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Post-Tensioned Concrete Fundamentals

004 x 888 355 sq in 0004 x 320 128 sq in use 125

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Unformatted text preview: ildings – Part One A SunCam online continuing education course Example Given: The post-tensioned beam shown below. 120" 7" 3" N A 20" 16" 58'‐0" clear span between face of supports Find: Determine the minimum area and length of bonded reinforcing required. Solution: Let's begin by finding , the area of that part of the cross section between the flexural tension face and the center of gravity of the cross-section for the top and bottom of the beam. The neutral axis has already been determined to be 10 inches from the top of the beam. Top Bottom = 3 x 16 + 7 x 120 = 888 sq. in. = 16 x20 = 320 sq. in. Now we can compute the minimum required area of bonded reinforcing using 0.004 : Top Bottom = 0.004 x 888 = 3.55 sq. in. = 0.004 x 320 = 1.28 sq. in. Use 12#5 Top Use 3#6 Bottom The ACI 318 states that this minimum bonded reinforcement shall be uniformly distributed as close as close as possible to the tension face. Therefore, the bottom www.SunCam.com Copyright 2010 John P. Miller Page 35 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course steel would be spaced approximately 6 inches on center, allowing for concrete cover on the side of the stem and beam stirrups. This seems like an appropriate spacing, but in all likelihood, flexural demands will require a larger area of steel and possibly more than three bars. The minimum bonded reinforcing in the top of the beam will be placed at both ends, where negative bending moments will occur due to support fixity. 12#5s were selected instead of 8#6s to avoid having fewer bars spaced farther apart. The 12#5s result in a spacing of approximately 10 inches on center, which seems to be better than almost 18 inches on center had 12#6s been selected. However, either spacing would probably meet the intent of the ACI 318. The minimum length of the bottom bars is one-third the clear span, or 58/3 = 19.33 feet. The top bars need to extend into the clear span by at least one-sixth the clear span, or 58/6 = 9.67 feet. Example Given: A continuous post-tensioned one-way slab is 5 1/2" thick. It is supported by 16" wide concrete beams that are at 22'-0" on center. Find: Determine the minimum area and length of bonded reinforcing required. Solution: for the and bottom will Since the concrete slab has a symmetric cross section, the be the same and equal to 12x5.5/2 = 33 sq. in. per foot. Using this, the minimum area of bonded reinforcing is: = 0.004 x 33 = 0.132 sq. in. per foot of slab Use #[email protected]" o.c. The minimum length of the bottom bars is one-third the clear span, or (22-1.33)/3 = 6.89 feet and the top bars need to extend into the clear span by at least one-sixth the clear span, or (22-1.33)/6 = 3.44 feet. The results are illustrated below. www.SunCam.com Copyright 2010 John P. Miller Page 36 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course #3 x 8'‐3 @ 14" o.c. #3 x 8'‐3 @ 14" o.c. #3 x 7'‐0 @ 14" o.c. 20'‐8" clear span Minimum Bonded Reinforcing – One-Way Slab Example Example Given: A two-way post-tensioned slab is 8" thick. It is supported by 16" x 16" columns that are at 20'-0" on center both ways. The 28-day specified concrete compressive strength is 5,000 psi and mild reinforcing with = 60,000 psi will be used. The extreme fiber tension at service loads in positive moment areas (in the bottom of the slab), after all pre-stress losses, is 350 psi. Find: Determine the minimum area, length, and distribution of bonded reinforcing required. Solution: Because the bays are equal in both directions, we need only investigate one direction and apply the results to both. Since the tensile stress in the bottom of the concrete slab 141 psi and less than 6 424 psi, minimum bonded is greater than 2 reinforcing is required in the bottom of the slab in the positive moment regions. Therefore, by referring to the figure on page 34, we have: 350 0.5 12 2 8,400 8,400 / 0.5 60,000 0.28 4 / . ./ This bottom reinforcing should be placed in the middle strip. From chapter 13 of ACI 318, the middle strip width is defined as being bounded by two column strips, which is www.SunCam.com Copyright 2010 John P. Miller Page 37 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course the smaller of the centerline spans of the slab. In this example, our column strip widths are 20/4 = 7'-6" and the middle strip width is 15'-0". Therefore, the total area of reinforcing is 15 x 0.28 = 4.20 sq. in. Recall that the minimum length of the bottom bonded reinforcing is one-third the clear span, or (20-1.33)/3 = 6.22 feet. So, we will use 14#5 bottom bars, 6'-3" long, equally spaced in a 15-foot wide middle strip, both ways. For the minimum area of bonded reinforcement in negative moment regions at the column supports, in this example is the entire bay width times the slab thickness, or 20 x 12 x 8 = 1920 sq. in. For columns...
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