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Quizzes > Quizzes for Business > Technology

Master the PE Exam Practice Quiz

Enhance Professional Engineering Skills with Practice Test

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art illustrating a fun PE Exam Practice Quiz

Dive into this PE exam practice quiz to sharpen your professional engineering skills with real-world scenarios and challenging practice questions. Whether you're preparing for an engineering license or looking for a quick knowledge check, this practice test adapts to your pace and learning style. Each question highlights critical concepts in mechanics and structural analysis to help boost your confidence. Feel free to customise any question in the quizzes editor for your own study plan. For additional preparation, explore our Exam Practice Quiz or try the Entrance Exam Practice Quiz.

What is the SI unit of the second moment of area (moment of inertia) used in bending calculations?
m^3
m^4
kg·m^2
N·m
The second moment of area is defined as an integral of y^2 dA, giving units of length to the fourth power. In SI, that unit is m^4. Other units like m^3 or N·m are not correct for area moments.
Young's modulus (E) is defined as the ratio of which two quantities?
Load to displacement
Stress to strain in the linear elastic region
Shear stress to shear strain
Bending moment to curvature
Young's modulus is the ratio of normal stress to normal strain within the elastic limit of a material. It characterizes stiffness under axial loading. Other ratios describe different material properties.
What is the formula for bending stress at the outer fiber of a beam section?
σ = I·c / M
σ = V·c / I
σ = M·c / I
σ = M·I / c
The bending stress formula is σ = M·c / I, where M is the bending moment, c is the distance to the outer fiber, and I is the second moment of area. This relationship comes directly from beam theory. Alternate forms with V (shear) or inverted terms are incorrect.
A material has an ultimate tensile strength of 400 MPa and is loaded to produce 200 MPa of stress. What is the factor of safety?
4
2
1
0.5
Factor of safety is defined as ultimate strength divided by working stress, so FS = 400 MPa / 200 MPa = 2. This ensures the design load is half of the material's failure capacity. Other values do not match this ratio.
What is the second moment of area (I) for a rectangle of width b and height h about its centroidal horizontal axis?
b·h^3 / 3
b^3·h / 12
(b·h)^3 / 12
b·h^3 / 12
For a rectangle about its centroidal axis parallel to the width, I = b·h^3 / 12. This formula is derived by integrating y^2 dA over the height. The other expressions do not match the standard derivation.
What is the Euler critical buckling load P_cr for a pinned - pinned column of length L, modulus E, and moment of inertia I?
π²·E·I / L²
π²·E·I / L
π²·G·J / L²
2·π²·E·I / L²
Euler's formula for a pinned - pinned column is P_cr = π²·E·I / L². It assumes elastic buckling with pinned ends. Variations with different end conditions have different factors, and G·J relates to torsional buckling, not Euler buckling.
For a simply supported beam of length L under a uniform load w, what is the maximum bending moment?
w·L² / 16
w·L² / 12
w·L² / 2
w·L² / 8
The maximum bending moment at midspan for a simply supported beam under uniform load is w·L² / 8. This comes from the bending moment diagram for a UDL. Other fractions correspond to different loading or support conditions.
What is the maximum deflection δ_max of a simply supported beam under a uniform load w?
5·w·L^4 / (384·E·I)
w·L^3 / (48·E·I)
3·w·L^4 / (384·E·I)
w·L^4 / (8·E·I)
The standard deflection formula for a simply supported beam with uniform load is δ_max = 5·w·L^4 / (384·E·I). This is derived from integrating the bending moment equation twice. Other coefficients correspond to different load cases.
What is the axial deformation " of a rod of length L, cross-sectional area A, and modulus E under axial load P?
P·A / E
P / (A·E)
P·L / A
P·L / (A·E)
Axial deformation is given by " = P·L / (A·E), derived from Hooke's law under axial loading. It relates load, geometry, and material stiffness. Other forms are incorrect rearrangements or missing terms.
Section modulus S of a beam section is defined as which of the following?
I / c
c / I
I / A
I·c
Section modulus is S = I / c, where I is the second moment of area and c is the distance from the neutral axis to the extreme fiber. It measures section strength under bending. Other expressions do not give section modulus.
A material has an ultimate strength of 300 MPa and a factor of safety of 2. What is its allowable working stress?
150 MPa
75 MPa
200 MPa
300 MPa
Allowable stress = ultimate strength / factor of safety = 300 MPa / 2 = 150 MPa. This ensures the working stress does not exceed half the failure capacity. Other values do not match the division by 2.
What is the maximum shear stress in a rectangular cross section under shear force V?
1.5·V / A
V / A
2·V / A
V / (2·A)
In a rectangular section, the maximum shear stress is τ_max = 1.5·V / A due to the parabolic distribution. The average value is V/A, but the maximum is higher. Other factors do not match the known distribution.
What is the modulus of resilience Ur for a material with yield strength σ_y and modulus E?
σ_y^2 / E
σ_y / (2·E)
σ_y^2 / (2·E)
2·E / σ_y^2
Modulus of resilience is the energy per unit volume up to yield, given by Ur = σ_y^2 / (2·E). It is the area under the stress - strain curve to the yield point. Other forms misplace factors of 2 or E.
If you have 240 minutes to answer 80 questions, what is the average time available per question?
3 minutes
4 minutes
5 minutes
2 minutes
Average time per question = total time / number of questions = 240 min / 80 = 3 min per question. This helps with pacing in exam conditions. Other values do not match the division.
Which formula correctly computes shear stress at a point in a beam cross-section?
τ = Q / (I·t)
τ = V·Q / (I·t)
τ = V / (I·t)
τ = V·I·t / Q
The shear formula is τ = V·Q / (I·t), where Q is the first moment of area about the neutral axis and t is the thickness at the point. This accounts for nonuniform shear distribution. Other expressions omit necessary factors or invert terms.
A column section carries an axial load P = 100 kN and moment M = 200 kN·m. Its cross-section has A = 2000 mm², I = 1.6 - 10^8 mm^4, and c = 200 mm. What is the maximum combined stress?
200 MPa
250 MPa
350 MPa
300 MPa
Axial stress = P/A = 100e3 N / 2000 mm² = 50 MPa. Bending stress = M·c/I = (200e6 N·mm·200 mm) / 1.6e8 mm^4 = 250 MPa. Total = 50 + 250 = 300 MPa. Other sums are incorrect.
A steel column has effective length factor K=1.0, unbraced length L=5000 mm, and radius of gyration r=50 mm. What is its slenderness ratio KL/r?
50
200
100
150
Slenderness ratio = K·L / r = 1.0·5000 mm / 50 mm = 100. This parameter determines whether Euler buckling formulas apply. Other values come from incorrect division.
For a stress state with σ_x = 120 MPa tension, σ_y = -50 MPa compression, and τ_xy = 30 MPa, what is the major principal stress σ_1 (approximate)?
95 MPa
-15 MPa
125 MPa
60 MPa
σ₝ = (σ_x+σ_y)/2 + sqrt[((σ_x'σ_y)/2)^2 + τ_xy^2] = 35 + sqrt(85^2 + 30^2) ≈ 35 + 90.1 ≈ 125 MPa. Other choices do not match this calculation.
In a truss joint with no external load where only two non-collinear members meet, which members carry zero force?
Neither member
Only the larger member
Both members are zero-force members
Only the stiffer member
If two non-collinear members meet at an unloaded joint, both carry no axial force (zero-force members). This is a standard truss analysis rule. Other interpretations are incorrect under these conditions.
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Learning Outcomes

  1. Analyse structural engineering problems relevant to the PE exam
  2. Apply core engineering formulas to solve complex questions quickly
  3. Evaluate design scenarios for safety and compliance standards
  4. Master time-management strategies for multiple-choice sections
  5. Identify key concepts in mechanics, structures, and materials
  6. Demonstrate problem-solving techniques under exam conditions

Cheat Sheet

  1. Combined Stress Formula Mastery - Tackle axial, bending, shear, torsion, and thermal stresses all at once with this unified approach to structural analysis. It turns a messy multi”load problem into a single, manageable calculation so you can breeze through your FE review. Why the Combined Stress Formula is the BEST Way to Ace Your FE Exam!
  2. Roark's Formulas for Stress and Strain - Dive into over 5,000 ready”to”use formulas that cover beams, plates, shells, and more to save hours of derivation time. This treasure trove of reference material lets you quickly look up solutions and verify your hand calculations. Roark's Formulas for Stress and Strain
  3. Fundamental Structural Analysis Equations - Nail down the Euler-Bernoulli beam equation, shear and moment diagrams, and other core relationships that reveal internal forces and deflections. Mastering these equations is like having a roadmap for any beam or frame problem you encounter. Fundamental Structural Analysis Equations to Know for Civil Engineering Systems
  4. Key Structural Engineering Formulas - Memorize your go-to equations for tension, compression, bending, and combined stresses to quickly assess material performance under load. Having these formulas at your fingertips will boost your speed and confidence in exam conditions. Structural Engineering Formulas
  5. Mechanics of Materials Deep Dive - Explore shear and moment diagrams, flexure theory, and deflection formulas to understand how structural elements deform and carry load. A firm grasp of these concepts helps you predict real”world behavior and design safer structures. Structural Engineering Teaching Guide | Learn Civil Engineering
  6. Beam Deflection Formula Practice - Use d = (5wL❴)/(384EI) to calculate deflection under a uniform load and get comfortable with units and boundary conditions. This exercise sharpens your ability to predict how beams bend and when they might fail code limits. Civil Engineering Formulas
  7. NCEES SE Exam Specs & Standards - Familiarize yourself with the exam layout, question types, and referenced design standards so there are no surprises on test day. Knowing the spec PDF inside out helps you target your study sessions for maximum efficiency. NCEES: SE Exam
  8. Statically Indeterminate Structure Analysis - Learn techniques like slope”deflection and moment distribution to solve problems that simple equilibrium can't handle. Mastering these methods unlocks tricky frame and continuous beam challenges you'll face on the SE. Structural Engineering Formulas
  9. Load Combination Essentials - Understand how dead, live, wind, seismic, and other loads interact so you can apply the correct factors and ensure safety. This knowledge is critical for designing structures that meet modern building codes. Structural Engineering Teaching Guide | Learn Civil Engineering
  10. Time”Management for Multiple Choice - Simulate timed practice sessions to develop a rhythm, decide when to guess, and avoid getting stuck on a single question. Effective pacing strategies can mean the difference between passing and nearly missing your target score. NCEES: SE Exam
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