- Eurocode 8: Structural types
- Eurocode 8: Ductility class
- Eurocode 8: Structural regularity
- Member reinforcement details correlation
- Eurocode 2: Modulus of Elasticity
- Design Compressive and Tensile Strengths
- Stress-strain relations
- Crack Control according to Eurocode 2
- Crack Control without calculation
- ACI 318-11: Minimum thickness of beams and one-way slabs
- ACI 318-11: Reinforced concrete beam design parameters
- ACI 318-11: Shear reinforcement
- Eurocode 8: Behavior Requirements
- Eurocode 8: Design spectrum
- Importance classes for buildings
- ACI 318-11: Development length for reinforcement
- Eurocode 8: Ground types
- Eurocode 2: Crack width calculation

Reinforcement Ratio

The amount of steel reinforcement in concrete members should be *limited*. Over-reinforcing (the placement of too much reinforcement)** **will not allow the steel to yield before the concrete crushes and there is a sudden failure.

The reinforcement ratio in concrete beam design is th following fraction:

The reinforcement ratio , ρ, must be less than a value determined with a concrete strain of 0.003 and tensile strain of 0.004 (minimum). When the strain in the reinforcement is 0.005 or greater, the section is tension controlled. (For smaller strains the resistance factor reduces to 0.65 because the stress is less than the yield stress in the steel.)

Maximum Reinforcement

Based on the limiting strain of 0.005 in the steel, *x(or c) = 0.375d *so

α = β_{1 }(0.375d) to find As-max

The values of β_{1 }are presented in the following Table:

Minimum Reinforcement

Minimum reinforcement is provided even if the concrete can resist the tension, in order to control cracking.

Minimum required reinforcement:

but not less than

where:

f_{y} is the yield strength in psi

b_{w} is the width of the web of a concrete T-Beam cross section

d is the effective depth from the top of a reinforced concrete beam to the centroid of the tensile steel

Cover for Reinforcement

Cover of concrete over/under the reinforcement must be provided to protect the steel from corrosion. For indoor exposure, 1.5 inch is typical for beams and columns, 0.75 inch is typical for slabs, and for concrete cast against soil, 3 inch minimum is required.

Bar Spacing

Minimum bar spacings are specified to allow proper consolidation of concrete around the reinforcement. The minimum spacing is the maximum of 1 in, a bar diameter, or 1.33 times the maximum aggregate size.

Effective width b_{eff}

In case of T-Beams or Gamma-Beams, the effective slab can be calculated as follows:

For *interior *T-sections, b_{eff}* *is the smallest of:

*L/4, bw + 16t, or center to center of beams*

For *exterior *T-sections, *bE *is the smallest of

*bw + L/12, bw + 6t, or bw + ½(clear distance to next beam)*

When the **web **is in tension the minimum reinforcement required is the same as for rectangular

sections with the web width (*bw*) in place of *b*.

When the **flange **is in tension (negative bending), the

minimum reinforcement required is the greater value of

where:

f_{y} is the yield strength in psi

b_{w} is the width of the web of a concrete T-Beam cross section

b_{eff} is the effective flange width

Compression Reinforcement

If a section is *doubly reinforced*, it means there is steel in the beam seeing compression. The force in the compression steel that may not be yielding is

*Cs = As´(f´s - 0.85f´c) *

The total compression that balances the tension is now: *T = Cc + Cs*.

The moment taken about the centroid of the compression stress is *Mn = T(d-a/2)+Cs(a-d’) *

where *As*‘ is the area of compression reinforcement

*d’ *is the effective depth to the centroid of the compression reinforcement

Because the compression steel may not be yielding, the neutral axis *x *must be found from the force equilibrium relationships, and the stress can be found based on strain to see if it has yielded.

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