All 8 sections — every topic explained with why it matters first, then built up through analogies, interactive visuals, and technical detail.
Everything you design in this course is made of one of these three materials — or a combination. Their fundamentally different behaviours under stress will dictate every sizing, shape, and reinforcement decision you ever make. Get this wrong conceptually and you'll be guessing your way through the rest of the textbook.
Think of plain concrete as a block of blackboard chalk — crushing-strong, snap-brittle. Reinforced concrete is that chalk encased in a steel skeleton — now it bends without snapping. Prestressed concrete is the chalk pre-squeezed so hard by rubber bands that any tension from bending must first undo that squeeze before cracking can start — this lets you span distances that would be impossible otherwise.
A carefully proportioned mixture of cement, sand, coarse aggregate, and water. Cement and water react chemically to bind the aggregate into a stone-like mass. Curing conditions (temperature, humidity) critically affect the final strength.
Great at: Compression — columns, arches, gravity dams. Compressive strength f'c typically 3,000–6,000 psi.
Terrible at: Tension and bending. Tensile strength is only ~8–12% of compressive strength. A plain concrete beam cracks at the tension face under surprisingly light loads.
Tension forms at the bottom of a loaded beam — plain concrete cracks there immediately.
Deformed steel bars (rebar) are placed in forms before pouring. Once hardened, the two materials act compositely: concrete handles compression, steel handles tension. Two key facts make this work perfectly:
Grade 60 rebar (60 ksi yield) is the most commonly used. The ACI Code limits usable yield to 100 ksi to control crack widths.
Rebar near the tension face prevents cracking. Stirrups (dashed squares) resist shear.
High-strength steel tendons (wires, strands, or bars — up to 270 ksi) are stretched and anchored against the concrete. This squeezes the concrete into pre-compression before any live load is applied.
The key insight: When live load bends the member and induces tension at the bottom, it must first overcome that pre-compression before cracking can occur. This allows much thinner sections and longer spans.
Enables spans of 100–300 ft. Used in bridges, parking garages, stadiums. Dramatically reduces deflection and crack widths.
The draped tendon profile follows the tension zone, pre-compressing it.
Choosing the right structural form is the first and most impactful decision in any design. It determines how efficiently loads travel to the ground, how much material you use, how much you spend, and what spans are achievable. An engineer who confuses these forms or applies them outside their optimal range will produce expensive, unsafe, or impractical structures.
Structural forms are like tools in a toolbox. A hammer, screwdriver, and wrench each do something the others can't. You don't drive a screw with a hammer just because you already have it out. Flat plates suit apartments; shells suit stadiums; arches suit bridges — force the wrong one onto the wrong job and you waste money or risk failure.
Click any card to see how that structural form works and when engineers choose it.
Every structural form is a different way to route loads down this same chain. Good engineers visualise this path intuitively.
Every design calculation you ever do starts with loads. If you misclassify a load, apply the wrong value, or ignore a load type, your structure will be either dangerously under-designed or wastefully over-designed. Understanding load types and their statistical nature is what separates a thoughtful engineer from someone who just plugs numbers into equations.
Think of loads like your monthly budget. Dead loads = rent (fixed, always there, known precisely). Live loads = groceries (varies month to month, but bounded). Wind/seismic = sudden car repair (rare but potentially huge). You plan for the regular ones and buy insurance for the surprises. Engineers do the same through load combinations — but with math instead of a bank account.
Self-weight of the structure + permanent fixtures (HVAC, flooring, ceilings). Calculated from dimensions and unit weights. Always present. Known precisely.
Occupancy loads — people, furniture, vehicles, stored goods. Varies with use and time. Code specifies minimum values by occupancy (40 psf residential → 250 psf warehouses).
Accumulation on roofs. Depends on geographic location and roof slope. Can be asymmetric (drift loads at parapets). A major cause of roof failures in cold climates.
Pressure and suction on all surfaces. Can cause net uplift on flat roofs. Varies with height, terrain, and building shape. Based on statistical return periods (ASCE 7).
Inertia forces during ground shaking. Proportional to mass — heavier structures attract more seismic force. Dynamic analysis required for complex/tall structures.
Fluid pressure (water tanks), lateral earth pressure (retaining walls), and temperature/settlement effects. Must be considered when applicable.
Drag the sliders to see how dead load, live load, and span affect beam deflection. The factored moment updates in real time — this is what you're designing against.
This is the philosophical core of structural engineering. Why do we multiply loads by 1.2 or 1.6? Why do we reduce calculated strength by 0.9 or 0.75? The answer is that both loads and strengths are random variables — they vary, and we can never know them exactly. This section teaches you to think probabilistically about structural safety instead of treating it as a magic recipe from a code book.
Imagine two overlapping bell curves on a number line — one for the loads a structure will see, one for the strength it actually has. Failure happens when a load exceeds the strength — the overlap of those two curves. Safety design means keeping that overlap (the failure probability) acceptably tiny — typically 1 in 100,000 for structural elements.
The goal: keep the curves far apart so the overlap (failure probability) is negligibly small.
Each source below is a reason we can't use exact values — and collectively they justify why we need safety factors. Click any item to learn more about why it matters.
You need to understand why modern concrete design works the way it does — and why it replaced what came before. This isn't just history: understanding the two competing philosophies tells you exactly what the strength design equations are trying to achieve, which makes them far easier to remember and apply correctly.
Imagine two ways to hire a taxi driver. The old method (working stress / ASD) says: "Keep your speed below 30 mph at all times" — a rule based on service conditions. The modern method (strength design / LRFD) says: "Your car must be able to physically survive a crash at 60 mph without killing anyone" — a rule based on the ultimate limit. The modern method is more rational because it designs against actual failure, not an arbitrary fraction of it.
Members are proportioned so their nominal strength, reduced by φ, meets or exceeds the required strength U from factored loads.
Design against the factored moment — the member must physically be able to resist collapse under extreme loads.
Members are proportioned so that stresses under service (unfactored) loads stay within allowable limits — typically half the failure stress.
ASD checks that elastic stresses under real loads stay below an arbitrary fraction of failure stress.
You will spend your entire career navigating and applying these documents. Understanding who writes them, why they exist, and how they relate to each other is essential — not just for passing exams, but because misapplying the wrong code or the wrong edition of a code to a project has caused structural failures and massive legal liability.
Think of design codes like traffic laws. The ACI Code is like the detailed traffic rulebook for concrete — specific technical requirements. The IBC is like the state law that says "you must follow the traffic rulebook." ASCE 7 is a separate standard that defines the loads (speed limits, essentially). No single document covers everything — they reference each other in a chain.
The United States — unlike many nations — has no single official government-sanctioned national code. Instead, codes are written by professional organisations (ACI, ASCE, AASHTO) and adopted by local jurisdictions through reference in laws like the IBC.
These are the actual numbers you will use in every single design calculation for the rest of this course and your career. The φ (phi) factors and load factors aren't arbitrary — each one is calibrated to reflect specific levels of uncertainty and consequence. Understanding the reason behind each value prevents you from blindly applying the wrong one and catching errors that others miss.
Think of φ factors like the safety margins on different parts of a car. The brakes (columns — sudden, catastrophic failure) get more redundancy (φ = 0.65). The seatbelts (beams — give ductile warning before failing) need less redundancy (φ = 0.90) because you can see a problem coming. The ACI calibrates each φ to give the same overall probability of failure regardless of how different each failure mode looks.
Each φ < 1.0 reduces the calculated nominal strength to account for real-world variability. Click any row to learn why that value was chosen.
| Action / Failure Mode | φ Value | Relative φ | Reason |
|---|---|---|---|
| Flexure (tension-controlled) | 0.90 | Ductile; warns before failure ▸ | |
| Shear and torsion | 0.75 | Less predictable; more sudden ▸ | |
| Compression-controlled (tied columns) | 0.65 | Sudden; catastrophic collapse ▸ | |
| Compression-controlled (spiral columns) | 0.75 | More ductile than tied ▸ | |
| Bearing on concrete | 0.65 | Localised, brittle ▸ | |
| Post-tensioned anchorage zones | 0.85 | High-quality PS construction ▸ |
This is where the theory becomes calculation. Every structural design starts with computing the factored loads — the actual numbers that go into your beam or column equations. Get this step wrong and everything downstream is wrong. This section walks you through the exact process used in professional practice, from gathering service loads to computing the governing factored design force.
Developing factored loads is like computing the worst-case bill you need to be able to pay. You list all your regular expenses (dead loads), estimate your maximum variable spending (live loads), multiply each by how uncertain it is (load factors), and check every possible month's scenario (load combinations). The highest total across all scenarios is your required "financial strength" — your Mu, the design demand.
List dead loads (self-weight of concrete at 150 pcf, slab fill, partitions, MEP, ceilings) and live loads (from ASCE 7 Table 4.3-1 based on occupancy). Don't forget roof live loads, snow, or other applicable loads.
The portion of the floor or roof that "feeds" loads to the beam or column being designed. For a beam with joists at 8 ft spacing, the tributary width is 8 ft. For a column, it's the surrounding floor area it supports.
Multiply load intensity (psf) × tributary width (ft) = load per linear foot (plf). This gives you the distributed load w on your beam or girder.
Check both U = 1.4D and U = 1.2D + 1.6L (plus others if snow/wind applies). The larger result governs.
Use statics to find maximum moment and shear. For a simply supported beam: Mu = wuL²/8, Vu = wuL/2. These are the demand values your design must satisfy.
Enter your service loads and span. The calculator checks all governing ACI combinations and highlights the one that controls design.
Each column or beam collects load from its surrounding "tributary" region. Interior columns carry more load than corner columns because they have a larger tributary area.
§1.1 Materials: Concrete is strong in compression (~4,000 psi), weak in tension (~400 psi). Rebar fills the tensile gap. Prestressing pre-compresses concrete so live load tension must overcome the squeeze before cracking — enabling long spans.
§1.2 Structural Forms: Each form (flat plate, slab-beam, arch, shell, joist, box girder) routes loads to the ground via a different mechanism, each suited to specific span ranges and load conditions. All good structural design starts with recognising the load path.
§1.3 Loads: Dead, live, snow, wind, seismic, and environmental loads each have different statistical characters. ACI load combinations (1.4D; 1.2D+1.6L; etc.) apply factors reflecting the uncertainty of each load type. All applicable combinations must be checked.
§1.4 Safety: Both loads and strengths are random variables with probability distributions. Safety means keeping the probability that strength < load acceptably tiny (~1:100,000). This motivates φ < 1.0 (reduce calculated strength) and γ > 1.0 (amplify design loads).
§1.5 Design Basis: Modern Strength Design (LRFD) proportions members to resist factored loads at failure — using nonlinear material behaviour. It replaced Working Stress Design, which kept elastic stresses at fractions of failure stress. SD is more realistic and rational.
§1.6 Design Codes: ACI 318 (concrete design) + ASCE 7 (loads) are the two primary standards, both referenced by the IBC. No single U.S. national government code exists. AASHTO governs bridges; AREMA governs railways. Know which code applies to your project.
§1.7 ACI Provisions: φ factors range from 0.65 (tied columns — sudden, catastrophic) to 0.90 (flexure — ductile warning). Load factors are calibrated to uncertainty: 1.2 for well-known dead loads, 1.6 for uncertain live loads. Each number has a specific engineering rationale.
§1.8 Factored Loads: The 5-step process: (1) identify loads, (2) find tributary area/width, (3) convert psf → plf, (4) apply load combinations to find wu, (5) compute Mu = wuL²/8 and Vu = wuL/2. The governing combination produces the design forces all subsequent calculations must satisfy.