A Study of Self-Supporting Spiral Stair
A STUDY OF SELF SUPPORTING HELICAL STAIRCASE
A Project
\
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
Harshad J. Shah April 1973
.
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)
Radial Horizontal Sheari S }1,8
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---·-------·-----·--·----:-------··-----------·-- -------
A Project
\
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
Harshad J. Shah April 1973
.
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)
Radial Horizontal Sheari S }1,8
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---·-------·-----·--·----:-------··-----------·-- -------
References: 1. Mattock, l. H. , "Desiqn .:md Construction of a Helical staircase," Concr~te and Constructional Enqineering (London), v. 52, No. 3. March 1957, pp. 99-105. Morgan, V. A., "Comparison of Analysis of Helical S·tairs," Concre·te 2nd Constructional En9ineering (London), v. 55, No. 3. March 1960, pp. 127-132. Cusens 1 A. R., and 'I 'ri.rojna Supachai, "Helicoidal St~ircasc Study ' ', A.C.I. Journal, Proceedings, v. 61. January 1964, pp. 85-101. Holmes 1 J. M. C., "Analysis of Helical Beams Under Symmetrical Loading", Proceedings 1 lSCE, v. 8 3, ST6, November 1957, pp. 1437-l to 1437-37. Scordelis, ZL C. , "Internal Forces ln Uniformly Loaded Helicoidal Girders," !~.C. I. ,Journal, Proceedings, v. 56, No. 10, April 1960, pp. 1013-1026. Bergman I v. R. I "Eelicoidal s·taircases of Reinforced Concrete," l:c.C.I. Journal, Proceedings v. 53, No. 4. October 1956, pp. 403-412. Cohen, J. S. , 11 Desig·n of Helical Staircases," Concrete and Constructional Engineering (London), v. 50, No. 5, May 1955, pp. 181-194. Magnel (:!., "!