Cover, Spacing, and Pullout of Reinforcement for an Experimental Beam
An Experiment in Reinforced Concrete
We are about to finish our `Code Checks' for our experimental beam. Code checks are not just `madness'; they have relevance; they are protecting us from something bad. Proper cover means the rebar will be protected (from fire, damage, other stuff), as well as help ensure the bars are developed. Likewise with spacing. If the bars are spaced too close to one another the concrete may not develop the bars; worse yet, if spaced too closely, the concrete may not properly cover or consolidate around the bars (aggregate may get `hung up' at the bars). And finally, we will do the pullout calc, to make sure the demand on the reinforcement doesn't grow faster than what the concrete bond can deliver at the rebar ends (where the need for rebar theoretically vanishes). Here goes ...
1. Cover
The ACI Code (Sec. 7.7) requires that the reinforcement in cast-in-place beams have at least 1.5 in. of cover. (See, also, pages 374-5 of your Ambrose text).
The reinforcement for our example experimental beam is centered 2 in. from the bottom. The closest concrete surface is the bottom of the beam. The minimum available cover is, then, 2 in. minus ½ of the diameter ... 2.0 in. - ½ of ¾ in. = 1-5.8 in. Since this is not less than 1.5 in. ... GOOD!
2. Spacing
Spacing requirements are covered in Section 7.6 of the ACI Code ...
7.6.1 - the minimum spacing between parallel bars in a layer shall be db, but not less than 1.0 in.
7.6.2 - where parallel reinforcement is placed in two or more layers, bars in the upper layers shall be placed directly above bars in the bottom layer with clear distance between layers not less than 1.0 in.
So, in our example, with ¾ in. diameter rebar, we end up needing 1.0 in. clear spacing between bars in a layer, and between layers. In our example we only have one bar, so ... not applicable to our example at hand.
3. Pullout
This pullout thing is covered in Section 12.11 of the Code and also ... here (equation in Item 3 and example in Item 5).
Pullout is prevented if the length available at the section of interest (in this case the ends of the beam) if the (bar is small enough so that the) development length of the bar does not exceed ...
... (1.0 or 1.3) Mn / Vu + la,
where
... the 1.0 or 1.3 represents a 30% increase if the reaction produces compression in the concrete at the support,
... Mn is the nominal bending strength at the location of interest (the ultimate condition of concrete crushing and steel yield, but this time examined at the end, not the mid-span) ...
... Vu = the factored shear at the section ... in this case the shear associated with the load that brings our beam to failure; and ...
... la is the amount of bar lap past the center of the support ... in our example, 2 in. (So, even though it's less than `Code' ... we still benefit from it.)
Here goes ...
... we'll use the 1.3 since our reaction does produce compression across the concrete at the supports ...
... Mn = 179,400 lb-in. ... from early on in this example (here) ... (and note how I left it in the lb-in. units) ...
Since we're looking at pullout in the condition of ultimate flexure failure, we'll use the P that causes that to determine our shear; likewise we use the actual self weight; so,
Vu = ω self weight (L/2) + Pult / 2 = ... with the self-weight and Pult values also from that lesson ...
Vu = 54.4 lb/ft (6 ft / 2) + 10,100 lb/2 = 163 lb + 5,050 lb = 5213 lb.
And ℓd = 17 in. ... from a lesson or two ago (here) ( ... for our example experimental beam ... # 6 bar, 4000 psi concrete, and so on).
So, ...
... is ℓd = 17 in. ≤ 179,400 lb-in. / 5213 lb + 2 in. = 34 in. + 2 in. = 36 in. ???
Yes, good.
So, we don't anticipate the reinforcing pulling out.
References
Building Code Requirements for Structural Concrete, ACI 318, American Concrete Institute, P.O. Box 9094, Farmington hills, Michigan, 48333.
Simplified Engineering for Architects and Builders, Ambrose, J. and P. Tripeny, 10th edition, John Wiley & Sons, Hoboken, New Jersey.
Basement Retaining Wall Design Continued, Jeff Filler, Associated Content.
Strength and Deflection Calculations for an Experimental Beam, Jeff Filler, Associated Content.
Development Length for an Experimental Beam, Jeff Filler, Associated Content.
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