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TRANSCRIPT
DESIGN OF STAIRCASE
Dr. Izni Syahrizal bin Ibrahim Faculty of Civil Engineering
Universiti Teknologi Malaysia
Email: [email protected]
T
G N
Introduction
T
G
R
N
h
Span, L
Flight Landing
T = Thread R = Riser G = Going h = Waist N = Nosing = Slope
Introduction
• Public building R 180 mm & G 255 mm • Private building R 200 mm & 250 mm
G 400 mm • For comfort: (2 R) + G = 600 mm
(UBBL, BS 5395, Reynold et al. 2007)
Types of Staircase
Straight stair spanning longitudinally
Free-standing stair
Helical stair
Types of Staircase
Slabless stair
Straight stair spanning horizontally Spiral stair
General Design Considerations
Loads • Permanent action: Weight of steps & finishes. Also consider
increased loading on plan (inclination of the waist) • Stairs with open well: Two intersecting landings at right-angles to
each other, loads on areas common to both spans may be divided equally between spans
Bending Moment & Shear Force • Stair slab & landing to support unfavourable arrangements of
design load • Continuous stairs: Bending moment can be taken as FL/10 (F is
the total ultimate load)
General Design Considerations
Effective Span • Stairs between beam or wall: Centreline between the supporting
beam or wall • Stairs between landing slab: Centreline of the supporting landing
slab, or the distance between edges of supporting slab + 1.8 m (whichever is the smaller)
Detailing • Ensure that the tension bar may not break through at the kink
General Design Considerations
Correct detailing
General Design Considerations
Incorrect detailing
Design Procedure
Step Task Standard
1 Determine design life, Exposure class & Fire resistance
EN 1990 Table 2.1 EN 1992-1-1: Table 4.1 EN 1992-1-2: Sec. 5.6
2 Determine material strength BS 8500-1: Table A.3 EN 206-1: Table F1
3 Select the waist, h and average thickness, t of staircase EN 1992-1-1: Table 7.4N EN 1992-1-2: Table 5.8
4 Calculate min. cover for durability, fire and bond requirements EN 1992-1-1: Sec. 4.4.1
5 Estimate actions on staircase EN 1991-1-1
6 Analyze structure to obtain maximum bending moments and shear forces
EN 1992-1-1: Sec. 5
7 Design flexural reinforcement EN 1992-1-1: Sec. 6.1
8 Check shear EN 1992-1-1: Sec. 6.2
9 Check deflection EN 1992-1-1: Sec. 7.4
10 Check cracking EN 1992-1-1: Sec. 9.3
11 Detailing EN 1992-1-1: Sec.8 & 9.3
Example 1
STRAIGHT STAIRCASE SPANNING LONGITUDINALLY
Example 1: Straight Staicase
G = 255 mm
R = 175 mm
h = 110 mm
L = 2800 mm
10 255 mm = 2550 mm 250 mm 250 mm
• Permanent action, gk = 1.0 kN/m2 (excluding selfweight)
• Variable action, qk = = 4.0 kN/m2 • fck = 25 N/mm2
• fyk = 500 N/mm2
• RC density = 25 kN/m3
• Cover, c = 25 mm • bar = 8 mm
Example 1: Straight Staircase
Determine Average Thickness of Staircase
𝑦 = ℎ𝐺2+𝑅2
𝐺= 110
2552+1752
255= 133 mm
Average thickness:
𝑡 =𝑦+(𝑦+𝑅)
2=
133+(133+175)
2= 𝟐𝟐𝟏 mm G
R y t
y
Example 1: Straight Staircase
Action Slab selfweight = 25.0 0.221 = 5.52 kN/m2
Permanent action (excluding selfweight) = 1.00 kN/m2
Characteristics permanent action, gk = 5.52 + 1.00 = 6.52 kN/m2
Characteristics variable action, qk = 4.00 kN/m2
Design action, nd = 1.35gk + 1.5qk = 14.81 kN/m2
Consider 1 m width, wd = nd 1 m = 14.81 kN/m/m width
Example 1: Straight Staircase
Note: F = wd L = 14.81 2.8 m = 41.47 kN
M = FL/10 = 11.6 kNm
M = FL/10 = 11.6 kNm M = FL/10 = 11.6 kNm
L = 2.8 m
Analysis
Example 1: Straight Staircase
Main Reinforcement Effective depth, d = 110 – 25 – 8/2 = 81 mm
𝐾 =𝑀
𝑓𝑐𝑘𝒃𝑑2 =11.6×106
25×𝟏𝟎𝟎𝟎×812 = 0.071 Kbal = 0.167
Compression reinforcement is NOT required
𝑧 = 𝑑 0.25 −𝐾
1.134= 0.93𝑑 0.95d
𝐴𝑠 =𝑀
0.87𝑓𝑦𝑘𝑧=
11.6×106
0.87×500×0.93×81= 𝟑𝟓𝟑 mm2/m
Example 1: Straight Staircase
Minimum & Maximum Area of Reinforcement
𝐴𝑠,𝑚𝑖𝑛 = 0.26𝑓𝑐𝑡𝑚
𝑓𝑦𝑘𝑏𝑑 = 0.26
2.56
5000.0013𝑏𝑑 ≥ 0.0013𝑏𝑑
As,min = 0.0013bd = 0.0013 1000 81 = 108 mm2/m As,max = 0.04Ac = 0.04bh = 0.04 1000 110 = 4400 mm2/m
Secondary Reinforcement As = 20% of the main reinforcement = 0.20 353 = 71 mm2/m
Main bar H8-125 (As = 402 mm2/m) Secondary bar H8-350 (As = 144 mm2/m)
Example 1: Straight Staircase
Shear
14.81 kN/m 11.6 kNm/m 11.6 kNm/m
VA VB 2.8 m
M @ B = 0 2.80VA – 11.6 + 11.6 – (14.81 2.80 1.4) = 0 VA = 20.7 kN/m VB = 20.7 kN/m
Example 1: Straight Staircase
Shear Maximum design shear force, VEd = 20.7 kN/m
𝑘 = 1 +200
𝑑= 1 +
200
81= 2.57 2.0 Use k = 2.0
𝜌𝑙 =𝐴𝑠𝑙
𝒃𝑑=
402
𝟏𝟎𝟎𝟎 × 81= 0.0050 ≤ 0.02
𝑉𝑅𝑑,𝑐 = 0.12𝑘 100𝜌𝑙𝑓𝑐𝑘1/3 𝒃𝑑
= 0.12 × 2.0 100 × 0.0050 × 25 1/3 𝟏𝟎𝟎𝟎 × 81 = 45011 N = 45.0 kN/m
𝑉𝑚𝑖𝑛 = 0.035𝑘3/2 𝑓𝑐𝑘 𝒃𝑑
= 0.035 × 2.03/2 25 𝟏𝟎𝟎𝟎 × 81 = 40093 𝑁 = 40.1 kN/m
VEd (20.7 kN/m) VRd,c (45.0 kN/m) OK
Example 1: Straight Staircase
Deflection Percentage of required tension reinforcement:
𝜌 =𝐴𝑠,𝑟𝑒𝑞
𝒃𝑑=
353
𝟏𝟎𝟎𝟎 × 81= 0.0044
Reference reinforcement ratio:
𝜌𝑜 = 𝑓𝑐𝑘 × 10−3 = 25 × 10−3 = 0.0050
Since o Use Eq. (7.16a) in EC 2 Cl. 7.4.2
Example 1: Straight Staircase
Factor or structural system, K = 1.5
𝑙
𝑑= 𝐾 11 + 1.5 𝑓𝑐𝑘
𝜌𝑜
𝜌+ 3.2 𝑓𝑐𝑘
𝜌𝑜
𝜌− 1
3/2
(l/d)basic = 1.5 (11 + 8.6 + 0.90) = 30.8 Modification factor for span less than 7 m = 1.00
Modification for steel area provided = 𝐴𝑠,𝑝𝑟𝑜𝑣
𝐴𝑠,𝑟𝑒𝑞=
402
353= 1.14 1.50
(l/d)allow = 30.8 1.00 1.14 = 35.0 (l/d)actual = 2800/81 = 34.6 (l/d)allow
Deflection OK
Example 1: Straight Staircase
Cracking h = 110 mm 200 mm Main bar: Smax, slab = 3h (330 mm) 400 mm 330 mm Max bar spacing = 125 mm Smax, slab OK Secondary bar: Smax, slab = 3.5h (385 mm) 450 mm 385 mm Max bar spacing = 350 mm Smax, slab OK
Cracking OK
Max bar spacing
Example 1: Straight Staircase
Detailing
10
1
75
= 1
75
0 m
m
10 255 mm = 2550 mm 250 mm 250 mm
840 mm 840 mm
H8-125
H8-350
H8-125
H8-350
Example 2
STAIRCASE WITH LANDING & CONTINUOUS AT ONE END
Example 2: Staircase with Landing & Continuous at One End
• Permanent action, gk = 1.2 kN/m2 (excluding selfweight)
• Variable action, qk = = 3.0 kN/m2 • fck = 25 N/mm2
• fyk = 500 N/mm2
• RC density = 25 kN/m3
• Cover, c = 25 mm • bar = 10 mm
G = 260 mm
R = 170 mm
h = 160 mm
L1 = 2700 mm
10 260 mm = 2600 mm 1500 mm 200 mm
L2 = 1600 mm
200 mm
L = 4300 mm
Example 2: Staircase with Landing & Continuous at One End
Determine Average Thickness of Staircase
𝑦 = ℎ𝐺2+𝑅2
𝐺= 160
2602+1702
260= 191 mm
Average thickness:
𝑡 =𝑦+(𝑦+𝑅)
2=
191+(191+170)
2= 𝟐𝟕𝟔 mm G
R y t
y
Example 2: Staircase with Landing & Continuous at One End
Action & Analysis Landing Slab selfweight = 25.0 0.160 = 4.00 kN/m2
Permanent action (excluding selfweight) = 1.20 kN/m2
Characteristics permanent action, gk = 4.00 + 1.20 = 5.20 kN/m2
Characteristics variable action, qk = 3.00 kN/m2
Design action, nd = 1.35gk + 1.5qk = 11.52 kN/m2
Consider 1 m width, wd, landing = nd 1 m = 11.52 kN/m/m width
Example 2: Staircase with Landing & Continuous at One End
Action & Analysis Flight Slab selfweight = 25.0 0.276 = 6.90 kN/m2
Permanent action (excluding selfweight) = 1.20 kN/m2
Characteristics permanent action, gk = 6.90 + 1.20 = 8.10 kN/m2
Characteristics variable action, qk = 3.00 kN/m2
Design action, nd = 1.35gk + 1.5qk = 15.43 kN/m2
Consider 1 m width, wd, flight = nd 1 m = 15.44 kN/m/m width
Example 2: Staircase with Landing & Continuous at One End
Note: F = wd L = (15.44 2.7 m) + (11.52 1.6 m) = 60.1 kN
M = FL/10 = 25.9 kNm
M = FL/10 = 25.9 kNm
L1 = 2.7 m
Analysis
L2 = 1.6 m
11.52 kN/m
Example 2: Staircase with Landing & Continuous at One End
Main Reinforcement Effective depth, d = 160 – 25 – 10/2 = 130 mm
𝐾 =𝑀
𝑓𝑐𝑘𝒃𝑑2 =25.9×106
25×𝟏𝟎𝟎𝟎×1302 = 0.061 Kbal = 0.167
Compression reinforcement is NOT required
𝑧 = 𝑑 0.25 −𝐾
1.134= 0.94𝑑 0.95d
𝐴𝑠 =𝑀
0.87𝑓𝑦𝑘𝑧=
25.9×106
0.87×500×0.94×130= 𝟒𝟖𝟓 mm2/m
Example 2: Staircase with Landing & Continuous at One End
Minimum & Maximum Area of Reinforcement
𝐴𝑠,𝑚𝑖𝑛 = 0.26𝑓𝑐𝑡𝑚
𝑓𝑦𝑘𝑏𝑑 = 0.26
2.56
5000.0013𝑏𝑑 ≥ 0.0013𝑏𝑑
As,min = 0.0013bd = 0.0013 1000 130 = 173 mm2/m As,max = 0.04Ac = 0.04bh = 0.04 1000 130 = 6400 mm2/m
Secondary Reinforcement As = 20% of the main reinforcement = 0.20 485 = 97 mm2/m
Main bar H10-150 (As = 524 mm2/m) Secondary bar H10-400 (As = 196 mm2/m)
Example 2: Staircase with Landing & Continuous at One End
Shear
15.44 kN/m 25.9 kNm/m
VA VB 2.7 m
M @ B = 0 4.30VA – 25.9 – (15.44 2.70 2.95) – (11.52 1.6 0.80) = 0 VA = 38.0 kN/m VB = 22.1 kN/m
11.52 kN/m
1.6 m
Example 2: Staircase with Landing & Continuous at One End
Shear Maximum design shear force, VEd = 38.0 kN/m
𝑘 = 1 +200
𝑑= 1 +
200
130= 2.24 2.0 Use k = 2.0
𝜌𝑙 =𝐴𝑠𝑙
𝒃𝑑=
524
𝟏𝟎𝟎𝟎 × 130= 0.0040 ≤ 0.02
𝑉𝑅𝑑,𝑐 = 0.12𝑘 100𝜌𝑙𝑓𝑐𝑘1/3 𝒃𝑑
= 0.12 × 2.0 100 × 0.0040 × 25 1/3 𝟏𝟎𝟎𝟎 × 130 = 67376 N = 67.4 kN/m
𝑉𝑚𝑖𝑛 = 0.035𝑘3/2 𝑓𝑐𝑘 𝒃𝑑
= 0.035 × 2.03/2 25 𝟏𝟎𝟎𝟎 × 130 = 64347 𝑁 = 64.3 kN/m
VEd (38.0 kN/m) VRd,c (67.4 kN/m) OK
Example 2: Staircase with Landing & Continuous at One End
Deflection Percentage of required tension reinforcement:
𝜌 =𝐴𝑠,𝑟𝑒𝑞
𝒃𝑑=
485
𝟏𝟎𝟎𝟎 × 130= 0.0037
Reference reinforcement ratio:
𝜌𝑜 = 𝑓𝑐𝑘 × 10−3 = 25 × 10−3 = 0.0050
Since o Use Eq. (7.16a) in EC 2 Cl. 7.4.2
Example 2: Staircase with Landing & Continuous at One End
Factor or structural system, K = 1.3
𝑙
𝑑= 𝐾 11 + 1.5 𝑓𝑐𝑘
𝜌𝑜
𝜌+ 3.2 𝑓𝑐𝑘
𝜌𝑜
𝜌− 1
3/2
(l/d)basic = 1.5 (11 + 10.1 + 3.18) = 31.5 Modification factor for span less than 7 m = 1.00
Modification for steel area provided = 𝐴𝑠,𝑝𝑟𝑜𝑣
𝐴𝑠,𝑟𝑒𝑞=
524
485= 1.08 1.50
(l/d)allow = 31.5 1.00 1.08 = 34.0 (l/d)actual = 4300/130 = 33.1 (l/d)allow
Deflection OK
Example 2: Staircase with Landing & Continuous at One End
Cracking h = 160 mm 200 mm Main bar: Smax, slab = 3h (480 mm) 400 mm 400 mm Max bar spacing = 150 mm Smax, slab OK Secondary bar: Smax, slab = 3.5h (560 mm) 450 mm 450 mm Max bar spacing = 400 mm Smax, slab OK
Cracking OK
Max bar spacing
Example 2: Staircase with Landing & Continuous at One End
Detailing
10 260 mm = 2600 mm 1500 mm 200 mm
10
1
70
= 1
70
mm
H10-150
H10-400
H10-150
H10-400
H10-400
200 mm
0.3L = 1290 mm
Example 3
STAIRCASE SUPPORTED BY LANDING
Example 3: Staircase Supported by Landing
Example 3: Staircase Supported by Landing
Plan View
200
1500
1500
100
50
50 200
200 1500
200 10 @ 260 = 2600
Example 3: Staircase Supported by Landing
G = 260
R = 170
h = 150
h = 150
• Permanent action, gk = 1.2 kN/m2 (excluding selfweight)
• Variable action, qk = = 3.0 kN/m2 • fck = 25 N/mm2
• fyk = 500 N/mm2
• RC density = 25 kN/m3
• Cover, c = 25 mm • bar = 10 mm
Section
Example 3: Staircase Supported by Landing
Determine Average Thickness of Staircase
𝑦 = ℎ𝐺2+𝑅2
𝐺= 150
2602+1702
260= 179 mm
Average thickness:
𝑡 =𝑦+(𝑦+𝑅)
2=
179+(179+170)
2= 𝟐𝟔𝟒 mm G
R y t
y
Example 3: Staircase Supported by Landing
For this type of staircase, design for LANDING and FLIGHT should be done
SEPARATELY !!!
Example 3: Staircase Supported by Landing
Action Landing Slab selfweight = 25.0 0.150 = 3.75 kN/m2
Permanent action (excluding selfweight) = 1.20 kN/m2
Characteristics permanent action, gk = 3.75 + 1.20 = 4.95 kN/m2
Characteristics variable action, qk = 3.00 kN/m2
Design action, nd = 1.35gk + 1.5qk = 11.18 kN/m2
Consider 1 m width, wd, landing = nd 1 m = 11.18 kN/m/m width
Example 3: Staircase Supported by Landing
Action Flight Slab selfweight = 25.0 0.264 = 6.61 kN/m2
Permanent action (excluding selfweight) = 1.20 kN/m2
Characteristics permanent action, gk = 6.61 + 1.20 = 7.81 kN/m2
Characteristics variable action, qk = 3.00 kN/m2
Design action, nd = 1.35gk + 1.5qk = 15.04 kN/m2
Consider 1 m width, wd, flight = nd 1 m = 15.04 kN/m/m width
Example 3: Staircase Supported by Landing
Analysis for Staircase
Effective span, Le = La + 0.5 (Lb1 + Lb2) La = Clear distance between supports = 2600 mm Lb1 = The lesser of width support 1 or 1.8 m = 200 mm Lb2 = The lesser of width support 2 or 1.8 m = 1500 mm
Le = 2600 + 0.5 (200 + 1500) = 3450 mm
Example 3: Staircase Supported by Landing
Note: F = wd L = (15.04 2.7 m) = 40.6 kN
M = FL/10 = 14.0 kNm
M = FL/10 = 14.0 kNm
L1 = 2.7 m L2 = 0.75 m
Le = Effective span
Support 1
Support 2
Analysis for Staircase
Example 3: Staircase Supported by Landing
Moment Design
Shear Check
Deflection Check
Cracking Check
Detailing
Self Study
Example 3: Staircase Supported by Landing
Analysis for Landing
w kN/m
L = 3.4 m
w = wlanding + Load from staircase = (11.18 1.5) + 11.8 (reaction from support 2) = 28.6 kN/m
𝑽𝒎𝒂𝒙 =𝒘𝑳
𝟐 𝟒𝟖. 𝟔 𝒌𝑵
𝑴𝒎𝒂𝒙 =𝒘𝑳𝟐
𝟖= 𝟒𝟏. 𝟑 𝒌𝑵𝒎
Example 3: Staircase Supported by Landing
Main Reinforcement Effective depth, d = 150 – 25 – 10/2 = 120 mm
𝐾 =𝑀
𝑓𝑐𝑘𝒃𝑑2 =41.3×106
25×𝟏𝟓𝟎𝟎×1202 = 0.077 Kbal = 0.167
Compression reinforcement is NOT required
𝑧 = 𝑑 0.25 −𝐾
1.134= 0.93𝑑 0.95d
𝐴𝑠 =𝑀
0.87𝑓𝑦𝑘𝑧=
41.3×106
0.87×500×0.93×120= 𝟖𝟓𝟒 mm2/m
Example 3: Staircase Supported by Landing
Minimum & Maximum Area of Reinforcement
𝐴𝑠,𝑚𝑖𝑛 = 0.26𝑓𝑐𝑡𝑚
𝑓𝑦𝑘𝑏𝑑 = 0.26
2.56
5000.0013𝑏𝑑 ≥ 0.0013𝑏𝑑
As,min = 0.0013bd = 0.0013 1500 120 = 240 mm2/m As,max = 0.04Ac = 0.04bh = 0.04 1500 120 = 9000 mm2/m
Main bar 17H10 (As = 1335 mm2/m)
Example 3: Staircase Supported by Landing
Shear Maximum design shear force, VEd = 48.6 kN/m
𝑘 = 1 +200
𝑑= 1 +
200
120= 2.29 2.0 Use k = 2.0
𝜌𝑙 =𝐴𝑠𝑙
𝒃𝑑=
1335
𝟏𝟓𝟎𝟎 × 130= 0.0074 ≤ 0.02
𝑉𝑅𝑑,𝑐 = 0.12𝑘 100𝜌𝑙𝑓𝑐𝑘1/3 𝒃𝑑
= 0.12 × 2.0 100 × 0.0074 × 25 1/3 𝟏𝟓𝟎𝟎 × 120 = 114350 N = 114.4 kN/m
𝑉𝑚𝑖𝑛 = 0.035𝑘3/2 𝑓𝑐𝑘 𝒃𝑑
= 0.035 × 2.03/2 25 𝟏𝟓𝟎𝟎 × 120 = 89095 𝑁 = 89.1 kN/m
VEd (48.6 kN/m) VRd,c (114.4 kN/m) OK
Example 3: Staircase Supported by Landing
Deflection Percentage of required tension reinforcement:
𝜌 =𝐴𝑠,𝑟𝑒𝑞
𝒃𝑑=
854
𝟏𝟓𝟎𝟎 × 120= 0.0047
Reference reinforcement ratio:
𝜌𝑜 = 𝑓𝑐𝑘 × 10−3 = 25 × 10−3 = 0.0050
Since o Use Eq. (7.16a) in EC 2 Cl. 7.4.2
Example 3: Staircase Supported by Landing
Factor or structural system, K = 1.0
𝑙
𝑑= 𝐾 11 + 1.5 𝑓𝑐𝑘
𝜌𝑜
𝜌+ 3.2 𝑓𝑐𝑘
𝜌𝑜
𝜌− 1
3/2
(l/d)basic = 1.0 (11 + 7.9 + 0.20) = 19.1 Modification factor for span less than 7 m = 1.00
Modification for steel area provided = 𝐴𝑠,𝑝𝑟𝑜𝑣
𝐴𝑠,𝑟𝑒𝑞=
1335
854= 1.56 1.50
(l/d)allow = 19.1 1.00 1.50 = 28.7 (l/d)actual = 3400/120 = 28.3 (l/d)allow
Deflection OK
Example 3: Staircase Supported by Landing
Cracking h = 150 mm 200 mm Main bar: Smax, slab = 3h (450 mm) 400 mm 400 mm
Max bar spacing =[1500−2 25 −10]
16= 90 𝑚𝑚 Smax, slab OK
Cracking OK
Example 3: Staircase Supported by Landing
Detailing
LETS DO IT
Example 4
TWO SPANS OF STAIRCASE INTERSECT AT RIGHT ANGLES
Example 4: Two Spans of Staircase Intersect at Right Angles
200 1500 10 @ 255 = 2550 200
200
1500
10 @ 255 = 2550
200
A A
Plan View
Example 4: Two Spans of Staircase Intersect at Right Angles
Section A-A
• Permanent action, gk = 1.0 kN/m2 (excluding selfweight)
• Variable action, qk = = 3.0 kN/m2 • fck = 25 N/mm2
• fyk = 500 N/mm2
• RC density = 25 kN/m3
• Cover, c = 25 mm • bar = 10 mm
G = 255
R = 170
h = 150
h = 150
Example 4: Two Spans of Staircase Intersect at Right Angles
Determine Average Thickness of Staircase
𝑦 = ℎ𝐺2+𝑅2
𝐺= 150
2552+1702
255= 180 mm
Average thickness:
𝑡 =𝑦+(𝑦+𝑅)
2=
180+(180+170)
2= 𝟐𝟔𝟓 mm G
R y t
y
Action & Analysis Landing Slab selfweight = 25.0 0.150 = 3.75 kN/m2
Permanent action (excluding selfweight) = 1.00 kN/m2
Characteristics permanent action, gk = 3.75 + 1.00 = 4.75 kN/m2
Characteristics variable action, qk = 3.00 kN/m2
Design action, nd = 1.35gk + 1.5qk = 10.91 kN/m2
Consider 1 m width, wd, landing = nd 1 m = 10.91 kN/m/m width
Example 4: Two Spans of Staircase Intersect at Right Angles
Action & Analysis Flight Slab selfweight = 25.0 0.265 = 6.63 kN/m2
Permanent action (excluding selfweight) = 1.00 kN/m2
Characteristics permanent action, gk = 6.63 + 1.00 = 7.63 kN/m2
Characteristics variable action, qk = 3.00 kN/m2
Design action, nd = 1.35gk + 1.5qk = 14.80 kN/m2
Consider 1 m width, wd, flight = nd 1 m = 14.80 kN/m/m width
Example 4: Two Spans of Staircase Intersect at Right Angles
Example 4: Two Spans of Staircase Intersect at Right Angles
Note: F = wd L = (5.46 1.6 m) + (14.80 2.65 m) = 48.0 kN
Analysis
M = FL/10 = 20.4 kNm
M = FL/10 = 20.4 kNm
L2 = 2.65 m L1 = 1.6 m
5.46 kN/m
Load on landing 2. WHY?
Example 4: Two Spans of Staircase Intersect at Right Angles
Main Reinforcement Effective depth, d = 150 – 25 – 10/2 = 120 mm
𝐾 =𝑀
𝑓𝑐𝑘𝒃𝑑2 =20.4×106
25×𝟏𝟎𝟎𝟎×1202 = 0.057 Kbal = 0.167
Compression reinforcement is NOT required
𝑧 = 𝑑 0.25 −𝐾
1.134= 0.95𝑑 0.95d
𝐴𝑠 =𝑀
0.87𝑓𝑦𝑘𝑧=
20.4×106
0.87×500×0.95×120= 𝟒𝟏𝟐 mm2/m
Example 4: Two Spans of Staircase Intersect at Right Angles
Minimum & Maximum Area of Reinforcement
𝐴𝑠,𝑚𝑖𝑛 = 0.26𝑓𝑐𝑡𝑚
𝑓𝑦𝑘𝑏𝑑 = 0.26
2.56
5000.0013𝑏𝑑 ≥ 0.0013𝑏𝑑
As,min = 0.0013bd = 0.0013 1000 120 = 160 mm2/m As,max = 0.04Ac = 0.04bh = 0.04 1000 120 = 6000 mm2/m
Secondary Reinforcement As = 20% of the main reinforcement = 0.20 412 = 82.4 mm2/m
Main bar H10-175 (As = 449 mm2/m) Secondary bar H10-400 (As = 196 mm2/m)
Example 4: Two Spans of Staircase Intersect at Right Angles
Shear Check
Deflection Check
Cracking Check
Detailing
Self Study
Other Types
Other Types