Stairs

1/7-Stairs

Stairs

2/7-Stairs

Design of step:

Steps are made of checkered plate

6/8 as shown

Assume o.w. of step = 20 kg / m\

L.L = 300 500 kg / m2

F.C. may be used

W =1000

20 + (F.C. + L.L.) b

Calculate M =8

2wa Q =2

wa

Fbcx = 1.4 t/cm2 (lip is small, so neglect L.T.B.)

Check f, q, aLL =300

d

Width of stairs is about 11.5 m

Slope is 1:2 in most cases.

Design of stair beam: (Usually used as channel)

26.5q

assume o.w. = 25 kg/m\

weight of step, handrail, (all steel structure)

ws = 70 kg/m2/hz proj

L.L = 300 500 kg / m2

F.C. = .. if any

W =1000

25 + (70 + F.C. + L.L.) (a/2)

Draw M, Q, (neglect normal)

M =8

2wL Q =2

wL

Lu act = zero

b = 30 cm

Checkered plate

5-7

a

(6.00)

a

(4.50)

(3.00)

aa

Beam at 1/2 floor level

R 1M

2M

w = ...... t/m'

12

Stairs

3/7-Stairs

Fbcx = 1.4 t/cm2

dmin of channel ????????

Check f, q, d

Design of connection using butt weld:

hhw=

h =weldh

2coschannel

C

13

2

Calculate Ix

Check yIM

x = ..< 0.7 ft (allowable of good butt weld subjected to tension due

to moment or due to tension). Look ECP page

Design of beam at 1/2 floor height: (Usually IPE)

R = Reaction of stair beam

Calculate M, Q

If channel is flushed & checkered plate is

welded, so Lu act = zero

If we use grating Lu act = a

Design of connection between channel & I beam:

Force = Rt Rss, Rb as before

3

2

1

0

L70*726.5

42h-2t

a a

R RR R

Stairs

4/7-Stairs

Solved example:

It is required a complete design of stairs

(steps, beam of stairs with its connection &

beam at 1/2 floor height)

Given that: L.L. = 400 kg/m2, F.C. =150

kg/m2

Solution:

Design of step:

Assume o.w. of step = 20 kg/m\

Take shape of step as Z section (assume b = 30cm) (checkered plate 6/8)

WDL = 20 + 150 * 0.3 = 65 kg/m\

WLL = 400 * 0.3 = 120 kg/m\

WT = 120 + 65 = 185 kg/m\

M = 0.185 *825.1 2 = 0.036 mt = 3.6 cmt

Q = 0.185 * (1.25/2) = 0.11 t

Ix = 126.0*30 3 (neglected) + 2

+ 2

35.2*4.4*6.0

124.4*6.0 = 41.52 cm4

Checks:

1. f =52.41

7.4*6.3 = 0.41 t/cm2 < 1.4 t/cm2

(Lip is small, so we can neglect L.T.B)

2. q =6.0*5*2

11.0 = 0.02 t/cm2

Stairs

5/7-Stairs

Design of stair beam:

Assume o.w. = 25 kg/m\

Weight of other steel structure is 70 kg/m\

WDL = 25 + (70 + 150) * (1.25 / 2)

= 162.5 kg/m\

WLL = 400 * (1.25 / 2) = 250 kg/m\

Wtotal = 250 + 162.5 = 412.5 kg/m\

M =8

5.5*41.0 2 = 1.56 mt

Q = 0.41 * (5.5 / 2) = 1.13 t

Assume Fbcx = 1.4 t/cm2

Sx = 156 / 1.4 = 111 cm3

Choose channel 160

Checks:

Lu act = zero So No L.T.B.

ftc =

05.105.175.05.6 -- = 4.48 < 10.9

w

wtd

= 11.6 / 0.75 = 15.5 < 82

Therefore, the section is not slender (simply symmetric channel)

1. f = 156 / 116 = 1.34 t/cm2 < 1.4 t/cm2

2. q =75.0*16

13.1 = 0.09 t/cm2 < 0.84 t/cm2

3. 64

.. 10*925*21005.5*25.0*

3845

=LLd = 1.53 cm < 550/300 = 1.83cm

1.13

w = 0.41 t/m'

1.561.41

Stairs

6/7-Stairs

Min channel:

94.92

2=

- th (From drawing)

cmt 1 h = 22 cm

Choose channel minimum 220

Design of connection butt weld:

M connection = 1.13 * 1.25 = 1.41 mt o25.132=

q

hweld = 25.13cos22 = 22.6 cm

Ix = 23

)225.1

26.22(*)9.08(*25.1*2

126.22*9.0

--+ = 2888.4 cm4

f = 55.02

6.22*4.2888

141= t/cm2 < 0.7*1.4 = 0.98 t/cm2

Design of connection between channel & beam at 1/2 floor beam:

R = 1.13 t (use only one angle)

Rss = 4*25.0*6.1*42p = 2.01t

tmin is smaller of 0.7 or 0.9 (tw of channel)

Rb = (0.8 * 3.6)*1.6*0.7 = 3.22 t

n = 1.13 / 2.01 = 0.56 use 2 bolts min

plateChequerd L70*7

=9.94

2h-2t30cm 5cm

L70*726.5

0

t=0.922.6

t=1.258

Stairs

7/7-Stairs

Design of beam B (at mid floor level)

Rtotal stair beam = 1.13 t, O.W. = 50 kg/m'

RLL stair beam = 0.25 * 5.5 / 2 = 0.69 t

(To be used in check of deflection)

Mconc = 2.385 x 2.25 1.13 x 1.25 0.05 x

1.252 /2= 3.83 mt

Q = 0.03 x 5 / 2 + 1.13 x 4 / 2 = 2.385 mt

Assume Fbcx = 0.64 Fy = 1.54 t/cm2

Sx = 383/ 1.54 = 259 cm3 choose IPE 220

Checks:

ftc =

92.02.1*259.011 -- = 8.7 < 10.9 ,

w

wtd

= 21.2 / 0.59 =35.9 < 82

Assume using checkered plate welded to upper flange of beam

So Lu act = zero Fbcx = 0.64 Fy1. f = 383 / 252 = 1.52 t/cm2 < 1.54 t/cm2

2. q = 2.3822*0.59

= 0.18 t/cm2 < 0.84 t/cm2

3.510.69 1.725

0.54 0.56

0.690.69 0.69

1.25 1.25

3. deflection due to live load only " RLL stair beam "

eM = 3.51 * 2.5 0.56 * (0.25/2) 0.54 * (0.5 + 1.25/3) 1.725 * (0.25 +

1.25/2) 0.69 * (0.25 + 1.25 + 1/3) = 5.43 m3t

2770*210010*43.5 6

.. =LLd = 0.93 cm < 550/300 = 1.67cm

1.25 1.25

1.13 1.13 1.13

1.00 1.000.5

0.05