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By Dr. Attaullah Shah Swedish College of Engineering and Technology Wah Cantt.

By Dr. Attaullah Shah Swedish College of Engineering and Technology Wah Cantt. Reinforced Concrete Design-8 Design of 2 way Slabs. One way vs Two way slab system. L>2S. As ≥ Temp. steel Min. Spacing ≥ ∅ main steel ≥ 4/3 max agg. ≥ 2.5 cm (1in) Max. Spacing ≤ 3 t ≤ 45 cm (17in).

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By Dr. Attaullah Shah Swedish College of Engineering and Technology Wah Cantt.

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  1. ByDr. Attaullah ShahSwedish College of Engineering and Technology Wah Cantt. Reinforced Concrete Design-8 Design of 2 way Slabs

  2. One way vs Two way slab system L>2S As ≥ Temp. steel Min. Spacing ≥ ∅ main steel ≥ 4/3 max agg. ≥ 2.5 cm (1in) Max. Spacing ≤ 3 t ≤ 45 cm (17in) Min slab thickness =

  3. Shear Strength of Slabs In two-way floor systems, the slab must have adequate thickness to resist both bending moments and shear forces at critical section. There are three cases to look at for shear. 1. 2. 3. Two-way Slabs supported on beams Two-Way Slabs without beams Shear Reinforcement in two-way slabs without beams.

  4. Shear Strength of Slabs Two-way slabs supported on beams The critical location is found at d distance from the column, where The supporting beams are stiff and are capable of transmitting floor loads to the columns.

  5. Shear Strength of Slabs The shear force is calculated using the triangular and trapezoidal areas. If no shear reinforcement is provided, the shear force at a distance d from the beam must equal where,

  6. Shear Strength of Slabs Two-Way Slabs without beams There are two types of shear that need to be addressed 1. 2. One-way shear or beam shear at distance d from the column Two-way or punch out shear which occurs along a truncated cone.

  7. One-way shear or beam shear at distance d from the column Two-way or punch out shear which occurs along a truncated cone. 1. 2. Shear Strength of Slabs

  8. Shear Strength of Slabs One-way shear considers critical section a distance d from the column and the slab is considered as a wide beam spanning between supports.

  9. Shear Strength of Slabs Two-way shear fails along a a truncated cone or pyramid around the column. The critical section is located d/2 from the column face, column capital, or drop panel.

  10. If shear reinforcement is not provided, the shear strength of concrete is the smaller of: bo = bc = perimeter of the critical section ratio of long side of column to short side Shear Strength of Slabs

  11. Shear Strength of Slabs If shear reinforcement is not provided, the shear strength of concrete is the smaller of: as is 40 for interior columns, 30 for edge columns, and 20 for corner columns.

  12. For plates and flat slabs, which do not meet the condition for shear, one can either - Increase slab thickness - Add reinforcement Reinforcement can be done by shearheads, anchor bars, conventional stirrup cages and studded steel strips. Shear Strength of Slabs Shear Reinforcement in two-way slabs without beams.

  13. Shearhead consists of steel I-beams or channel welded into four cross arms to be placed in slab above a column. Does not apply to external columns due to lateral loads and torsion. Shear Strength of Slabs

  14. Anchor bars consists of steel reinforcement rods or bent bar reinforcement Shear Strength of Slabs

  15. Shear Strength of Slabs Conventional stirrup cages

  16. Shear Strength of Slabs Studded steel strips

  17. Shear Strength of Slabs The reinforced slab follows section 11.12.4 in the ACI Code, where Vn can not The spacing, s, can not exceed d/2. If a shearhead reinforcement is provided

  18. Example Problem Determine the shear reinforcement required for an interior flat panel considering the following: Vu= 195k, slab thickness = 9 in., d = 7.5 in., fc = 3 ksi, fy= 60 ksi, and column is 20 x 20 in.

  19. Example Problem Compute the shear terms find b0 for

  20. Example Problem Compute the maximum allowable shear Vu =195 k > 135.6 k Shear reinforcement is need!

  21. Example Problem Compute the maximum allowable shear So fVn >Vu Can use shear reinforcement

  22. Example Problem Use a shear head or studs as in inexpensive spacing. Determine the a for

  23. Example Problem Determine the a for The depth = a+d = 41.8 in. +7.5 in. = 49.3 in.  50 in.

  24. Example Problem Determine shear reinforcement The fVs per side is fVs / 4 = 14.85 k

  25. Example Problem Determine shear reinforcement Use a #3 stirrup Av = 2(0.11 in2) = 0.22 in2

  26. Example Problem Determine shear reinforcement spacing Maximum allowable spacing is

  27. Example Problem Use s = 3.5 in. The total distance is 15(3.5 in.)= 52.5 in.

  28. Example Problem The final result: 15 stirrups at total distance of 52.5 in. So that a = 45 in. and c = 20 in.

  29. Direct Design Method for Two-way Slab Method of dividing total static moment Mo into positive and negative moments. Minimum of 3 continuous spans in each direction. (3 x 3 panel) Rectangular panels with long span/short span 2 Limitations on use of Direct Design method 1. 2.

  30. Direct Design Method for Two-way Slab Limitations on use of Direct Design method 3. 4. Successive span in each direction shall not differ by more than 1/3 the longer span. Columns may be offset from the basic rectangular grid of the building by up to 0.1 times the span parallel to the offset.

  31. Direct Design Method for Two-way Slab Limitations on use of Direct Design method 5. 6. All loads must be due to gravity only (N/A to unbraced laterally loaded frames, from mats or pre-stressed slabs) Service (unfactored) live load 2 service dead load

  32. Direct Design Method for Two-way Slab Limitations on use of Direct Design method For panels with beams between supports on all sides, relative stiffness of the beams in the 2 perpendicular directions. Shall not be less than 0.2 nor greater than 5.0 7.

  33. Definition of Beam-to-Slab Stiffness Ratio, a Accounts for stiffness effect of beams located along slab edge reduces deflections of panel adjacent to beams.

  34. Definition of Beam-to-Slab Stiffness Ratio, a With width bounded laterally by centerline of adjacent panels on each side of the beam.

  35. Two-Way Slab Design Static Equilibrium of Two-Way Slabs Analogy of two-way slab to plank and beam floor Section A-A: Moment per ft width in planks Total Moment

  36. Two-Way Slab Design Static Equilibrium of Two-Way Slabs Analogy of two-way slab to plank and beam floor Uniform load on each beam Moment in one beam (Sec: B-B)

  37. Two-Way Slab Design Static Equilibrium of Two-Way Slabs Total Moment in both beams Full load was transferred east-west by the planks and then was transferred north-south by the beams; The same is true for a two-way slab or any other floor system.

  38. Basic Steps in Two-way Slab Design 1. 2. 3. Choose layout and type of slab. Choose slab thickness to control deflection. Also, check if thickness is adequate for shear. Choose Design method • Equivalent Frame Method- use elastic frame analysis to compute positive and negative moments • Direct Design Method - uses coefficients to compute positive and negative slab moments

  39. Basic Steps in Two-way Slab Design Calculate positive and negative moments in the slab. Determine distribution of moments across the width of the slab. - Based on geometry and beam stiffness. Assign a portion of moment to beams, if present. Design reinforcement for moments from steps 5 and 6. Check shear strengths at the columns 4. 5. 6. 7. 8.

  40. Minimum Slab Thickness for two-way construction Maximum Spacing of Reinforcement At points of max. +/- M: Min Reinforcement Requirements

  41. Distribution of Moments Slab is considered to be a series of frames in two directions:

  42. Distribution of Moments Slab is considered to be a series of frames in two directions:

  43. Distribution of Moments Total static Moment, Mo where

  44. Moments vary across width of slab panel Design moments are averaged over the width of column strips over the columns & middle strips between column strips. Column Strips and Middle Strips

  45. Column Strips and Middle Strips Column strips Design w/width on either side of a column centerline equal to smaller of l1= length of span in direction moments are being determined. l2= length of span transverse to l1

  46. Column Strips and Middle Strips Middle strips: Design strip bounded by two column strips.

  47. Positive and Negative Moments in Panels M0 is divided into + M and -M Rules given in ACI sec. 13.6.3

  48. Moment Distribution

  49. Positive and Negative Moments in Panels M0 is divided into + M and -M Rules given in ACI sec. 13.6.3

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