Two unjointed 6-inch slabs are placed under identical conditions over identical bases using identical materials and methods. One slab contains continuous deformed 4x4-4/4 welded wire reinforcement under 1 inch of cover; the other #4 deformed bars at 12 inches both ways under 1½ inches of cover. If post-installation treatments and environments also are identical, which slab will develop tighter, more closely spaced cracks?
Per Rule 14a (see the July issue), each layer of the 4-gage mesh (in each direction) has R% (percent reinforcement) values of 0.167, and each layer of the #4 mat has R% values of 0.272. Per Rule 14h (see the August issue), the top layers of both the WWR and #4 rebars have crack inducement ability (Ai) values of about 1.82. But the bottom layer of the WWF (being slightly deeper in the slab) has an Ai of 1.49, while the bottom layer of #4s has an Ai of only 0.88.
With their top layers having nearly identical Ai values, both reinforcements should produce simliar crack spacings and crack widths in the directions of their top layers. In the directions of their bottom layers, however, because the bottom layer of the WWR has a much larger Ai value than the bottom layer of the #4 mat, the mesh should produce much smaller crack spacings and much tighter cracks than the rebars.
Ignoring overlaps and splices, the 4-gage mesh weighs 0.85 psf, while the mat of #4s weighs 1.33 psf. If the costs per ton installed are the same, then the WWR reinforcement is not only the better technical choice, but also the more economical one.
Rule No. 14i: To maintain a joint’s vertical stability under wheeled traffic, the joint must be fitted with mid-depth dowels.
Owing to the appreciable joint growths (typically, 0.0005 times the joint spacing) induced by the panels’ shrinkage and curling, formed keys at construction joints and “aggregate interlock” at control joints are both useless for preventing joint rocking. Mid-depth dowels are the only reliable approach.
Rule No. 14j: For both construction and control joints, the appropriate spacingSdfor mid-depth steel dowels is given by the smaller of 15568As/(f´c½t) or 3t, whereAsis the cross sectional area of the dowel at the joint line,tis the slab thickness in inches, andf´cis the compressive strength of the concrete.
The first expression in Rule No. 14j equates the shear strength of the dowels to the shear strength of the unbroken slab, while also assuming that the dowels will remain perfectly embedded and subjected only to simple shear. The second provision—which limits the dowel spacing in all cases to three times the slab thickness—recognizes the highly localized action of each dowel and limits significant relative cross-joint movements between the dowels.
For a 5-inch-deep 3000-psi slab to be doweled with ½-inch-diameter smooth round steel bars, the rule’s first expression requires a dowel spacing of 11 inches. For a 6-inch-deep 4000-psi slab to be doweled with ¾-inch-diameter smooth round steel bars, both rule provisions set the spacing at 18 inches. For an 8-inch-deep 4500-psi slab to be doweled with ¼-inch-thick 4½-inch square plate dowels (fitted at 45 degrees to the joint line), the second three-times-slab-thickness limit keeps the spacing at 24 inches, even though the first expression would allow a 46-inch spacing.
Rule No. 14k: Bar dowels through construction joints should be 12 inches long. Bar dowels through control joints should be 18 inches long.
Because of the lifting and counter rotation of the abutting slab elements that inevitably occurs at every joint due to curling, the use of embedded steel dowels is problematic. The minimum dowel lengths given in Rule No. 14j ensure the dowels, if centered on the joints, will retain sufficient effectiveness.
Rule No. 14l: The ideal dowel would be a hinge.