drill fatigue analysis: practice modified Goodman, Soderberg, Gerber, and Morrow with both fully reversed and combined loading

3Memorize canonical formulas: tau_max = 16T/(pi*d^3), helical spring k = G*d^4/(8*D^3*Na), ball bearing L10 = (C/P)^3

4Practice GD&T tolerance stack-ups (worst-case and RSS) and MMC bonus tolerance problems on real drawings

5Review failure theories side-by-side: Tresca vs von Mises vs Mohr-Coulomb; pick the right one for ductile vs brittle materials

6Work through bolted-joint problems: C = kb/(kb+km), preload Fi = 0.75*Fp, separation force P_sep = Fi/(1-C)

7Brush up engineering economics: present worth (P/F), annual worth (A/P, A/F), MARR and rate-of-return analysis

8Review the NSPE Code of Ethics — competence, conflicts of interest, and the public-safety override

9Practice unit conversions between US Customary and SI; the exam uses both

10Take a full 80-question timed simulation at least twice in the final two weeks

Frequently Asked Questions

What is the PE Mechanical Machine Design and Materials exam?

It is one of three sub-discipline exams under the NCEES PE Mechanical umbrella, focused on mechanical machinery design, failure analysis, materials, and manufacturing. Examinees pick this discipline at registration. The 80-question computer-based test takes a 9-hour appointment (8 hours of testing plus tutorial and break) at Pearson VUE.

How is this exam different from PE Mechanical HVAC or PE Mechanical Thermal & Fluid Systems?

Machine Design and Materials emphasizes solid mechanics, fatigue, gears, bearings, shafts, springs, fasteners, GD&T, AGMA, and AWS — the design and durability of mechanical components. HVAC focuses on psychrometrics, refrigeration cycles, and load calculations. Thermal & Fluid Systems emphasizes thermodynamic cycles, heat exchangers, and fluid system design. All three share Principles and Professional Practice content.

What is the pass rate for the Machine Design exam?

NCEES publishes pass rates by sub-discipline annually. Recent first-time pass rates for PE Mechanical Machine Design have run roughly 60-65%, comparable to the other PE Mechanical sub-disciplines. Repeat-taker pass rates are typically 30-40%. Pass rates depend on the candidate pool's preparation, not just exam difficulty.

What references are provided during the exam?

NCEES provides the PE Mechanical Reference Handbook as a searchable PDF during the exam. No personal references are allowed. The handbook includes equations, tables, and selected charts for fatigue criteria, gear and bearing analysis, GD&T concepts, and standard material data. Practice extensively with the handbook to learn its layout before exam day.

How should I prepare for the calculation-heavy portions?

Master the canonical equations: tau_max = 16T/(pi*d^3) for shafts; modified Goodman 1/n = sigma_a/Se + sigma_m/Sut; Marin factors ka*kb*kc*kd*ke*kf*Se'; bolted-joint stiffness C = kb/(kb+km); helical spring k = G*d^4/(8*D^3*Na); ball bearing L10 = (C/P)^3. Practice 100+ problems spanning these formulas using only the NCEES handbook. Time yourself at 6 minutes per question.

What codes and standards should I review?

Focus on ASME Y14.5 GD&T (datum/feature control frames, MMC bonus tolerance, tolerance stack-up), AGMA gear standards (bending Lewis equation, AGMA 2015-1 quality), ASME BPVC Section VIII Division 1 for pressure vessels, AWS D1.1 for steel welding, ASTM material specs (E8 tensile, A36 structural), and ANSI/RIA R15.06 for robot safety. The NSPE Code of Ethics and engineering economics formulas also appear.