Reinforced Concrete Design
Designs reinforced concrete beams, slabs, and columns for flexure, shear, and axial-flexure interaction per ACI 318.
Section progress
0% of the workflow complete
Structural Engineering · Load path, member selection, connections and limit-state verification to AISC, ACI and ASCE 7.
Deliverable: Concrete member design calculations with flexure, shear, and reinforcement detailing summary.
Minimum tables, figures and equations for Reinforced Concrete Design
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 Reinforced Concrete Design lecture and the worked example so you know what "Concrete member design calculations with flexure, shear, and reinforcement detailing summary." 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.
Reinforced Concrete Design
Designs reinforced concrete beams, slabs, and columns for flexure, shear, and axial-flexure interaction per ACI 318.
Section B
Engineering story
A real project situation that frames this module
Week 4: reinforced concrete design is the item standing between the team and a reviewable calculation package and framing drawings. Designs reinforced concrete beams, slabs, and columns for flexure, shear, and axial-flexure interaction per ACI 318. Review stalls on a single line: the team cannot show the record behind whitney stress block and flexural strength design of singly/doubly reinforced sections.
The team treats shear design and stirrup spacing requirements 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 minimum and maximum reinforcement ratios, ductility (tension-controlled) requirements, 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 whitney stress block and flexural strength design of singly/doubly reinforced sections, and is that record in the project data inventory?
- Does ACI 318-19 (2019), Ch. 22, 9, govern here — and is that the edition adopted by the jurisdiction?
- What is the acceptance criterion for shear design and stirrup spacing requirements, and was it written before the result was known?
- Is φMn = φ·As·fy·(d − a/2) 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. Footing reinforcement and formwork before placement — the physical form of a bearing-capacity calculation.
Wikimedia Commons, public domain
Section C
Why this matters
Professional
A licensed engineer defending reinforced concrete design cites ACI 318-19 (2019), Ch. 22, 9, and shows the record behind each input. Your concrete member design calculations with flexure, shear, and reinforcement detailing summary. is reviewed the same way — traceability is assessed before arithmetic.
Technical
Whitney stress block and flexural strength design of singly/doubly reinforced sections is what makes φMn = φ·As·fy·(d − a/2) 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 development length and splice requirements for reinforcement, 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 whitney stress block and flexural strength design of singly/doubly reinforced sections; 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
Reinforced concrete capacity must be re-verified whenever geometry or loading changes after design Occupants who rely on the structure performing through its design life and design event live with that outcome long after the semester ends.
Section D
Learning objectives
By the end of this module you will be able to:
- 1.Explain whitney stress block and flexural strength design of singly/doubly reinforced sections, using this project's own conditions rather than a textbook case.
- 2.Evaluate shear design and stirrup spacing requirements, using this project's own conditions rather than a textbook case.
- 3.Interpret minimum and maximum reinforcement ratios, ductility (tension-controlled) requirements, using this project's own conditions rather than a textbook case.
- 4.Apply column interaction diagrams (P-M) for combined axial and flexure, using this project's own conditions rather than a textbook case.
- 5.Compute the governing quantity from φMn = φ·As·fy·(d − a/2) and a = As·fy/(0.85·f'c·b) and Pn = 0.80·φ·[0.85·f'c·(Ag − Ast) + fy·Ast], with a unit audit on every term.
- 6.Apply ACI 318-19 (2019), Ch. 22, 9, and cite the section that governs your acceptance decision.
- 7.Reproduce the worked example for determine φMn for a rectangular beam and defend the interpretation of the result.
- 8.Produce concrete member design calculations with flexure, shear, and reinforcement detailing summary. 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
Reading reinforced concrete design as a practising engineer
Designs reinforced concrete beams, slabs, and columns for flexure, shear, and axial-flexure interaction per ACI 318. That single sentence hides the substance of the module: whitney stress block and flexural strength design of singly/doubly reinforced sections, and shear design and stirrup spacing requirements. 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. Minimum and maximum reinforcement ratios, ductility (tension-controlled) requirements — 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.
- Whitney stress block and flexural strength design of singly/doubly reinforced sections
- Shear design and stirrup spacing requirements
- Minimum and maximum reinforcement ratios, ductility (tension-controlled) requirements
- Column interaction diagrams (P-M) for combined axial and flexure
- Development length and splice requirements for reinforcement
Photo 1. Reading reinforced concrete design as a practising engineer in practice — Footing reinforcement and formwork before placement — the physical form of a bearing-capacity calculation.
Wikimedia Commons, public domain
Governing relationships and how they are applied here
The relationships below govern reinforced concrete design. φMn = φ·As·fy·(d − a/2); a = As·fy/(0.85·f'c·b); Pn = 0.80·φ·[0.85·f'c·(Ag − Ast) + fy·Ast] — each is valid only inside the parameter range this project occupies, so state that range before substituting.
Shear design and stirrup spacing requirements sets the values you place into these expressions. Any code-prescribed factor must match ACI 318-19 (2019); a factor lifted from a different edition silently changes the answer.
φMn = φ·As·fy·(d − a/2)
- φ = 0.90 (tension-controlled)
- As — tension steel area
- fy — yield strength
- d — effective depth
- a — depth of stress block
a = As·fy/(0.85·f'c·b)
- f'c — concrete compressive strength
- b — section width
Pn = 0.80·φ·[0.85·f'c·(Ag − Ast) + fy·Ast]
- Maximum axial capacity of a tied column, ACI 318-19 Sec. 22.4.2
Photo 2. Governing relationships and how they are applied here in practice — Footing reinforcement and formwork before placement — the physical form of a bearing-capacity calculation.
Wikimedia Commons, public domain
Constraints, adopted standards and the safety case for reinforced concrete design
ACI 318-19 (2019), Ch. 22, 9, governs this module: Flexural and axial-flexure design provisions
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 development length and splice requirements for reinforcement together with an independent check by someone who did not perform the work.
- Controlling criterion for this module: whitney stress block and flexural strength design of singly/doubly reinforced sections.
- Adopted reference: ACI 318-19 (2019) — cite Ch. 22, 9 by number.
- Failure mode guarded: an element loaded beyond its governing limit state.
- Evidence produced: Concrete member design calculations with flexure, shear, and reinforcement detailing summary..
Photo 3. Constraints, adopted standards and the safety case for reinforced concrete design in practice — Footing reinforcement and formwork before placement — the physical form of a bearing-capacity calculation.
Wikimedia Commons, public domain
Where this method stops being valid
The worked example — determine φMn for a rectangular beam — holds only while its assumptions hold. Compare φMn to Mu from the governing load combination; verify εt ≥ 0.005 for tension-controlled behavior before accepting φ=0.90. 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 development length and splice requirements for reinforcement. 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 — Footing reinforcement and formwork before placement — the physical form of a bearing-capacity calculation.
Wikimedia Commons, public domain
Section F
Engineering workflow
Steps
- 1. Assemble the inputs this module needs — whitney stress block and flexural strength design of singly/doubly reinforced…; shear design and stirrup spacing requirements — each with a unit and a source record.
- 2. Confirm ACI 318-19 (2019) is the adopted edition and locate Ch. 22, 9.
- 3. State the assumptions and the acceptance criterion for whitney stress block and flexural strength design of singly/doubly reinforced sections.
- 4. Evaluate φMn = φ·As·fy·(d − a/2) and a = As·fy/(0.85·f'c·b) and Pn = 0.80·φ·[0.85·f'c·(Ag − Ast) + fy·Ast] term by term, carrying one extra significant figure.
- 5. Test the result against minimum and maximum reinforcement ratios, ductility (tension-controlled) requirements.
- 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 concrete member design calculations with flexure, shear, and reinforcement detailing summary. and submit it to the plan reviewer at the building department for review.
Decision points
- Is every input behind whitney stress block and flexural strength design of singly/doubly reinforced sections traceable? If not — stop and collect the record.
- Does the result satisfy shear design and stirrup spacing requirements? 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: whitney stress block and flexural strength design of singly/doubly reinforced sections
- Documented: shear design and stirrup spacing requirements
- Documented: minimum and maximum reinforcement ratios, ductility (tension-controlled) requirements
- ACI 318-19 Ch. 22, 9 cited by section number
- Units audited on every expression
- Acceptance criterion recorded before the result
- Independent check signed and dated
- Concrete member design calculations with flexure, shear, and reinforcement detailing summary. attached and named per the course convention
Section H
Interactive visualization
Reinforced Concrete Design — 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
ACI 318-19
2019 · Ch. 22, 9
Adopted design/analysis reference governing this module.
Relevance: Flexural and axial-flexure design provisions
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 whitney stress block and flexural strength design of singly/doubly reinforced sections as a given instead of establishing it from a project record.
- Producing concrete member design calculations with flexure, shear, and reinforcement detailing summary. without showing how shear design and stirrup spacing requirements was satisfied.
- Substituting into φMn = φ·As·fy·(d − a/2) outside the range where it is valid, and reporting the number anyway.
- Missing development length and splice requirements for reinforcement, 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.
- Ignoring constructability: a design that cannot be built safely is not a completed design.
- Omitting the safety check because the strength check passed.
- Referencing figures, tables, or sources that never appear in the reference list.
Section L
Industry case study
Sampoong Department Store Collapse (Seoul, 1995)
Five-story reinforced concrete retail building
Official findings
- Government investigation found columns undersized and reduced from the original design, with slabs overloaded by unauthorized floor additions and heavy rooftop AC units
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
- Reinforced concrete capacity must be re-verified whenever geometry or loading changes after design
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
- φMn = φAsfy(d−a/2)
- a = Asfy/(0.85f'cb)
Weak results here feed your FE Civil Academy weak-area queue for targeted practice.
Question 1 of 2
Score: 0/2In reinforced concrete design, which item must be established BEFORE the analysis is run?
Section N
Apply it to your project — Reinforced Concrete Design
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 — Reinforced Concrete Design
Your firm has been retained to deliver the reinforced concrete design 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
No files uploaded yet.
Section R
Deliverable and advisor review
Concrete member design calculations with flexure, shear, and reinforcement detailing summary.
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
Concrete member design calculations with flexure, shear, and reinforcement detailing summary. 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
ACI 318-19 (2019)
Adopted reference — cite section numbers, do not reproduce text.
Reinforced Concrete Design — 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.