Course syllabus · 1.0
Beam Section Properties: Calculate, Interpret & Verify
OB-CE-SECT-101 · Author: Tamer Hijjawi, P.Eng. · Optimal Beam Inc.
Learning outcomes
By the end, a learner should be able to define the section and its axes; calculate area, centroid, second moments, elastic and plastic moduli; distinguish principal directions; interpret shear and torsion properties; reconcile a section report; and transfer a verified property into a stated beam calculation.
Prerequisites and materials
Basic algebra, statics vocabulary and unit conversion. A calculator and space for handwritten calculations are sufficient. No prior software subscription or paid external reference is required. The existing Beam Analysis course is useful background but not compulsory.
Required learning sequence and workload
Each lesson uses short explanations, exact geometry diagrams, worked calculations and a new application. Predictions and independent calculations are part of the required learning activity. Solutions are available for self-checking; drawings and notes are not individually instructor-graded. The checked numerical record, guided choices and understanding checks provide the saved evidence.
| Lesson and outcome | Explain / practise / check | Total |
|---|---|---|
| 1. Read the section and choose the property Connect a cross-section to its beam, choose the bending axis and keep units consistent. | 10 / 7 / 3 min | 20 min |
| 2. Area, centroid and openings Break a section into parts, subtract an opening and locate the area centroid. | 10 / 12 / 3 min | 25 min |
| 3. Second moment of area Calculate how material distribution and axis position change bending properties. | 12 / 15 / 3 min | 30 min |
| 4. Elastic modulus, stress and stiffness Use the correct extreme-fibre distances and distinguish a stress check from a deflection check. | 12 / 15 / 3 min | 30 min |
| 5. Plastic axis and plastic modulus Balance the yielded areas, split a crossing component and calculate its plastic modulus. | 10 / 12 / 3 min | 25 min |
| 6. Unsymmetric sections and principal axes Read product of inertia and principal directions before trusting a bending calculation. | 14 / 13 / 3 min | 30 min |
| 7. Shear and torsion properties Interpret Q, shear area, J, warping and shear centre without confusing their meanings. | 18 / 14 / 3 min | 35 min |
| 8. Verify a section and make a decision Reconcile a flawed report, compare two section depths and complete the applied assessment. | 5 / 20 / 20 min | 45 min |
| Required core, including final assessment | 91 / 108 / 41 min | 240 min |
Lesson 8 uses 5 minutes for the brief, 20 for the capstone and 20 for assessment. Enter that lesson’s study time separately from assessment time to avoid counting it twice. Optional linked references and further software exploration are not needed to reach the planned core workload. The plan will be revised if actual trials show a materially different duration.
Completion and feedback
Submit eight correct calculation records and all 21 understanding-check answers, then pass a 20-question assessment at 80% or higher. Every attempt covers all eight modules from a 48-question applied bank. Notes and a calculator are allowed. Feedback is shown after submission; another attempt is available after review. Successful completion provides a numbered certificate, calculation workbook and actual study-time record. Earlier private draft records do not satisfy the released course requirements.
Scope and limits
Homogeneous geometry, sharp-corner teaching models, small-deformation elastic bending, ideal plastic section properties and interpretation of common advanced properties. The course introduces unsymmetric bending and shear/torsion interpretation without deriving a general cross-section solver. It excludes full material-code member design, connection design, transformed mixed-material sections, fatigue and a complete restrained-torsion analysis. A geometric built-up section assumes appropriate structural connection action, which must be verified separately.
Reference conventions
x is horizontal across the section; y is vertical. Centroid coordinates use a stated drawing origin. S denotes elastic modulus and Z plastic modulus, even where other sources use different symbols. Ixy uses ∫(x−x̄)(y−ȳ)dA. Principal angles are measured counterclockwise from positive x and paired with the associated inertia. Units and display scale accompany every numerical input.
Technical references and tools
- University of Illinois Mechanics Reference: bending — elastic flexure, section geometry and stress.
- University of Illinois Mechanics Reference: torsion — circular-shaft torsion and its assumptions.
- sectionproperties analysis documentation — geometric, warping and plastic analyses and their respective outputs.
- Optimal Beam section-properties calculator and section builder — optional comparison tools. Available advanced outputs depend on geometry and successful analysis; missing results are not zero.
All course drawings and dimensioned examples are original teaching geometry. They are not nominal catalog shapes. A real catalog comparison requires its exact designation, edition, geometry and property definitions.
Support and corrections
Report an unclear explanation or suspected error through course support, including the module and example. Your purchase includes ongoing access and version 1.x corrections. See course terms for access and refund details.