ACI 318/Reinforced Concrete

LRFD strength reduction factor (Phi)

• ACI Table 21.2.1

• 0.75 for shear

• Typically 0.9 for flexural but depends on additional calc and ranges from 0.65-0.9

  • Need to use Table 21.2.2 to determine based on strain values

  • To determine strain value, use similar triangles from stress block in Diagram/Figure below ACI Table or in Handbook

    • et = ecu * (d-c) / c

    • c can then be found based on Beta value in Handbook Concrete section definitions table with compressive strength values

      • Beta = a / c, so c = a / Beta

      • And a can obviously be calculated from main equation in Handbook a = AsFy/.85f’cb

Section strength letter

• Phi letter n

• M for flexural

• V for shear

• T for torsional

• P for axial

Ultimate/factored section demand letter

• Letter u

• M for flexural

• V for shear

• T for torsional

• P for axial

Total Concrete Shear strength

• 22.5

• Vn = Vc + Vs

Concrete shear strength

• 22.5.5

• Vc = 2*sqrt(f’c)*bw*de

Steel shear strength

• 22.5.8

• Vs = Av * fy * de / s

• Have to iterate for this unless bar size and ultimate shear demand already given, then just solve Vn = Phi(Vc + Vs) for Vs using Vn = Vu

• Max = 4*sqrt(f’c)*bw*de

  • Because equation used for max shear reinforcement/stirrup spacing from Table 9.7.6.2.2

Lambda

• Concrete weight reduction factor

• 1.0 for normal weight

• 0.75 for lightweight

Required spacing of shear reinforcement/stirrups

• 22.5.8.5.3

• Note, uses nominal steel shear strength

Weight of normal weight concrete

150pcf, page 34

Weight of lightweight concrete

115pcf, ACI 318, page 33

Over reinforced concrete beam failure

• Over reinforcing a concrete beam will result in sudden crushing failure on the compression side of the beam, which is unsafe and not recommended

• Instead, we want the steel tensile strength on the tension side of the beam to be less than the compressive strength of concrete so the steel yields first which allows a slower, safer failure

Deformed rebar

Steel bars with ribbed edges to enhance grip/tension with concrete

Max aggregate size

• ACI 26.4.2 part 5, chapter 26 construction documents and inspection will be a fraction of the distance b/t forms, slab thickness or clear spacing b/t rebar

• Intent is to allow wet concrete workability to prevent air pockets and honeycombing

Interaction

• When a component is under both tension/moment and shear loads, most typical for an anchor bolt

• V/Vallow + T/Tallow < 1.0

• ACI 17.6 - Anchoring to Concrete, Interaction of Tensile and Shear Forces

  • ACI states throughout pretty much each design section of the codebook that interaction must be considered when it applies

• AISC pg 15-5 has this equation

(Icr) Cracked Moment of Inertia

• ACI 11.8.3.1 chapter 11 is walls

  • For a beam zero out the Pu term completely there no axial load

• Icr considers a more realistic I for cracked concrete, taking 2 blocks/sections (a tension and compression) into account

  • Transforms rebar area into equivalent concrete area

• Icr technically derived from parallel axis theorem, didn’t spend time to figure out derivation though

Distance from top compression fiber to neutral axis

• c = kd = a/Beta

  • kd is in Handbook 4.3.2.3 diagram where it gives kd/3 instead of c/3

    • k and j are just random factors for the stress block

  • Can use kd whenever a and Beta can’t be determined

Flexural Strength

Use Handbook, Mn equations dependent on controlling/lower value of allowable concrete compressive strength f’c or rebar tensile yield strength fy

Punching shear failure mode

• This failure is like someone literally punched through something, so the strength actually lies in the perimeter of the material and the depth of the material

• Punching shear strength = concrete shear strength * critical perimeter (b0) * effective depth (de)

  • ACI 22.6.4.1 describes critical perimeter

Stirrups

• Only help in shear strength, not bending

• And vice versa with tension bars that only help in bending, not shear

Meaning of Rebar Markings

• First letter/symbol is the manufacturer

• The first number is the bar size/#

• The second letter is the steel type

  • S = Carbon steel A615

    • Stronger than A706

  • W = Low alloy steel A706

    • Higher ductility so better for seismic than A615 and better weldability than A615

  • A = Axle steel A996

  • SS = Stainless steel A955

  • CS = low carbon chromium A1035

• The second number is the grade mark or the yield strength like 60ksi

Strap footing

• A strap footing is really like a reinforced concrete beam installed over spray foam between (2) spot footings. Its purpose is to make the two footings act uniformly so that the total force from both footings is combined and the pressure under each footing is equivalent, and equal to the total Force divided by the total footing/bearing area (not including the strap footing area obviously)

Required flexural strength of footing supporting column with given axial load

• Get Pressure = column Force / footing Area

• Now think of punching shear and where footing would fail, at column edges. The footing portions not below the column would experience an upward curling movement like cantilevered beams

• So find Mmax for a theoretical cantilevered beam (Mmax = w * l² / 2 per handbook), where l = largest footing edge not below column = (largest footing width - column width) / 2

• That is the Mmax per foot, for a 1’ wide strip of the concrete footing. To get the required flexural strength for the whole thing we would multiply Mmax by the other footing width direction

Minimum rebar

• Typically this will be 0.0018 * Ag, where Ag is the gross area of concrete section = width times thickness/depth

Flexural demand on heel of retaining wall

• Critical section is at transition from heel to wall edge, per usual, where the heel would break off

• Do sum of moments at critical section considering heel weight, soil weight, and any surcharge load

  • Note that per ACI 5.3.8 if lateral earth pressure (retained soil) is present, it should have a 1.6 load factor

Concrete mix design

• Type 1 = Normal application

• Type 2 = Sea water exposure

• Superplasticizer = reduces water/cement ratio so more durable and less permeable, good for coastal exposure, also enhances workability

• Chemical accelerator = accelerates curing time and increases early strength, BAD for coastal

How to determine max factored negative moment in a continuous one way slab spanning across 5 integrated concrete beams with dead/live load psf provided?

• Table 6.5.2 from Chapter 6 Structural Analysis, 6.5 Simplified Method of Analysis for Nonprestressed Continuous Beams and One Way Slabs

• Have to first verify all parameters in 6.5.1

• Then just use table and most conservative equation (that would create the highest/maximum moment)

  • See subnote 1 that ln is the avg of the adjacent CLEAR SPANS