Structural Analysis
Runs the structural analysis model (linear static or modal) that produces member demands for design.
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Structural Engineering · Load path, member selection, connections and limit-state verification to AISC, ACI and ASCE 7.
Deliverable: Analysis model file with reaction/equilibrium check and governing demand envelope.
Minimum tables, figures and equations for Structural Analysis
Tables — at least 6
- Table — trial sections or sizes considered, with the capacity of each and the selection decision
- Table — final selected geometry for every element: dimensions, thickness, grade, spacing, elevation
- Table — ultimate limit state check summary: demand, capacity, ratio, pass or fail, governing clause
- Table — serviceability check summary: deflection, crack width, settlement, freeboard or velocity against its limit
- Table — factors of safety achieved against the factor required, per failure mode
- Table — strength, service, fatigue and extreme-event checks with ratios
Figures — at least 5
- Figure — free body diagram of each isolated element, fully labelled with loads, reactions, dimensions and axes
- Figure — shear and moment (or pressure and velocity) diagrams for each force-carrying element
- Figure — dimensioned section or plan of each designed element
- Figure — capacity versus demand plot, interaction diagram, or rating curve as applicable
- Figure — girder, bearing and substructure elevation with dimensions
Equations — at least 7
- Equation — equilibrium equations written out for each free body (sum of forces and sum of moments, or continuity and energy)
- Equation — the internal force relations V(x) and M(x), or the momentum/thrust relation, used to compute each element's demand
- Equation — the resulting demand at the critical section of each element, with numeric substitution
- Equation — the capacity expression for each element type, shown with full numeric substitution and units
- Equation — the sizing criterion that sets the final dimension (for example required area, depth or diameter)
- Equation — each limit state check written as demand over capacity with numbers substituted
- Equation — the factor of safety calculation for each failure mode checked
Number every table and figure (Table 4.x, Figure 4.x), caption it, and refer to it by number in your text. Number displayed equations and show the substitution with units. These counts are minimums — add whatever else your design needs.
Engineering documentation standard — required in every Chapter 4 subsection
These rules are graded on every subsection. Work that misses them is capped on technical accuracy, exhibits, codes and communication, whatever the quality of the prose.
Code and standard references
- Every requirement, factor, coefficient, limit and allowable you apply cites the governing document AND the exact section, article or sub-article number — e.g. ACI 318-19 §22.5.5.1, AISC 360-22 Chapter J, Section J3.6, AASHTO LRFD 10th Ed. Article 3.6.1.2.2, ASCE 7-22 §12.8.1, ASTM D2487, state DOT manual section, local stormwater manual chapter.
- Give the edition or year of every document the first time it appears, then use a consistent short form.
- Where a code equation is used, quote the equation number (e.g. Eq. 22.5.5.1) next to your displayed equation.
- Where you depart from a code provision, state the clause you are departing from and the engineering justification.
- List every code, standard and manual actually used in a Codes and Standards table at the start of the subsection.
Citations for statements
- Every statement of fact, value taken from elsewhere, material property, soil parameter, rainfall depth, unit cost or published method carries an in-text citation (APA) to its source.
- Field and lab data cite the report, boring log, gauge, survey file or test number and its date.
- Manufacturer data cites the product literature and revision date; software results cite the program, version and model file name.
- Uncited assertions are treated as assumptions and must appear in the assumptions table with a justification.
- Every in-text citation resolves to a full entry in the reference list.
Step-by-step calculations
- Structure every calculation the same way: (1) objective, (2) governing code clause, (3) equation in symbolic form with the equation number, (4) definition of each symbol, (5) numerical substitution, (6) result with units, (7) comparison against the limit and the pass/fail statement.
- Show the substitution line — never jump from the formula to the answer.
- Number displayed equations sequentially (Eq. 4.1, 4.2, …) and refer to them by number in the text.
- State the load or flow combination governing each calculation by name.
- Carry consistent significant figures and round only at the reported result; state the rounding convention once.
- Present repetitive element checks in a calculation table with one row per element and the same column order throughout.
Free body diagrams and figures
- Draw a separate free body diagram for each isolated element — no combined sketches standing in for several members.
- Dimension every FBD: span, depth, thickness, cover, eccentricity, embedment, slope, pipe diameter, wall height — with the dimension lines and values shown.
- Label every force, pressure, reaction and moment with its symbol, magnitude and units, and show the sign convention and coordinate axes.
- Show supports and boundary conditions explicitly (pin, roller, fixed, elastic, buoyant, hydrostatic).
- Accompany each FBD with its shear, moment, thrust, pressure or hydraulic grade diagram at the same scale reference.
- Number and caption every figure (Figure 4.x) and refer to it by number in the narrative; add a scale or north arrow to plans.
Units and notation
- Every number in text, tables, figures and equations carries its unit — no bare numbers.
- Use one unit system throughout (US customary or SI); if both appear, give the converted value in parentheses consistently.
- Check dimensional homogeneity of each equation and say so — the units of both sides must match.
- Provide a nomenclature table defining every symbol with its unit.
Checking and verification
- Every calculation is checked by an independent route — hand check against software, alternative method, order-of-magnitude estimate, or a published worked example — and the check is shown, not just claimed.
- Report demand-to-capacity ratios and factors of safety against the required values, with the source clause for each required value.
- Include a verification/checking table: item, method of check, expected, obtained, difference, accept or revise.
- Sanity-check every result (magnitude, direction, plausibility) and state the conclusion.
- Record who checked the work and on what date; flag anything still unverified as an open item.
- State limitations and the range over which the result is valid.
How to complete this section
Do this next: Read the Structural Analysis lecture and the worked example so you know what "Analysis model file with reaction/equilibrium check and governing demand envelope." has to contain.
Not sure how to start or how much depth is expected? Read the fully written model example for this deliverable first — it shows the structure, tables and level of justification your advisor grades against.
Structural Design Office — what this workspace teaches
Load path, member selection, connections and limit-state verification to AISC, ACI and ASCE 7.
- ASCE 7 load derivation: dead, live, snow, wind and seismic
- LRFD and ASD load combinations and which governs
- AISC steel member design: flexure, shear, compression, stability
- ACI concrete design: flexure, shear, development, detailing
- Load path and lateral force-resisting systems
- Connection design: bolted, welded, base plates, force transfer
- Failure modes: yielding, rupture, buckling, punching, bearing
- Serviceability: deflection, vibration, drift limits
- Constructability, durability and structural alternatives
End-of-term milestones
- Tuesday, November 17, 2026 — Poster printed and ready. 36 in × 48 in poster finalized and printed one week before the November 24 showcase.
- Wednesday, November 18, 2026 — Final document package uploaded for scoring. Chapters 4–5, calculation package, drawings and appendices uploaded in the app for advisor scoring.
- Wednesday, November 18, 2026 — Poster presentation to faculty and industry. Wednesday poster session — printed 36 in × 48 in poster presented in person; industry reviewers score communication and impact.
- Wednesday, November 25, 2026 — Oral presentation and defense (scored). Scored oral presentation and defense held on Wednesday, November 25.
Structural Analysis
Runs the structural analysis model (linear static or modal) that produces member demands for design.
Section B
Engineering story
A real project situation that frames this module
The team opens week 4 believing structural analysis is a formality, because the proposal treated it in a single sentence. Runs the structural analysis model (linear static or modal) that produces member demands for design. The first review question is not about arithmetic — it is where the basis for linear elastic analysis vs came from.
The team treats boundary condition idealization as a background assumption instead of an input that must be established and recorded. The result is an element loaded beyond its governing limit state, discovered only after the design of record that drawings, quantities and cost are generated from has already been built on it.
Building occupants, erection crews and the structural engineer of record carry the consequence. On this module specifically, the exposure runs through load case combinations and envelope of demands, and the cost of correction rises every week the calculation package and framing drawings moves closer to issue.
Decisions the engineer must make
- What record establishes linear elastic analysis vs, and is that record in the project data inventory?
- Does ASCE 7-22 (2022), Sec. 12.8.7, govern here — and is that the edition adopted by the jurisdiction?
- What is the acceptance criterion for boundary condition idealization, and was it written before the result was known?
- Is δ = δ1st/(1 − ΣPΔ/(ΣH·hsx)) valid over the parameter range this project actually occupies?
- If the check fails, does the team revise the calculation package and framing drawings or raise a change request against the locked baseline?
Photo 1. Structural framing of a pedestrian bridge: members, connections and the load path a designer must trace.
Wikimedia Commons, CC BY-SA 4.0
Section C
Why this matters
Professional
A licensed engineer defending structural analysis cites ASCE 7-22 (2022), Sec. 12.8.7, and shows the record behind each input. Your analysis model file with reaction/equilibrium check and governing demand envelope. is reviewed the same way — traceability is assessed before arithmetic.
Technical
Linear elastic analysis vs is what makes δ = δ1st/(1 − ΣPΔ/(ΣH·hsx)) usable on this project rather than a formula copied from a reference. Get it wrong and every quantity derived from it is wrong by the same factor.
Safety
The failure mode this module guards against is an element loaded beyond its governing limit state. It reaches people through p-delta effects and second-order analysis triggers, which is why the safety check is recorded explicitly here rather than inferred from a passing strength or performance check.
Economic
The design of record that drawings, quantities and cost are generated from is priced from this work. Quantities, unit costs and schedule float all trace to linear elastic analysis vs; a late correction here is paid for as a change order, not a redline.
Environmental
Environmentally, this module fixes embodied carbon in concrete and steel, and the demolition waste of a redesign. Choosing conservatively without justification is not free — the excess shows up as material, energy and land that the project consumes for no measurable gain.
Community
Occupants who rely on the structure performing through its design life and design event inherit whatever this module decides — performance, accessibility, cost of ownership and resilience are set here, not at the ribbon-cutting.
Section D
Learning objectives
By the end of this module you will be able to:
- 1.Justify linear elastic analysis vs, using this project's own conditions rather than a textbook case.
- 2.Evaluate boundary condition idealization, using this project's own conditions rather than a textbook case.
- 3.Apply load case combinations and envelope of demands, using this project's own conditions rather than a textbook case.
- 4.Analyze model verification, using this project's own conditions rather than a textbook case.
- 5.Compute the governing quantity from δ = δ1st/(1 − ΣPΔ/(ΣH·hsx)), with a unit audit on every term.
- 6.Apply ASCE 7-22 (2022), Sec. 12.8.7, and cite the section that governs your acceptance decision.
- 7.Produce analysis model file with reaction/equilibrium check and governing demand envelope. at a standard the plan reviewer at the building department would accept without a second revision cycle.
Section E
Instructional content
Full lecture notes with figures and governing equations
Structural Analysis — what the work actually is
Runs the structural analysis model (linear static or modal) that produces member demands for design. That single sentence hides the substance of the module: linear elastic analysis vs, and boundary condition idealization. Both must be established from project evidence before anything downstream is credible.
In structural engineering, this work is the input to the calculation package and framing drawings. Load case combinations and envelope of demands — which is why this page asks you to record the source of every quantity, not just its value. The design of record that drawings, quantities and cost are generated from depends on it.
- Linear elastic analysis vs. modal response spectrum vs. nonlinear pushover — selection criteria
- Boundary condition idealization: pinned, fixed, and semi-rigid connections
- Load case combinations and envelope of demands
- Model verification: reaction sums, deflected shape sanity check, mesh/element convergence
- P-delta effects and second-order analysis triggers
Photo 1. Structural Analysis — what the work actually is in practice — Structural framing of a pedestrian bridge: members, connections and the load path a designer must trace.
Wikimedia Commons, CC BY-SA 4.0
Governing relationships and how they are applied here
The relationships below govern structural analysis. δ = δ1st/(1 − ΣPΔ/(ΣH·hsx)) — each is valid only inside the parameter range this project occupies, so state that range before substituting.
Boundary condition idealization sets the values you place into these expressions. Any code-prescribed factor must match ASCE 7-22 (2022); a factor lifted from a different edition silently changes the answer.
δ = δ1st/(1 − ΣPΔ/(ΣH·hsx))
- Second-order amplification of story drift, ASCE 7-22 Sec. 12.8.7
Photo 2. Governing relationships and how they are applied here in practice — Structural framing of a pedestrian bridge: members, connections and the load path a designer must trace.
Wikimedia Commons, CC BY-SA 4.0
Constraints, adopted standards and the safety case for structural analysis
ASCE 7-22 (2022), Sec. 12.8.7, governs this module: P-delta stability coefficient limit
The safety case is explicit here. The failure mode is an element loaded beyond its governing limit state; the people exposed are building occupants, erection crews and the structural engineer of record; the control that prevents it is p-delta effects and second-order analysis triggers together with an independent check by someone who did not perform the work.
- Controlling criterion for this module: linear elastic analysis vs.
- Adopted reference: ASCE 7-22 (2022) — cite Sec. 12.8.7 by number.
- Failure mode guarded: an element loaded beyond its governing limit state.
- Evidence produced: Analysis model file with reaction/equilibrium check and governing demand envelope..
Photo 3. Constraints, adopted standards and the safety case for structural analysis in practice — Structural framing of a pedestrian bridge: members, connections and the load path a designer must trace.
Wikimedia Commons, CC BY-SA 4.0
Where this method stops being valid
Every method has a domain of validity. State the range of geometry, loading, material behaviour or flow regime over which your approach holds, and state what you would do instead beyond it.
For this project, the boundary you are most likely to push is p-delta effects and second-order analysis triggers. If you cross it, say so in writing, bound the error, and carry the limitation into your results chapter. A disclosed limitation is professional practice; a silent extrapolation is not.
Photo 4. Where this method stops being valid in practice — Structural framing of a pedestrian bridge: members, connections and the load path a designer must trace.
Wikimedia Commons, CC BY-SA 4.0
Section F
Engineering workflow
Steps
- 1. Assemble the inputs this module needs — linear elastic analysis vs; boundary condition idealization — each with a unit and a source record.
- 2. Confirm ASCE 7-22 (2022) is the adopted edition and locate Sec. 12.8.7.
- 3. State the assumptions and the acceptance criterion for linear elastic analysis vs.
- 4. Evaluate δ = δ1st/(1 − ΣPΔ/(ΣH·hsx)) term by term, carrying one extra significant figure.
- 5. Test the result against load case combinations and envelope of demands.
- 6. Audit units and run an order-of-magnitude check by hand before the number leaves your desk.
- 7. Obtain an independent check from a teammate who did not perform the work, and record their name and date.
- 8. Assemble analysis model file with reaction/equilibrium check and governing demand envelope. and submit it to the plan reviewer at the building department for review.
Decision points
- Is every input behind linear elastic analysis vs traceable? If not — stop and collect the record.
- Does the result satisfy boundary condition idealization? If not — revise the work, never the criterion.
- Would the correction change the design of record that drawings, quantities and cost are generated from? If yes — raise a change-control request before proceeding.
Quality checklist
- Documented: linear elastic analysis vs
- Documented: boundary condition idealization
- Documented: load case combinations and envelope of demands
- ASCE 7-22 Sec. 12.8.7 cited by section number
- Units audited on every expression
- Acceptance criterion recorded before the result
- Independent check signed and dated
- Analysis model file with reaction/equilibrium check and governing demand envelope. attached and named per the course convention
Section H
Interactive visualization
Structural Analysis — step-through
Advance one frame at a time. Each frame adds one engineering decision to the previous state.
Step 1 of 6
Start from the confirmed inputs: geometry, materials, loads or flows, each with a source.
Section I
Applicable codes and standards
ASCE 7-22
2022 · Sec. 12.8.7
Adopted design/analysis reference governing this module.
Relevance: P-delta stability coefficient limit
Reference the section number and edition in your calculation package. Do not reproduce code text.
Section J
Worked examples
Full engineering solution format
Section K
Common mistakes and how to avoid them
- Treating linear elastic analysis vs as a given instead of establishing it from a project record.
- Producing analysis model file with reaction/equilibrium check and governing demand envelope. without showing how boundary condition idealization was satisfied.
- Substituting into δ = δ1st/(1 − ΣPΔ/(ΣH·hsx)) outside the range where it is valid, and reporting the number anyway.
- Missing p-delta effects and second-order analysis triggers, which is exactly the path to an element loaded beyond its governing limit state.
- Designing to the average condition when the governing condition is the controlling one.
- Freezing a design before the constructability and access review that would have changed it.
- Omitting the safety check because the strength check passed.
- Referencing figures, tables, or sources that never appear in the reference list.
- Carrying an assumption forward after the governing condition changed, without re-checking the result.
Section L
Industry case study
Documented failure related to structural analysis
A constructed civil works project where this module's decision was made incorrectly or skipped.
Official findings
- Published investigation identified a breakdown between analysis assumption and constructed condition.
Field observations
- The controlling assumption was documented nowhere in the design record.
- No independent check existed at the stage where the error entered the work.
Engineering interpretation
- Interpretation below is student analysis for instructional purposes, not an official finding.
- Map the failure to a step in your own workflow and state where your process would have caught it.
Lessons learned
- Document the assumption, then have someone else check it before it becomes construction.
Source: Summarize the published investigation; cite it in your reference list. Do not reproduce copyrighted report text.
Section M
FE Civil exam connection
Handbook FE Reference Handbook — structural engineering section (record the section number from your handbook edition).
Exam topics
Handbook formulas
- δ = δ1st/(1 − ΣPΔ/(ΣH·hsx))
Weak results here feed your FE Civil Academy weak-area queue for targeted practice.
Question 1 of 2
Score: 0/2In structural analysis, which item must be established BEFORE the analysis is run?
Section N
Apply it to your project — Structural Analysis
Complete this using your own capstone project data. Every field is saved to your project record and routed to your advisor with this module's submission.
Inputs and sources
Every value needs a traceable source.
| Quantity | Value | Unit | Source / record |
|---|
Assumptions and consequences
| Assumption | Basis | Consequence if wrong |
|---|
Self-check before submission
Section O
Design challenge
Consulting challenge — Structural Analysis
Your firm has been retained to deliver the structural analysis scope for a municipal client on a compressed schedule. Produce the technical position your firm would defend at a public meeting.
Client request: The client wants a defensible recommendation, the basis of design, and an honest statement of what remains unresolved.
Constraints
- Adopted local code edition governs; no exceptions without written variance.
- Budget and schedule are fixed; scope changes require change control.
- Public safety and accessibility requirements are non-negotiable.
Deliverables
- One-page basis of design
- Supporting calculation extract
- Risk and limitation statement
Evaluation
- Technical correctness
- Standard compliance
- Clarity of engineering judgment
- Honest treatment of uncertainty
Section P
Documentation workspace
Write the report section for this module in the academic editor
Section Q
File uploads
Accepted: PDF, DOCX, XLSX, CSV, PNG, JPG, ZIP, STAAD, SAP2000, ETABS, OpenSees
No files uploaded yet.
Section R
Deliverable and advisor review
Analysis model file with reaction/equilibrium check and governing demand envelope.
Submissions route to your assigned faculty advisor and are scored independently by faculty and administrator rubrics.
Reflection
What was the hardest engineering judgment in this module, and how did you resolve it?
Section S
ABET outcome mapping
Analysis model file with reaction/equilibrium check and governing demand envelope. with advisor review and dual scoring.
Assessment: Faculty rubric score and administrator rubric score on this module's submission.
Rubric: Engineering design · Target: 70% of students at or above 'meets expectations'.
Analysis model file with reaction/equilibrium check and governing demand envelope. with advisor review and dual scoring.
Assessment: Faculty rubric score and administrator rubric score on this module's submission.
Rubric: Engineering design · Target: 70% of students at or above 'meets expectations'.
Section T
References and further study
ASCE 7-22 (2022)
Adopted reference — cite section numbers, do not reproduce text.
Structural Analysis — instructor design procedure
Course template for the calculation package format expected in the final report appendix.
NCEES FE Reference Handbook
Locate the equations used here and note the handbook section for exam recall.
Advisor meeting agenda item
Bring the unresolved decision from this module to your next weekly advisor meeting.