CVLE 372 · FUNDAMENTALS OF REINFORCED CONCRETE / VIRTUAL LABORATORY
See the forces.
Size the steel.
Reinforced concrete works because steel and concrete share the load — concrete takes compression, steel takes tension, and they hold hands through bond. Explore every step of the theory: pull sections apart, move the neutral axis, place stirrups, push columns around their interaction curve.
Start with the materialsExplore the five modules
14 interactive experimentsBehaviour & materials
Concrete and steel stress–strain curves, the three stages of a bending member, loads and safety factors, ductile versus brittle failure.
Weeks 1–2 02 / FLEXUREFlexure
Whitney stress block on singly, doubly and T-sections — analyse an existing beam or design the steel when the moment is given.
Weeks 3–7 03 / SHEAR & TORSIONShear & torsion
Diagonal tension, Vc and Vs, stirrup spacing zones along the beam, and closed stirrups that fight twisting.
Weeks 10–11 04 / COLUMNSColumns
Axial capacity, eccentricity, live interaction diagrams for tied and spiral columns, and the moment magnifier for slender ones.
Weeks 12–14 05 / DEVELOPMENT & DETAILINGDevelopment & detailing
Development length, hooks, splices, and where bars may safely stop when the moment fades away.
Week 15MODULE 01 / BEHAVIOUR & MATERIALS
Two materials,
one member.
Before any formula, meet the materials. Concrete crushes at 0.003; steel yields at fy/Es and keeps stretching. Learn how their stress–strain curves write every design rule that follows.
Open lab 1.1Explore behaviour & materials
4 learning modulesConcrete & steel get real
Slide f'c and the steel grade. Watch Ec, the yield strain, the modulus of rupture and the crushing strain move.
Interactive stress–strain bench 1.2 / BEHAVIOURThree stages of a beam
Load a beam from zero to failure: uncracked elastic, cracked elastic, then the ultimate Whitney block. See Mcr, kd and Mn arrive in order.
The exam sketch, alive 1.3 / SAFETYLoads & safety
Build the required strength U from D, L, W and E. See which ACI load combination governs — and why nothing is designed for service load.
ACI combinations explorer 1.4 / FAILURE MODESDuctile or brittle?
Turn the steel area up and watch the failure switch from ductile to brittle — and the φ factor follow the net tensile strain.
φ-factor laboratory NEXT MODULEModule 02 · Flexure
Once you know the materials, put them to work: the Whitney block, singly and doubly reinforced sections, and T-beams.
Weeks 3–7MODULE 02 / FLEXURE
Balance the couple,
find the bars.
The heart of the course: replace the real stress distribution with the Whitney block, equate tension and compression, and take the lever arm. Then run it backwards — design the steel for a required moment.
Open lab 2.1Explore flexure
4 learning modulesSingly reinforced · analysis
Given b, d, As, f'c and fy — find a, Z, Mn and εt, and check that the steel really yielded. The lecture example is one click away.
Step-by-step solver 2.2 / DESIGNSingly reinforced · design
Given Mu — choose the design ratio, solve for the depth, then pick real bars and verify φMn. As,min and As,max are checked for you.
Design workspace + bar picker 2.3 / DOUBLYDoubly reinforced
When the section is squeezed, compression steel adds the second couple. Check whether A's yields — Condition I or Condition II.
Two-couple decomposition 2.4 / T-SECTIONST-beams
The slab joins the party. Find the effective flange width, then let the stress block decide: rectangular T or true T?
Flange laboratory NEXT MODULEModule 03 · Shear & Torsion
Flexure tells half the story. Now follow the diagonal tension and the twisting moment.
Weeks 10–11MODULE 03 / SHEAR & TORSION
Diagonal cracks
need a corset.
Shear turns the principal stresses diagonal. Concrete gives Vc; stirrups must carry everything above it — close enough together. Torsion wraps the beam the other way, and closed stirrups plus corner bars are the answer.
Open lab 3.1Explore shear & torsion
2 learning modulesShear & stirrups
Compute Vc and the stirrup demand, then lay out real spacing zones along the beam with every spacing limit checked.
Stirrup layout bench 3.2 / TWISTTorsion
When must torsion be taken seriously? Build the closed stirrup and the longitudinal steel that resist it.
Threshold + design NEXT MODULEModule 04 · Columns
Load meets moment. Build the interaction diagram and keep the demand point inside it.
Weeks 12–14MODULE 04 / COLUMNS
Load meets moment.
Stay inside the curve.
No column is truly axially loaded. Every real column is a P–M problem — draw the interaction diagram, drop the demand point on it, and read the failure type. Short columns first, then the magnifier that tame slender ones.
Open lab 4.1Explore columns
2 learning modulesShort columns · interaction
P0, the 0.80 and 0.85 caps, eccentricity, and a live interaction diagram you can park a demand point on.
Live P–M curve 4.2 / SLENDERNESSSlender columns
When does buckling bite? Find Pc, watch the moment magnifier grow, and learn when slenderness may be neglected.
Moment magnification NEXT MODULEModule 05 · Development
The design is done — now anchor it. Development lengths, hooks and cutoff points.
Week 15MODULE 05 / DEVELOPMENT & DETAILING
Every bar needs
a grip.
A bar is only as strong as the length over which it can hand its force to the concrete. Compute development lengths, add hooks and splices, and find exactly where a bar may be cut without stealing strength.
Open lab 5.1Explore development & detailing
2 learning modulesDevelopment & hooks
Every ψ and λ explained: top bars, epoxy coating, bar size, cover and confinement. Straight ld, hook ldh and lap splices.
Anchorage laboratory 5.2 / CUTOFFBar cutoff
The moment diagram is a hill; the capacity diagram is a staircase. Walk the bars down the moment — always ld past the last drop.
Detailing challenge FULL WORKSTATIONRC beam analysis & design app
When you want the full ACI 318-19 workstation for flexural and shear design of beams — the tool behind the course projects.
Opens the professional appMODULE 01 / LAB 1.1
Concrete & steel get real.
Concrete is strong in compression and brittle in tension; steel is equally strong in both and yields with plenty of warning. Slide their properties and watch the two curves — every design rule in this course lives inside them.
The materials
The fixed reference strains from the notes: concrete reaches its peak stress near ε = 0.002 and is assumed to crush at ε = 0.003. Steel is elastic up to fy, then runs on an almost flat plateau.
NUMBERS TO CARRY FORWARD
ACI 318 (SI): Ec = 4700√f'c, fr = 0.62λ√f'c, εy = fy/Es with Es = 200 GPa. The curves use a Hognestad-type concrete model and an elastic–perfectly plastic steel model — the shapes your lecture notes sketch.
MODULE 01 / LAB 1.2
Three stages of a beam.
Pull a simply supported beam from zero load to failure. First it behaves elastically and uncracked, then cracks open at the modulus of rupture, and finally the steel yields while the concrete heads for 0.003. Drag the moment and watch every diagram redraw.
The load
f'c = 28 MPa, fy = 420 MPa, b = 250 mm, d = 600 mm (h = 650 mm) unless the preset changes the steel. Stage boundaries: cracking at Mcr, first yield at My, ultimate at Mn — the design strength is φMn.
MODULE 01 / LAB 1.3
Loads & safety.
Structures never see "the load" — they see combinations of dead, live, wind and earthquake effects. Multiply each by its ACI load factor, find the worst case, and that U is what the member must resist. Build your own combination below.
Service moments
Values are service moments on the member. The lecture's design rule: φ Sn ≥ U — the design strength must cover the most critical factored combination.
THE COMBINATIONS
Load combination list follows the ACI Code factors as taught in week 2: 1.4D; 1.2D plus 1.6L or 1.6S; wind and seismic combinations with the companion-load 0.5 or 0.2 factors; and the 0.9D "uplift" cases where the dead load works against you. The companion factors recognise that snow, wind and earthquake rarely peak together.
MODULE 01 / LAB 1.4
Ductile or brittle?
The failure mode of a beam is decided by its steel area. Too little steel and it snaps when it cracks; too much and the concrete crushes with no warning. Slide As and watch the net tensile strain εt move the φ factor.
The steel area
Section fixed: b = 250 mm, d = 600 mm, f'c = 28 MPa, fy = 420 MPa — your As sits at of the balanced steel. As,balance = mm²; the course ceiling As,max = 0.75 As,balance = mm²; minimum steel As,min = mm².
MODULE 02 / LAB 2.1
Balance the forces.
Here is the idea behind every flexure formula: the compression in the concrete block and the tension in the steel must be equal — ΣH = 0. Drag the neutral axis yourself, feel which side wins, and discover the one depth where the beam is in equilibrium.
Set the scene
Grab and drag the red neutral-axis line right in the drawing — or use the slider. There is exactly one depth where NC = NT.
THE BALANCE
MODULE 02 / LAB 2.2
Size it yourself.
A factored moment is looking for a home. You choose the width, the depth and the bars — the lab reviews you like a checker: capacity, minimum steel, the ductility cap, and whether the bars even fit. Find a passing section, then try to beat it with less concrete.
Your design
REVIEWER'S CHECKLIST
Your reinforcement ratio ρ = .
MODULE 02 / LAB 2.3
The second couple.
When the architecture caps the depth, the trick is steel in the compression zone — it responds to the extra tension steel with a couple of its own. Add A's bar by bar and watch the section change: how much capacity it buys, how much ductility it buys, and when the compression bars are still too lazy to yield.
The section
Without any compression steel this same section would reach φMn = kN·m.
MODULE 02 / LAB 2.4
The flange effect.
Cast a slab monolithically over your beams and it quietly joins the compression team. Move the steel, the flange thickness and the beam spacing and watch the stress block decide: does the slab keep it shallow (a free wide rectangle), or does the block dive into the web where the overhangs start pulling their own weight?
The floor system
Ignoring the slab, the same steel would only reach φMn = kN·m.
MODULE 03 / LAB 3.1
Build the stirrup layout.
The shear diagram is tallest at the support; the concrete only ever points ½, and everything above φVc has to be caught by stirrups. You set a spacing for each quarter of the half span — the lab checks every zone and counts the steel. Goal: all four zones green, as few stirrups as possible.
The beam & load
Your spacing schedule
MODULE 03 / LAB 3.2
Twist it.
Twist a beam and the damage is sneaky: diagonal tension that spirals around all four faces. Concrete alone can take a little of it (up to Tcr); past that the section needs a corset — closed stirrups plus corner bars. Drag the torque, set your cage, and feel the three zones of torsion.
Twist the beam
MODULE 04 / LAB 4.1
Move the load around.
No column carries load alone — every real one carries load and moment together. Push the axial force Pu and the eccentricity e and watch the demand point wander over a live interaction diagram. The lesson: eccentricity doesn't just add moment, it steals axial capacity too.
The column
The load
Utilisation of the interaction capacity:
MODULE 04 / LAB 4.2
Push it to the edge.
A slender column bends under its own load: the bow adds deflection, the deflection adds moment, the moment bows it further. Pull the length and the load up and watch the magnifier δ stop growing gently — and start exploding as Pu closes on 0.75 Pc.
The column
The load
MODULE 05 / LAB 5.1
The grip.
A bar is only as strong as the length over which it can hand its force to the concrete. Pull a bar at As·fy and watch how far it must stay buried: change the bar size, tick "top bar", add epoxy, crowd the bars together — then see what a standard hook buys you when the geometry gives no room.
The bar & its conditions
MODULE 05 / LAB 5.2
The moment hill.
Bars cost money; moments fade toward the supports. So why not stop some bars early? Because a bar may only stop where the remaining bars can still carry the moment — and then it must run ld past that point. Slide the two cutoffs and keep the amber hill under the green staircase.