Force and Motion Forces in Buildings A Historical Review

Transcription

1 Science Teaching Kit for Senior Secondary Curriculum Force and Motion Forces in Buildings A Historical Review [Teacher notes] Organizer Sponsor Research Team

2 Contents Preamble Teaching plan Lesson 1 : Forces in Buildings A Historical Review 1.1 Concepts of Forces in Historic Buildings 1.2 Structural Systems in Historic Buildings The Step Pyramid in Saqqara (2600 BC) Lion Gate in Mycenae (1200 BC) Aqueduct in Segovia (50 AD) Colosseum in Rome (80 AD) Pantheon in Rome (126 AD) Romanesque Architecture ( AD) Gothic Architecture ( AD) Renaissance Architecture ( AD) i Summary, Key words and Further reading 18 Disclaimer Create Hong Kong of the Government of the Hong Kong Special Administrative Region provides funding support to the project only, and does not otherwise take part in the project. Any opinions, findings, conclusions or recommendations expressed in these materials/events (or by members of the project team) do not reflect the views of the Government of the Hong Kong Special Administrative Region Hong Kong Institute of Architects

3 Topic 01 Forces in Buildings A Historical Review Major teaching areas Physics: Chapter II Force and Motion Force and motion Interdisciplinary teaching areas Design and Applied Technology: Strand 2 Technological Principles Strand 3 Value and Impact Learning objectives To appreciate historic buildings for the performance of their structure To understand how forces are transferred in basic structural elements To learn how ancient builders transformed basic structural elements to satisfy different needs and requirements Teaching plan Lesson Lesson 1 Forces in Buildings A Historical Review Contents Review of Newton s Laws of force and motion Principles of force and basic structural elements in ancient buildings in chronological order 1 The Step Pyramid in Saqqara (2600 BC) 2 Lion Gate in Mycenae (1200 BC) 3 Aqueduct in Segovia (50 AD) 4 Colosseum in Rome (80 AD) 5 Pantheon in Rome (126 AD) 6 Romanesque Architecture ( AD) 7 Gothic Architecture ( AD) 8 Renaissance Architecture ( AD) i

4 Lesson 1 Forces in Buildings A Historical Review 01

5 Lesson 1 Forces in Buildings A Historical Review Passion can create drama out of inert stone. Le Corbusier 1.1 Concepts of Forces in Historic Buildings Sir Isaac Newton ( ) first published his concepts of force, motion, inertia and gravity in Since then, Newton s laws of force and motion have been widely used in the physical sciences. However, even before Newton s theory appeared, architects, engineers and builders had long been coming up with innovative structural solutions based on available materials and methods. When an object is in equilibrium, the sum of all net forces equals to zero. This is true of a building as it is for a smaller object. A stable building structure supports three types of loads, or forces: live load, dead load and environmental load. Different structural systems some of them quite aesthetically pleasing were developed to withstand these loads in the most efficient way possible. [Discussion] 1 Can you outline the three laws of motion stated by Sir Isaac Newton? Possible perspectives First Law: Every object remains in its state of rest, or of uniform motion in the same direction, when the net force on the object equals to zero. Second Law: F = ma ; where F equals to the net force acting on the object parallel to its motion, m is the mass of the object, and a is the rate of change of its velocity. Third Law: When two objects exert a force on each other, these forces, namely the action and the reaction, are equal in magnitude, but opposite in direction. p Newton s First and Second Laws of motion were stated in his Mathematical Principles of Natural Philosophy, published in

6 1.2 Structural Systems in Historic Buildings The Step Pyramid in Saqqara (2600 BC) Tentoila - Wikipedia User [Discussion] 1 Tilted surfaces were used to reduce the loads of the building. In the following diagram, illustrates how the forces on the tilted surfaces of the pyramid can be resolved into vertical and horizontal components and transferred to the earth. What are the advantages and disadvantages of this geometry? Possible perspectives F H1 F H2 The Step Pyramid, Saqqara Height : 62 m Sum of horizontal force = F H1 + F H2 A triangle with a small top and wide base has a low centre of gravity. The Step Pyramid (ziggurat) in Saqqara was built for an ancient Egyptian King Djoser, the founder of the Third Dynasty. It is the first great stone step pyramid of tomb architecture. It is 62 m high, with a base of 109 m x 125 m. In this structure, for the first time, mud brick was replaced by stone. This was a new form of the earlier tombs shaped like great brick rectangles, with the walls sloping inward and a flat roof, commonly referred to as mastabas. A pyramid is a very efficient structure made of converging triangles. The Step Pyramid is part of the UNESCO World Heritage site that also includes Egypt s most famous pyramids. Load-bearing wall The walls of the pyramid are load-bearing. Stone blocks were stacked up to make the structure, and mortar was used to glue pieces together for extra strength. A well-built load-bearing wall is very effective in resisting compressive forces, but stone is relatively weak in tension. Force on the load-bearing wall F V1 F V2 Force on Centre of Gravity = F V1 + F V2 Advantages: The pyramid geometry can resolve the force into horizontal and vertical components. Part of the total force is distributed horizontally and the horizontal components can be balanced by each other. Support of the roof is not necessary because it is formed by the walls. Also, the tilted surfaces made it easier to build the pyramid, as it is believed that stones were dragged up the sides using pulleys. Counteracting internal force Reaction force on the wall from the earth p Forces in a load-bearing wall Disadvantages: Interior space of a pyramid is limited and inefficient, but this does not significantly affect its function as a tomb. 03

7 1.2.2 Lion Gate in Mycenae (1200 BC) The Lion Gate is the main entrance to the ancient Greek citadel at Mycenae. It is a simple example of a load-bearing wall that accommodates an opening of 3.10 m by 2.95 m. Two huge columns, carved of monolithic stone, flank the gateway and are capped by an equally massive lintel of 4.5 x 2.0 x 0.8 m. (Bong, 2008) Lintel (Beam-and-Column structure) The lintel - the horizontal member atop the doorway - acts as a kind of beam spanning over an opening and resting on two vertical supports (columns). In ancient times, lintels were commonly made of stone or wood. Compression at upper part Stress point Force on the beam Tension at lower part p Internal forces in a beam-and-column structure Arch Like a column-and-beam structure, an arch spans an opening and supports a load. However, in an arch, all the forces inside each element are resolved into compressive stresses which serve to hold the arch together in equilibrium. An arch tends to push outwards at the base, so an abutment may be used to retain this outward force. Force on the arch Lion Gate, Mycenae Lintel [Discussion] 1 Can you distinguish which part of the gate is beamand-column structure? Which part is an arch? 2 Why do you think the lintel is thicker in the middle? Possible perspectives David Monniaux - Wikipedia User 1 The additional part above the opening is an arch formed by the masonry blocks. It lightens the load carried by the lintel. Compression in each structural piece Horizontal and vertical components Corbelled arch 2 The stress point of the lintel was thickened. Thicker at the middle (Stress point) Beam-and-column structure p Internal forces and load path in an arch Teaching Tips Students can try forming an arch with a piece of paper to see how the force is acting. 04

8 Ten Books on Architecture (100 BC) Vitruvius, a Roman architect, wrote in his Ten Books on Architecture that a building should possess the qualities of firmitas, utilitas, venustas which can be translated as firmness, usefulness and beauty or structure, function and aesthetics. He also suggested that all buildings should have a sense of proportion derived from the human body Aqueduct in Segovia (50 AD) The ancient Roman aqueduct in Segovia was built to channel a constant flow of clean water to the city. Water was brought from as far as 18 km away using only gravity; the aqueduct is built with an average slope gradient of 1%, and the water simply ran downhill, an ingenious civil-engineering solution to an infrastructural challenge that occurred throughout the Roman Empire. This particular aqueduct is the best known example owing to its monumentality, its excellent state of conservation, and its location in one of the most beautiful urban sites in the world. In order to reach the rocky contrefort on which the city was perched the builders had to erect an enormous construction of masonry 813 m in length, consisting of four straight segments and two superimposed arcades borne by 128 pillars. At the lowest point of the valley, the aqueduct stands at a height of 28.5 m above ground. (Source: UNESCO website) Rows of repeating arches The aqueduct in Segovia was built with two tiers of arches. The outward forces at the base of each arch push against their neighbours to form a very stable structure. Aqueduct, Segovia Colosseum in Rome (80 AD) Agamemnus - Wikipedia User The Colosseum is the largest amphitheatre ever built by the ancient Romans, a public venue that could hold tens of thousands of spectators during events and entertainments. The structure uses vaulting and arches to create a multi-level space that is elliptical in plan, 189 m long and with a base area of 24,000 m 2. Tiers of seating line the sides. The outer wall, which is 48 m high, is estimated to have required over 100,000 cubic metres of travertine stones that were set without mortar and held together by 300 tonnes of iron clamps. The building s original perimeter was 545 m. Vaults A vault can be envisioned as an extruded arch (an arch that has been multiplied or pulled to become long). It shares the same structural characteristics of a single arch, and is a very efficient way to make structure and enclosure at once. Colosseum, Rome u Section of Colosseum. Vaults form hallways inside the building. (Source: Lexikon der gesamten Technik, 1904) 05

9 Mike Hui Tension ring 7 Tension ring 6 Tension ring 5 Tension ring 4 Tension ring 3 Tension ring 2 Tension ring 1 Oculus Main wall Pantheon in Rome (126 AD) The Pantheon or Temple to All Gods in Rome is the largest unreinforced concrete dome in the world. Ancient concrete was made with volcanic sand lime mortars, and seven tension rings were installed to withstand the outward pushing forces at different levels and to prevent the lower support columns from collapsing. The thickness of the wall of the dome is 6.4 m at the base and decreases to 1.2 m at the oculus, a design feature that lowers the overall weight of the structure without sacrificing its stability. Dome A dome is a hemispheric roof structure. Structurally, it can be analysed as an arch that has been rotated around a central axis. Like an arch, a dome enables large spaces without interior support. Tension rings can be used to withstand the outward pushing forces of the dome. p Section of the Pantheon. A sphere of 43.3m diameter could fit inside. (Source: Meyers Konversationslexikon, 1885) q Diagrams showing the forces on a dome. Compression in each structural piece Force on the dome Pantheon, Rome Outward pushing forces at the base of the dome Tension ring The ring is in tension to counteract the outward pushing forces Inner surface of a dome 06

10 The oculus provides the only natural light source in the Pantheon. Mike Hui 07

11 1.2.6 Romanesque Architecture ( AD) Structural Elements in Romanesque Architecture Rounded arch Romanesque architecture can usually be recognized by its semicircular arches. These rounded arches were used for doors and windows, for vaults and for arcades. They were also used in naves and aisles of churches to create tall, wide spaces. Barrel vaults In Romanesque churches, barrel vaults - simple arched vaults - were often built flanking the central nave. They could support the structure of the central space against lateral forces, while also providing covered space for the congregation. Walls and buttresses Wall in Romanesque buildings were relatively thick because they were load-bearing. Buttresses were often added outside to support the walls against lateral forces. Duomo, Pisa Arcade An arcade is a covered walkway formed of a row of arches supported by piers or columns. In Romanesque architecture, massive piers or columns were used to support arches. The small scale of the arcade was usually for decoration, while larger scale elements served structural purposes. t The Duomo in Pisa features arches on the interior and the exterior. q San Miniato al Monte has been called the most beautiful Romanesque church in the world. The rounded arches date back to the original structure, and the painted wood trusses were added later. San Miniato al Monte, Florence Counteracting force p Load-bearing wall with additional buttress support 08

12 The rounded vault at Speyer Cathedral, Germany. The construction of the church begun in Its depth is 134 m, with nave 33 m tall and 14 m wide internally. Berthold Werner - Wikipedia User 09

13 1.2.7 Gothic Architecture ( AD) York Minster, Yorkshire Structural Elements in Gothic Architecture Gothic architecture further transformed the basic structural elements of Romanesque architecture to improve the spatial quality and natural lighting of the interiors. Pointed arch The rounded arch so characteristic of the Romanesque period was replaced by the pointed arch. Ribbed vault A ribbed vault is formed when two vaults intersect at right angles. Adding ribs at the lines of intersection offers extra structural stability, making a lighter-weight ceiling possible. tq Decorative ribbed vaults at York Minster 1 What is the advantage of the pointed arch over the rounded arch? Possible perspectives F [Discussion] F θ θ Outward pushing force at the base = F cosθ (0 < θ < 90 o ) When the angle θ increases in magnitude, cosθ will decrease, and hence the outward pushing force at the base will be smaller. A pointed arch has a larger angle θ than a rounded arch so its outward pushing force will be less significant. Therefore, given the same structural base, a pointed arch can create a higher vertical space than a rounded arch. 10

14 Typical buttress Flying buttress [Discussion] p 1 Discuss why a flying buttress is better than the typical buttresses and barrel vaults used in earlier times. Possible perspectives The earlier buttresses were bulky and the spaces between them could not be used. Barrel vaults could be used to make passageways, but they were dark, lacking natural lighting. Flying buttresses could create usable space around the central hall, lit by natural light. The lighter structure also required less building materials. Combination of flying and typical buttresses in the Canterbury Cathedral, Kent. The space underneath the flying buttress is enclosed to form the aisles on the two sides of the nave. Buttresses at the ground level need not be massive. Flying buttress Buttress on the side of the load-bearing wall are bulky and create unusable and dark spaces in between. The flying buttress was invented to transfer the lateral forces overhead from the main hall structure to the side structure. A visitor passage around the main hall was created and natural light could pass through the space. q Canterbury Cathedral, Kent Different solutions for lateral forces: typical buttress, barrel vault and flying buttress (left to right) 11

15 The flying buttress of Notre Dame de Paris. Jean Lemoine Jean Lemoine 12

16 1.2.8 Renaissance Architecture ( AD) Courtyard of Palazzo Strozzi, Florence Characteristics of Renaissance Architecture Symmetry Proportion Geometry Regularity of parts t The courtyard of the Palazzo Strozzi in Florence employs simple geometric shapes - semi-circles, circles and rectangles - that were thought to echo the perfection of God. St Peter s Basilica in Italy (1506 AD) The enormous St Peter s Basilica is the seat of the Papacy and the Catholic Church. It was designed by Michelangelo in Renaissance style, with the addition of a later colonnade and piazza designed by the prominent Baroque architect and sculptor Bernini. q St Peter s Basilica and its piazza 13

17 t q The spaces of St Peter s Basilica are formed by vaults. Michelangelo s symmetrical design for St Peter s Basilica has five domes. Two-layered dome St Peter s huge dome is supported by four structural piers. It has a perimeter of 71 m and a height of 120 m from the ground to the roof of the lantern. The diameters of the outer and inner dome are 42 m and 41.5 m respectively. Mike Hui St Peter s Basilica was built as tall as possible to overlook Vatican City and the rest of Rome. Therefore, view from distance was taken into account when designing the height of the dome. Drum was added to raise the whole dome higher. Two layers of dome were built. From exterior view, the taller and outer dome appears pointing to the heaven without being hidden by the building mass in the front; while the inner dome appears as a perfect hemisphere from interior view. 120 m Outer dome For visual expression from exterior Inner dome For visual expression from interior u Section of St Peter s Basilica Drum The cylindrical wall at the base of a dome 14

18 Perspective Expressions Affecting the Structure of the Dome 1 When a single perfect dome was built... Perspective plan 2 When a drum was added... Perspective plan Perfect dome Drum Visual Expression Visual Expression 3 When a taller outer dome was added... Perspective plan Outer dome Visual Expression p View points from distance (Left) and visual expressions (Right) of three cases of dome structure 15

19 The cylindrical wall at the base of a dome is called the drum. It serves to hold the dome s base in tension. This drum is 20 m high with 16 windows. Mike Hui 16

20 [Discussion] 1 What are the common building materials used in ancient and historic buildings? What are their structural strengths and limitations? 2 How does the arch work with the structural limitations of these materials? What other structural systems are derived from the arch? 3 What are the downsides of the arch? What did architects, engineers and builders do to solve these problems? 4 How do modern buildings deal with structural challenges? Possible perspectives 1 Mud brick, stone and concrete are the common materials in historic buildings. They are strong in compressive force but relatively weak in tensile force. 2 In an arch, the structural pieces experience compressive force only. Vaults and domes were derived from the arch system and shared similar structural characteristics. 3 The arch tends to push outwards at the base. The lower support of an arch might collapse due to this horizontal force. Abutments can withstand the horizontal pushing force at the base of an arch. A row or ring of arches could be built so that the outward pushing force of each arch will counteract each other. Tension rings can be added to a dome to hold its hemispheric shape. 4 Modern architectural solutions: Steel is strong in both compression and tension. It is one of the most common building materials used today. Concrete is reinforced with steel to increase its tensile strength. A truss is a kind of structural system that can replace the use of beam. It distributes the compressive and tensile stresses throughout the whole structure and gives long spans. Cable is good in withstanding tensile forces on a building. Cross-bracing provides lateral support against horizontal forces. Teaching Tips To appreciate architecture on the other perspective, please refer to Arts Topic 01 Art and Architecture and Topic 05 VIDEO: Form and Space in Architecture. Teaching Tips More information about modern architectural solutions against forces can be found in Science Topic 03 Model Making Workshop Structure of Tall Buildings and Towers. 17

21 Summary 1. Before Newton s theories of force and motion, architects, engineers and builders had already been finding solutions for structural stability, based on their intelligence, experience, and available materials and technology. 2. The form of the structural systems transformed continuously to enhance structural stability, spatial experience and building aesthetics. 3. Structural systems commonly found in historic buildings are load-bearing walls, beam-and-column systems, arches, vaults, buttresses and domes. Key words Load-bearing wall Beam-and-column Arch Vault Buttress Dome Abutment Further reading 1. Ching, Francis D.K. Building Construction Illustrated, 4th ed. New Jersey: John Wiley & Sons Inc, Bong, Wun Chok. The Gods Machines: From Stonehenge to Crop Circles. Berkeley, California: Frog Books, Semper, G. Style in the Technical and Tectonic Arts; or, Practical Aesthetics. Los Angelos: Getty Research Institute, 2004 Organizer Sponsor Research Team