RC — Introduction & Material Properties

1.1 What is Concrete? What is Reinforced Concrete?

Concrete is a mixture of sand, gravel, crushed rock (or other aggregates) held together by a paste of Portland cement and water. Admixtures may be added to modify workability, durability, early strength, or set time. Like most rock-like materials, concrete has high compressive strength but very low tensile strength. Reinforced concrete pairs concrete with embedded steel reinforcing bars so the steel carries the tensile forces the concrete cannot.

Concrete = coarse aggregate + fine aggregate (sand) + cement paste, with rebar taking over wherever tension develops.

Plain vs reinforced concrete under a point load — the same beam that snaps brittlely in plain concrete carries load ductilely once rebar is added.

1.2 Advantages of Reinforced Concrete as a Structural Material

• High compressive strength per unit cost compared to nearly every other structural material.
• Fire and water resistance. Concrete cover shields the rebar from ordinary fires — after a typical fire the surface spalls but the structural core is intact.
• Rigidity. RC frames deflect and vibrate far less than steel or timber frames of equal span.
• Low maintenance and long service life. Concrete strength increases with age (continued hydration of the cement paste).
• Cast into any shape. Slabs, shells, arches, domes, folded plates — anything the formwork can hold.
• Uses inexpensive local materials. Only the cement and rebar need to be shipped in; sand and gravel are usually local.
• Lower-skill labor. Placing and finishing concrete needs a less specialized crew than a structural-steel erection team.

1.3 Disadvantages — and Their Practical Consequences

1. Very low tensile strength → reinforcing is mandatory wherever bending, shear, or restraint tension develops.
2. Formwork is expensive. Formwork and shoring can be one-third to two-thirds of the total cost of an RC structure — so economizing formwork (repeat bays, standard depths, flat soffits) is where most cost savings come from.
3. Heavy dead load. Low strength per unit weight → members get large, and dead-load moments dominate long spans. Lightweight aggregates can help.
4. Large member sizes reduce clear headroom and useable floor area, matters for tall buildings.
5. Property variability. Field-mixed/placed concrete varies more than shop-fabricated steel — mix design, curing, and inspection matter.
6. Shrinkage & creep. Long-term deformations from water loss and sustained load — see §1.11 below.

1.5 Concrete vs Structural Steel — When to Pick Which

Consideration	Favors Reinforced Concrete	Favors Structural Steel
Height	Low to mid-rise; increasingly competitive over 20 stories	Traditionally > 20 stories, though RC now competes
Speed of erection	Slower — cure time before form stripping	Faster erection sequence
Fire rating	Inherent — no extra fireproofing	Needs sprayed or board fireproofing
Foundations	Adds weight — needs good soil	Lighter — poor soil sites
Vibration/stiffness (e.g. hospitals, railway bridges)	Stiffer, better for vibration control	Springier
Short-span bridges	Very competitive (girders, box, slab bridges)	Long-span cable/truss

Notable RC records: the 74-story, 859-ft Water Tower Place (Chicago) — tallest RC building for many decades; the 1,465-ft CN Tower (Toronto) — tallest RC structure. Roughly 9 of 10 U.S. buildings are 3 stories or less and under 15,000 ft², where RC and steel are both viable choices.

1.6 Compatibility of Concrete & Steel

• Bond. Concrete adheres chemically to bar surfaces; deformations (ribs) rolled onto rebar force mechanical interlock. Slippage is negligible under service loads.
• Corrosion protection. The alkaline concrete cover passivates the steel — as long as the cover is intact and chlorides are kept out, the steel does not corrode.
• Thermal compatibility. α_steel ≈ 6.5×10⁻⁶/°F, α_concrete ≈ 4–7×10⁻⁶/°F (avg ~5.5). Because they expand almost the same amount, temperature changes don't shear the bond apart.
• Fire. Cover keeps rebar below its critical temperature — a 1½-in cover typically buys a 1-hour rating for beams.

1.10 Admixtures — Tuning the Concrete

Admixture	What it does	When to use
Air-entraining (ASTM C260/C618)	Introduces microscopic air bubbles; freeze–thaw & deicing-salt resistance	Any exterior slab, pavement, or freeze-exposed member
Accelerating (e.g. calcium chloride)	Faster early strength gain; earlier form removal	Cold weather. Never with embedded aluminum, galvanized forms, or prestressed steel — corrosion risk (ACI 3.6.3).
Retarding (acids, sugars)	Slows set; keeps concrete plastic longer	Hot weather; long pours; architectural exposed-aggregate finishes
Superplasticizer (organic sulfonates)	Very high workability at low w/c — either lower water or higher strength at same water	High-strength concrete, congested reinforcement, self-consolidating concrete
Waterproofing (soaps, asphalt emulsions)	Slows water penetration into porous concrete	Not a substitute for dense, well-cured concrete — treat as insurance only

1.11 Properties of Concrete

a) Compressive strength f'_c

Determined at 28 days on standard 6×12-in cylinders (or 4×8-in). Typical values:

Concrete class	f'c (psi)	Typical use
Ordinary	3,000 – 4,000	Beams, slabs, footings, walls
Prestressed	5,000 – 6,000	Precast/PT beams, bridge girders
High-strength	8,000 – 19,000+	Lower-story columns of tall buildings

Because the actual placed concrete varies, the mix must be designed for a higher average strength f'_cr > f'_c (see ACI §5.3). This is the overdesign factor a mix designer applies to hit the specified value reliably.

Family of concrete stress–strain curves (f'_c = 2–6 ksi). Key observations: (a) linear only up to ~⅓ to ½ f'_c, (b) peak stress near ε ≈ 0.002, (c) ACI assumes crushing at ε_cu = 0.003, (d) weaker concretes are less brittle (larger failure strain).

b) Static Modulus of Elasticity E_c

Concrete has no single "the" modulus — the curve is nonlinear. ACI adopts a secant modulus taken from the origin to the point ≈ 0.45f'_c (roughly the service-load stress):

Quick numbers (f'_c = 4,000 psi, normal-weight): E_c = 57,000·√4,000 ≈ 3,605 ksi. Compare with steel: E_s = 29,000 ksi — steel is ≈8× stiffer.

c) Modulus of Rupture (tensile cracking stress)

Quick number: f'_c=4,000 psi → f_r ≈ 474 psi — only ~12% of f'_c, and ~130× smaller than f_y of Grade-60 rebar. That gap is the whole reason we reinforce.

d) Shrinkage — water leaving hardened concrete

Fresh concrete needs more mixing water than the cement actually consumes (called hydration). The excess water evaporates over time and the paste contracts — the concrete shrinks and often cracks. Shrinkage continues for years but roughly 90% occurs in the first year. To limit it: (1) use the lowest workable water content, (2) cure well, (3) place in small pours with construction joints, (4) use shrinkage reinforcement (temperature & shrinkage steel — see the one-way slab chapter), (5) prefer dense, low-absorption aggregates.

e) Creep — deformation under sustained load

Under long-term compressive load, concrete keeps deforming after the instantaneous elastic shortening. This time-dependent extra strain is called creep (or plastic flow). Final creep is typically 2–3× the initial elastic deformation, and ~75% of it occurs in the first year. Practical consequence (Ch. 6): long-term deflections of RC beams are 2–3× short-term deflections — which is why ACI applies a multiplier to sustained-load deflections.

Shrinkage vs creep on a log-time axis. Shrinkage happens whether the member is loaded or not; creep only under sustained compressive load.

f) Tensile strength — small, brittle, but critical

Concrete's tensile strength is only about 8% – 15% of f'_c. The tensile strength does not vary linearly with f'_c; it varies approximately with √f'_c. Direct axial tension tests are impractical (grip stress concentrations, alignment problems), so two indirect tests are used: the modulus-of-rupture flexure test and the split-cylinder test.

Why don't we rely on concrete tension in design? Concrete cracks at such small tensile strain that the co-existing stress in the rebar would be tiny — so far below f_y that using it would be uneconomical. Once cracking occurs, the concrete has essentially no tensile strength and the rebar carries all of it. That is why the flexure and shear derivations you'll see next intentionally set the concrete tensile contribution to zero.

Third-point flexural test — plain concrete beam, span L, loaded to first bottom-face crack.

ACI's code value from hundreds of such tests: f_r = 7.5·λ·√f'_c (psi) — the same expression already introduced above.

Split-cylinder test — compressive P is applied along the length of the cylinder; failure occurs by a tensile split down the vertical diameter.

g) Shear strength — never measured in "pure" shear

"Pure" shear is nearly impossible to isolate in the lab because normal stresses always develop. Reported concrete shear strengths range from ⅓ to 4/5 of f'_c — a huge scatter. In design (Ch. 7), you'll see V_c written as a conservative multiple of √f'_c, not a fraction of f'_c, precisely to sidestep that scatter.

1.12 Aggregates & Lightweight Concrete

Aggregates occupy about ¾ of the concrete volume, so aggregate properties dominate concrete cost, workability, and strength. Fine aggregate passes a No. 4 sieve (¼″ openings); coarser material is coarse aggregate.

Maximum aggregate size (ACI 26.7.22.1(a)(1)) must not exceed:

• ⅕ of the narrowest form dimension,
• ⅓ of the depth of the slab, or
• ¾ of the minimum clear spacing between reinforcing bars.

Larger stones can be used only if the engineer is satisfied no honeycomb or voids will result. Aggregates must be strong, durable, clean — dust or clay coating destroys the paste-to-aggregate bond.

Concrete category	Air-dry unit weight	Notes
Normal-weight	≈ 145 pcf	Standard use; λ = 1.0
Structural lightweight (f'c ≥ 2,500 psi, wc ≤ 115 pcf)	90 – 115 pcf	Expanded shales/slag/fired clay aggregate
All-lightweight	lowest	Both coarse & fine LW; λ = 0.75
Sand-lightweight	intermediate	Only coarse is LW; λ = 0.85

Lightweight modifier λ. Because lightweight concrete has lower tensile capacity, ACI reduces every √f'_c term by λ. Linear interpolation is allowed between the tabulated values, or if the average splitting tensile strength f_ct is known:

λ affects f_r, V_c, coefficient of friction (shear-friction), and development length ℓ_d — a single factor that ripples through every RC chapter.

1.13 High-Strength Concrete (HSC)

Concretes with f'_c > 6,000 psi are called high-strength (or high-performance) concretes. Modern ready-mix trucks routinely deliver 9,000 – 10,000 psi, and lab mixes above 20,000 psi have been achieved. Landmark project: Two Union Square, Seattle, at 19,000 psi.

• Where it pays off: lower stories of tall building columns (loads up to 1,000+ kips), precast/prestressed girders, shear walls, offshore & long-span structures.
• What drives strength: low water–cement ratio (aided by superplasticizers), silica fume, well-graded strong & rough coarse aggregate, careful curing.
• Cost/benefit rule of thumb (from McCormac): a 12,000–15,000 psi mix costs ≈ 3× a 3,000 psi mix but delivers 4–5× the strength — favorable for column sizes and prestressed members.
• Design implications: β₁ decreases with f'_c (see the flexure chapter), so extra strength does not translate linearly into extra moment capacity. Also more brittle → detailing rules tighten.

1.14 Fiber-Reinforced Concrete (FRC)

Adding 1–2 % by volume of discrete fibers (steel, glass, plastic, or synthetic) does not significantly raise the compressive strength — instead it dramatically increases toughness, crack-width control, impact resistance, and fatigue life. Rebar reinforces in one direction; fibers reinforce in all directions, which is why FRC is popular for slabs on grade, industrial floors, shotcrete linings, thin shells, and pavements.

Property	Typical range
Fiber length	0.25 – 3 in
Fiber diameter	0.01 – 0.03 in
Aspect ratio ℓ/d	25 – 150 (≈100 average)
Volume dose	1 – 2 % of concrete volume

Steel fibers are most common (durable when protected by cover). Glass fibers must be alkali-resistant — ordinary glass deteriorates in cement paste. Toughness improvements are measured with ASTM C1018 third-point beam loading.

1.15 Concrete Durability

In many projects the compressive strength is dictated by durability, not by structural demand. ACI 318 Ch. 19 imposes exposure categories that limit w/c, require entrained air, and set minimum f'_c:

Exposure	Typical requirement
Freeze–thaw (F1/F2/F3)	Air entrainment + limit on w/c (max 0.45)
Deicing chemicals (F3)	Limit on fly-ash / pozzolan replacement
Sulfates (S1/S2/S3)	Type II or Type V cement + max w/c
Corrosion (C1/C2)	Increased cover, low w/c, admixtures, coated/stainless bars

1.16 Reinforcing Steel — Bars, Grades, and Areas

Reinforcement is supplied as plain or deformed bars (welded wire fabric is also used). Deformed bars — with rolled-on ribs — are used almost everywhere; plain bars are used only for spiral wrapping in columns. In the U.S. bar numbers equal eighths of an inch of nominal diameter: #4 = 4/8″ = 0.5″, #8 = 1″. Standard sizes are #3–#11, plus large sizes #14 and #18.

Grade	Minimum fy	εy = fy/Es	Where used
Grade 40	40 ksi (300 MPa)	0.00138	Older / small work
Grade 50	50 ksi (350 MPa)	0.00172	Some ties, stirrups
Grade 60 (default)	60 ksi (420 MPa)	0.00207	Almost all ordinary RC
Grade 75 / 80 / 100	75 – 100 ksi (520 – 700 MPa)	0.00259 – 0.00345	Heavily loaded columns/walls, special detailing

Bar cross-sectional areas — memorize the top row. #n bar area (in²) ≈ π·(n/16)² (check yourself: #8 → π·(0.5)² = 0.785, matches the tabled 0.79 in²).

Table 1.1 — Reinforcement Bar Sizes and Areas (inch-pound & soft-metric)

Bar No.	Diameter (in.)	Area (in²)	SI Bar No.	Diameter (mm)	Area (mm²)
3	0.375	0.11	10	9.5	71
4	0.500	0.20	13	12.7	129
5	0.625	0.31	16	15.9	199
6	0.750	0.44	19	19.1	284
7	0.875	0.60	22	22.2	387
8	1.000	0.79	25	25.4	510
9	1.128	1.00	29	28.7	645
10	1.270	1.27	32	32.3	819
11	1.410	1.56	36	35.8	1006
14	1.693	2.25	43	43.0	1452
18	2.257	4.00	57	57.3	2581

1.18 SI Bar Sizes & Material Strengths (ACI 318M)

• Bar numbers in ACI 318M = bar diameter in millimeters, rounded (so #10 ≈ 9.5 mm, #13 ≈ 12.7 mm — see Table 1.1 above).
• Yield strengths f_y: 300, 350, 420, 520 MPa — the metric equivalents of Grades 40, 50, 60, and 75.
• Concrete strengths f'_c: 17, 21, 24, 28, 35, 42 MPa — corresponding to 2,500, 3,000, 3,500, 4,000, 5,000, 6,000 psi.

1.19 Corrosive Environments — Extra Protection

In marine, deicing-salt, or industrial chloride environments the alkaline cover eventually breaks down and rebar corrodes. Corrosion products occupy ~2–3× the original steel volume, spalling the cover and destroying bond. ACI §20.5.1 requires increased cover, tighter w/c limits, and mix additives. Additional lines of defense:

• Epoxy-coated bars (ASTM A775) — handled carefully so the coating isn't chipped; development lengths must be lengthened (ψ_e factor in Ch. 7).
• Dual-coated bars (A1055) — zinc under epoxy, added to ACI 318 in 2011.
• Stainless-steel bars — highest cost, longest life (bridge decks, marine piers).
• Cathodic protection — sometimes retro-fitted to parking-garage slabs.

1.20 Identifying Marks on Reinforcing Bars

Every deformed bar carries four rolled marks. Learn to read them on site — a substituted grade or wrong bar size is a code violation waiting to happen.

ASTM standard rolled-on markings — every deformed bar carries mill, size, steel type, and grade.

📘 ACI 318-19 — the code you will live by

ACI 318-19 — Building Code Requirements for Structural Concrete (companion standard for every RC chapter)

Every equation in the next five chapters comes from ACI 318-19. Learn to navigate it: chapter numbers are stable across editions — Ch. 5 load combinations, Ch. 9 beams, Ch. 10 columns, Ch. 19 concrete properties (E_c, f_r), Ch. 21 strength-reduction factors φ, Ch. 22 sectional strength, Ch. 25 anchorage and development.