Known and Unknown Values
Students classify every variable in the governing equation set into known and unknown categories and confirm the system is solvable.
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Computational Engineering · Build, calibrate, verify and validate the numerical model that supports your design decisions.
Deliverable: Known/unknown variable table with degrees-of-freedom verification.
Minimum tables, figures and equations for Known and Unknown Values
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 — slab, beam, column and shear wall schedule with governing demand
- 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
Figures — at least 4
- 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
Equations — at least 8
- 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
- Equation — punching shear, drift and deflection checks with limits
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 Known and Unknown Values lecture and the worked example so you know what "Known/unknown variable table with degrees-of-freedom verification." 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.
Modeling & Simulation Center — what this workspace teaches
Build, calibrate, verify and validate the numerical model that supports your design decisions.
- Selecting analysis software for the engineering question (STAAD, SAP2000, ETABS, HEC-RAS, OpenRoads, Civil3D, ArcGIS, MATLAB, Python)
- Model geometry idealization and simplification
- Boundary conditions, supports, restraints and their effect on results
- Load application and load-case management in software
- Mesh and element selection; convergence studies
- Model calibration against measured or benchmark data
- Sensitivity analysis of governing input parameters
- Verification (solving the equations right) vs. validation (solving the right equations)
- Exporting, documenting and archiving model results
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.
Known and Unknown Values
Students classify every variable in the governing equation set into known and unknown categories and confirm the system is solvable.
Section B
Engineering story
A real project situation that frames this module
The team opens week 3 believing known and unknown values is a formality, because the proposal treated it in a single sentence. Students classify every variable in the governing equation set into known and unknown categories and confirm the system is solvable. The first review question is not about arithmetic — it is where the basis for degrees of freedom check came from.
Attempting to solve an indeterminate system using only equilibrium equations. Because statically determinate vs, the error does not stay local: it is carried into the calculation package a reviewer must be able to reproduce line by line, and every downstream product inherits it before anyone notices.
The owner, the reviewing agency and the engineer of record carry the consequence. On this module specifically, the exposure runs through iterative vs, and the cost of correction rises every week the project record moves closer to issue.
Decisions the engineer must make
- What record establishes degrees of freedom check, and is that record in the project data inventory?
- Which adopted document governs this decision, and who confirmed it applies in this jurisdiction?
- What is the acceptance criterion for statically determinate vs, and was it written before the result was known?
- Is DOF = Nunknowns − Nequations valid over the parameter range this project actually occupies?
- If the check fails, does the team revise the project record or raise a change request against the locked baseline?
Photo 1. Field review: the conversation in which a scope, a constraint or a decision is actually settled.
Capstone Studio instructional photograph
Section C
Why this matters
Professional
Known and Unknown Values is judged on whether an independent engineer can follow your reasoning to the same conclusion. Your known/unknown variable table with degrees-of-freedom verification. is the evidence that they can.
Technical
Degrees of freedom check is what makes DOF = Nunknowns − Nequations 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 a decision made without a traceable basis. It reaches people through sensitivity ranking — which unknown most affects the final result, which is why the safety check is recorded explicitly here rather than inferred from a passing strength or performance check.
Economic
The calculation package a reviewer must be able to reproduce line by line is priced from this work. Quantities, unit costs and schedule float all trace to degrees of freedom check; a late correction here is paid for as a change order, not a redline.
Environmental
Environmentally, this module fixes material use, land disturbance and the waste stream generated by rework. 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
The residents and agencies who inherit the completed work 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.Explain degrees of freedom check, using this project's own conditions rather than a textbook case.
- 2.Interpret statically determinate vs, using this project's own conditions rather than a textbook case.
- 3.Compare iterative vs, using this project's own conditions rather than a textbook case.
- 4.Justify sensitivity ranking — which unknown most affects the final result, using this project's own conditions rather than a textbook case.
- 5.Compute the governing quantity from DOF = Nunknowns − Nequations, with a unit audit on every term.
- 6.Reproduce the worked example for a truss has 14 members, 3 reaction components, and 8 joints and defend the interpretation of the result.
- 7.Produce known/unknown variable table with degrees-of-freedom verification. at a standard the advisor of record would accept without a second revision cycle.
Section E
Instructional content
Full lecture notes with figures and governing equations
Known and Unknown Values — what the work actually is
Students classify every variable in the governing equation set into known and unknown categories and confirm the system is solvable. That single sentence hides the substance of the module: degrees of freedom check, and statically determinate vs. Both must be established from project evidence before anything downstream is credible.
In civil engineering practice, this work is the input to the project record. Iterative vs — which is why this page asks you to record the source of every quantity, not just its value. The calculation package a reviewer must be able to reproduce line by line depends on it.
- Degrees of freedom check: number of unknowns vs. number of independent equations
- Statically determinate vs. indeterminate systems and the implication for solution method
- Iterative vs. closed-form solution paths when unknowns cannot be isolated directly
- Sensitivity ranking — which unknown most affects the final result
Photo 1. Known and Unknown Values — what the work actually is in practice — Field review: the conversation in which a scope, a constraint or a decision is actually settled.
Capstone Studio instructional photograph
Governing relationships and how they are applied here
The relationships below govern known and unknown values. DOF = Nunknowns − Nequations — each is valid only inside the parameter range this project occupies, so state that range before substituting.
Statically determinate vs sets the values you place into these expressions. Any prescribed factor must be traced to the document your jurisdiction adopted, not to a lecture slide.
DOF = Nunknowns − Nequations
- Nunknowns = number of independent unknown quantities
- Nequations = number of independent governing equations available
Photo 2. Governing relationships and how they are applied here in practice — Field review: the conversation in which a scope, a constraint or a decision is actually settled.
Capstone Studio instructional photograph
Constraints, adopted standards and the safety case for known and unknown values
No single code section governs this module, so the constraint set comes from the approved proposal, the owner's requirements and professional practice. Write those constraints down; an unwritten constraint is not enforceable at review.
The safety case is explicit here. The failure mode is a decision made without a traceable basis; the people exposed are the owner, the reviewing agency and the engineer of record; the control that prevents it is sensitivity ranking — which unknown most affects the final result together with an independent check by someone who did not perform the work.
- Controlling criterion for this module: degrees of freedom check.
- Adopted reference: confirm with the jurisdiction before you rely on it.
- Failure mode guarded: a decision made without a traceable basis.
- Evidence produced: Known/unknown variable table with degrees-of-freedom verification..
Photo 3. Constraints, adopted standards and the safety case for known and unknown values in practice — Field review: the conversation in which a scope, a constraint or a decision is actually settled.
Capstone Studio instructional photograph
Where this method stops being valid
The worked example — a truss has 14 members, 3 reaction components, and 8 joints — holds only while its assumptions hold. The truss is statically indeterminate to the first degree; the model cannot be solved by statics alone and requires a compatibility-based method (e.g., force method or stiffness method) before member forces can be reported. Outside that envelope the arithmetic still returns a number, and the number is wrong in a way no unit check will catch.
For this project, the boundary you are most likely to push is sensitivity ranking — which unknown most affects the final result. 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 — degrees of freedom check; statically determinate vs — each with a unit and a source record.
- 2. Confirm which document governs, and record who verified that it applies here.
- 3. State the assumptions and the acceptance criterion for degrees of freedom check.
- 4. Evaluate DOF = Nunknowns − Nequations term by term, carrying one extra significant figure.
- 5. Test the result against iterative vs.
- 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 known/unknown variable table with degrees-of-freedom verification. and submit it to the advisor of record for review.
Decision points
- Is every input behind degrees of freedom check traceable? If not — stop and collect the record.
- Does the result satisfy statically determinate vs? If not — revise the work, never the criterion.
- Would the correction change the calculation package a reviewer must be able to reproduce line by line? If yes — raise a change-control request before proceeding.
- Have you ruled out the most common error on this module — attempting to solve an indeterminate system using only equilibrium equations?
Quality checklist
- Documented: degrees of freedom check
- Documented: statically determinate vs
- Documented: iterative vs
- Governing document cited
- Units audited on every expression
- Acceptance criterion recorded before the result
- Independent check signed and dated
- Known/unknown variable table with degrees-of-freedom verification. attached and named per the course convention
Section H
Interactive visualization
Known and Unknown Values — step-through
Advance one frame at a time. Each frame adds one engineering decision to the previous state.
Step 1 of 6
List all variables appearing in the governing equation set.
Section I
Applicable codes and standards
Section J
Worked examples
Full engineering solution format
Section K
Common mistakes and how to avoid them
- Attempting to solve an indeterminate system using only equilibrium equations.
- Treating a variable as 'known' because it appeared in a similar past project, without a project-specific source.
- Treating degrees of freedom check as a given instead of establishing it from a project record.
- Producing known/unknown variable table with degrees-of-freedom verification. without showing how statically determinate vs was satisfied.
- Substituting into DOF = Nunknowns − Nequations outside the range where it is valid, and reporting the number anyway.
- Missing sensitivity ranking — which unknown most affects the final result, which is exactly the path to a decision made without a traceable basis.
- Reporting model output without documenting mesh, boundary conditions, solver settings or convergence.
- Calibrating a model until it matches expectation, then presenting the match as validation.
- Confusing results (what the analysis produced) with conclusions (what the engineer decided).
- Ignoring constructability: a design that cannot be built safely is not a completed design.
- Omitting the safety check because the strength check passed.
Section L
Industry case study
Documented failure related to known and unknown values
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 — civil engineering practice section (record the section number from your handbook edition).
Exam topics
Handbook formulas
- DOF = Nunknowns − Nequations
Weak results here feed your FE Civil Academy weak-area queue for targeted practice.
Question 1 of 2
Score: 0/2In known and unknown values, which item must be established BEFORE the analysis is run?
Section N
Apply it to your project — Known and Unknown Values
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 — Known and Unknown Values
Your firm has been retained to deliver the known and unknown values 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
No files uploaded yet.
Section R
Deliverable and advisor review
Known/unknown variable table with degrees-of-freedom verification.
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
Known/unknown variable table with degrees-of-freedom verification. with advisor review and dual scoring.
Assessment: Faculty rubric score and administrator rubric score on this module's submission.
Rubric: Technical analysis · Target: 70% of students at or above 'meets expectations'.
Known/unknown variable table with degrees-of-freedom verification. with advisor review and dual scoring.
Assessment: Faculty rubric score and administrator rubric score on this module's submission.
Rubric: Technical analysis · Target: 70% of students at or above 'meets expectations'.
Section T
References and further study
Known and Unknown Values — 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.