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

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
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Geometrical Classification
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Geometrical Classification
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Structural Classification-Stair
spanning longitudinally
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2. Lecture Notes 15 July 2010
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Structural
Classification-Stair
spanning
transversely
Parts of a stair
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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
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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
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Stair spanning horizontally
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Stair spanning horizontally
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Stair spanning horizontally
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Stair spanning longitudinally
Slab between beams
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Stair spanning longitudinally
Slab between landings
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Stair spanning longitudinally
Slab between walls
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Dead Loads
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Live Loads
• Live Load (IS 875)
– Residential building without overcrowding – 2 kN/m2
– Public building with overcrowding – 5 kN/m2
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Depth of Section
• One way reinforced slab
– Longitudinally spanning – min thickness = W
– Transverse spanning – average depth of step; D/2
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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
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Calculation of Dead Loads and
Effective Depth
• Transverse Stair
– Effective span = width of stair
– Individual steps of width = G and span = width of
stair
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Calculation of Dead Loads and
Effective Depth
• Longitudinally spanning Stair
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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
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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
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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.
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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

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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
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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
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Homework
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LOADS AT SECTION 1-1
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