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Stairs rajesh sir

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SHAMJITH KM
SHAMJITH KM

Dr. B. Rajeevan gave a lecture on designing stairs on July 15, 2010. The lecture covered: - Geometrical and structural classifications of stairs - Design requirements for public and residential staircases - Empirical relationships for rise and going dimensions - Designing stairs that span horizontally and longitudinally - Calculating dead and live loads - Determining effective depth and reinforcement requirements - Worked examples of designing transverse and longitudinal staircases

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Lecture Notes 15 July 2010 Dr. B. Rajeevan 1 Dr. B. Rajeevan Senior Lecturer Department of Civil Engineering Govt. College of Engineering Kannur E-mail: rajeevan@gcek.ac.in Mob: 9495 333 088 ContactTime: 4 pm – 5 pm DESIGN OF STAIRS STRUCTURAL DESIGN 15 July 2010 Dr. B. Rajeevan 2 Geometrical Classification 15 July 2010 Dr. B. Rajeevan 3 Geometrical Classification 15 July 2010 Dr. B. Rajeevan 4 15 July 2010 Dr. B. Rajeevan 5 Structural Classification-Stair spanning longitudinally 15 July 2010 Dr. B. Rajeevan 6
Lecture Notes 15 July 2010 Dr. B. Rajeevan 2 15 July 2010 Dr. B. Rajeevan 7 Structural Classification-Stair spanning transversely Parts of a stair 15 July 2010 Dr. B. Rajeevan 8 15 July 2010 Dr. B. Rajeevan 9 Public Buildings Rise = 150 mm Tread = 270 mm to 300 mm Residential Buildings Rise = 160 mm Tread = 250 mm Number of rise in one flight < 12 15 July 2010 Dr. B. Rajeevan 10 Empirical relation 550 < (2R + G) < 750 (in mm) (2R + G) = 600 (approx) Principles of Design • Cl. 33 of IS 456-2000 – Stair spanning horizontally (transversely) – Stair spanning longitudinally 15 July 2010 Dr. B. Rajeevan 11 Stair spanning horizontally 15 July 2010 Dr. B. Rajeevan 12
Lecture Notes 15 July 2010 Dr. B. Rajeevan 3 Stair spanning horizontally 15 July 2010 Dr. B. Rajeevan 13 Stair spanning horizontally 15 July 2010 Dr. B. Rajeevan 14 Stair spanning longitudinally Slab between beams 15 July 2010 Dr. B. Rajeevan 15 Stair spanning longitudinally Slab between landings 15 July 2010 Dr. B. Rajeevan 16 Stair spanning longitudinally Slab between walls 15 July 2010 Dr. B. Rajeevan 17 Dead Loads 15 July 2010 Dr. B. Rajeevan 18
Lecture Notes 15 July 2010 Dr. B. Rajeevan 4 Live Loads • Live Load (IS 875) – Residential building without overcrowding – 2 kN/m2 – Public building with overcrowding – 5 kN/m2 15 July 2010 Dr. B. Rajeevan 19 Depth of Section • One way reinforced slab – Longitudinally spanning – min thickness = W – Transverse spanning – average depth of step; D/2 15 July 2010 Dr. B. Rajeevan 20 Structural Detailing • Maximum BM – simply supported = wl2/8 – One half of tension steel taken to supports • Maximum BM – slab built-in to beams at supports = (0.9) wl2/8; – 2/3 of tension steel to support as negative steel • Maximum BM – slab continuous over beams at supports = wl2/10; – Full tension steel to support as negative steel • Distributors– 0.0012bD or 0.0015bD in transverse direction; – Full tension steel to support as negative steel 15 July 2010 Dr. B. Rajeevan 21 15 July 2010 Dr. B. Rajeevan 22 15 July 2010 Dr. B. Rajeevan 23 Calculation of Dead Loads and Effective Depth • Transverse Stair – Effective span = width of stair – Individual steps of width = G and span = width of stair 15 July 2010 Dr. B. Rajeevan 24
Lecture Notes 15 July 2010 Dr. B. Rajeevan 5 Calculation of Dead Loads and Effective Depth • Longitudinally spanning Stair 15 July 2010 Dr. B. Rajeevan 25 Design Example 1 A staircase has the following dimensions: waist W = 75 mm; nosing N = 25 mm; rise R =175 mm; going G = 225 mm. The live load expected is 2 kN/m2. Calculate the factored loads and effective depths for design if the staircase is spanning (a) transversely , and (b) longitudinally 15 July 2010 Dr. B. Rajeevan 26 15 July 2010 Dr. B. Rajeevan 27 Ref Step Calculations Output 1 wu=2.3kN/m 2 2 2 2 2 250 175 305 tan 1 25 1.08 / 1 2 0.225 2 0.45 / , 1.5( ) 2.295 /u B G R mm Slab spanning seversely RT DL WB kN m LL kN m Design Load w DL LL kN m cover cos 2 2 161.5 ( 12 ) W R d mm Use mmdia 161.5d mm 15 July 2010 Dr. B. Rajeevan 28 Ref Step Calculations Output 1 wu=10.22 kN/m 2 2 2 2 2 250 175 305 tan 1 25 4.81 / 2 2 / , 1.5( ) 10.22 /u B G R mm Slab spanning seversely RT DL WB kN m G LL kN m Design Load w DL LL kN m cover 2 54 ( 12 ) d W mm Use mmdia 54d mm Design Example 2 A longitudinal type of stair spans a distance of 3.75 m c/c of beams. R = 175 mm, T =250 mm. The treads have 15 mm granite finish and consists of 15 steps. Use M25 grade concrete and Fe 415 steel. Take Live load = 5 kN/m2. Width of stair = 1.5 m. 15 July 2010 Dr. B. Rajeevan 29 15 July 2010 Dr. B. Rajeevan 30 Ref Step Calculations Output IS 456 Cl. 26.4 1 Thickness of waist slab, W Assume l/d =30, d = 3750/30 = 125 W = 125 + cover + /2 = 125 + 15 + 6 = 146 mm = 150 mm (say) d = 150 -15 -6 =129 mm W = 150 mm d = 129 mm 2 Loads – Dead Load DL = Design Load = 1.5(DL + LL) = 18.48 kN/m2 SP 16 Table D 3 Bending Moment, Mu, Check for Mu,lim SP16 Table 3 4 Area of main steel 2 2 2 2 250 175 305B G R mm 21 25 23.5 7.32 / 2 RT FT WB kN m G G 2 18.48 /uw kN m 2 26 / 10 w kN m ,limu uM M 2 2 1.56, 0.472 606 100 u st M p bd pbd A mm
Lecture Notes 15 July 2010 Dr. B. Rajeevan 6 15 July 2010 Dr. B. Rajeevan 31 Ref Step Calculations Output SP 16 Table 96 5 Compute Spacing Provide 12 mm dia bars at 180 mm c/c Max spacing 3d or 300 mm 12 mm dia bars at 180 mm c/c IS 456 Cl. 25.5.2.1 SP 16 Table 96 6 Distributors Provide 8 mm dia @ 270 mm c/c Max spacing 5d or 450 mm 8 mm dia @ 270 mm c/c IS456 Table 19 7 Shear Check No shear reinforcement necessary IS 456 Fig 4 8 Check for Deflection (l/d)allowed = 1.2 x 26 =31.2 (l/d)assumed = 30 < 31.2 (l/d) ratio OK 2 ,min 0.12 /100 180stA bD mm 34.65 ; / 0.27 2 0.36 ; Noshear reinforcement v c v c w V kN V bd MPa MPa Design Example 3 15 July 2010 Dr. B. Rajeevan 32 Design a waist slab type stair shown in Figure. Landing slab A is supported on beams along JK and PQ, while the waist slab and landing slab B are spanning longitudinally as shown in Figure. The finish load and Live load are 1 kN/m2 and 5 kN/m2 , respectively. Use R = 160 mm and T = 270 mm, concrete grade = M20 and steel grade = Fe 415 15 July 2010 Dr. B. Rajeevan 33 15 July 2010 Dr. B. Rajeevan 34 15 July 2010 Dr. B. Rajeevan 35 15 July 2010 Dr. B. Rajeevan 36
Lecture Notes 15 July 2010 Dr. B. Rajeevan 7 15 July 2010 Dr. B. Rajeevan 37 15 July 2010 Dr. B. Rajeevan 38 15 July 2010 Dr. B. Rajeevan 39 15 July 2010 Dr. B. Rajeevan 40 15 July 2010 Dr. B. Rajeevan 41 15 July 2010 Dr. B. Rajeevan 42
Lecture Notes 15 July 2010 Dr. B. Rajeevan 8 15 July 2010 Dr. B. Rajeevan 43 15 July 2010 Dr. B. Rajeevan 44 15 July 2010 Dr. B. Rajeevan 45 Homework 15 July 2010 Dr. B. Rajeevan 46 15 July 2010 Dr. B. Rajeevan 47 15 July 2010 Dr. B. Rajeevan 48
Lecture Notes 15 July 2010 Dr. B. Rajeevan 9 15 July 2010 Dr. B. Rajeevan 49 15 July 2010 Dr. B. Rajeevan 50 LOADS AT SECTION 1-1 15 July 2010 Dr. B. Rajeevan 51 15 July 2010 Dr. B. Rajeevan 52 15 July 2010 Dr. B. Rajeevan 53 15 July 2010 Dr. B. Rajeevan 54
Lecture Notes 15 July 2010 Dr. B. Rajeevan 10 15 July 2010 Dr. B. Rajeevan 55 15 July 2010 Dr. B. Rajeevan 56 15 July 2010 Dr. B. Rajeevan 57

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Stairs rajesh sir

  • 1. Lecture Notes 15 July 2010 Dr. B. Rajeevan 1 Dr. B. Rajeevan Senior Lecturer Department of Civil Engineering Govt. College of Engineering Kannur E-mail: rajeevan@gcek.ac.in Mob: 9495 333 088 ContactTime: 4 pm – 5 pm DESIGN OF STAIRS STRUCTURAL DESIGN 15 July 2010 Dr. B. Rajeevan 2 Geometrical Classification 15 July 2010 Dr. B. Rajeevan 3 Geometrical Classification 15 July 2010 Dr. B. Rajeevan 4 15 July 2010 Dr. B. Rajeevan 5 Structural Classification-Stair spanning longitudinally 15 July 2010 Dr. B. Rajeevan 6
  • 2. Lecture Notes 15 July 2010 Dr. B. Rajeevan 2 15 July 2010 Dr. B. Rajeevan 7 Structural Classification-Stair spanning transversely Parts of a stair 15 July 2010 Dr. B. Rajeevan 8 15 July 2010 Dr. B. Rajeevan 9 Public Buildings Rise = 150 mm Tread = 270 mm to 300 mm Residential Buildings Rise = 160 mm Tread = 250 mm Number of rise in one flight < 12 15 July 2010 Dr. B. Rajeevan 10 Empirical relation 550 < (2R + G) < 750 (in mm) (2R + G) = 600 (approx) Principles of Design • Cl. 33 of IS 456-2000 – Stair spanning horizontally (transversely) – Stair spanning longitudinally 15 July 2010 Dr. B. Rajeevan 11 Stair spanning horizontally 15 July 2010 Dr. B. Rajeevan 12
  • 3. Lecture Notes 15 July 2010 Dr. B. Rajeevan 3 Stair spanning horizontally 15 July 2010 Dr. B. Rajeevan 13 Stair spanning horizontally 15 July 2010 Dr. B. Rajeevan 14 Stair spanning longitudinally Slab between beams 15 July 2010 Dr. B. Rajeevan 15 Stair spanning longitudinally Slab between landings 15 July 2010 Dr. B. Rajeevan 16 Stair spanning longitudinally Slab between walls 15 July 2010 Dr. B. Rajeevan 17 Dead Loads 15 July 2010 Dr. B. Rajeevan 18
  • 4. Lecture Notes 15 July 2010 Dr. B. Rajeevan 4 Live Loads • Live Load (IS 875) – Residential building without overcrowding – 2 kN/m2 – Public building with overcrowding – 5 kN/m2 15 July 2010 Dr. B. Rajeevan 19 Depth of Section • One way reinforced slab – Longitudinally spanning – min thickness = W – Transverse spanning – average depth of step; D/2 15 July 2010 Dr. B. Rajeevan 20 Structural Detailing • Maximum BM – simply supported = wl2/8 – One half of tension steel taken to supports • Maximum BM – slab built-in to beams at supports = (0.9) wl2/8; – 2/3 of tension steel to support as negative steel • Maximum BM – slab continuous over beams at supports = wl2/10; – Full tension steel to support as negative steel • Distributors– 0.0012bD or 0.0015bD in transverse direction; – Full tension steel to support as negative steel 15 July 2010 Dr. B. Rajeevan 21 15 July 2010 Dr. B. Rajeevan 22 15 July 2010 Dr. B. Rajeevan 23 Calculation of Dead Loads and Effective Depth • Transverse Stair – Effective span = width of stair – Individual steps of width = G and span = width of stair 15 July 2010 Dr. B. Rajeevan 24
  • 5. Lecture Notes 15 July 2010 Dr. B. Rajeevan 5 Calculation of Dead Loads and Effective Depth • Longitudinally spanning Stair 15 July 2010 Dr. B. Rajeevan 25 Design Example 1 A staircase has the following dimensions: waist W = 75 mm; nosing N = 25 mm; rise R =175 mm; going G = 225 mm. The live load expected is 2 kN/m2. Calculate the factored loads and effective depths for design if the staircase is spanning (a) transversely , and (b) longitudinally 15 July 2010 Dr. B. Rajeevan 26 15 July 2010 Dr. B. Rajeevan 27 Ref Step Calculations Output 1 wu=2.3kN/m 2 2 2 2 2 250 175 305 tan 1 25 1.08 / 1 2 0.225 2 0.45 / , 1.5( ) 2.295 /u B G R mm Slab spanning seversely RT DL WB kN m LL kN m Design Load w DL LL kN m cover cos 2 2 161.5 ( 12 ) W R d mm Use mmdia 161.5d mm 15 July 2010 Dr. B. Rajeevan 28 Ref Step Calculations Output 1 wu=10.22 kN/m 2 2 2 2 2 250 175 305 tan 1 25 4.81 / 2 2 / , 1.5( ) 10.22 /u B G R mm Slab spanning seversely RT DL WB kN m G LL kN m Design Load w DL LL kN m cover 2 54 ( 12 ) d W mm Use mmdia 54d mm Design Example 2 A longitudinal type of stair spans a distance of 3.75 m c/c of beams. R = 175 mm, T =250 mm. The treads have 15 mm granite finish and consists of 15 steps. Use M25 grade concrete and Fe 415 steel. Take Live load = 5 kN/m2. Width of stair = 1.5 m. 15 July 2010 Dr. B. Rajeevan 29 15 July 2010 Dr. B. Rajeevan 30 Ref Step Calculations Output IS 456 Cl. 26.4 1 Thickness of waist slab, W Assume l/d =30, d = 3750/30 = 125 W = 125 + cover + /2 = 125 + 15 + 6 = 146 mm = 150 mm (say) d = 150 -15 -6 =129 mm W = 150 mm d = 129 mm 2 Loads – Dead Load DL = Design Load = 1.5(DL + LL) = 18.48 kN/m2 SP 16 Table D 3 Bending Moment, Mu, Check for Mu,lim SP16 Table 3 4 Area of main steel 2 2 2 2 250 175 305B G R mm 21 25 23.5 7.32 / 2 RT FT WB kN m G G 2 18.48 /uw kN m 2 26 / 10 w kN m ,limu uM M 2 2 1.56, 0.472 606 100 u st M p bd pbd A mm
  • 6. Lecture Notes 15 July 2010 Dr. B. Rajeevan 6 15 July 2010 Dr. B. Rajeevan 31 Ref Step Calculations Output SP 16 Table 96 5 Compute Spacing Provide 12 mm dia bars at 180 mm c/c Max spacing 3d or 300 mm 12 mm dia bars at 180 mm c/c IS 456 Cl. 25.5.2.1 SP 16 Table 96 6 Distributors Provide 8 mm dia @ 270 mm c/c Max spacing 5d or 450 mm 8 mm dia @ 270 mm c/c IS456 Table 19 7 Shear Check No shear reinforcement necessary IS 456 Fig 4 8 Check for Deflection (l/d)allowed = 1.2 x 26 =31.2 (l/d)assumed = 30 < 31.2 (l/d) ratio OK 2 ,min 0.12 /100 180stA bD mm 34.65 ; / 0.27 2 0.36 ; Noshear reinforcement v c v c w V kN V bd MPa MPa Design Example 3 15 July 2010 Dr. B. Rajeevan 32 Design a waist slab type stair shown in Figure. Landing slab A is supported on beams along JK and PQ, while the waist slab and landing slab B are spanning longitudinally as shown in Figure. The finish load and Live load are 1 kN/m2 and 5 kN/m2 , respectively. Use R = 160 mm and T = 270 mm, concrete grade = M20 and steel grade = Fe 415 15 July 2010 Dr. B. Rajeevan 33 15 July 2010 Dr. B. Rajeevan 34 15 July 2010 Dr. B. Rajeevan 35 15 July 2010 Dr. B. Rajeevan 36
  • 7. Lecture Notes 15 July 2010 Dr. B. Rajeevan 7 15 July 2010 Dr. B. Rajeevan 37 15 July 2010 Dr. B. Rajeevan 38 15 July 2010 Dr. B. Rajeevan 39 15 July 2010 Dr. B. Rajeevan 40 15 July 2010 Dr. B. Rajeevan 41 15 July 2010 Dr. B. Rajeevan 42
  • 8. Lecture Notes 15 July 2010 Dr. B. Rajeevan 8 15 July 2010 Dr. B. Rajeevan 43 15 July 2010 Dr. B. Rajeevan 44 15 July 2010 Dr. B. Rajeevan 45 Homework 15 July 2010 Dr. B. Rajeevan 46 15 July 2010 Dr. B. Rajeevan 47 15 July 2010 Dr. B. Rajeevan 48
  • 9. Lecture Notes 15 July 2010 Dr. B. Rajeevan 9 15 July 2010 Dr. B. Rajeevan 49 15 July 2010 Dr. B. Rajeevan 50 LOADS AT SECTION 1-1 15 July 2010 Dr. B. Rajeevan 51 15 July 2010 Dr. B. Rajeevan 52 15 July 2010 Dr. B. Rajeevan 53 15 July 2010 Dr. B. Rajeevan 54
  • 10. Lecture Notes 15 July 2010 Dr. B. Rajeevan 10 15 July 2010 Dr. B. Rajeevan 55 15 July 2010 Dr. B. Rajeevan 56 15 July 2010 Dr. B. Rajeevan 57