# A Study of Self-Supporting Spiral Stair

Topics: Shear stress, Force, Concrete Pages: 23 (1570 words) Published: August 28, 2012
A STUDY OF SELF SUPPORTING HELICAL STAIRCASE

A Project
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Presented to the Department: of Civil Engineering Science Brigham Young University

In Partial Fulfillment of the Requirements for the Degree Master of Civil. Engineering

by

.
This project, by Harshad J. Shah, is accepted in its present form by the Department of Civil Engineering Science of Brigham Young University as satisfying in part the requirements for the degree of Master of Civil Engineering.

--~~~~~~=~~~---Arnold Pilson, Committee Chairman
~d-

/

4.

-~ ~
I

/jG

, L I ________., / /
X
--~---.1.

~f:>i

;{

,A

_tc•) )
/
PLAN

~/3(10~--=-42)
1i

-

4
2

3

=

7·45'

--

=

=

) X 100 3·14(10 4 2 ) x 100 26376 lbs 26·5 kips (say)

(H

2

-

r

2

10

he B

PLAN

DEVELOPED ELEVli'l'ION

Using the formula developed by V. A. Morgan, and using his substitutions a - 8-y and 8 = 8 + B/2 In this problem, y = 0, a = 8 __ M',)n \ TL., r•-:_i r

0

- 18 0

X

TI

(4)

12 Force Across the Waist of the Stairs Sno

= wR 1 8 Cos ¢ - H Sin 8 Sin ¢ =
1•6
X

7·45

X

e

x

180

--

11

X

0•9527 -

37•0

X

Sin 8

X

•3038

S

no

= 11·35

X

8 X 'IT ·- 11 • 2 4 S in 8 180

(5)

Force
( 6)

= H Cos 9 - 37·0 Cos G

Now substituting value of G from 0° to ± 180° in equations (l) to

(6), different values are obtained which are plotted.

Following are the maximum values which are used in design. See Figures (l) to (4).

)I'

y

In X Direction Max. + JVIax. Max. + Max. ve
V'C

ve

M
I-1

r

- 133·2 k. ft.

@8 =
@8

oo
120°

r

=
::::

81·7 k. ft.

=

s1.1
c

+ 37·0 k.
37·0 k.

@
€.1

e = oo
0
-"·

''h

::::

± 180°

14

(\ ---~--r
501----

-l

·------j \

I

J

0 1---·-------·-----·--·----:-------··-----------·-- ------- ----"--·--------!

-so~+--

~

~--

-100~--------·------------------

-1800 -150° -120°-90°-60° -30°

0

Values of 8

Fig. l. Showina relationships between radial moment and angle of turning.

16

200

150

/-~

I

100

[_.______ ~---·------·-----·--J
I \
\--

1 r

f

~\

'

I-

sol
0 r-·-----

\ ·--\

-50 ! - - - - - - - - - - -

J

~100

----------->q--------·~---------1

-150

l
-60
--------------------------~

-200 -180 -150 -120 -90 -30
0

30

60

90

120

150

180

Values of 8 Fiq, 3. --Shm1ing rolo.tionships between torsion and angle of turning.

15

150

r----~-~

1

100

I

50
li-~

-JJ
!

/r-\ I I ' ,---.,----------

I
I I
I

!

1-

I
j

.q
r-1

rc: ):!
rd
U)

0

_____L ____

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