This is a Lecture Series. Find other parts in profile Contact for Guest lecture and Seminars https://armanav.wixsite.com/studio8d

1. Domes and Space framesDomes and Space frames
Part 4
Appropriate technologies
Ar. Manav Mahajan

2. CCONSTRUCTING A DOMEONSTRUCTING A DOME
by TRIANGULATION combines two of the most stable structures i.e.
THE TRIANGLE WITH THE HEMISPHERE
•All the triangles are near equilateral triangles, but are never so.
•The basic triangle of AN ICOSAHEDRON is subdivided into smaller triangles.
• Each NODE lifted to meet the surface of the sphere.
• More the SUB-DIVISIONS, smoother the dome.
• Each side of the sub-divided triangle = chord factor,
which is multiplied by the radius to give the straight length
of each member.

3. GENERATION OF DOME _ ICOSAHEDRONGENERATION OF DOME _ ICOSAHEDRON
METHOD OF CONSTRUCTIONMETHOD OF CONSTRUCTION
1. Draw a Pentagon of side “ A” on XY
plane . Draw the medians to find the
centre of the “Polyhedron”.
2. Draw a line CB along Z – axis ( where ,
length of the line CB, R = A/ 1.051) .
Draw another line CD in ZX – plane
subtending angle 63 d 26 min 5.47
sec to line CB.
here R is the radiusR is the radius of the Geodesic Dome
to be constructed
1. ALIGN the mid point of vertical line CB
to meet the centre of the pentagon and
inclined line CD to meet the vertex of the
same.
2. Join all the vertices of pentagon to the
point B of the vertical line.
5. Duplicate & Rotate all the five faces such
that it forms a dihedral angle
(angle between the adjacent faces of the
icosahedron ) of 138 d 11’
6. Repeat the process for the second half.
Rotate it and join it with the former half.
A
B
D
B
D
B
D
R
A
R
R

4. GGENERATION OF DOME _ ICOSAHEDRONENERATION OF DOME _ ICOSAHEDRON
METHOD OF CONSTRUCTIONMETHOD OF CONSTRUCTION
7. An ICOSAHEDRON is
obtained.
8. The faces (triangular) of the
Icosahedron are
subdivided into smaller
triangles. Based on the
required accuracy of the
curvature, More
subdivisions ensure
smoother sphere.
9. Join the vertices of the
triangle to the centre, C.
10. Extend the lines (equal to
radius =R) so as they
provide the points lying
at the sphere. These
points are now the new
vertices.
11. Join all these points
(vertices) to get the
spherical triangle as
shown.
12. Repeat the process with
other faces to get final
Geodesic
B
R
B’

5. GENERATION OF DOME
GEODESIC DOME SHOWING THE BASIC ICOSAHEDRON

7. THE GREAT EGYPTIAN MUSEUM

8. ELEVATION

11. DDODECAHEDRONODECAHEDRON

12. 1. Draw a Regular pentagon
and similar pentagons on each of
its side.
2. Rotate the outer Pentagons
around the common edges as an
axis, such that it forms an angle of
116 d 34’ with the other pentagons.
( 116 d 34’ is the angle between
any two faces of Dodecahedron)
3. Half of the Dodecahedron
is formed . Repeat the process for
the second half . Rotate it and
join it with the former half.
Dodecahedron is complete.
GGENERATION OF DOME _ DODECAHEDRONENERATION OF DOME _ DODECAHEDRON
METHOD OF CONSTRUCTIONMETHOD OF CONSTRUCTION
4. Join any of the vertices
( say A) with the opposite
vertex ( say B) , to get the
Diameter AB of the sphere
with C as its centre.
( radius of geodesic, R = ½
AB)
5. All the edges are the
chords of the sphere
A
B
C

13. GGENERATION OF DOME _ DODECAHEDRONENERATION OF DOME _ DODECAHEDRON
METHOD OF CONSTRUCTIONMETHOD OF CONSTRUCTION
6. Chord factors = length
of the members (chords)
for radius of sphere
equal to 1. therefore,
scale down the drawing
of Dodecahedron by 1/ R
so that the radius
becomes equal to 1 unit.
7. Join the centre of the
pentagon with the
centre C and lengthen it
to 1 unit so that it
touches the sphere.
8. From this elevated point
join all the vertices of
that particular
Pentagon . Five triangles
are formed . Based on
the required accuracy of
the curvature, subdivide
the triangles into
smaller triangles. More
subdivisions ensure
smoother sphere..
9. Join the vertices of
subdivided triangle to the
Centre and lengthen them to
1 unit . Extended lines provide
the points lying at the sphere.
These points are now the new
vertices. Join all these points
(vertices) to get the spherical
triangle as shown.
10. Measure all the distances
between two adjacent
vertices, which are the Chord
Factors. Categorize them
such that same lengths fall in
one category ( say A1, B1, C1)
A
B
C
A
B
C
A
B
C
A
B
C

14. OOCTAGEDULECTAGEDULE
BHARTIYAMGRAM , DELHIBHARTIYAMGRAM , DELHI

15. GGENERATION OF _OCTAGEDULEENERATION OF _OCTAGEDULE
METHOD OF CONSTRUCTIONMETHOD OF CONSTRUCTION
1. Draw two tetrahedra of
same size and join them
at the base to form an
octahedron.
2. Join the opposite
extreme vertices to
form the diameter - AB
of the octagedule.
3. The faces (triangular) of
the Octahedron are
subdivided into smaller
triangles. Based on the
required accuracy of the
curvature. More
subdivisions ensure
smoother sphere.
4. Join the vertices of the
subdivided triangle to the
Centre. Lengthen them to
1 unit . Extended lines
provide the points lying at
the sphere. These points
are now the new vertices.
A
B
A
B
C
5. Join all these points
(vertices) to get the
spherical triangle as
shown.
6. Repeat the process
Measure all the distances
between two adjacent
vertices, which are the
Chord Factors.
Categorize them such
that same lengths fall in
one category ( say A1,
B1, C1)
A
B

17. ELEVATION
SECTION

18. BHARATYAMGRAM

19. BHARATYAMGRAM

20. COMPLEX JOINERY SYSTEM
CONVENTIONAL BALL JOINT
CCONVENTIONAL JOINTSONVENTIONAL JOINTS
Each joint weighs 250
kgms costing Rs. 22000/-

22. PPLATE JOINT SYSTEMLATE JOINT SYSTEM

24. PPLATE JOINT SYSTEMLATE JOINT SYSTEM

25. PLATE JOINTS

26. Construction of a geodesic
dome

27. Construction of a geodesic
dome

28. SSPACEFRAMESPACEFRAMES
• EXPOSITION CENTRE, BANGALOREEXPOSITION CENTRE, BANGALORE
• JOB, BALLABGARH, NEAR DELHIJOB, BALLABGARH, NEAR DELHI
• STADIUM, NOIDASTADIUM, NOIDA

29. • A BALL JOINT which serves as the connector
for tubular steel members.
• MANUFACTURE of the ball joint is a complex affair
• The reliance of the joint only ON THE THREADING
is not an entirely appropriate solution.
• A HINGED NODE - cannot be assembled on the ground
and hoisted into position.
• An EXPENSIVE DECKING at the level of the assembly is
often required WATER PROOFING IN 5 LAYERS
FERROCEMENT 30 MM THK
ALL PIPES CENTRE
TO CENTRE OF
BALL 80 MM
NOMINAL BORE
HEAVY DUTY PIPES
150X150X5 MM PLATE SCREWED INTO
BALLOR SEATING FRAME FOR
FERROCEMENT
THREADED ENDS MUST BE
AT LEAST AS STRONG AS
THE PIPES THEY CONNECT
AA FLAWEDFLAWED CONVENTIONAL SYSTEM- THE USE OF BALLCONVENTIONAL SYSTEM- THE USE OF BALL
NODESNODES

30. SSIMPLIFIED _ SPACE FRAMESIMPLIFIED _ SPACE FRAMES
A FAR SUPERIOR SOLUTIONA FAR SUPERIOR SOLUTION - THE WELDED NODE- THE WELDED NODE
• a simple and cost effective node.
• without butt welds
• fabricated on the ground – checked –
hoisted into position
• with the help of simple derricks and winches.

31. SPACE FRAMES
SPACE FRAME USING WELDED JOINTS (1979)