smaller one and if the smaller is sufficiently

The Effects of Scale

This essay was first written in 1953 as a Master's thesis titled The Tall Building: The Effects of Scale.

6]

^Over

the

years it has been revised and

expanded

^to

incorporate

n e w e r

insights

^and developments; the current revision ^{w a s} prepared tor this publication.

Introduction

In the seventeenth century, Galileo summarized

the prevailing opinion on the relation of size to

structure in the Dialogues Concerning Two New Sciences (1638) as follows:

"If a machine be constructed in such a way that

its parts bear to one another the same ratios as in a

smaller

^{o n e}

^and

^if

the ^smaller

^is

sufficiently

strong ^for

^its

purpose, I

^{do not s e e}

^why

^the

larger is not." [4]

Galileo refuted this proposition by saying that the size of an organism or artifact has a decisive influence on its structure and its function. He proved his theory with the utmost possible clarity, and with a great wealth of illustration

drawn from animate and inanimate structures:

"You can plainly see the impossibility of increas- ing the size of structures to vast dimensions either in art or in

nature,

likewise the

impossi-

bility of building ships, palaces or temples of

enormous size in such a way that their oars,

yardbeams, iron-bolts and in short all their parts

can holad together; nor can nature produce trees of

extraordinary

size because their

branches would break down under their own weight; soo also

^it

would

be

impossible

^to

^build

up the

bony

structures of _men, horses or

other animals

^{so as}

to

hold together ^and perform

^their

^normal

function

it these

animals

^were to be

increased enormously

ⁱⁿ

height,

^{for this}

increase

in

height

c a n be

accomplished only by employing

^a

material

which is harder and

stronger

^than

usual,

^{o r}

by enlarging

the size of

bones thus

changing

^their

shape

until the form and appear

ance of the animals

suggest

^a

monstrosity."

Sketch of comparative bones by Galileo

"To

illustrate briefly

^I

have sketched

a

bone whose

natural

length

^{has been}

increased

three times

and whose thickness has been multiplied

until, fora correspondingly large animal, it

would perform the same function which the

smaller bone

pertorms

tor its small animal. From these

tigures,

^{you can see} how out ot

proportion

8

the large bone appears (fig. 1). Clearly then, if

one wishes to maintain in a great giant the same proportion ot limb as that found in an ordinary

man, he must find a harder and stronger

material ^for making the bones

^or

^he

^must

^admit

a diminution of strength." [4]

In this remarkable work Galileo formulates the idea of an ultimate size for structures:

"Among heavy prisms or cylinders of similar figure there is one and only one which under the

stress of its own weight lies just on the limit

between breaking and not breaking so that every larger one is unable to carry the load of its own weight and breaks while every smaller one is able to withstand some additional force tending to break it." [4

The principles dealing with the effects of magnitude, laid down by Galileo, have since been extended and elaborated in many fields,

such as biology, mathematics, philosophy, and

engineering. Sir D'Arcy Wentworth Thompson in his work On Growth and Form cites many

examples from these fields:

"We learn in elementary mechanics the simple case of two similar beams supported at both ends and carrying no other weight than their own. Within the limits of their elasticity they tend to be deflected, or to sag downwards, in

proportion to the squares ot their linear dimen-

sions. If a match stick be 2" and a similar beam 6 (or thirty-six times as long) the latter will sag under its own weight thirteen hundred times as much as the other. To counteract this tendency, as the size of an animal increases the limbs tend to become thicker and shorter and the whole skeleton bulkier and heavier; bones make up some eight per cent of the body of mouse or wren, 13 or 14% of goose or dog and 17 or

18% of the body ofa man. Elephant and

hippopotamus have grown clumsy as well as big, and the elk is of necessity less graceful than the gazelle. It is of high interest, on the other hand, to observe how little the skeletal proportions differ in a little porpoise and a great whale, even in the limbs and limb bones; for the whole

influence ^of gravity has become negligible,

^or

nearly so, in both of these." [9]

Concerning limitations on height, Thompson observes that the tall tree tends to bend under

its own weight and mentions how Greenhill

showed that a British Columbian pine tree 221

feet high and 21 inches in diameter at the base could not have grown beyond 300 teet, the very limitation on growth for trees anticipated by

Galileo.

Analogies to the tapering pine tree are to be

found in Smeaton's lighthouse and the Eiffel Tower, whose profiles follow a logarithmic curve so that the structural strength is uniform through- out their height. Thompson continues:

From

the examples ^cited

^{s o}

far,

^it

would seem

that every increase in size is accompanied by a decrease in efficiency. This is not always true, and there are many structures whose increasing efficiency due to increasing volume with propor tionately decreasing surface continues up to the limits of the strength of the materials. If we

consider the case of two similar obelisks of different size it can be shown that as long as the strength of the material is not exceeded the

larger wil resist winds that will blow down the smaller, and in the case of similar chimneys the larger may be expected to be capable of standing a greater storm than the smaller. In these c a s e s the

overturning

^{torces a r e}

_propor

tional to the areas exposed to the wind, while the stabilizing forces are proportional to the volumes; since every increase in size is accomn-

panied by

^a

disproportionately higher increase

in volume than _{in area,} these structures become

more stable a s

they increase

in size."

9

Also, there is a series of structures whose pertormance does not change over a wide range of sizes. The tank for containing fluid is

o n e such structure, and the

chart (fig. 2)

^shows

the

weight

per

gallon

^{contained a s} the

capacity

increases. The

weight

is constant over a wide range [2]. There are also structures such as the

bridges

discussed below whose

performances

follow

typical optimization

^curves with their

greatest efficiency occurring neither at their

largest or smallest sizes.

In

1947, after studying

On Growth

and Form,

became convinced that

different scales required

different

structures. I

examined

the

applicability

of this

principle

^{to modern}

engineering

^struc-

tures. The

study

^{shows a}

comparison

^of the spans of

different types

of

bridge

structures

(fig.

3) [8]. Each type

^{has an} upper and

lower

limit.

The

longest plate girder

span is 980 feet while the

simple

^truss has been used _{up to} spans of 720 feet and

continuous

truss has been carried to a span of

1,200

feet.

Thereafter

_{the span} 10

,.500

4p00 000

3500

Jpco

2500

a200 00

100

apoo

SPAN IN FEET po0

CAPACITY I THOUSAN0S OF GALLONS

2

Chart showing the decrease in weight ^{of tank per}

gllon

^of

fluid as the capacity increases

3 SUSPENSION

Weights of railroad bridges 4

Spans of different types of bridge structures

CANTILEVER TRUSS

STEEL ARCH

CONTINUOUS TRUSSS

PLATE GIRDER

SIMPLE TRUSS

30 35 40 45 50

SPAN IN HUNDREDS OF FEET 20 25

A ^{5 0 15}

increases rapidly, the arch-bridge spanning

1,600 feet, the cantilever bridge 1,800 feet and

finally the suspension bridge reaching a present maximum of 4,600 feet with predictable limits in

the ^region

^of

^15,000

teet. Thus it ^{c a n} be seen

that at certain limits

^the

structural system

^{has to}

be changed. The reason tor the upper limit of

structural systems becomes clear by comparing

the

weights

of railroad

bridges

^{ot ditterent} span

(fig. 4). It is seen thata 150-foot

span structure weighs 400,000 pounds whereas a 600-foot

structure ^weighs 4,500,000 pounds,

^a

^four-fold

increase in span and an eleven-fold increase in weight. The curve of the graph shows that at 600-toot span the increments ot weight increase rapidly tor every increase in span, and it can be expected that the maximum span tor this type ot construction will be reached not far beyond 700 feet

[7].

^The

steel skeletons

of

multi-story buildings exhibit similar

behavior. An

eight-story

building requires 10 pounds of steel per square

foot

[3]

^{while a}

100-story building requires

³⁰

pounds.

In summing up, it can be said that every structure has a maximum and minimum size. For example, in the bridge structures there is a region between 4000 feet and 700 feet where

now one and

then

^another

type

^is

used;

^but

above 2,000

^{feet the}

suspension bridge reigns

supreme,

while below

400 feet the

suspension bridge is minimally efficient. (A relatively new

type of bridge has been developed the

cable-stayed bridge. Some engineers claim that

it will

replace

^the

suspension bridge

^for

long

spans; ^at

present

1300 teet is the

longest

span for this

type bridge.) In

^the

^final analysis,

^an

optimum size may be tound somewhere between these extremes and its exact

determination

wil be at its

point

^ot

maximum etticiency.

Scale and the Tall Building

The effects

of

magnitude

^as

^stated previously

will now be

examined

in

relation

to the

tall

building

and the choice of its

structural system.

Brick

structures are at

their greatest efficiency

ⁱⁿ

low buildings ^where

^the

^thickness

^of

wall

required

^for

protection against

^the

elements

is

sufficiently strong

^to carry the

floors and roof.

The

maximum height

^of

brick office

structures

was

reached in

^the

16-story ^{Monadnock Buil-}

ding (fig.

⁵

and 6) of Burnham and Root, built

in

Chicago

ⁱⁿ

1891. The building's ^walls

^{are six}

feet

12

5

Monadnock Building, Chicago, 1891 6

Monadnock Building (section) 7

Promontory Apartment Building (section), Chicago, 1948

8

Promontory Apartment

Building

B

5 6

thick at the

base, decreasing gradually through

the upper stories to thirty inches in thickness. The internal columns are of cast iron; the external walls of brick act as bearing walls and stabilize the structure by their mass.

A reinforced concrete skeleton is a monolithic structure in which all the vertical loads are

carried by means of columns, while the hori- zontal loads are resisted by the columns stiff- ened by the beams and girders. The Promon- tory Apartment Building by Mies van der Rohe (Chicago, 1948) is a good example of this

structural type. The thickness of the floor construction

remains constant for _every

story (fig. 7 and 8) whereas the columns and girders

must increase in the lower stories due to the increase of vertical and horizontal loads. The

skeleton type permits great flexibility

ⁱⁿ

internal planning, since the vertical members are relati- vely small and isolated; but the increasing size of the principal members in the lower stories of

tall

buildings

^{tends to}

interfere

with the use and

flexibility of the interior space. As a conse-

quence, the practical limit on height for this

structural type

^has

been

about

twenty-five

stories.

The limitations inherent

in

the moment-resisting

concrete frame were

rapidly

^overcome in the

fifties and

_sixties

by the introduction

of a

whole

new series ot concrete structures: the frame and shear wall

combination,

the concrete

tube where

^the

exterior resists lateral forces), ^and

various combinations

of

these. This advance

came

about through

^a

series

of

Master's theses

in

architecture

at

IIT (see

pp.

147-183) for which

protessors Myron Goldsmith, the late Fazlur Khan, and David Sharpe ^served

^as

advisors.

^It

was

buildings designed by the Chicago office of first realized

in a

series of revolutionary Skidmore, Owings & Merrill. An example of the

framed

_concrete

tube

is

the Chestnut-Dewitt

Apartment Building (fig. 9) designed by SOM

(Bruce Graham, Design Partner; Myron ^Gold-

smith, Senior Designer; and Fazlur Khan, Struc-

tural Engineer).

In 1968,

^a

116-story

^concrete

braced tube office

building

^was

designed

^{as a}

Master's thesis by Robin Hodgkison

^at

IT, with Myron Goldsmith,

Fazlur Khan, and David Sharpe

^as

principal advisors. (fig. 10) Two subsequent buildings using ^this structural system, both designed ^by SOM,

^are

the 50-story ^office building

^at

⁷⁸⁰

14

T

9

Chestnut-Dewitt Apartment Building, Chicago, 1963 10

116-story concrete, high-rise building for llinois Center, Chicago, 1968

11

Structural systems for high-rise

buildings

ⁱⁿ

steel,

^{Fazlur Khan}

9 10

11

Third

^Avenue

in New York (1983, ^{Raul De} Armas, Design ^Partner;

^Robert

Rosenwasser/

Assoc.,

Structural

Engineer;

^the

late Fazlur Khan, Consulting Structural Engineer),

^and

^Onterie Center,

^a

60-story ^oftice and ^{apartment building}

in Chicago (1986, ^{Bruce Graham,} Design Partner; ^Fazlur Khan, Sirinvasa lyengar, ^Struc- tural Engineers). Simultaneously, work

^at

lT ^and

SOM also produced

^a

^similar development of steel

structures

for tall buildings, ^{and Fazlur}

Khan subsequently identified the heights

^at

which

various steel structural

systems

^were

economical (fig. 11).

A further effect of scale

^on

the tall building ^is

found in the proportionately greater area

required for elevators as the building's height increases. Recent developments in elevatoring tall buildings which recognize this need are the double-deck elevators and sky lobbies found in the World Trade Center, New York, and Sears Tower, Chicago.

The proliferation of new structural systems has led to their corresponding architectural expres- sions in such diverse structures as the John

Hancock ^Building (fig. 13) and the Sears Tower

(Fig. 12). Incredibly, ^the desire for

^new

^architec- tural expressions became ^the driving ^{force in the}

development of these alternative structural systems.

Scale and Long Span Roofs

Just

^as

with bridges ^{and tall} buildings, ^there

^must

be

^a

change ^of structural systems ^{in roots} _as

their spans increase. In his 1962 Master's thesis

at

lIT, Davis Sharpe produced

^a

^chart _(fig. 14) showing how the weight of a steel structure increases with ^the magnitude of its span

ⁱⁿ

long

span roof spans in the range of 50 roofs. At the lower end of the 100 feet, all of chart, ^with

the structural ^types

^are

nearly equal with weights ot approximately ^five _{pounds per}

square beyond _diverge, foot. ¹⁰⁰ _{and it} However, _feet,

_soon

the _becomes different

^as

^the spans increase _types increasingly

apparent which

type is appropriate ^for which _{span. As each}

curve

becomes _steeper, that particular structural type reaches the limit of _its efficiency. According

to

this chart, the rigid frame reaches its

maximum efficient _span

_at

about 275 feet, ^the

steel _truss system

^at

about 350 feet and steel

arches

at

about 450 feet. Beyond ⁴⁵⁰ feet, the

16

Sears Tower, Chicago, 1974 12 13

John Hancock Building, Chicago, 1969 14

Weights

^{of long spon roofs}

12

-uMGED AECAS

LAMELAcMES

OFODSIC d o u s

14

SPAN IN

17

N G E O A C

choices decrease, but the lamella dome main-

tains

^{a very}

^good

etticiency

beyond

⁶⁵⁰

feet,

the diameter necessary to accommodate a

football or baseball stadium.

As

Dr. Khan's

diagram and

^David

Sharpe's ^chart

demonstrate, there is a wide range of options

for structural systems at smaller scales which

permit making

choices for architectural and aesthetic reasons. The options decrease, however, with large scale structures.

Scale and the Environment

Large scale intrusions into the environment can

have both beneficial and harmful effects. These effects are often complex, are difficult to assess

in

advance, and

^are

subject

^to

rapid change or

even reversal with passing time as the result of

economic, political, and social forces.

In the language of economics, the reduction in cost achieved by increased size is called an economy of scale. The tankership industry has

sought economy

^of

scale by building ^larger

^and

larger oil tankers to lower the cost of transpor

ting oil and thereby lower the price of petroleum products (fig. 15) [10]. In 1952, Japanese

shipyards were building 38,000-ton tankers; by

1975, a 484,000-ton tanker, which is now

operating, was carrying oil from Saudi Arabia to Japan. The larger tankers have produced economy of scale in ^both construction ^and

operation. The following table from a major oil

company shows the reduction in oil transport

cost as the size of the tanker increases:

Tanker Size 45,000 70,000 100,000 200,000 300,000

Relative 100 Cost of Oil 83

52

35 29 (Tons)

Transport

It is

clear from

the

table that increasing tanker

size

from 45,000

tons to

100,000

^tons

reduces

transport cost 48%. But increasing capacity to

200,000 tons achieves only 17% additional cost reduction, and further expansion to 300,000

tons

yields just

^6%

additional reduction.

Critics of

supertankers, concerned about disas-

trous oil

spillage ^and

^water

pollution, point

^to

two

separate tanker accidents

in the late

seventies

which

killed

multitudes

of

birds and

fish and

polluted

^resort

beaches. These calamities,

coupled

^with

decreasing ^demand for oil from

18

15

Oil Supertanker 16

Walking Dragline, 220 yards 17

City ^of Chicago looking ^north

to the city center

15

16

the Middle East and such factors as Suez Canal

improvements and difticulty ot collecting largee

cargoes at ^{o n e} port, have led to a decline in usage of tankers of over 225,000 tons. A July

1985 survey by Drewry Shipping Consultants

reported in the Chicago Tribune found that only

11.1 % of tankers below that size were laid up,

as compared with 40.8 % of 225,000-to-300,000

ton tankers and 61.4% of those above 300,000 tons. Unless supertanker usage revives because

of a sharp increase in the demand for oil, it

seems likely that their environmental impact will

diminish and will have been relatively short- lived.

Mining machinery has a similar economy of

scale. Enormous excavating machines weighing thousands of tons, moving earth thousands ot

feet, now make it economical to reshape land,

create lakes and canals, and remove over-

burden hundreds of feet thick from coal and

ores. The

walking dragline ^{(fig. 16)} weighs

15,000 tons, has a bucket capacity of 220 cubic yards and a boom length of 310 feet. Built almost

twenty

years ago, it is

the

^world's

largest,

and moves earth at about 5 % of the cost of a small machine; its yearly capacity is 60 million cubic yards [1]. Development of large exca- vators led to the manufacture of enormous trucks

which

^{c a n haul}

^hundreds of tonsof

material in a

single

load. One

truck for mining

operations has a capacity of 350 tons and is

more than

^{50 feet}

long: with

^its

body

ⁱⁿ

^raised

position, it soars to the height of a six-story

building [5]. As in the case of tankers, cost ot

construction

^and

^operation has been reduced due to the enormous size of these machines.

Their size has not been exceeded in the years

since their introduction, however, since the current trend has been to achieve _economny

through standardization of smaller machines.

This

equipment

^{has been}

primarily

^used

for stripp

mining, and tor many years huge areas ot the United States have been devastated through its

Use.

Conversely,

^these

^machines

have also

been

Used

to convert stripped

land into

recreational

areas,

farmlands,

^and

_pastures.

Ecologically, these examples of large scale can

be very destructive o r can lead to

great

^benetits when their ^use is

carefully controlled. Large

construction can produce large-scale changes in the environment.

Enhancement

of the environ- 20

ment

^{and the}

protection ^{of human}

health and

well-being should be foremost in our minds.

Scale and the City

The effects of scale on the ^city are

^a

fruitful and

important topic of study beyond the scope of this essay. Such effects are complex and inter related and require on-going investigation by

an interdisciplinary team of architects, demo-

graphers, sociologists, city planners, traffic engi-

neers, etc.

However,

^{as a}

native ^of Chicago, ^I

would like to make a few observations about

that city.

The photo of Chicago (fig. 17) shows the extensive rail and highway network connecting the outlying areas of the city with its center. This system ^was

originally

^{built to} s e r v e the needs of a major port and manufacturing city located on

Lake Michigan in the population center of the United States. Today, due in large part to the existence of this original transportation network, more than 80% of the people entering the center of the city arrive by public transportation.

The core of the city has an extremely high density which is surrounded by vast areas of

low-density neighborhoods. This concentration

permits easy access to a majority of the city's

cultural, political, business, and commercial insti-

tutions, which can be found in a roughly one

square mile ^area. Thus it is both

pleasant

^and

efficient to travel on foot within this area. This configuration of the city, served by a compre hensive system of public transportation, is a distinguishing characteristic of Chicago not found in many other cities, both large and smal, whose configuration requires almost exclusive use of the automobile for transportation.

Chicago demonstrates that

^some

^of the ^negative

effects of large scale on the city can be

minimized when a high-density commercial core

is surrounded by low-density neighborhoods linked by efficient public transportation.

Summary

I believe it is impossible to examine anything in

depth without an understanding of the influence

of scale. The realities of scale exist in all aspects

of construction and life. The right means to the

right ^ends

^must

^be found;

^i.

^e., the ^means

^must

be in scale with the ends, and a philosophic

21

base must be used to ijudge the relationship of structure, scale, and architecture.

Several major conclusions about structure and scale are:

1. Every structural type, whether organism or artifact, has a maximum and minimum size.

2. In the tall building, there are both structural

and functional limitations on height.

3. Increasing the magnitude of a building

beyonda

certain size requires

changes

ⁱⁿ

the structural and ^other systems.

4. A new structural system gives the possibility

of a new aesthetic expression.

5. Size and scale have important implications environmentally and functionally. Engineer- ing for efficiency is not the last and only determinant; it is possible to make a choice

from several efficient schemes because of

architectural, aesthetic, and environmental reasons. The

human needs ^must

give

^the

directions.

22

Relerences

[1] Bucyrus-Erie, Manufacturer s Data

2] Chicago Bridge and Iron Company. Manufocturers Dato.

3] Clark, W C. and Kingston, J. C, The Skyscraper A Study ⁱⁿ the Economic Height ^{of Modern} Ofice Bunl

dings,

^{New York: 1930, p. 50.}

4)

Golilei, Galileo,

Dialogues

Concerning ^{Two New} Sciences, Henry Crew and Alfonse De ^{Salvio, trans.,} Chicago: 1914

5]

General Motors, Manufacturer's Data.

6

Goldsmith, Myron, unpublished ^Master's thesis, The Tall Building: The Effects of ^Scale, lIT, Chicago, ^{1953. (Rev.}

1977, 1986.)

7)

^{Ketchum, Milo S.,} Structural Engineers ^{Handbook, New} York: 1924, p. 204.

8] Steinman, ^David B., ^The World's Most Notable Brid-

ges,'

Engineering News Record, (rev. Myron Goldsnith), December 9, 1948, pp. 92-94.

9

^{Thompson, Sir D'Arcy} Wentworth, On Growth ^and Form, Cambridge: 1948.

[10] Tourk, Chairy A., "Supertankers: ^A Bird's Eye ^{View, IT} Technology and Human Affairs, Vol. 5, No. 3, Fall 1973.

pp. 11-14.

23