The work package for a slab on grade includes the concrete for the slab, the area to be finished, forms, and rebar or wire mesh. The concrete is treated as a volumetric good, the forms are treated as a linear component, rebar is treated as a linear component, and wire mesh is treated as a sheet good. The quantity takeoff for a slab on grade is shown in the fol- lowing examples.
EXAMPLE 5-8
Determine the volume of concrete in cubic yards, the area to be finished, the lineal feet of forms, and number of 20-foot bars of #4 rebar needed to complete a slab on grade 100 feet long by 40 feet wide. The slab is reinforced with #4 rebar at 18 inches on center.
⫽ 64.34 ft2
⫹ (16 ft ⫺ 2 ⫻ 1 ft 4 in)(1 ft) Area⫽ 2(16 ft)(1.5 ft) ⫹ 2(1 ft)(1.5 ft)
Area⫽ 2(Area of Side) ⫹ 2(Area of End) ⫹ Area of Bottom Volumewith Waste⫽ (0.89 yd3)a1 ⫹
5 100b ⫽ 0.93 yd 3 Volume⫽ 0.89 yd3 ⫽ (16 ft)(1.5 ft)(1 ft)a1 yd 3 27 ft3˛˛b Volume⫽ (Length)(Width)(Thickness)
BEAMS
The same principles that were used to determine the quan- tity of concrete, forms, and rebar for footings, columns, and walls can be used for determining the quantities for beams.
FIGURE 5-17 Beam Section
EXCEL QUICK TIP 5-6 Slab on Grade with Rebar
The volume of concrete and the number of bars of rebar needed for a slab on grade are set up in a spreadsheet by entering the data and formatting the cells as follows:
A B C 1 Slab Length 100 ft 2 Slab Width 40 ft 3 Slab Thickness 4 in 4 Waste 12 % 5 Bar Spacing 18 in 6 Bar Size 4 # 7 Bar Length 20 ft 8 Lap 36 # of dia. 9 10 Area 4,000 sft 11 Volume 55.31 cyd 12 No. of Bars 299 each
Include 12% waste in the calculated volume of concrete, and express the volume of concrete in quarter-yard increments. Provide 36 bar diameters of lap on the rebar.
Solution: The volume of concrete is calculated as follows:
Add the waste using Eq. (4-22) as follows:
Rounding up to quarter-yard increments, we get 55.50 cubic yards. The area to be finished is calculated as follows:
The length of the forms is calculated as follows:
The number of 100-foot-long bars needed to cover the slab in the long direction is calculated using Eq. (4-1) as follows:
The number of 40-foot-long bars needed to cover the slab in the short direction is calculated using Eq. (4-1) as follows:
Number⫽100 ft 1.5 ft ⫹ 1 ⫽ 68 bars Number⫽ 40 ft 1.5 ft⫹ 1 ⫽ 28 bars ⫽ 280 ft ⫽ 2(100 ft) ⫹ 2(40 ft)
Length⫽ 2(Length of Side1)⫹ 2(Length of Side2)
Area⫽ (100 ft)(40 ft) ⫽ 4,000 ft2 Volumewith Waste⫽ (49.38 yd3)a1 ⫹
12 100b ⫽ 55.31 yd 3 ⫽ (100 ft)(40 ft)(4 in)a 1 ft 12 inba 1 yd3 27 ft3b ⫽ 49.38 yd 3 Volume⫽ (Length)(Width)(Thickness)
The total length of rebar is calculated as follows:
The lap is 18 inches (36⫻ 0.5 in) or 1.5 feet. The number of 20-foot bars is calculated using Eq. (4-6) as follows:
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Number⫽ 5,520 ft
(20 ft⫺ 1.5 ft) ⫽ 299 each
EXCEL QUICK TIP 5-7 Wire Mesh–Reinforced Slab on Grade
The volume of concrete and the number of rolls/sheets of wire mesh needed for a slab on grade are set up in a spreadsheet by entering the data and formatting the cells as follows: A B C 1 Slab Length 100 ft 2 Slab Width 40 ft 3 Slab Thickness 4 in 4 Waste 12 % 5 Wire Mesh Length 150 ft 6 Wire Mesh Width 5 ft 7 Wire Mesh Lap 6 in 8
9 Area 4,000 sft 10 Volume 55.31 cyd 11 Wire Mesh 7 each
EXAMPLE 5-9
Determine the number of 150-foot by 5-foot rolls of wire mesh that would be needed for the slab in Example 5-8 if the #4 rebar were re- placed by wire mesh. The wire mesh will need to be lapped 6 inches. Solution: Run the rolls the long direction in the slab. Using the row and column method, determine the number or rows of wire mesh needed to cover the 40-foot width of the slab using Eq. (4-12) as follows:
The number of columns is calculated using Eq. (4-15) as follows:
The number of rolls is calculated using Eq. (4-18) as follows:
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Number⫽ (9 rows)(0.67 columns) ⫽ 6.03 rolls NumberColumns⫽ 100 ft (150 ft⫺ 0.5 ft) ⫽ 0.67 columns NumberRows⫽ 40 ft (5 ft⫺ 0.5 ft) ⫽ 9 rows
RAISED SLABS
The estimating of raised slabs is similar to the estimating of slabs on grade, with two exceptions. First, the thickness of the slab may vary because the bottom of the slab is poured over an intentionally uneven surface (such as a metal deck) and because the structure supporting the slab may sag under the weight of the concrete, making the slab thicker at the center of the spans than near the supports. To account for the uneven surface of the deck, the average slab thickness must be determined.
For the metal deck shown in Figure 5-18, the average thickness is determined by the following equation:
(5.1)
where
T⫽ Distance from Top of Slab to Top of Metal Deck W1⫽ Width of the Metal Deck Cell at the Top W2⫽ Width of the Metal Deck Cell at the Bottom
D⫽ Depth of the Metal Deck Cell S⫽ Spacing of the Metal Deck Cells
TAve⫽ T ⫹ (W1⫹ W2) (D)
2S
FIGURE 5-18 Metal Deck The following formulas need to be entered into the
associated cells: Cell Formula B10 =B1*B2 B11 =(B1*B2*(B3/12)/27)*(1+B4/100) B12 =ROUNDUP((ROUNDUP(B1*12/B5+1,0)* B2+ROUNDUP(B2*12/B5+1,0)*B1)/ (B7-B8*(B6/8)/12),0)
The data for the slab is entered in Cells B1 through B8. The data shown in the foregoing figure is from Example 5-8.
The following formulas need to be entered into the associated cells: Cell Formula B9 =B1*B2 B10 =(B1*B2*(B3/12)/27)*(1+B4/100) B11 =ROUNDUP(ROUNDUP(2*B2/(B6-B7/ 12),0)/2*B1/(B5-B7/12),0)
The formula for Cell B11 rounds the number of rows up to the nearest half row. The data for the slab is entered in Cells B1 through B7. The data shown in the foregoing figure is from Example 5-9.
FIGURE 5-19 Metal Deck Dimensions
EXAMPLE 5-10
A 100-foot by 50-foot by 3-inch-thick slab is poured over the metal deck shown in Figure 5-19. The depth of the slab is measured from the top of the slab to the top of the metal deck. Determine the aver- age thickness of the slab and the number of yards of concrete needed to pour the slab. Add 10% waste.
Solution: The average thickness is determined using Eq. (5-1) as follows:
The volume of concrete is calculated as follows:
Add the waste using Eq. (4-22) as follows:
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Volumewith Waste⫽ (59.80 yd3)a1 ⫹
10 100b ⫽ 65.78 yd 3 ⫽ (100 ft)(50 ft)(3.875 in)a 1 ft 12 inba 1 yd3 27 ft3b ⫽ 59.80 yd 3 Volume⫽ (Length)(Width)(Thickness) TAve⫽ 3 in ⫹ (4 1>2 in ⫹ 2 1>2 in)(1 1>2 in) 2⫻ 6 in ⫽ 3.875 in
The amount of concrete needed to account for the sag is a function of how much a structure deflects under the weight of the concrete as it is being poured. This additional concrete is treated in the same manner as waste; identify the historical amount of concrete needed to account for the sag as a percentage of the estimated volume of concrete. Typically, sag adds 10% to 15% to the amount of concrete needed to pour the slab.
The second way that estimating raised slabs differs from estimating slabs on grade is that the bottom of the slab must be formed. There are three basic ways to form the bottom of the slab. The first is to form the bottom of the slab with removable forms with a structural support that are removed after the concrete has cured to the point that it can support its own weight. In this case, the cost of the forms and supporting structure is often based on the square footage of the slab. A second way is to use a self-support- ing metal deck as the form. In this case, the metal deck and the building structure that supports it remain as part of the building after the construction of the slab is complete. The metal deck and supporting structure are included in the materials needed for the construction of the building. The third way is to use a metal deck that is not capable of sup- porting the weight of the concrete, which must be sup- ported until the concrete has cured to the point that it can support its own weight, as is the case with composite slabs. When the concrete has cured, the support structure is re- moved, leaving the metal deck and concrete. In this case the support structure is included in the forming, and the metal deck is included in the materials needed for the con- struction of the building.
STAIRS
The volume of concrete needed for stairs can be estimated by determining the cross-sectional area of the stairs and multi- plying the cross-sectional area by the width of the stairs as shown in the following example.
EXAMPLE 5-11
Determine the volume of concrete needed to construct the stairs in Figure 5-20.
Solution: The cross-sectional area of the stairs can be treated as a parallelogram and seven triangles as shown in Figure 5-21.
The area of the parallelogram equals the length of two of the parallel sides multiplied by the perpendicular distance between the two sizes and is calculated as follows:
The area of the triangles is one-half the base times the height mul- tiplied by the number of stairs. The area of the seven triangles is calculated as follows: Area⫽ (7 ea)a1 2b(10 in)(7 in)a 1 ft 12 inb 2 ⫽ 1.70 ft2
Area⫽ (6.5 in)(5.25 ft)a 1 ft
12 inb ⫽ 2.84 ft
2
EXCEL QUICK TIP 5-8 Concrete Slab on Metal Deck
The volume of concrete needed for a concrete slab on a metal deck similar to Figure 5-18 is set up in a spreadsheet by entering the data and formatting the cells as follows:
The following formula needs to be entered into Cell B9:
=B1*B2*((B3+(B5+B6)*B4/(2*B7))/12)/27* (1+B8/100)
The data for the slab is entered in Cells B1 through B8. The data shown in the foregoing figure is from Example 5-10.
A B C 1 Slab Length 100 ft 2 Slab Width 50 ft 3 T 3.00 in 4 D 1.50 in 5 W1 2.50 in 6 W2 4.50 in 7 S 6.00 in 8 Waste 10 % 9 Volume 65.78 cyd
FIGURE 5-21 Stair Cross-Sectional Area
The cross-sectional area is 4.54 square feet (2.84 ft2⫹ 1.70 ft2). The volume is calculated as follows:
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