327985515-helical-staircase.xlsx
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NGASI CONSULTING ENGINEE
P. O BOX 2680 NAIROBI - 00202 TEL: 3860246, 2016972 FA NCCK JUMUIA CONFERENCE CENTRE, L FITNESS CENTRE HELICAL STAIRCASE CALCULATION
REF REINFORCED
Materials
CONCRETE
Concrete
fcu
=
20
N/mm2
DESIGNER'S
Reinforcement
fy
=
500
N/mm2
fyv
=
250
N/mm2
HANDBOOK
( C. E
REYNOLDS & J. C. STEEDMAN)
Cross section Depth of section
h
=
Width of stair
b
=
Cover
=
Diameter of main reinforcement
=
Internal radius, Ri
=
500
mm
External radius, Ro
=
1753
mm
Load Calculation Dead Load Concrete slab, gslab Steps, gsteps
=
h/1000*24
=
170 mm /1000 * 24
g = gslab
+ gsteps
Live Load q=
4
Ultimate Load Case =
1.4 g
+
For helical stair case of
1.200
m
kN/m2 1.6 q
width
W=
m. w
Design Moment, shear and torsion Total angle subtended by helix in plan,
β
Slope of tangent to helix centerline
φ
measured from horizontal Radius of centerline of loading, R1
=
2( Ro3-Ri3) 3( Ro2-Ri2)
Radius of Centerline of steps, R2
b =
=
R1 = R2
8.00
h Chart table
0.5* ( Ro+Ri )
1.10
Parameters
176 k1
=
k2
-0.01
=
Redundant moment acting tangentially at midspan Mo = k1.W.R22 Horizontal redundant force at midspan H = k2.W.R2 Vertical moment at supports Mvs = k3.W.R22 At support
θ=
0.5*β
0.70
NGASI CONSULTING ENGINEE
REF
P. O BOX 2680 NAIROBI - 00202 TEL: 3860246, 2016972 FA NCCK JUMUIA CONFERENCE CENTRE, L FITNESS CENTRE HELICAL STAIRCASE CALCULATION Lateral moment Mn = Mo.Sin(θ).Sin(φ) - H.R2.θ.Tan(φ).Cos(θ).Sin(φ) H.R2.Sin(θ)Cos(φ) + W.R1.Sin(φ).(R1Sin(θ)-R2.θ) Torsional moment T = (Mo.Sin(θ)- H.R2.Cos(θ).Tan(φ) + W.R12Sin(θ) - W.R1.R2.θ).Cos(φ) + H.R2.Sin(θ)Sin(φ) Vertical moment My = Mo.Cos(θ) + (H.R2.θ.Tan(φ).Sin(θ)) - W.R12.(1-Cos(θ)) Thrust N = -H.Sin(θ).Cos(φ) - W.R1.θ.Sin(φ) Lateral shearing force across stair Vn = W.R1.θ.Cos(φ) - H.Sin(θ).Sin(φ) Radial horizontal shearing force Vh = H.Cos(θ)
Design of edge tension reinforcement Design moment
=
Lateral Moment, Mn
�= 𝑀/(𝑓_𝑐𝑢 ℎ 〖� _1 〗 _^2 ) �= �_1 [0.5+ √((0.25− �/0.9) )]
= k
=
�= �_1 [0.5+ √((0.25− �/0.9) )]
Reinforcement
�_(𝑠 )= 𝑀/ (0.95𝑓_𝑦 �)
Provide
z
=
�_𝑠
=
�_(𝑠 𝑝𝑟𝑜𝑣)
3 Y12
=
Design of tension reinforcement Design moment
=
Vertical Moment, My
�= 𝑀/(𝑓_𝑐𝑢 𝑏�_^2 )
k
=
z
=
�_𝑠
=
�= �_1 [0.5+ √((0.25− �/0.9) )]
Reinforcement
�_(𝑠 )= 𝑀/ (0.95𝑓_𝑦 �)
Provide
5 Y10
Distribution reinforcement Provide
Y8 @
=
=
�_(𝑠 𝑝𝑟𝑜𝑣)
=
0.13/10 0 𝑏ℎ
= �_(𝑠 𝑝𝑟𝑜𝑣)
150 mm centers
Shear reinforcement Design shear
=
Lateral shearing force across stair, Vn Average shear stress,
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 (5, 0.8√(𝑓_𝑐𝑢 ))
𝑣= 𝑉_𝑛/𝑏�
Limiting shear =
𝑣_𝑐= 0.79/1.25 × [(100�_𝑝𝑟𝑜𝑣)/𝑏�]^(1/3) × [400/�]^(1/4) ∴
𝑣_𝑙𝑖 𝑚
𝑣_𝑐= 0.79/1.25 × [(100�_𝑝𝑟𝑜𝑣)/𝑏�]^(1/3) × [400/�]^(1/4) ∴
No shear reinforcement required
NGASI CONSULTING ENGINEE
P. O BOX 2680 NAIROBI - 00202 TEL: 3860246, 2016972 FA NCCK JUMUIA CONFERENCE CENTRE, L FITNESS CENTRE HELICAL STAIRCASE CALCULATION
REF
Torsional resistance Design torsion =
Ttor
Check torsion reinforcement
hmin = hmax =
Shear stress induced by torsion
=
𝑣_𝑡 = (2 𝑇_𝑡𝑜𝑟)/( 〖ℎ _𝑚𝑖𝑛 〗 ^2 [ℎ_𝑚𝑎𝑥 − ℎ_𝑚𝑖𝑛/3] )
Limiting torsional shear stress Provide torsional reinforcement Links
6
Distance to center of links Link dimensions Link spacing
=
Torsional resistance
Y10
t=
35
𝑥_1=𝑏−2𝑡
150 mm
𝑇_𝑟=0.8[�_𝑠𝑣/𝑠_𝑣 . 𝑥_1. 𝑦_1. 〖 0.95𝑓 〗 _𝑦𝑣 ]
Check for torsion combined with bending and shear stress v = v t + vf Total shear Limiting shear ∴
=𝑀𝑖𝑛(5 , 0.8√(𝑓_𝑐𝑢 ))
=
3.58
Safe for torsion combined with bending and shear stress
CONSULTING ENGINEERS
202 TEL: 3860246, 2016972 FAX: 2016973 MUIA CONFERENCE CENTRE, LIMURU FITNESS CENTRE HELICAL STAIRCASE CALCULATION
150
mm
1200
mm
25
mm
12
mm
12/303
PAGE
1
DATE
Jun-12
MADE BY
JWM
OUTPUT
d= d1=
kN/m3
=
3.75
kN/m2
kN/m3
=
4.25
kN/m2
=
8
kN/m2
=
17.6
kN/m2
w
JOB NO
119
mm
1169
mm
W
=
21.12
kN/m
=
219
°
=
3.82
rads
=
35.49
°
=
0.62
rads
R1
=
1.24
m
R2
=
1.13
m
k3
=
-0.20
Mo
=
-0.17
kNm
H
=
16.57
kNm
Mo
=
-5.25
kNm
θ
=
1.91
rads
( Ro+Ri )
m
CONSULTING ENGINEERS
202 TEL: 3860246, 2016972 FAX: 2016973 MUIA CONFERENCE CENTRE, LIMURU FITNESS CENTRE HELICAL STAIRCASE CALCULATION
0.01
�_1
12/303
PAGE
2
DATE
Jun-12
MADE BY
JWM
OUTPUT
Mn
=
-24.44 kNm
T
=
-11.18 kNm
My
=
-17.77 kNm
N
=
-41.84 kN
Vn
=
31.77
kN
Vh
=
-5.53
kN
R12Sin(θ) - W.R1.R2.θ).Cos(φ) +
-24.44 kNm
JOB NO
0.95
�_1
46
mm2
339
mm2
�_(𝑠 𝑟𝑎𝑡𝑖𝑜 )
=
0.19 %
�_(𝑠 𝑟𝑎𝑡𝑖𝑜 )
=
0.22 %
-17.77 kNm 0.05
0.94 �_1
�_(𝑠 𝑝𝑟𝑜𝑣)
335
mm2
393
mm2
234
mm2
=
335
mm2
=
31.77
kN
=
0.22
N/mm2
=
5.00
N/mm2
=
0.53
N/mm2
v
<
vc
CONSULTING ENGINEERS
202 TEL: 3860246, 2016972 FAX: 2016973 MUIA CONFERENCE CENTRE, LIMURU FITNESS CENTRE HELICAL STAIRCASE CALCULATION
JOB NO
12/303
PAGE
3
DATE
Jun-12
MADE BY
JWM
OUTPUT
-11.18 kNm 150
mm
1200
mm
𝑇_𝑡𝑜𝑟)/( 〖ℎ _𝑚𝑖𝑛 〗 ^2 − ℎ_𝑚𝑖𝑛/3] )
𝑣 _ 𝑡
𝑣_(𝑡 𝑚𝑖𝑛)
mm mm
Asv
0.86
N/mm2
=
0.40
N/mm2
=
471 mm2
𝑦_1=ℎ−2𝑡 𝑇_𝑟 =
v= 3.58
=
N/mm2
ned with bending and shear stress
54 kNm
1.09
N/mm2
vt
>
vtmin
x1
=
1130
mm
y1
=
80
mm
P. O BOX 2680 NAIROBI - 00202 TEL: 3860246, 2016972 FA NCCK JUMUIA CONFERENCE CENTRE, L FITNESS CENTRE HELICAL STAIRCASE CALCULATION
REF REINFORCED
Materials
CONCRETE
Concrete
fcu
=
20
N/mm2
DESIGNER'S
Reinforcement
fy
=
500
N/mm2
fyv
=
250
N/mm2
HANDBOOK
( C. E
REYNOLDS & J. C. STEEDMAN)
Cross section Depth of section
h
=
Width of stair
b
=
Cover
=
Diameter of main reinforcement
=
Internal radius, Ri
=
500
mm
External radius, Ro
=
1753
mm
Load Calculation Dead Load Concrete slab, gslab Steps, gsteps
=
h/1000*24
=
170 mm /1000 * 24
g = gslab
+ gsteps
Live Load q=
4
Ultimate Load Case =
1.4 g
+
For helical stair case of
1.200
m
kN/m2 1.6 q
width
W=
m. w
Design Moment, shear and torsion Total angle subtended by helix in plan,
β
Slope of tangent to helix centerline
φ
measured from horizontal Radius of centerline of loading, R1
=
2( Ro3-Ri3) 3( Ro2-Ri2)
Radius of Centerline of steps, R2
b =
=
R1 = R2
8.00
h Chart table
0.5* ( Ro+Ri )
1.10
Parameters
176 k1
=
k2
-0.01
=
Redundant moment acting tangentially at midspan Mo = k1.W.R22 Horizontal redundant force at midspan H = k2.W.R2 Vertical moment at supports Mvs = k3.W.R22 At support
θ=
0.5*β
0.70
NGASI CONSULTING ENGINEE
REF
P. O BOX 2680 NAIROBI - 00202 TEL: 3860246, 2016972 FA NCCK JUMUIA CONFERENCE CENTRE, L FITNESS CENTRE HELICAL STAIRCASE CALCULATION Lateral moment Mn = Mo.Sin(θ).Sin(φ) - H.R2.θ.Tan(φ).Cos(θ).Sin(φ) H.R2.Sin(θ)Cos(φ) + W.R1.Sin(φ).(R1Sin(θ)-R2.θ) Torsional moment T = (Mo.Sin(θ)- H.R2.Cos(θ).Tan(φ) + W.R12Sin(θ) - W.R1.R2.θ).Cos(φ) + H.R2.Sin(θ)Sin(φ) Vertical moment My = Mo.Cos(θ) + (H.R2.θ.Tan(φ).Sin(θ)) - W.R12.(1-Cos(θ)) Thrust N = -H.Sin(θ).Cos(φ) - W.R1.θ.Sin(φ) Lateral shearing force across stair Vn = W.R1.θ.Cos(φ) - H.Sin(θ).Sin(φ) Radial horizontal shearing force Vh = H.Cos(θ)
Design of edge tension reinforcement Design moment
=
Lateral Moment, Mn
�= 𝑀/(𝑓_𝑐𝑢 ℎ 〖� _1 〗 _^2 ) �= �_1 [0.5+ √((0.25− �/0.9) )]
= k
=
�= �_1 [0.5+ √((0.25− �/0.9) )]
Reinforcement
�_(𝑠 )= 𝑀/ (0.95𝑓_𝑦 �)
Provide
z
=
�_𝑠
=
�_(𝑠 𝑝𝑟𝑜𝑣)
3 Y12
=
Design of tension reinforcement Design moment
=
Vertical Moment, My
�= 𝑀/(𝑓_𝑐𝑢 𝑏�_^2 )
k
=
z
=
�_𝑠
=
�= �_1 [0.5+ √((0.25− �/0.9) )]
Reinforcement
�_(𝑠 )= 𝑀/ (0.95𝑓_𝑦 �)
Provide
5 Y10
Distribution reinforcement Provide
Y8 @
=
=
�_(𝑠 𝑝𝑟𝑜𝑣)
=
0.13/10 0 𝑏ℎ
= �_(𝑠 𝑝𝑟𝑜𝑣)
150 mm centers
Shear reinforcement Design shear
=
Lateral shearing force across stair, Vn Average shear stress,
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 (5, 0.8√(𝑓_𝑐𝑢 ))
𝑣= 𝑉_𝑛/𝑏�
Limiting shear =
𝑣_𝑐= 0.79/1.25 × [(100�_𝑝𝑟𝑜𝑣)/𝑏�]^(1/3) × [400/�]^(1/4) ∴
𝑣_𝑙𝑖 𝑚
𝑣_𝑐= 0.79/1.25 × [(100�_𝑝𝑟𝑜𝑣)/𝑏�]^(1/3) × [400/�]^(1/4) ∴
No shear reinforcement required
NGASI CONSULTING ENGINEE
P. O BOX 2680 NAIROBI - 00202 TEL: 3860246, 2016972 FA NCCK JUMUIA CONFERENCE CENTRE, L FITNESS CENTRE HELICAL STAIRCASE CALCULATION
REF
Torsional resistance Design torsion =
Ttor
Check torsion reinforcement
hmin = hmax =
Shear stress induced by torsion
=
𝑣_𝑡 = (2 𝑇_𝑡𝑜𝑟)/( 〖ℎ _𝑚𝑖𝑛 〗 ^2 [ℎ_𝑚𝑎𝑥 − ℎ_𝑚𝑖𝑛/3] )
Limiting torsional shear stress Provide torsional reinforcement Links
6
Distance to center of links Link dimensions Link spacing
=
Torsional resistance
Y10
t=
35
𝑥_1=𝑏−2𝑡
150 mm
𝑇_𝑟=0.8[�_𝑠𝑣/𝑠_𝑣 . 𝑥_1. 𝑦_1. 〖 0.95𝑓 〗 _𝑦𝑣 ]
Check for torsion combined with bending and shear stress v = v t + vf Total shear Limiting shear ∴
=𝑀𝑖𝑛(5 , 0.8√(𝑓_𝑐𝑢 ))
=
3.58
Safe for torsion combined with bending and shear stress
CONSULTING ENGINEERS
202 TEL: 3860246, 2016972 FAX: 2016973 MUIA CONFERENCE CENTRE, LIMURU FITNESS CENTRE HELICAL STAIRCASE CALCULATION
150
mm
1200
mm
25
mm
12
mm
12/303
PAGE
1
DATE
Jun-12
MADE BY
JWM
OUTPUT
d= d1=
kN/m3
=
3.75
kN/m2
kN/m3
=
4.25
kN/m2
=
8
kN/m2
=
17.6
kN/m2
w
JOB NO
119
mm
1169
mm
W
=
21.12
kN/m
=
219
°
=
3.82
rads
=
35.49
°
=
0.62
rads
R1
=
1.24
m
R2
=
1.13
m
k3
=
-0.20
Mo
=
-0.17
kNm
H
=
16.57
kNm
Mo
=
-5.25
kNm
θ
=
1.91
rads
( Ro+Ri )
m
CONSULTING ENGINEERS
202 TEL: 3860246, 2016972 FAX: 2016973 MUIA CONFERENCE CENTRE, LIMURU FITNESS CENTRE HELICAL STAIRCASE CALCULATION
0.01
�_1
12/303
PAGE
2
DATE
Jun-12
MADE BY
JWM
OUTPUT
Mn
=
-24.44 kNm
T
=
-11.18 kNm
My
=
-17.77 kNm
N
=
-41.84 kN
Vn
=
31.77
kN
Vh
=
-5.53
kN
R12Sin(θ) - W.R1.R2.θ).Cos(φ) +
-24.44 kNm
JOB NO
0.95
�_1
46
mm2
339
mm2
�_(𝑠 𝑟𝑎𝑡𝑖𝑜 )
=
0.19 %
�_(𝑠 𝑟𝑎𝑡𝑖𝑜 )
=
0.22 %
-17.77 kNm 0.05
0.94 �_1
�_(𝑠 𝑝𝑟𝑜𝑣)
335
mm2
393
mm2
234
mm2
=
335
mm2
=
31.77
kN
=
0.22
N/mm2
=
5.00
N/mm2
=
0.53
N/mm2
v
<
vc
CONSULTING ENGINEERS
202 TEL: 3860246, 2016972 FAX: 2016973 MUIA CONFERENCE CENTRE, LIMURU FITNESS CENTRE HELICAL STAIRCASE CALCULATION
JOB NO
12/303
PAGE
3
DATE
Jun-12
MADE BY
JWM
OUTPUT
-11.18 kNm 150
mm
1200
mm
𝑇_𝑡𝑜𝑟)/( 〖ℎ _𝑚𝑖𝑛 〗 ^2 − ℎ_𝑚𝑖𝑛/3] )
𝑣 _ 𝑡
𝑣_(𝑡 𝑚𝑖𝑛)
mm mm
Asv
0.86
N/mm2
=
0.40
N/mm2
=
471 mm2
𝑦_1=ℎ−2𝑡 𝑇_𝑟 =
v= 3.58
=
N/mm2
ned with bending and shear stress
54 kNm
1.09
N/mm2
vt
>
vtmin
x1
=
1130
mm
y1
=
80
mm
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