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Contents | 1. Introduction to structural design | 2. Loads | 3. Wood | 4. Steel |

Introduction to reinforced concrete | Material properties | Sectional properties | Design approaches | Construction systems | Tension elements | Columns | Beams |

Reinforced concrete elements are not ordinarily "connected" in the usual sense of the term; rather, they are most often cast together into a monolithic assembly. Of course, there are construction joints between sections of the structure cast separately, but even at such joints, opposite faces of concrete brought together in compression bear against each other just as if they had been monolithically cast; and steel reinforcement in tension is made to extend through each construction joint so that tensile forces in the bars continue from one side of the joint to the other.

The following discussion therefore does not include any reference to the types of welds, bolts, screws, or nails commonly found in wood or steel construction, where discrete structural elements subjected to tension, compression, or bending must be explicitly connected in order to function together as a coherent structural system. Instead, two "quasi-connections," both typical of reinforced concrete construction, shall be examined: the end condition of a continuous beam, and the lapped splicing of reinforcing bars where the bottom of one column is cast against the top of another column.

The fact that much reinforcing steel is subjected to tension raises an important question: what prevents such steel bars from being pulled out of, or slipping within, the concrete into which they have been placed? As can be seem in Figure 5.48, any bending of a structural element literally stretches the tension region while the compression region shortens.

Figure 5.48: Extension of rebar in tension zone of reinforced concrete element

If the surface between the reinforcing bars and adjacent concrete were smooth and frictionless, the bars would remain "unstretched" as the beam bent; in general, it is the bond between the steel bars and concrete that guarantees that such slippage will not occur. This bond is primarily a result of bumps, or deformations, placed on the surface of the reinforcement that create a mechanical interlocking of the steel and concrete surfaces, as shown schematically in Figure 5.49.

Figure 5.49: Schematic representation of a deformed reinforcing bar (rebar)

The strength of this bond, per unit of bar
length, has been measured experimentally, so
the total necessary bar length required to resist
any tendency for the bar to be pulled through
the concrete can be determined for any given
tension stress. This required bar length is called
the development length, *l _{d}*, and is shown in
Equation 5.29 for No. 7 or larger uncoated bars with normalweight concrete and adequate bar spacing, or adequate spacing plus confinement with ties or stirrups, to prevent splitting of the concrete. Specifically, as illustrated in Figure 5.50, the bars must have a clear space between them at least equal to twice the bar diameter, that is, at least equal to 2

Figure 5.50: Clear cover and spacing requirements for reinforced concrete beams

Alternatively, if adequate stirrups or ties are used throughout the development length region to confine the bars and prevent splitting of the concrete, the minimum clear spacing requirement may be reduced to *d _{b}*.

(5.29)

In Equation 5.29, *l _{d}* is the development length for tension (in.),

Development length is influenced primarily by three factors: assuming adequate bar spacing and/or ties to prevent splitting of the concrete, the required development length becomes larger if the tensile strength of the concrete decreases (concrete's tensile strength is proportional to the square root of its compressive strength); the required development length also increases if the stress in the bar increases (that stress being at most equal to the yield stress of the steel); and the development length increases as well if the surface area of the bar decreases (the surface area being proportional to the bar diameter). These three parameters can all be found in Equation 5.29.

If we imagine an isolated and discrete concrete beam within a continuous concrete structure, it is easier to see where and how the concept of development length becomes important. As can be seen in Figure 5.51, a typical reinforced concrete beam-girder "connection" must resist the shear force and bending moment that occur at the surface where they come together. The shear force is resisted through the shear resistance of the concrete itself, the longitudinal steel bars, and the steel ties or stirrups provided for that purpose (the latter not shown in Figure 5.51 for clarity).

Figure 5.51: Development length of straight bars and standard hook: (*a*) section through typical slab and girder; (*b*) exploded view showing "connection" between beam and girder (with slab omitted for clarity); and (*c*) required development length of hook (in girder) and straight bar (in beam)

The bending moment, in turn, is resolved into a compressive force (the resultant of the stress distribution
shown below the neutral axis for "negative" bending) and a tensile force (carried by the
longitudinal steel reinforcement shown above the neutral axis). The compressive force presents no
particular problems, as the concrete in the beam "pushes" against the concrete in the girder. The
tensile force, however, could pull the bars out of the girder and beam, unless those bars develop sufficient bond with the concrete to resist that tendency or are otherwise anchored into the concrete.
In the case of the beam, sufficient space is available to develop that bond strength by making
sure that the bars extend into the beam for a distance at least as great as the required development
length, *l _{d}* (see Equation 5.29). For an exterior girder, however, it is likely that sufficient space is not available, and a 90° or 180° hook is often required.
As shown in Figure 5.51

(5.30)

In this equation, *l _{dh}* is the development length for hooks (in.),

It is possible to reduce this length if certain requirements are met that increase the level of confinement
of the hook or provide more concrete cover, making it less likely to split the concrete: First,
the tabular values for development length can be divided by 1.6 if the centerline spacing between
hooked bars is at least 6*d _{b}* or if the total area of ties or stirrups confining the hooked bars is not less than 0.4 times the total area of the hooked bars. Second, the tabular values for development length
can be divided by 1.25 if the cover on the side of the hooked bars (i.e., perpendicular to their longitudinal
direction) is at least equal to 6

** Problem definition.** A reinforced concrete beam
frames into an exterior girder, as shown in Figure
5.52, and the negative moment at the connection
is resisted using No. 8 bars with 6 in.
clear spacing between them. The required area
for each bar = 0.74 in

Figure 5.52: Required rebar development length for Example 5.9

** Solution overview.** Find the nominal development lengths for a No. 8 bar, using 4000-psi concrete, in
Appendix Table A-5.10 (for the beam) and Appendix Table A-5.11 (for the hook in the girder). Multiply
these base values by the appropriate factors shown in the notes below each table.

*Problem solution*

**1.** The nominal development length required for the No. 8 bar in the beam is 62 in. (Appendix Table A-5.10). This value is not divided by 1.3 (see Note 2) and also can be reduced by the ratio
of required steel bar area to provided steel bar area = 0.74/0.79 = 0.937 (see Note 3), so that
the final value for the required development length, *l _{d}* = 62(0.937) = 58.1 in. or, rounded up to the nearest inch, 59 in. The required area for each bar = 0.74 in

**2.** The nominal development length for the 90-degree hook in the beam is 30 in. (Appendix Table A-5.11). This value can be modified as follows: it can be divided by 1.6 since the 6 in. centerline spacing of the hooked bars is no less than 6*d _{b}* = 6 in. (see Note 4 in Appendix Table A-5.11); and it can be divided by 1.25 since the side cover is no less than 6

There are two other requirements for tension reinforcement in continuous beams. First, for so-called
positive-moment reinforcement — where tension occurs at the bottom of reinforced concrete
beams — one-fourth of the rebars need to be extended at least 6 in. into the supports at each end
of the beam. Second, for negative-moment reinforcement — where tension occurs at the top of the
beam, typically in the vicinity of supports — at least one-third of the rebars need to extend beyond
the point of inflection (where the negative moment becomes zero and the curvature changes from
negative to positive) a distance of either *d*, 12*d _{b}*, or

For a steel reinforcing bar in compression, much of the stress in the steel can be transferred to the
concrete through direct bearing of the bar end on the concrete. For that reason, the required development
length in compression, *l _{dc}*, is smaller than that required when bars are stressed in tension,
and is given by the greater of the following values:

(5.31)

In these equations, *l _{dc}* is the development length (in.) for normalweight concrete in compression;

Since the length of reinforcing bars is limited by manufacturing and transportation constraints, it is
often necessary to splice them together, at least in cases where the continuity assumed in design
indicates lengths greater than those available from a single bar. While it is possible to weld bars together,
or to use special mechanical splicing devices, the most common method for creating continuity
between two bars in tension is by lapping them a sufficient distance so that tensile stresses can be
transferred through the bond developed between the steel bars and adjacent concrete. For virtually
all tension splices, the required lap distance is taken as 1.3*l _{d}*, where the development length,

Columns are almost always cast floor by floor, with longitudinal reinforcement left extending vertically
beyond the current floor level, so that it can be spliced into the column steel for the next floor
being cast. For *f _{y}* ≤ 60 ksi and

required compressive lap distance = 0.0005*f*_{y} *d*_{b}

(5.32)

This required lap distance equals 30*d _{b}* for 60 ksi steel bars, with an absolute minimum lap distance of 12 in. For rebars with

Figure 5.53: Column lap splice parameters

For a column resisting only compressive forces, the required lap length is determined for the bars
originating in the upper column; the bars extended upwards from the lower column that terminate
in the upper column must satisfy the requirements for compressive development length (Equation
5.31). In practice, the larger of these two criteria (compressive development length for the lower
bars and required lap splice length for the upper bars) determines the minimum splice length. Since
loads typically are smaller in upper-level columns, it is possible that smaller bars sizes can be used
in the upper columns; these smaller bars can be spliced with larger bars extending upward from
the lower column. In such cases, different bar diameters, *d _{b}*, must be used in determining lap splice length and development length.

** Problem definition.** A 12 in. × 16 in. reinforced concrete column is configured as shown in Figure 5.53.
The longitudinal (vertical) bars in the lower column consist of four No. 9 bars, which extend into the
upper column. Four No. 8 bars originate in the upper column, and are spliced to the lower column
bars as shown. The longitudinal steel is confined by No. 3 ties spaced at 9 in. on center. Assuming
only compressive stress in the column, with

** Solution overview.** Find the compressive lap splice length based on the diameter of the No. 8 bars in the upper column. Find the required compressive development length based on the No. 9 bars extended into the upper column. Use the larger of these two values for the column splice length.

*Problem solution*

**1.** Lap splice. From Equation 5.32, the minimum lap splice length for the No. 8 bars = 0.0005*f _{y}*

**2.** Development length. From Equation 5.31, we get:

The bar diameter, *d _{b}*, is found in Appendix Table A-5.2. Using the larger value and rounding up, the minimum development length,

**3.** Comparing the requirements for lap splice length and development length, the larger of the two values will be used: 25 in.

© 2020 Jonathan Ochshorn; all rights reserved. This section first posted November 15, 2020; last updated November 15, 2020.