Design of steel staircase
Design of step
Design of Flat
INPUT
Density of steel
Try Flat of size
Width
Thickness
Tread of step
Number of Flats provided per tread
Grade of steel
Allowable bending stress
Allowable shear stress
bt = 0.66fy
b
t
T
fy
vm = 0.4fy
kN/m3
mm
mm
mm
=
=
=
=
=
78
30
4
220
8
=
=
=
250 N/mm2
165 N/mm2
100 N/mm2
ISMC 200
Loads
1) Live Load =
Live load on each flat =
2) Dead load of each flat (Trying a flat of crossection 30x4 mm 2)
Combination
(Dead load + Live load) on each flat
Maximum Bending Moment on each w
flatl2/ 8
Z = I /y = bd2/6
5 kN/m2
0.157143 kN/m
0.00936 kN/m
0.166503 kN/m
0.020813 kNm
Z = I /y = bd2/6
Section Modulus
600 mm3
b
y
d
x
Flat section
Actual max. Bending Stress in each flat
M/Z
Net Effective Ares of crossection
A
v
Actual shear stress
=
=
34.6881 N/mm2
O.K
120 mm2
0.693762 N/mm2
O.K
Actual Bending stress and shear stress is Less than Allowable Bending stress and shear stress
respectively hence the tried section is ok
Design of Double Angle section
Trying a section (2 ISA 40x40x4)
Length of Equal angle section
Load
Live Load
Dead load of Double angle section
Total Dead + Live load of Flats
Dead load + Live load transfer to each double angle
=
=
=
=
5
0.047
1.332023
3.027325
3.027325 KN/m
0.22 m
kN/m2
kN/m
KN
kN/m
Load Combination
( Total Dead Load + Live Load)
Maximum Bending Moment
w l2/ 8
0.018315 kNm
Section Modulus
Z = 2 * Ixx / y
Z
Ixx
3125 mm3
y
y
4.5 cm4
2.88 cm
From Steel Table
5.861 N/mm2
2 ISA 40x40x4
Actual Bending Stress
=
=
M/Z
O.K
Net Effective Area of cross-section as per IS: 800claus 4.2.1
For untacked double angle section
NEA available = 2* ( NEA of single angle )
= 2* (A1 + K A2)
A1 = (l1 - t/2 - nd')xt
A1
98 mm2
A2 = (l2 -t/2)xt
A2
152 mm2
K
NEA
=
=
0.659193
396.3946 mm2
K = 3A1/(3A1+A2)
Actual shear stress
0.84 N/mm2
O.K
Actual Bending stress and shear stress is Less than Allowable Bending stress and shear stress
respectively hence the tried section is ok
Design of Bolted connection
input
Thickness of web of ISMC 200 as per Steel Table
Thickness of Angle section ( ISA 40x40x4 )
Assuming Nominal Dia. of Bolt
Bolt in clearance holes
tw
t
d
=
=
=
6.1 mm
4 mm
12 mm
Permissible Shear stress in Bolts as per IS: 800
vf
80 N/mm2
Permissible Bearing stress in Bolts as per IS: 800
pf
250 N/mm2
2 ISA 40x40x4
Back to Back
tw
ISMC 200
e=
ISMC 200
20 mm
20 mm
2 ISA 40x40x4
In calculating the shear and bearing stress of bolt the effective diameter of a bolt is used that is its
nominal diameter as per IS : 800 clause 8.9.1
Gross dia of Bolt
Strength of Bolt in Bearing
d'
d tmin pf
=
=
=
Strength of Bolt in single shear
d 2* vf / 4
=
=
9047.787 N
9.048 kN
9.048 kN
0.666011 kN
Bolt value
Total Load which is to be transfered
No. of Bolt required
P
Bolt value
13.5 mm
12000 N
12 kN
0.07361
1 Bolt
Min Edge distance as per IS: 800 Table 8.2
emin r
17 mm
Provide Edge distance
eprovide
20 mm
=
=
=
4 mm
0.22 m
62.4 N/m
Provide M12 Bolt of Length
Design of side plate:
Try a plate of cross-section (200 x 4)
Length of plate
Dead Load of Plate
Load Combination
(Total Dead Load(Plate+Double angle section+Flats) + Live Load)
3.136725 KN/m
Maximum Bending Moment
0.018977 kNm
26666.67 mm3
0.711644 N/mm2
O.K
800 mm2
w l2/ 8
Section Modulus
Z = Ixx /y = bd2/6
b
y
d = 200
x
Actual Bending Stress
Net Effective Ares of crossection
mm
M/Z
A
v
0.862599 N/mm2
O.K
Actual Bending stress and shear stress is Less than Allowable Bending stress and shear stress
Actual shear stress
respectively hence the tried section is ok
