FOLDED PLATES - THEORY OF STRUCTURE

FOLDED PLATES

REPORT ON

FOLDED PLATES Submitted in partial fulfilment of the requirement for the award of degree of Bachelor of Architecture Submitted by MOHD FARHAN Guided by AR. MANSI BEDI ER. Md. IRFAN ANSARI

FACULTY OF ARCHITECTURE & EKISTICS JAMIA MILLIA ISLAMIA NEW DELHI-110025 2018-2019

Faculty of Architecture & Ekistics, Jamia Millia Islamia, New Delhi B. ARCH SFS IVTH YEAR – THEORY OF STRUCTURE

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FOLDED PLATES

Certificate In the partial fulfilment of the B. Arch degree program, this is to certify that ‘MOHD FARHAN’ has worked on the REPORT entitled “FOLDED PLATES” under my guidance and supervision.

AR. MANSI BEDI ER. Md. IRFAN ANSARI Dissertation Guide

Prof. HINA ZIA Dean

External Examiner 1

External Examiner 2

External Examiner 3

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ACKNOWLEDGEMENT

First of All, I Thanks to Almighty, for guiding me to select “FOLDED PLATES” as a topic of my Report. After studying Folded Plates I discovered a totally new Philosophy of Structure which has enhanced my understanding to a great extent.

Sincere thanks to Ar. Mansi Bedi Mam for guiding me in analysing the project & understanding the Philosophy of my topic.

I would also like to thank my parents whose continuous backing & support always kept my morale high.

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TABLE OF CONTENT 1. ABSTRACT…………………………………………………………………………………………………………………………………….5 2. INTRODUCTION…………………………………………………………………………………………………………………………………..6 3. HISTORY OF EMERGENCE…………………………………………………………………………………………………………………….8 4. TYPOLOGY……………………………………………………………………………………………………………………………………………9 4.1 LINEAR FOLDED PLATE STRUCTURE…………………………………………………………………………………………………9 4.2 RADIAL FOLDED PLATE STRUCTURE………………………………………………………………………………………………..9 4.3 SPATIAL FOLDED PLATE STRUCTURE……………………………………………………………………………………………….9 5. DESIGN OF FOLDED PLATES…………………………………………………………………………………………………………………10 6. ANALOGY………………………………………………………………………………………………………………………………………….…12 7. APPLICATIONS……………………………………………………………………………………………………………………………………..13 7.1 ROOF STRUCTURE………………………………………………………………………………………………………………………….13 7.2 WALL STRUCTURE…………………………………………….……………………………………………………………………………14 7.3 FLOOR PLATES……………………………………………………………………………………………………….………………………15 7.4 SHEET PILES……………………………………………………………………………………………………………………………………16 8. TYPOLOGY (MATERIALS)………………………………………………………………………………………………………………………17 8.1 WOOD………………………………………………………………………..…………………………………………………………………17 8.2 STEEL……….……………………………………………………………………………………………………………………………………17 8.3 PLASTIC..………………………………………………………………………………………………………………….……………………18 9. MODERN ADAPTATION…………………………………………………………………………………………………….…………………19 9.1 ORIGAMI………………………………………………………………………………………………………………………………………19 10. CASE STUDY……………………………………………………………………………………………………………………………………….21 10.1 USAFA CADET CHAPEL……………………………………………..…………………………………………………………………21 10.2 THE LIBRARY……………………………………………………………………………………………………………………………….23 11. CONCLUSION……………………………………………………………………………………………………………………………….……24 12. BIBLIOGRAPHY………………………………………………………………………………..…………………………………………………25

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ABSTRACT Folded structures are three-dimensional structures - spatial structures and they belong to the structural systems. The term folded structure defines a folded form of construction, including structures derived from elements which form a folded structure by their mutual relationship in space.

Figure 1 FOLDED PLATES EXAMPLE

B. ARCH SFS IVTH YEAR – THEORY OF STRUCTURE

Figure 2 FOLDED PLATES EXAMPLE

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INTRODUCTION There are different ways of constructing folded structure in terms of their forms and the application of different materials they are made of. Based on the research and analysis of the formal potential of the folded constructions the systematization of folded structures was done in terms of shape and geometry.

Figure 3 TYPES OF DOMES IN FOLDED PLATES

Figure 4 TYPICAL ROOF IN FOLDED PLATES

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The term folded structure defines a folded form of construction, including structures made of plates and structures made of sticks which make a folded form by their mutual relationship in space. Some authors also call a folded structure the origami construction.

Figure 5 FOLDED STRUCTURES IN MODERN ARCHITECTURE

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HISTORY OF EMERGENCE Design and construction of folded structures occurs at the beginning of the twentieth century and is associated with the development of reinforced concrete. The basic idea of creating this type of construction is striving to achieve more constructive height and greater rigidity and reduce the net weight of the structural element. The strength and stiffness of folded construction is achieved primarily by proper design of the structure and to a lesser extent, by thickness and dimension of the elements that form it. This solution was possible to realize due to the development of structural systems and the use of reinforced concrete.

Engineer Eudene Freyssinet performed the first roof with the folded structure in 1923 as an aircraft hangar at Orly Airport in Paris. In technological terms this folded construction is made of prefabricated elements, with pre-stressed structure, which is a remarkable engineering undertaking of the time.

Figure 6 ORLY AIRPORT PARIS

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TYPOLOGY The shape of folded structures affects the transmission of load and direction of relying of folded structures. Based on these parameters we can do the division in: • linear folded plate structure • radial folded plate structure • spatial folded plate structure

Figure 7 TYPOLOGY ON THE BASIS OF FORM

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DESIGN OF FOLDED PLATES The following are the recommended steps that comprise the entire procedure for the analysis and design of folded plates.

• Step 1 (Figure a) Consider an imaginary one-foot strip cut along the center line of the proposed folded plate. Calculate one-way slab moments (in footpounds) as it were fully supported at every ridge and valley. Balance all unequal fixed-end-moments (FEM’s) by using the moment distribution method.

• Step 2 (Figure b) Determine plate loads in the plane of the plates (in pounds per linear foot) as resulting from slab loads.

• Step 3 (Figure c) Consider plates disconnected at ridges and valleys, find extreme fiber stresses (in pounds per square inch) at the center line of plate span.

• Step 4 Connect plates together again. Balance unequal stresses (PSI) at joints by using the stress distribution method (similar to moment distribution).

• Step 5 (Figure d) Consider plates disconnected once more, calculate deflections based on the distributed extreme fiber stresses. Those deflections must be on the plane of the plate.

• Step 6 (Figure e) Plot the deflected positions of the plate vertices (joints) at the centerline of the plate span.

• Step 7 Scale deflection magnitudes from the Williot Diagram. Deflections are to be translated perpendicular to the plate.

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Figure 8 DIAGRAM OF FORCES ACTING ON FOLDED PLATES

• Step 8 As in steps #5, 6 and 7, the slab transverse bending strength was neglected. Deduct the FEM’s from the deflections perpendicular to the plates in step #7. Those moments will tend to be unequal and large.

• Step 9 Apply the above corrected FEM’s to the transverse section as it was done with the gravity loads in step #1. Repeat steps 1 through 8 and continue the cycles until the corrections converge.

• Step 10 Determine and summarize all moments and shears. Calculate all required reinforcing steel accordingly.

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ANALOGY

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APPLICATIONS Folded structures have found the application in architectural buildings and engineering structures. Based on the position in the architectural structure, this type of construction can be divided into: roof, floor and wall folded constructions. In engineering structures, bridges and retaining walls, various structural elements can be constructed on the principle of folded structures.

The principle of greater stiffness of individual constructive element, by the introduction of folded form, has found application in many consumer products.

• Roof Structure

Figure 9 EXAMPLE OF ROOF STRUCTURE

Figure 10 EXAMPLE OF ROOF STRUCTURE

Figure 11 EXAMPLE OF ROOF STRUCTURE

Figure 12 EXAMPLE OF ROOF STRUCTURE

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• Wall Structure

Figure 13 EXAMPLE OF WALL STRUCTURE

Figure 14 EXAMPLE OF WALL STRUCTURE

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• Floor plates

Figure 15 MAKING OF FLOOR PLATES

Figure 16 LIVE PHOTO FLOOR PLATES

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• Sheet Piles

Figure 17 PROFILES

Figure 18 LIVE PHOTO OF PROFILE

Figure 19 SECTION

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TYPOLOGY (MATERIALS) • Wood

Figure 20 WOOD AS FOLDED PLATES

• Steel

Figure 21 STEEL AS FOLDED PLATES

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• Plastic

Figure 22 PLASTIC AS FOLDED PLATES

Figure 23 PLASTIC MODULES

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MODERN ADAPTATION • ORIGAMI Traditional origami uses paper. However, most engineering applications require materials with definitive thickness and enough strength and stiffness to properly perform. That's where metamaterials come in.

An origami expert can turn a few basic folds into a complex design.

The challenge for engineers is to create a system of folds that is structurally sound and can be reproduced.

Figure 24 ORIGAMI PATTERNS

Figure 25 ORIGAMI PATTERNS

Figure 26 ORIGAMI EXAMPLES

Figure 27 ORIGAMI PATTERNS

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Figure 28 ORIGAMI MAKING STYLES

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CASE STUDY • USAFA CADET CHAPEL The Protestant Chapel is the largest chapel and is designed to seat 1200 people. The nave is 92 feet tall at its highest peak, and measures 64x168 feet. The tetrahedrons form the walls of the chapel with stained glass windows in between them that progress from darker to lighter as they approach the altar, creating a beautifully lit majestic space.

Figure 29 USAFA CADET CHAPEL

The USAFA Cadet Chapel is an icon of modernism, a memorable icon of religious architecture ahead of its time, and in 2004 it was named a United States National Historic Landmark.

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Figure 30 USAFA CADET CHAPEL LIVE PHOTO

Figure 31 USAFA CADET CHAPEL INTERIOR

Figure 32 SECTION USAFA CADET CHAPEL

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• THE LIBRARY

Figure 33 THE LIBRARY DESIGNED FOLDED PLATE STRUCTURE

Figure 34 THE LIBRARY RENDERED

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CONCLUSION Spatial system of constructions consisting of flat elements mutually set at an angle represents a folded construction. First folded structures are related to reinforced concrete structures and for long time there has been present a prejudice that this type of construction can be performed only in that material.

In the second half of the twentieth century folded structures were made of other materials: steel, wood, polyester resin and glass, and in their combination.

Applying the principles of unification and systematization as basic elements of the structural system, with a few different elements you get a flexible system of building folded structures in terms of technology and facilitate the process of production, transport and installation of folded structures.

In terms of design and visual effect forming folded structures by using different materials interesting forms and design solutions can be obtained. That makes the structures obtained in this way different and special compared to other, less complex, spatial forms.

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BIBLIOGRAPHY • https://pdhonline.com/courses/s275/s275content.pdf • https://www.ijser.org/researchpaper/Study-of-Fold-and-Folded-Platesin-Structural-Engineering.pdf • https://www.slideshare.net/RohanNarvekar2/folded-plates • http://www.doiserbia.nb.rs/img/doi/0354-4605/2012/035446051201001S.pdf • https://www.designingbuildings.co.uk/wiki/Folded_plate_construction • https://www.scribd.com/document/112139729/Folded-Plates • https://in.pinterest.com/search/pins/?rs=ac&len=2&q=folded%20plates &eq=FOLDED%20PLATES&etslf=12623&term_meta[]=folded%7Cautoco mplete%7C1&term_meta[]=plates%7Cautocomplete%7C1

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