bridges - Ecent.nl

BRIDGES
A p h y s i c s u n i t f o r 14/15
year o l d s t u d e n t s .
PHYSICS CURRICULUM DEVELOPMENT PROJECT
*
*
*
*
The Physics Curriculum Development Project (PLON) was started in
1972 under the auspices of the Physics Curriculum Innovation Committee (CMLN). lts terms of reference were to develop teaching packages
on physics for junior and senior general secondary and pre-university
schools, to evaluate such material by means of research, and to draw up
a plan for directing its introduction into schools.
The PLON is supervised by a steering group whose members have been
drawn from schools, establishments of further education, educational
support institutes, secondary teacher training institutions and the Ministry of Education and Science.
The Project has been assigned to the Physics Education Department of
the State University of Utrecht, which is also concerned with activities
relating to the upper forms of senior general secondary schools. The
development of instructional material for the upper forms of pre-university schools is carried out in cooperation with the Universities of Amsterdam (Municipal University) and Groningen and a group of teachers.
Address: PLON, Lab. Vaste Stof, Postbus 80.008, 3508 TA Utrecht.
Tel.no. 030-532717.
Copyright 1984 State University of Utrecht, PLON
No part of this book may be reproduced in any f o r m by print, photoprint, m i c r o f i l m or any other
means w i t h o u t prior permission of the publisher.
Experimental edition.
-2-
PREFACE
This p u b l i c a t i o n contains t r a n s l a t e d parts
Bruggen ( B r i d g e s ) :
the o r i e n t a t i o n , two
(out of 4) and
i n v e s t i g a t i o n (out
one
T e x t s have not been
One
of the PLON-unit
c h a p t e r s of
of 6 ) . The
theory
Reading
translated.
of the purposes of t h i s p u b l i c a t i o n i s to i l l u s t r a t e
the
s t r u c t u r e of PLON-units f o r j u n i o r secondary e d u c a t i o n .
The
r e a d e r w i l l a l s o get an i m p r e s s i o n of the way
deal
w i t h p u p i l a c t i v i t i e s and w i t h p h y s i c a l
We
would l i k e to thank Mrs.
for
their contributions
the u n i t s
concepts.
Yolande Samwel and Mr.
Robin M i l l a r
to t h i s t r a n s l a t i o n .
A t a b l e of c o n t e n t s of the o r i g i n a l u n i t Bruggen has
p r i n t e d on page 5.
More c o p i e s of t h i s u n i t are a v a i l a b l e
PLON
P h y s i c s E d u c a t i o n Department
S t a t e U n i v e r s i t y of U t r e c h t
P.O.
Box
3508 TA
The
80.008
Utrecht
Netherlands
Price
ƒ6,-
( i n c l . postage and
packing)
-3-
at
been
CONTENTS
INTRODUCTION
ORIENTATION
1. B r i d g e s i n your neighbourhood
2. The shape of b r i d g e s
3. Expansion and c o n t r a c t i o n i n b r i d g e s
THEORY
1.
2.
3.
4.
15
17
18
26
2 7
Stress i n bridges
S t r e n g t h and shape
Weight and counterweight
Stability
29
36
INVESTIGATIONS
1. B u i l d i n g , l o a d i n g and r e i n f o r c i n g a b r i d g e
2. B u i l d i n g a crane
3. A crane and moments i n e q u i l i b r i u m
4. E x p l o r i n g s t r e n g t h and shape
5. E x p l o r i n g r o t a t i o n
6. S t a b i l i z i n g d i f f e r e n t o b j e c t s
READING T E X T S
1. The h i s t o r i c a l development of b r i d g e s
2. P r e - s t r e s s e d c o n c r e t e
3. The M o e r d i j k - b r i d g e
4. Stayed g i r d e r b r i d g e near E w i j k
5. The B r i t t a n n i a b r i d g e
6. B r i d g e s and t r a f f i c - j a m s
-5-
52
T h e new W i l l e m s b r i d g e o v e r t h e r i v e r M a a s i n R o t t e r d a m ,
i t was
o p e n e d i n 1981.
I t i s a stayed girder bridge with
b r i d g e - d e c k suspended from the A-shaped
pylons.
WHAT T H I S BOOK IS
This
ABOUT
jook d e a l s w i t h b r i d g e s
and
I t b e g i n s w i t h an I n t r o d u c t i o n
similar constructions.
to the theme Bridges
3
f o l l o w e d by
four
s e c t i o n s : O r i e n t a t i o n , Theory, I n v e s t i g a t i o n s and Reading T e x t s .
In the O r i e n t a t i o n s e c t i o n you w i l l
i n a way
t h a t i s p r o b a b l y new
In the Theory s e c t i o n you w i l l
cranes and
the m a t e r i a l s
to
l e a r n to look at b r i d g e s
and
cranes
you.
l e a r n more about the shapes of b r i d g e s
and
used i n t h e i r c o n s t r u c t i o n . T h i s s e c t i o n i s
e s s e n t i a l core m a t e r i a l which a l l s t u d e n t s s h o u l d complete.
Each group of p u p i l s then chooses one
i n v e s t i g a t i o n from the
Investigation
s e c t i o n to c a r r y out. A f t e r c o m p l e t i n g the i n v e s t i g a t i o n , the groups
report
t h e i r f i n d i n g s back to the whole c l a s s .
The
Reading T e x t s s e c t i o n
contains
a number of t e x t s which may
ful
i n c a r r y i n g out your i n v e s t i g a t i o n or i n p r e p a r i n g
vou
can
a l s o read them j u s t f o r p l e a s u r e .
We
but
compulsory.
contents.
hope you'11 have l o t s of fun l o o k i n g , l e a r n i n g , b u i l d i n g and
-7-
use-
your r e p o r t ,
These t e x t s are not
Each s e c t i o n s t a r t s w i t h a d e t a i l e d t a b l e of
be
reading!
just before
a steel
The b r i d g e a t W e s s e m u n d e r c o n s t r u c t i o n ( a b o v e ) a n d c o m p l e t e d ( b e l o w ) . By
c h o o s i n g the r i g h t b u i l d i n g scheme, m a t e r i a l s and shape, the e n g i n e e r s
have
s u c c e e d e d i n c o n s t r u c t i n g a s t r o n g b r i d g e w i t h o u t c a u s i n g t o o much
hindrance
to s h i p t r a f f i c . The b r i d g e c o n s i s t s o f p r e s t r e s s e d c o n c r e t e s e c t i o n s ( s e e
R e a d i n g T e x t 2,
) and i s c o n s t r u c t e d u s i n g t h e ' t a n t i l e v e r " method.
The p h o t o g r a p h a b o v e
deck from below.
clearly
shows
the concrete
"tubes"
supporting
the bridge-
INTRODUCTION
WHY
In
BRIDGES ?
the N e t h e r l a n d s , t h e r e are b r i d g e s everywhere. They are so f a m i l i a r you
h a r d l y e v e r n o t i c e them. Yet you can't do w i t h o u t them. Perhaps you c r o s s
a b r i d g e on your way
to school. J u s t imagine how much l o n g e r your r o u t e
would be i f t h a t b r i d g e weren't there'. Every y e a r , m i l l i o n s of g u i l d e r s
are
spent on b r i d g e s . The new W i l l e m s b r u g i n Rotterdam f o r i n s t a n c e , which
was opened i n J u l y 1981,costs about 100 m i l l i o n g u i l d e r s
This t e l l s
the
us something about how
(£25
million).
i m p o r t a n t b r i d g e s a r e . But t h a t i s not
o n l y r e a s o n f o r d e v o t i n g a whole theme t o b r i d g e s (and c r a n e s ) .
B r i d g e s can t e a c h you a l o t about o t h e r c o n s t r u c t i o n s you use i n your
everyday l i f e , not j u s t i f you happen to become a b r i d g e - b u i l d e r . F o r
example:
how
can a wobbly bookcase o r a t e l e v i s i o n a e r i a l be secured?
How
can a garden gate be s t r e n g t h e n e d ?
A l s o , i t w i l l be e n j o y a b l e t o come t o understand something about b r i d g e s by
w o r k i n g on them w i t h your hands and your head. Enough good reasons to get
s t a r t e d w i t h the theme.'
HOW
ARE
Bridges
THE
LESSONS ORGANIZED ?
i s the f i r s t theme f o r the t h i r d y e a r of the mavo-havo-vwo c o u r s e .
You w i l l be w o r k i n g on i t f o r about one month. I n the orientation
and your group w i l l
stage
you
f i n d out about the shape of b r i d g e s and cranes and the
m a t e r i a l s used t o make them by l o o k i n g around i n your neighbourhood
examining p i c t u r e s and photographs. You w i l l
s e v e r a l s i m p l e experiments and
and
l e a r n some t h e o r y by d o i n g
t a s k s ; t h i s can be done as a group. A l s o ,
your t e a c h e r may w i s h t o e x p l a i n p i e c e s of t h e o r y to the c l a s s as a whole.
The i n v e s t i g a t i o n stage
i s o r g a n i z e d as f o l l o w s : you and y o u r group are
g o i n g to b u i l d a b r i d g e or a c r a n e , and then t r y to improve the d e s i g n .
Or you may
to
i n v e s t i g a t e the s t r e n g t h of paper f o l d e d i n t o d i f f e r e n t
shapes
l e a r n about b a l a n c e and s t a b i l i t y . Your group w i l l p r e s e n t the r e s u l t s
and c o n c l u s i o n s of the i n v e s t i g a t i o n i n a r e p o r t o r a d e m o n s t r a t i o n to the
c l a s s . The theme finishes
with
a t e s t on the t h e o r y and on the main
c o n c l u s i o n s reached i n the i n v e s t i g a t i o n s which the d i f f e r e n t groups have
c a r r i e d out. P a r t of the t e s t w i l l
a l s o d e a l more i n d e t a i l w i t h your
i n v e s t i g a t i o n s , so t h a t p a r t w i l l be d i f f e r e n t f o r each group.
I f y o u r t e a c h e r d e c i d e s to o r g a n i z e the l e s s o n s d i f f e r e n t l y from t h i s
o u t l i n e , he o r she w i l l t e i l you so.
-9-
own
WHAT CAN YOU LEARN FROM T H I S THEME ?
I n the Orientation
section
you w i l l
l e a r n how to r e c o g n i z e d i f f e r e n t
types
of b r i d g e s , and you w i l l become f a m i l i a r w i t h the m a t e r i a l s used i n the
c o n s t r u c t i o n o f b r i d g e s . You w i l l a l s o l e a r n t h a t b r i d g e s need t o have
some " p l a y " t o be a b l e t o expand on h o t days.
The
Theory section
contains four
chapters:
Chapter 1 d e a l s w i t h s t r e s s e s i n m a t e r i a l s : c o m p r e s s i o n , t e n s i o n and b e n d i n g
stress.
In Chapter 2 you w i l l
choosing
l e a r n how t o make a b r i d g e as s t r o n g as p o s s i b l e by
the r i g h t m a t e r i a l and shape.
Chapter 3 d e a l s w i t h b a l a n c e
cranes.
and
You w i l l
and c o u n t e r b a l a n c e
i n movable b r i d g e s and
l e a r n how t o c a l c u l a t e w i t h w e i g h t s ,
counterweights
d i s t a n c e s from the a x i s o f r o t a t i o n .
Chapter 4 te l i s you how t o d e s i g n an o b j e c t
f a l l over ( s t a b i l i t y ) . You w i l l
(e.g. a crane) so t h a t i t doesn't
l e a r n how t o determine the c e n t r e o f g r a v i t y ,
and what the r e l a t i o n i s between the p o s i t i o n of the c e n t r e o f g r a v i t y and
the s t a b i l i t y o f an o b j e c t .
In the investigations
you need t o use t h i s theory t o improve the c o n s t r u c t i o n s
which you make y o u r s e l f .
Investigation
1: B u i l d i n g and l o a d i n g a b r i d g e . T r y t o make i t as s t r o n g as
p o s s i b l e ; t h i n k of how p a r t s o f a b r i d g e deform and what s t r e s s e s t h e
m a t e r i a l i s exposed t o .
I n v e s t i g a t i o n 2: B u i l d i n g a crane and i m p r o v i n g
i t as d e s c r i b e d i n I n v e s t i -
g a t i o n 1.
I n v e s t i g a t i o n 3: Working out the maximum l o a d o f a crane a t d i f f e r e n t p l a c e s .
N o t i n g the e f f e c t of the c o u n t e r p o i s e .
I n v e s t i g a t i o n 4: Making p i e r s , beams and b r i d g e - d e c k s
(e.g. out of p a p e r ) ,
l o a d i n g and i m p r o v i n g
o f d i f f e r e n t shapes
them.
I n v e s t i g a t i o n 5: E x p l o r i n g r o t a t i o n .
I n e s t i g a t i o n 6: Making d i f f e r e n t o b j e c t s and s t a b i l i z i n g them u s i n g a l l s o r t s
of
tricks.
The d i f f e r e n t groups t e i l each o t h e r about the r e s u l t s and c o n c l u s i o n s o f
t h e i r i n v e s t i g a t i o n s by p r e s e n t i n g
demonstrations.
WORKING IN A GROUP
As i n the second y e a r , you w i l l spend. a l o t of the t h i r d y e a r w o r k i n g as a
member o f a group. One of the major t a s k s f o r the group i s w o r k i n g o u t a
p l a n t o g e t h e r and d e v i d i n g up the t a s k s . You w i l l need t o d i s c u s s
-10-
things
t o g e t h e r , and t h i s may t u r n o u t t o be
a t h e r d i f f i c u l t a t times.
To make the d i s c u s s i o n s u c c e s s f u l ,
i t i s o f t e n necessary t o :
- prepare
group, but you may decide t o
the d i s c u s s i o n
choose one member o f the group
thoroughly
- s t i c k t o your s u b j e c t
to keep t h e d i s c u s s i o n i n o r d e r .
- see t o i t t h a t the group
I f you are a l a r g e group, t h i s
members don't speak a l l a t the
may be the b e s t way t o do i t . I f
same time
one o r two o f y o u r d i s c u s s i o n
- keep an eye on the c l o c k
s e s s i o n s have been u n s u c c e s s f u l ,
- see t o i t t h a t t h e group
you r e a l l y should t h i n k about
members don't j u s t t a l k , but
appointing a "discussion leader".
a l s o l i s t e n t o each o t h e r .
T h i s doesn't have t o be the same
p e r s o n every
You can t r y to do a l l t h i s as a
- See to it that
olear
time.
you are a l l
about what you are
going
to do.
A f t e r w a r d s , you can ask i f i t ' s
The
clear
d i s c u s s i o n l e a d e r can t r y
to s t a t e t h i s
t o everyone, and i f t h e r e
are any q u e s t i o n s . Don't go on
clearly
but he o r she can a l s o ask:
b e f o r e you're c e r t a i n
that
"Is
everybody has grasped
what i t ' s
there anybody who wants to
a l l going t o be about'.
summarise what we a r e going t o
Students o f t h e " R i j k s s c h o l e n g e m e e n s c h a p Schagen (a High School) have c o n s t r u c t e d
a r e a l b r i d g e , s p a n n i n g a d i t c h o f 7,5 m w i d e . T h e b r i d g e i s l o a d e d w i t h t h e
teacher'.
-1 1-
- See
to it that
stands
everyone
what is being
embarassed. I f someone doesn't
want t o g i v e h i s or h e r o p i n i o n , he
said.
I t o f t e n happens t h a t people
j u s t don't understand
i t ? " Try n o t to make anybody f e e l
under-
or she s h o u l d n ' t be f o r c e d t o .
each
o t h e r : someone says something,
At the end
and someone e l s e r e p l i e s i n a
of the disaussion
way
When the d i s c u s s i o n i s n e a r i n g
t h a t doesn't make any
sense
sum
up what the
results
are.
at a l l . You can h e l p t o make
i t s end
(because a d e c i s i o n has
c l e a r what o t h e r people say by
been taken or because time i s
a s k i n g , f o r i n s t a n c e , " I don't
r u n n i n g o u t ) , you w i l l have to
understand what P e t e r s a i d .
sum up the r e s u l t s . You.can s t a r t
Could you repeat what you were
l i k e t h i s : "So we've d e c i d e d t o . . "
just saying,Peter?"
- See
to it that
opportunity
everyone
to express
has
the
his/her
opinion.
You may
have someone i n your
group who
i s n ' t good at
listening
and i s always t a l k i n g . In the
end, no-one e l s e has been a b l e
to say a word. You
can
t h i s by a s k i n g every now
prevent
and
then
"We
a r e n ' t sure y e t i f . . " "We
" A l l r i g h t , t h a t ' s your o p i n i o n ;
don't y e t agree about.." I f the
what do the o t h e r s t h i n k about
group i s l a r g e you can s p l i t
up
the t a s k o f the d i s c u s s i o n l e a d e r
Be q u i e t please.
by a p p o i n t i n g someone t o see t o
;
i t t h a t everybody s t i c k s t o the
s u b j e c t , a n o t h e r t o make sure
t h a t everyone understands
going on, and another
what's
t o keep an
eye on the c l o c k . J u s t t r y i t
and see how
i t works o u t .
You s h o u l d a l s o t r y to keep a l l t h i s i n mind when you are doing
your
i n v e s t i g a t i o n s and making your a c t u a l b r i d g e . You w i l l be w o r k i n g as a group, and
everyone s h o u l d take p a r t i n the c o n s t r u c t i o n and g i v e t h e i r i d e a s on
s u b j e c t . And
the
of course everyone s h o u l d know what i s going on d u r i n g the
i n v e s t i g a t i o n . A f t e r you have planned
and c a r r i e d out an
investigation,
every member of the group s h o u l d be a b l e t o t e i l what the r e s u l t s a r e .
keep each o t h e r informed and
l e t the whole group prepare
together'.
-12-
the
So
demonstration
INVESTIGATION
MORE A B O U T
In
IN THE T H I R D
YEAR:
"WORKINC'QUESTIONS AND
"SEARCH"QUESTIONS
the second y e a r you have l e a r n e d how t o p l a n and c a r r y out an i n v e s t i -
g a t i o n . One o f the main t h i n g s you l e a r n e d was t o make sure t h a t t h e
problem you were t o i n v e s t i g a t e was w e l l d e f i n e d . You d i d t h i s by a s k i n g
"working" q u e s t i o n s and " s e a r c h " q u e s t i o n s .
- Try to e x p l a i n what i s meant by "working" and " s e a r c h " q u e s t i o n s .
While you were c a r r y i n g out experiments,
the w o r k i n g q u e s t i o n s
turned
out t o be most i m p o r t a n t . F o r i n s t a n c e , when i n v e s t i g a t i n g a w a t e r p i s t o l ,
you c o u l d ask the w o r k i n g q u e s t i o n : W i l l the water s q u i r t f u r t h e r i f I
widen the n o z z l e ?
In Bridges
and a l s o i n the o t h e r themes i n the t h i r d y e a r c o u r s e , the
w o r k i n g q u e s t i o n s w i l l a g a i n p l a y an i m p o r t a n t r o l e i n the i n v e s t i g a t i o n s .
But
as you know a l o t more about p h y s i c s now, you are a b l e t o ask w o r k i n g
q u e s t i o n s which are more d i f f i c u l t ,
as you can see i n the n e x t example:
E r i c and Jacob want t o b u i l d a b r i d g e f o r t h e i r model r a i l w a y , and they
s t a r t l o o k i n g around t o f i n d the b e s t way t o do i t . They d i s c o v e r that
most r a i l w a y b r i d g e s are made o f i r o n beams, and wonder i f they
should
a l s o use i r o n beams i n t h e i r own r a i l w a y b r i d g e . But how can they get
i r o n beams s m a l l enough t o f i t i n t o t h e i r model b r i d g e ? Maybe they
should
use another m a t e r i a l , but i f s o , what m a t e r i a l ? To f i n d o u t , they must
know what t h e advantages are of i r o n beams i n the c o n s t r u c t i o n o f r a i l w a y
b r i d g e s . " W e l l " , Jacob s a y s , " I know from a theme we d i d e a r l i e r , Man and
Me t a l
3
t h a t i r o n i s a s t r o n g m a t e r i a l . So l e t ' s use w i r e f o r o u r b r i d g e " .
"Wire i s n ' t s t r o n g enough. I t bends e a s i l y and i t i s n ' t e l a s t i c . Why e l s e
do you t h i n k they use i r o n beams? Couldn't we use wooden s t i c k s and p a i n t
them t o l o o k l i k e
iron?"
T h i s example shows t h a t E r i c
to
and Jacob use the knowledge they've a c q u i r e d
draw up a w o r k i n g q u e s t i o n . I n t h i s theme you w i l l a l s o l e a r n new t h i n g s
(e.g. about s t r e s s e s i n m a t e r i a l s ) t h a t you can use l a t e r t o ask a new
w o r k i n g q u e s t i o n . I f , f o r i n s t a n c e , you want t o r e i n f o r c e a b r i d g e , you
can ask y o u r s e l f : W i l l my b r i d g e become s t r o n g e r i f I use wood i n s t e a d o f
w i r e , s i n c e wood i s b e t t e r a t w i t h s t a n d i n g bending? You can put t h i s i n a
diagram l i k e
this:
knowledge about:
problem :
- stresses i n bridges
- strenght of the m a t e r i a l s
wood and w i r e
How do I r e i n f o r c e my
bridge
working question :
W i l l t h e b r i d g e Decome s t r o n g e r
j i f I u s e wooden s t i c k s i n s t e a d
of w i r e ?
f
Carry out the experiment.
Has t h e b r i d g e become
stronger?
t
- What have I l e a r n e d ?
- D i d t h a t f i t i n w i t h what I
knew a l r e a d y ?
- Have I a p p l i e d my k n o w l e d g e
t h e r i g h t way ?
-14-
new
working
question
ORIENTATION
contents
1
B r i d g e s i n your neighbourbood
2
The shape of b r i d g e s
3
E x p a n s i o n and c o n t r a c t i o n i n 1
T h i s p h o t o g r a p h s h o w s some o f t h e t h i n g s d i s c u s s e d i n t h i s
theme:
d i f f e r e n t t y p e s o f b r i d g e s ( a doublé b a s c u l e b r i d g e
and a l i f t i n g b r i d g e ) a n d a b i g f l o a t i n g d e r r i c k
c r a n e by a
t u g - b o a t . T h e p h o t o g r a p h was t a k e n i n D o r d r e c h t .
-16-
1 bridges in your neighbourhood
I n any town o r v i l l a g e you are l i k e l y
waterways o r r o a d s , d r a w - b r i d g e s ,
to f i n d b r i d g e s : b r i d g e s
over
r a i l w a y b r i d g e s , f l y o v e r s , e t c . There
are many d i f f e r e n t types of b r i d g e s and you can see t h a t they a l l have
t h e i r own c h a r a c t e r i s t i c shape. The shape of a b r i d g e depends on:
- the p e r i o d when the b r i d g e was b u i l t
- what was f a s h i o n a b l e d u r i n g t h a t p e r i o d
- the m a t e r i a l the b r i d g e i s made of
- the l e n g t h of the span
- the amount of t r a f f i c which passes over the b r i d g e
- whether the b r i d g e has t o be movable
- ( i f t h e b r i d g e i s over a waterway) whether i t s c o n s t r u c t i o n w i l l
interfere
with shipping.
In t h i s theme, you are going t o look at the shapes of b r i d g e s and at the
m a t e r i a l s used i n t h e i r c o n s t r u c t i o n . You w i l l
l e a r n something about the
s t r e s s e s o c c u r r i n g i n a b r i d g e and about m a t e r i a l s which a r e a b l e t o
w i t h s t a n d these s t r e s s e s . When b u i l d i n g your own b r i d g e , you w i l l put i n t o
p r a c t i c e what y o u have l e a r n e d . You w i l l a l s o l e a r n about weight and
counterweight
i n a swing b r i d g e . S t a b i l i t y i s the l a s t t o p i c i n t h i s theme.
A b r i d g e s h o u l d be s t a b l e enough t o w i t h s t a n d s t r o n g winds. The n o t i o n s
of w e i g h t , counterweight and s t a b i l i t y are a l s o a p p l i e d t o o t h e r c o n s t r u c t i o n s ,
such as cranes and d e r r i c k s .
task 1
1• Examine the b r i d g e s y o u see on your way from home t o
s c h o o l , and any o t h e r b r i d g e s i n your neighbourhood.
W h a t i s t h e name o f t h i s v e r y w e l l - k n o w n b r i d g e ?
I t l o o k s t o t a l l y d i f f e r e n t now, b u t t h i s i s h o u
i t l o o k e d u n t i l a few y e a r s ago. The b r i d g e i s
one o f t h e i m p o r t a n t l i n k s b e t w e e n t h e n o r t h
and t h e s o u t h o f t h e N e t h e r l a n d s .
-17-
2. Make s k e t c h e s
of a few of these b r i d g e s
book. T r y t o see e x a c t l y how the b r i d g e
i n your e x e r c i s e -
i s made. How a r e the
d i f f e r e n t p a r t s connected t o one another? I n which
direction
do the b a r s , the c a b l e s o r t h e beams run?
3. Which m a t e r i a l s are most commonly
used i n the b r i d g e s y o u
have drawn? A r e t h e r e any m a t e r i a l s t h a t can be used f o r
one p a r t of a b r i d g e , but a r e u n s u i t a b l e f o r a n o t h e r p a r t ?
What d i f f e r e n c e s do you n o t i c e between the m a t e r i a l s used i n
modern b r i d g e s
task 2
and i n o l d e r
Answer the same q u e s t i o n s
bridges?
f o r a crane ( t h e k i n d t h a t i s used
on a c o n s t r u c t i o n s i t e ) .
2 the shape of bridges
The s i m p l e s t type of b r i d g e i s the beam b r i d g e : a beam t h a t runs from
one bank t o the o t h e r . I f the span i s too l o n g , the beam can be s u p p o r t e d
by a number o f p i e r s . I n Reading Text 1, you w i l l see a photograph o f a
very o l d E n g l i s h beam b r i d g e .
BEAM BRIDGE
I f the b r i d g e raust be movable, a b a s c u l e b r i d g e i s one of the
possibilities.
The
roadway can be s t r e n g t h e n e d
by s u p p o r t i n g i t w i t h a d d i t i o n a l beams o r
an a r c h .
In
the mountains
you c a n f i n d
many o p e n a r c h
bridges
A b r i d g e can be s t r e n g t h e n e d
The m e d i e v a l
stone
arch
bridge
i n Maastricht
(and t h e span i n c r e a s e d ) when a s u p e r s t r u c t u r e
i s used. T h i s i s a s t a y e d g i r d e r b r i d g e ( t h e roadway i s suspended from
cables c a l l e d stays).
The G a l e c o p p e r b r i d g e o v e r t h e A m s t e r d a m - R h i n e
near Utrecht (stayed girder
type)
SUSPENSION
BRIDGE
canal
T h e r e a r e n o t many
suspension
bridges
i n the
Netherlands
Another way o f s t r e n g t h e n i n g a b r i d g e i s suspending
The
the deck from an a r c h .
a r c h i s u s u a l l y made of c o n c r e t e o r i r o n , and the deck i s suspended
from s t e e l c a b l e s .
ARCH
Two a r c h b r i d g e s s i d e b y s i d e : t h e r a i l w a y b r i d g e
and t h e r o a d b r i d g e o v e r t h e A m s t e r d a m - R h i n e c a n a l
n e a r U t r e c h t . The c h i m n e y s b e l o n g t o a powerstat ion.
-21-
BRIDGE
In s t e e l b r i d g e s , the s u p e r s t r u c t u r e o f t e n c o n s i s t s o f s t e e l
triangles.
This makes the b r i d g e much s t r o n g e r . There a r e s e v e r a l forms.
TRUSS BRIDGE
This
trusi
bridge
near
SWING BRIDGE
-22-
Sluiskil
rotaces
round
the c e n t r a l
pier
R BRIDGE
The M o e r d i j k b r i d g e t h e way i t l o o k e d u n t i l 1978 was a l a t t i c e
g i r d e r b r i d g e . Now, t h e e n t i r e b r i d g e h a s b e e n r e p l a c e d b y a rauch
wider beam-type b r i d g e , c o n s i s t i n g o f s e c t i o n s o f p r e s t r e s s e d
c o n c r e t e ( s e e R e a d i n g T e x t 3 ) . The t r u s s b r i d g e i n the b a c k g r o u n d
is a railway bridge.
'V
I f t h e r e has t o be room f o r t a l l
s h i p s t o pass under a t r u s s
b r i d g e , the l i f t i n g b r i d g e i s
the coramonest type. P a r t of
the b r i d g e i s l i f t e d by means
of
ING BRIDGE
-23
counterweights.
The o l d r o a d b r i d g e a t K e i 2 e r s v e e r w a s a c r u s s e d a r c h b r i d g e . Now, t h i s
b r i d g e h a s been r e p l a c e d by s e c t i o n s o f t h e M o e r d i j k b r i d g e ( s e e R e a d i n g
Text 3 ) .
task 3
T r v
t o
m a k
e out from the photographs o f b r i d g e s i n t h i s
c h a p t e r which m a t e r i a l s are used i n t h e i r c o n s t r u c t i o n . How
can you t e i l ?
The
shape of a b r i d g e i s v e r y much determined
by the m a t e r i a l used. U n t i l
around 1800, almost every b r i d g e was made o f stone o r wood. T h e i r span
c o u l d never be very l o n g . But then s t e e l b r i d g e s came i n t o use, and t h i s
c r e a t e d a l o t of new p o s s i b i l i t i e s .
-24-
Since
1945, s t e e l has been p r o g r e s s i v e l y r e p l a c e d by r e i n f o r c e d c o n c r e t e .
Nowadays by u s i n g p r e s t r e s s e d c o n c r e t e
(see Reading Text 2) and the s o -
c a l l e d " l i g h t - w e i g h t " c o n c r e t e , spans can be i n c r e a s e d
considerably
w i t h o u t the need of a s u p e r - o r a s u b s t r u c t u r e .
The b r i d g e o v e r t h e r i v e r I J s s e l a t Z u t p h e n
i s made o f p r e s t r e s s e d l i g h t w e i g h t c o n c r e t e ,
l t s m a x i m u m s p a n i s 126 m.
I n the s k e t c h below, you see a diagram o f the s t r u c t u r e of a b r i d g e and
the m a t e r i a l s used i n b r i d g e - b u i l d i n g .
SUPERSTRUCTURE
S T R U C T U R E OF A
BRIDGE
BASE
KSUBSTRUCTURE
PUILDING MATERIALS
WOOD
CAST
STONE
WROUGHT IRON
IRON
STEEL
-25-
l
I
CONCRETE
REINFORCED
PRESTRESSED
3 expansion and contraction in bridges
L i k e a l l o t h e r m a t e r i a l s , b r i d g e m a t e r i a l s expand and c o n t r a c t when the temperature
changes. To p r e v e n t damage when the b r i d g e expands on h o t days, the deck i s f a s t e n e d
o n l y a t one end. A t the o t h e r end, t h e r e i room f o r i t t o expand. Hinges o r r o l l e r s
are used t o a l l o w t h i s t o happen.
Choose a b r i d g e near s c h o o l . On s e v e r a l
days (choose a warm and a c o l d d a y ) ,
measure:
- the temperature of the b r i d g e - d e c k ,
by c a r e f u l l y f i t t i n g a thermometer
against i t
- the space between the b r i d g e - d e c k
and the road-way, u s i n g a c a l l i p e r .
Do you g e t d i f f e r e n t r e s u l t s on warm
and on c o l d days?
When t h e b r i d g e e x p a n d s ( i . e . w h e n t h e t e m p e r a c u r e r i s e s ) ,
t h e h i n g e s o r r o l l e r s move a l o n g w i t h t h e e x p a n d i n g d e c k .
Draw a s k e t c h ( o r take a photo) of a
movable deck of a b r i d g e i n your
neighbourhood.
Tower
bridge
expanded
Uhen
the parts
move
towards
of a bridge-deck
each
expand,
the steel
edRes
cooled
other.
-26-
i n London d u r i n g
s o rouch
by w a t e r
that
from
a heatwave.
the b r i d g e
the r i v e r .
couldn't
The b r i d g e - d e c k
be c l o s e d .
had
I t was
THEORY
contents
Chapter
1
Stress i n bridges
page 29
1.1
Bending o f the b r i d g e - d e c k
29
1.2
Stress i n d i f f e r e n t parts of a bridge
31
1.3
Bending
34
Chapter 2
S t r e n g t h and shape
36
2.1
Roofed b r i d g e s
36
2.2
Bridge-decks
39
2.3
Trusses
41
2.4
Arches
44
2.5
S t r e n g t h and m a t e r i a l
47
Chapter 3
Weight and c o u n t e r w e i g h t
Chapter 4
Stability
-27-
On 7 t h N o v e m b e r 1 9 4 0 , d u r i n g a g a l e , t h e
new T a c o m a B r i d g e i n t h e U n i t e d S t a t e s
c o l l a p s e d . I t could not withstand the
enormous s t r e s s e s .
The Van B r i e n e n o o r d b r u g
i n R o t t e r d a m has the l o n g e s t span
i n t h e N e t h e r l a n d s : 2 8 7 m. T h e a r c h t r a n s f e r s t h e s t r e s s e s
in the bridge-deck
to the p i e r s .
-28-
1 stress in bridges
In t h i s c h a p t e r , we w i l l examine the s t r e s s e s on the d i f f e r e n t p a r t s o f
a b r i d g e . The type o f m a t e r i a l chosen f o r the c o n s t r u c t i o n o f each p a r t
depends upon the s t r e s s e s which i t has t o w i t h s t a n d .
1.1 BENDING OF THE BRIDGE DECK
A l o a d on a b r i d g e makes the b r i d g e
bend. T h i s causes s t r e s s i n t h e
bridge-deck.
This simple bridge w i l l
hold the c y c l i s t
easily
(mass 80 k g ) ; a
c a r (mass 1000 kg) w i l l make the
b r i d g e bend a l i t t l e more.
The b r i d g e w i l l not h o l d a 6-ton l o r r y . I t w i l l bend so much under the l o r r y ' s
weight t h a t i t w i l l break. I t cannot w i t h s t a n d such l a r g e s t r e s s e s .
The
weight
o f t h e c a r makes t h e b r i d g e
bend.
Would i t h e l p i f the b r i d g e - d e c k
were t h i c k e r ? Maybe, b u t a t h i c k e r b r i d g e -
deck i s a l s o h e a v i e r . l t s own weight would make i t bend. I f the b r i d g e - d e c k
i s t o o heavy, i t can b a r e l y support
i t s own w e i g h t .
What e x a c t l y happens t o the b r i d g e - d e c k
You can f i n d t h i s out by doing
when i t bends?
the f o l l o w i n g e x p e r i m e n t .
-29-
experiment 1 B e n d i n g of a f o a m - r u b b e r
bridge
Draw some v e r t i c a l l i n e s on a p i e c e o f foam-rubber, as shown
i n the f o l l o w i n g photograph. Make a b r i d g e u s i n g the foamrubber, and put a l o a d on i t . Watch the l i n e s . What do you see?
In t h i s e x p e r i m e n t y o u l e a r n t h a t the foam-rubber i s compressed
(pushed
i n ) a t t h e top and s t r e t c h e d a t the bottom. The foam-rubber i s under
bending
stress.
material
in compression
O
O
0
O
0
O
O
O
O
O
O
0
O
O
O
O
O
O
O
O
O
O
0
O
O
O
O
O
O
O
O
O
O
O
O
O
j
material in t e n s i o n
In a r e a l b r i d g e the same t h i n g happens. You u s u a l l y don't see i t ,
because b r i d g e s are made of a s t r o n g e r m a t e r i a l than foam-rubber. The
b e n d i n g s t r e s s i n the b r i d g e - d e c k i s a b l e t o p r e v e n t i t from c o l l a p s i n g
under the weight o f the c a r , by t r a n s m i t t i n g the c a r ' s weight t o the
supports ( o r p i e r s ) .
-30-
neutral
layer
1.2
STRESS IN DIFFERENT PARTS OF A BRIDGE
Compression
Many b r i d g e s n o t o n l y have
s u p p o r t s on b o t h s i d e s b u t
are a l s o s u p p o r t e d by a p i e r
i n the m i d d l e . T h i s makes the
b r i d g e much s t r o n g e r , because
the p i e r won't l e t the b r i d g e deck bend t o o much. The p i e r
i s compressed
by the c a r ' s
w e i g h t , but the m a t e r i a l the
p i e r i s made o f can w i t h s t a n d
t h i s s t r e s s , and w i l l keep the
b r i d g e - d e c k i n p l a c e . The s t r e s s
The
pier
keeps
the bridge-deck
from
bending
t o o much.
which t h e p i e r undergoes i s
c a l l e d aompressive
stress
or
compression.
You can e x e r t compression on a
b a r by p u s h i n g a g a i n s t b o t h
ends w i t h your hands, as shown
i n the drawing. The b a r (and
BAR
your hands t o o ) a r e pushed i n
a l i t t l e b i t , b u t t h e b a r does
n o t c o l l a p s e nor bend n o r b r e a k ,
u n l e s s i t i s a v e r y t h i n one.
T h i s means t h a t the b a r i s good
a t w i t h s t a n d i n g compressive
stress.
experiment 2 Compression and materials
I n v e s t i g a t e which of the f o l l o w i n g m a t e r i a l s are good and
which are bad a t w i t h s t a n d i n g compression:
- wood
- modelling clay
- paper
- elastic
- cardboard
- rope
Which o f these m a t e r i a l s would be most s u i t a b l e f o r b u i l d i n g
a p i e r f o r a b r i d g e - m o d e l i n the classroom?
task
1
T h e
m a t e r i a l s most f r e q u e n t l y used i n the c o n s t r u c t i o n o f
b r i d g e s are wood, s t o n e , i r o n and r e i n f o r c e d c o n c r e t e . Which
o f these m a t e r i a l s are most commonly used f o r b r i d g e - p i e r s
i n b r i d g e s n e a r y o u r s c h o o l (or i n the photographs i n t h i s book)?
If a bridge
two arrows
element
pointing
is subjected
towards
to compression,
each
we w i l l indicate
this
by
other.
compression
Th«
t
pier
i s under
compression
Tension
A n o t h e r way
of s t r e n g t h e n i n g
bridge-decks
i s suspending
them
from c a b l e s . These c a b l e s (sometimes c a l l e d s t a y s ) are a t t a c h e d t o towers
c a l l e d p y l o n s . A b r i d g e c o n s t r u c t e d t h i s way
a c a b l e c a n t i l e v e r b r i d g e . The
are s t r e t c h e d i s c a l l e d tensile
w e i g h t of the load onto the
i s c a l l e d a stayed g i r d e r or
s t r e s s which the c a b l e s undergo when they
stress
o r tension.
pylons.
-32-
T h i s t r a n s f e r s the
T h e man i n t h e p h o t o g r a p h a r e i n v o l v e d i n a t u g - o f - v a r . T h e men
at t h e o t h e r end o f t h e r o p e a r e a l a o p u i l i n g as h a r d a s they
c a n . The r o p e b e t v e e n t h e t u o teams i s u n d e r a l o t o f s t r e s s ,
but f o r t u n a t e l y i t i s good a t w i t h s t a n d i n g t e n s i o n .
experiment 3 T e n s i o n and materials
Test the m a t e r i a l s l i s t e d i n experiment 2 f o r t e n s i l e
Which
a
task 2
stress.
of these m a t e r i a l s would you use t o make the s t a y s of
stayed g i r d e r b r i d g e ?
Which of the m a t e r i a l s l i s t e d i n task 1 a r e s u i t a b l e f o r use
in
s t a y e d g i r d e r b r i d g e s and which are not?
What i s your c o n c l u s i o n about the r e s i s t a n c e o f these
m a t e r i a l s to t e n s i l e s t r e s s ?
If a bridge
element
arrows pointing
is subjected
away from each
to tension,
other.
-33-
we w i l l indioate
this
by two
1.3
BENDING
In Experiment 1 we found t h a t a l o a d on a foam-rubber b r i d g e - d e c k compresses
the top l a y e r s o f the b r i d g e - d e c k and s t r e t c h e s the lower l a y e r s : the m a t e r i a l
i s i n compression a t the top and i n t e n s i o n
below.
When a b r i d g e - d e c k b e n d s ,
i t undergoes
compressive
and t e n s i l e
Bending i s a c o m b i n a t i o n o f compression and t e n s i o n . A m a t e r i a l which i s
n o t good a t w i t h s t a n d i n g
compression ( e . g . paper) o r t e n s i o n
i s a l s o bad at w i t h s t a n d i n g
(e.g. stone)
b e n d i n g s t r e s s e s . Only m a t e r i a l s which a r e s t r o n g
under b o t h c o m p r e s s i o n and t e n s i o n (e.g. wood o r i r o n ) a r e s u i t a b l e f o r t h e
construction of bridge-decks.
C o n c r e t e i s weak under t e n s i o n , and t h e r e f o r e weak when made t o bend. Y e t
many roadways a r e made o f c o n c r e t e .
This
c o n c r e t e needs t o be r e i n f o r c e d
w i t h s t e e l r o d s , which a r e p o s i t i o n e d i n the lower l a y e r s of the c o n c r e t e
-34-
stresses.
to absorb the t e n s i l e s t r e s s . The compressive s t r e s s i n the top l a y e r s
of the roadway can be e a s i l y h a n d l e d by the c o n c r e t e i t s e l f .
Reinforcement
makes the c o n c r e t e much s t r o n g e r . Text n r . 2 i n the Reading s e c t i o n d e a l s
w i t h the t e c h n o l o g y o f " p r e s t r e s s e d " c o n c r e t e .
I r o n b a r s o r rods a r e a l s o used i n c o n c r e t e f l o o r s o f houses, and i n
c o n c r e t e beams.
E x p l a i n why the r e i n f o r c i n g r o d i s p o s i t i o n e d a t the top o f
the b a l c o n y beam b u t a t the bottom of the f l o o r beam.
-35-
2 strength and shape
In t h i s c h a p t e r y o u w i l l f i n d o u t how b r i d g e s can be s t r e n g t h e n e d , and
you'11 l e a r n how i m p o r t a n t the shape o f a b r i d g e i s .
A l s o , you a r e going t o a p p l y what you have l e a r n e d about s t r e s s e s i n
m a t e r i a l s i n c h a p t e r 1.
2.1
ROOFED BRIDGES
In the b r i d g e on the
photograph, the r a i l w a y
i s roofed. This i s not
just a shelter against
the r a i n , i t a l s o makes
the b r i d g e s t r o n g e r . In
the next
experiment
you w i l l f i n d out why.
experiment
1
A paper
Brittannia
bridge
bridge
i n England
(see Reading Text
You s h o u l d u s e t h e same a m o u n t o f m a t e r i a l ,
o t h e r w i s e y o u w o n ' t b e a b l e t o make a f a i r
comparison.
- Make a " b r i d g e " o f two f o l d e d sheets o f paper, r e s t i n g on
two books. W i l l t h i s make a s t r o n g b r i d g e ?
- Then f o l d the sheets as shown below.
-36-
5)
W i l l t h i s make the b r i d g e s t r o n g e r ?
What w i l l happen t o the r a i s e d edges i f y o u put t o o much l o a d
on the b r i d g e ?
In what p a r t o f the edges do you n o t i c e t e n s i l e s t r e s s ?
Where do you n o t i c e compressive
s t r e s s ? How can you t e i l ?
SECOND SHEET
ILVuv u i u
u r n i il
Minu^r
- Now r e i n f o r c e your b r i d g e by g l u e i n g the two sheets of paper
t o g e t h e r t o form a tube.
Has
t h e b r i d g e become s t r o n g e r ?
-' How can you r e i n f o r c e your b r i d g e even more?
In
t h i s experiment,
you have s t r e n g t h e n e d
a f l a t sheet by f o l d i n g i t i n t o
a r e c t a n g u l a r shape. Paper i s n ' t a v e r y s t r o n g m a t e r i a l , y e t i t i s s t r o n g
enough t o make a f a i r l y s t r o n g b r i d g e . There a r e many ways you can change
the shape o f a sheet of paper; some a r e difficult» some are easy.
Deforming
paper
BENDING
Paper bends e a s i l y
PUSHING
Paper b u c k l e s e a s i l y when compressed
PULLING
Paper w i l l t e a r o n l y i f you
p u l l h a r d . I t doesn't
deform e a s i l y under
tensile
-37-
stress.
(pushed)
These c h a r a c t e r i s t i c s o f paper e x p l a i n how, i n the experiment,
your b r i d g e
became s t r o n g e r when the edges were r a i s e d . You c r e a t e d t e n s i l e s t r e s s i n
the lower p a r t o f the edges. T h i s p r e v e n t e d
paper w i t h s t a n d s
the b r i d g e from bending,
since
t e n s i o n b e t t e r than compression and d e f l e c t i o n . So t o
make your b r i d g e as s t r o n g as p o s s i b l e , y o u must choose the shape w h i c h i s
b e s t at s u b j e c t i n g the paper t o t e n s i l e
stress.
LOAD
When the b r i d g e i s too h e a v i l y l o a d e d , the upper p a r t o f the paper s t a r t s
to b u c k l e . You can h e l p t o p r e v e n t
t h i s by g l u e i n g the second sheet o f
paper on top of the f i r s t one. P a r t of the t e n s i l e s t r e s s w i l l be t r a n s m i t t e d
to
the second s h e e t . As you see, paper i s f a i r l y
s t r o n g , so l o n g as i t i s
tube-shaped.
In o t h e r m a t e r i a l s t o o , shape can add c o n s i d e r a b l y t o s t r e n g t h . The
B r i t t a n n i a b r i d g e ( r e a d i n g t e x t 5) has a tube made o f s t e e l . S t e e l i s much
s t r o n g e r than paper and a l s o w i t h s t a n d s
compression much b e t t e r . I n the
r e a d i n g t e x t you w i l l read how a b i g f i r e a f f e c t e d the s t r e n g t h o f the
Brittannia bridge.
-38-
task 1
- I s the b r i d g e i n t h i s photograph s t r o n g e r w i t h the r a i l i n g s
than
without?
- Are the r a i l i n g s under t e n s i o n o r under compression when
the b r i d g e i s loaded?
2.2
BRIDGE-DECKS
B r i d g e s a r e s t r o n g e r when the b r i d g e - d e c k s
have r a i s e d edges.
Connections
between the edges make them even s t r o n g e r .
task 2
P o i n t out the edges and the c o n n e c t i o n s
on the photograph
What would happen i f t h e r e were no c o n n e c t i o n s ?
I n d i c a t e which p a r t s a r e under t e n s i o n and which under
compression.
A b r i d g e made f r o m p a p e r a n d g l u e o n l y ' . I t i s a b o u t 10 m l o n g
w i d e ; i t c a n h o l d a 4 - t o n l o r r y . l t s own w e i g h t i s 2 0 0 k g s .
-39-
and 5 m
Under the c o n c r e t e decks of some b r i d g e s you can see c o n c r e t e t u b e s ,
which p r e v e n t the deck from b e n d i n g . They make the b r i d g e - d e c k
thicker
withoud making i t too much h e a v i e r .
Concrete
task 3
tubes
underneeth
a motorvay
flyover
i n Utrecht.
Where e x a c t l y do you t h i n k the s t e e l rods a r e i n the c o n c r e t e
tubes: i n the upper p a r t , i n the lower p a r t or i n the s i d e s ?
In i r o n b r i d g e s , you'11 o f t e n see H o r T-shaped g i r d e r s . These are almost
as s t r o n g as s o l i d beams, but much l i g h t e r and f a r l e s s b u l k y . A g r e a t d e a l
of the s t r e n g t h o f s o l i d beams i s used t o support t h e i r own w e i g h t , so they
are not o f t e n used.
H-SHAPED
GIRDER
experiment 2
T-SHAPED
GIRDER
SOLID BEAM
Make an H-shaped paper g i r d e r and l o a d i t . Where i s i t
exposed t o t e n s i o n and where t o compression?
How can you
teil?
What can you do t o p r e v e n t the paper
-40-
flattening?
task 4
Why do you t h i n k i r o n b a r s o r c a b l e s are used i n b r i d g e
elements under t e n s i o n , and H o r T-shaped g i r d e r s i n elements
under compression o r bending s t r e s s e s ?
2.3
The
TRUSSES
B r i t t a n n i a bridge
(see page 36
and r e a d i n g
t e x t 5) i s s t r e n g t h e n e d
by r a i s e d s i d e s made o f s t e e l p l a t e s , f o r which a l o t o f i r o n was r e q u i r e d .
S t r o n g s i d e s can a l s o be made u s i n g l e s s m a t e r i a l . T h i s i s done i n the
construction of truss bridges
The
(see p. 45 ) .
b a s i c shape o f the t r u s s b r i d g e
i s shown i n the photograph and t h e
drawing below.
Primitive
The
bridge
i n Albania
s i d e s of the p r i m i t i v e t r u s s b r i d g e a r e made o f wooden s t a k e s , r e i n f o r c i n g
the b r i d g e - d e c k at the c e n t r e
The
wooden t r u s s
( t h e drawing shows how the f o r c e s w o r k ) .
weight o f the c a r makes the b r i d g e - d e c k bend down. Member A moves down
too, but i s h e l d back by members B and C; t h e r e f o r e , the b r i d g e - d e c k does
not bend so much. Member A i s under t e n s i o n , B and C are under compression.
The
w e i g h t o f the l o a d i s t r a n s m i t t e d t o the p i e r s by the t r u s s and a l s o
by the roadway.
task 5
Which o f the members A, B and C c o u l d be r e p l a c e d by a cable?
task 6
A b r i d g e - d e c k can a l s o be r e i n f o r c e d by a t r u s s on the unders i d e . I n d i c a t e which members, i n the drawing below, are
under t e n s i o n and which are under compression.
-41-
When the span i s v e r y l o n g , a d d i t i o n a l v e r t i c a l c o n n e c t i o n s
give e x t r a
s t r e n g t h t o the t r u s s .
Look a t the shape ABCD i n the drawing below. Shapes l i k e t h i s tend t o
deform e a s i l y , but i t i s easy t o make them s t r o n g e r . You w i l l see how i n
the n e x t experiment.
A
LOAD
- P u l l down a t B w h i l e h o l d i n g CD. See how the shape deforms.
-Fit
i n a b a r BD and compare the s t r e n g t h o f t h i s c o n s t r u c t i o n
to the former one.
- F i t i n a b a r AC and compare a g a i n . Can b a r BD be r e p l a c e d
by a rope? And AC? Try i t .
-42-
By f i t t i n g a d i a g o n a l b a r , you c r e a t e two t r i a n g l e s . A t r i a n g l e i s a v e r y
s t r o n g shape, which i s why i t i s o f t e n used i n b r i d g e s and o t h e r c o n s t r u c t i o n s
such as c r a n e s , r o o f s e t c .
So the b r i d g e can be s t r e n g t h e n e d
like
this:
S5V
but n o t l i k e
this:
I
W&ftXff/A&ffl.'K'llSiK'lSi^"<WW9Sftt<96N^\W
^ V V V ^ A V ^ A V ^ ^ ^
I f the b r i d g e i s loaded a t p o i n t B - e.g. by a c a r - the shape ABCD deforms,
AC becoming s h o r t e r and BD l o n g e r . (Check t h i s w i t h y o u r r e s u l t s from
experiment 3.)
T h i s means t h a t member AC i s under compression,
I r o n i s s t r o n g under compression,
whereas BD i s under t e n s i o n .
but even s t r o n g e r under t e n s i o n . B e s i d e s ,
t e n s i o n can be absorbed by a s i m p l e b a r , whereas compression u s u a l l y
r e q u i r e s an H-shaped beam, which makes the b r i d g e b u i k i e r and h e a v i e r . That
i s why i t makes more sense t o use a b a r BD. B e s i d e s , BD t r a n s f e r s the
w e i g h t o f the l o a d towards the p i e r s , u n l i k e AC!
task 7
How c o u l d you f i t i n a d d i t i o n a l b a r s
to r e i n f o r c e the b r i d g e i n the drawing
on the r i g h t ? W i l l
exposed
these b a r s be
t o t e n s i o n or t o c o m p r e s s i on
1 '//.\ W / A V W r / A M l B W A \ l f / / . V l
WfS.VMW/MWW.
Compare your s o l u t i o n to the photograph of the M o e r d i j k b r i d g e i n
Reading Text 3.
2.4
ARCHES
In a t r u s s e d a r c h b r i d g e , the t r i a n g u l a r shape o f the t r u s s i s r e p l a c e d
by an a r c h . An example o f a t r u s s e d a r c h b r i d g e i s the r a i l w a y b r i d g e
at
Culemborg.
The r a i l w a y b r i d g e ac Culemborg (1865) i s Che oldesC r a i l w a y
b r i d g e i n Che NeCherlands. T h i s c r u s s e d a r c h b r i d g e i s s c i l l
i n use.
task 8
E x p l a i n why the b a r s towards the o u t s i d e a r e t h i c k e r than
those i n the m i d d l e .
task 9
.As y o u can see i n t h e photograph
o f the Culemborg b r i d g e ,
the b a r s a r e p o s i t i o n e d t o b o t h l e f t and r i g h t o f the c e n t r e ,
p o i n t i n g towards the c e n t r e o f the b r i d g e - d e c k . E x p l a i n why
they are p o s i t i o n e d l i k e t h i s :
-44-
The a r c h i s a s t r o n g e r shape than the t r i a n g l e . The experiment below
you
tells
why:
experiment 4
Make a model of a t r u s s b r i d g e , as i n the drawing. Load
the
t r i a n g l e by suspending w e i g h t s from A. F i n d out which are
the weakest p o i n t s i n the t r i a n g l e .
The b r i d g e i s loaded at A, g e n e r a t i n g t e n s i l e s t r e s s i n AD and
compressive
s t r e s s i n DC and DB. T h i s has the e f f e c t of t r a n s f e r r i n g the w e i g h t to
the p i e r s . P o i n t s B, C and D are exposed
and must be a b l e t o w i t h s t a n d a l l t h i s
In
an a r c h , the
t o s t r e s s from d i f f e r e n t
directions
stress.
compressive
s t r e s s i s spread o v e r the
a r c h as a whole. T h i s i s t r u e
b o t h f o r arches above b r i d g e decks and f o r arches
under-
neath b r i d g e - d e c k s .
The b r i d g e - d e c k i s compressed
a l i t t l e by the c a r ' s w e i g h t ,
resulting in a slight
compression of a r c h A. I f
the m a t e r i a l the a r c h i s made
of
i s s t r o n g enough, the
b r i d g e - d e c k w i l l not be
a f f e c t e d by t h i s
compression.
T h i s p r i n c i p l e ( w i t h suspended
as w e l l as s u p p o r t e d b r i d g e - d e c k s ) i s w i d e l y
used i n the c o n s t r u c t i o n of b r i d g e s .
-45-
task
10
Examine these two b r i d g e s and work out what s t r e s s e s the
d i f f e r e n t elements a r e exposed t o .
I n the drawing below, you see an (axaggerated) diagram of the f o r c e s
o c c u r r i n g i n a s p e c i a l type of a r c h b r i d g e .
The
combination
of forces prevents
the b r i d g e c o l l a p s i n g under the c a r ' s
w e i g h t . The weight i s t r a n s f e r r e d t o the p i e r s .
task 11
I n d i c a t e the p l a c e s where the concrete
needs t o be r e i n f o r c e d w i t h i r o n
2.5
i n the b r i d g e above
rods.
STRENGTH AND MATERIAL
You have l e a r n e d from the experiments t h a t s t r o n g b r i d g e s can be made u s i n g
"weak" m a t e r i a l such as paper o f cardboard.
Y e t these m a t e r i a l s a r e never
used i n r e a l b r i d g e s . The reason i s n o t o n l y t h a t r e a l b r i d g e m a t e r i a l s
need t o be much s t r o n g e r s t i l l , b u t a l s o t h a t the m a t e r i a l s i n r e a l
bridges
need t o s a t i s f y o t h e r requirements as w e l l . T h e y s h o u l d , f o r i n s t a n c e , be
h i g h l y r e s i s t a n t t o f i r e and t o m o i s t u r e .
That i s why cardboard
i s not
used at a l l , and wood o n l y r a r e l y , i n b r i d g e - b u i l d i n g .
Two o t h e r reasons f o r n o t u s i n g wood a r e the maintenance i t r e q u i r e s and
the way i t s w e l l s when i t gets wet. A wooden b r i d g e deforms c o n s i d e r a b l y
when the wood s w e l l s due t o m o i s t u r e .
A f i n a l f a c t o r which i s important
i n the c h o i c e o f m a t e r i a l i s the c o s t .
M a t e r i a l s commonly used f o r b r i d g e - b u i l d i n g a r e :
stone:
very d u r s b l e , s t r o n g under compression, but weaker under t e n s i o n .
oonavete:
v e r y d u r a b l e , s t r o n g under compression, but weaker under
t e n s i o n . An advantage over stone i s t h a t i t can be c a s t i n
any d e s i r e d shape and can be r e i n f o r c e d w i t h i r o n
iron
or s t e e l : s t r o n g under b o t h compression and t e n s i o n . R e q u i r e s
some maintenance.
-47-
rods.
quite
The q u a l i t i e s of i r o n and c o n c r e t e are o f t e n combined i n r e i n f o r c e d
c o n c r e t e . The
reinforcement
i s p o s i t i o n e d where the b r i d g e i s exposed to
t e n s i o n . So the i r o n i n s t e a d of the c o n c r e t e absorbs the t e n s i o n .
O f t e n , the s t e e l b a r s i n b r i d g e s are p o s i t i o n e d i n such a way
experience
are
t e n s i o n ; stone and c o n c r e t e
to e x p e r i e n c e
used o n l y where they w i l l e x p e r i e n c e
as to
compression.
Cables
t e n s i o n . S t e e l under compression
i s u s u a l l y i n the form o f T of H-shaped g i r d e r s r a t h e r than b a r s .
task 12
Check t h i s by l o o k i n g at some of the b r i d g e s i n the photographs i n t h i s book.
exercises
1. E x p l a i n why
Why
2. Why
the a r c h of the Twente c a n a l b r i d g e i s made of c o n c r e t e .
are the c a b l e s made of s t e e l ?
was
an a r c h chosen i n s t e a d of two s l a n t i n g beams?
Trussed
3. The b r i d g e i n the photograph above has
arch bridge
s t r o n g u p r i g h t "edges''. I n
the
c e n t r a l p a r t , the edges p o i n t upwards, i n the r i g h t p a r t downwards, below
the roadway. E x p l a i n ( u s i n g your knowledge of t e n s i l e and
f o r c e s ) why
compressive
i t makes more sense t o c o n s t r u c t b r i d g e s w i t h downward edges.
Why
then were upward edges used i n the c e n t r a l p a r t of t h i s
Why
i s the support
bridge?
i n the c e n t r a l p a r t h i g h e r than i n the r i g h t h a n d
part?
-48-
4. The c a r p e n t e r has made a h i n g e d garden gate u s i n g loose boards (see the
d r a w i n g ) . How can t h i s gate be s t r e n g t h e n e d by f i t t i n g
i n j u s t one more
board? Check the garden gates near s c h o o l o r near where you l i v e !
6. Look a t the s u s p e n s i o n b r i d g e below and work out which p a r t s
of the
b r i d g e a r e under compression and w h i c h a r e under t e n s i o n . C o n s i d e r the
p y l o n s , the suspending s t a y s and the v e r t i c a l c a b l e s between the b r i d g e deck and t h e s t a y s . N o t i c e the m a t e r i a l used f o r each p a r t .
Suspension bridge
over
Che r i v e r
R h i n e , E n m e r i c h , 1965.
5. Work out which elements of t h e b r i d g e i n the photograph below a r e under
compression, and which a r e under t e n s i o n . C o n s i d e r the a r c h , the b a r s
between arch and b r i d g e - d e c k , and the p i e r s .
What m a t e r i a l s a r e these d i f f e r e n t p a r t s of the b r i d g e made o f ? Do you
see any p a r t s t h a t a r e there j u s t f o r d e c o r a t i o n , so t h a t t h e b r i d g e
would be as s t r o n g w i t h o u t them?
-49-
The F o r c h B r i d g e over che P i r c h of F o r c h near
( c o n a c r u c c e d i n 1890).
Queensferry
A l i v i n g model of che Forch B r i d g e
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m
co
—I
O
>
H
O
Z
CO
INVESTIGATÏONS
contents
1
B u i l d i n g , l o a d i n g and r e i n f o r c i n g a b r i d g e
2
B u i l d i n g a crane
3
A crane and moments i n e q u i l i b r i u m
4
E x p l o r i n g s t r e n g t h and shape
5
Exploring rotation
6
S t a b i l i z i n g d i f f e r e n t objects
52
-
-51-
1 building, loading and reinforcing a bridge
1.1
B U I L D I N G A B R I D G E : A B U I L D I N G SCHEME
In t h i s i n v e s t i g a t i o n , y o u r group i s going to b u i l d a b r i d g e . You
may
choose one of the b r i d g e s shown i n the O r i e n t a t i o n s e c t i o n , o r you
p i e k any o t h e r one,
know e x a c t l y how
e.g.
one near your s c h o o l . I t i s i m p o r t a n t
may
t h a t you
the b r i d g e i s put t o g e t h e r and what the f u n c t i o n of
each p a r t i s .
I f more than one group chooses to b u i l d a b r i d g e , you can make a
c o m p e t i t i o n of i t . Which one h o l d s the h e a v i e s t
load?
Before s t a r t i n g the c o m p e t i t i o n , make sure you agree on the f o l l o w i n g
points:
- Length of the span
- Width of the
bridge-deck
- M a t e r i a l s used (e.g. paper, c a r d b o a r d ,
g l u e , s t a p l e s , rope)
- Time a l l o w e d f o r the c o n s t r u c t i o n
- Is the b r i d g e to be movable?
- W i l l b r i d g e s of the same type be compared, o r of d i f f e r e n t
types?
A b r i d g e u n d e r c o n s c r u c c i o n a r o u n d che c u r n o f che
cencury.
E a c h p a r e d e l i v e r e d c o Che s i t e i s r e a d y co be f i c c e d i n c o c h e
s c r u c c u r a . The c o n s c r u c c i o n s c r i c c l y f o l l o w s che b u i l d i n g s c h e m e .
As soon as a l l t h i s has been s e t t l e d , the group can p r o c e e d to draw up a
building
soheme. I f you s t a r t b u i l d i n g r i g h t away, t h i n g s w i l l
certainly
go wrong'. Bef ore the c o n s t r u c t i o n of a r e a l b r i d g e , t h e r e are y e a r s
d e s i g n i n g , c a l c u l a t i n g and
preparing.
-52-
of
A b u i l d i n g scherae may c o n t a i n the f o l l o w i n g p o i n t s :
- a d e t a i l e d d e s i g n o f the b r i d g e . I n d i c a t e f o r each p a r t t h e m a t e r i a l you
are g o i n g
to use.
- a l i s t of the m a t e r i a l s needed (amounts, d i m e n s i o n s , e t c . )
- i n f o r m a t i o n on where you w i l l get t h e m a t e r i a l s and who w i l l
of
take
care
this.
- the o r d e r
i n which the d i f f e r e n t p a r t s a r e t o be c o n s t r u c t e d and
assembled.
- a d i v i s i o n o f t a s k s w i t h i n the group.
- t a s k s t o be done a t s c h o o l and a t home.
1.2
B U I L D I N G YOUR BRIDGE
B u i l d i n g a s u c c e s s f u l b r i d g e means: be c o o p e r a t i v e and l i s t e n t o each
other!
S t i c k t o the b u i l d i n g scheme. I f , d u r i n g the p r o c e s s , the scheme
turns o u t t o be wrong, change i t t o g e t h e r . W r i t e down i n your r e p o r t why
i t had t o be changed.
1.3
L O A D I N G YOUR BRIDGE
When the b r i d g e i s f i n i s h e d , you l o a d i t by suspending from i t a bucket
f i l l e d w i t h w e i g h t s o r sand. Measure the weight you have a p p l i e d by means
of a s p r i n g b a l a n c e .
Your b r i d g e w i l l bend under the l o a d : the t e n s i l e
and compressive s t r e s s e s w i l l
You
t r a n s m i t the w e i g h t of the l o a d t o the p i e r s .
can measure the b e n d i n g u s i n g a bending gauge.
HOW TO MAKE A BENDING GAUGE
With t h i s gauge, you can measure t h e bending of a b r i d g e under l o a d . The
gauge i n t h i s drawing i s a s e n s i t i v e one, so t h a t even a s m a l l amount of
bending shows on the s c a l e . T h i s i s because the a x i s of r o t a t i o n of the
d r i n k i n g straw i s p o s i t i o n e d near the l e f t - h a n d end.
-53-
1. C o n s t r u c t a bending gauge as shown i n the drawing.
2. Test t h e gauge by p u s h i n g down the bead 1 cm and marking
1 cm on the
s c a l e at the o t h e r end of the s t r a w . Do the same f o r a s e r i e s o f o t h e r
v a l u e s , 0,5 cm a p a r t . Mark m i l l i m e t r e d i v i s i o n s on the s c a l e .
3. Use t h i s gauge t o measure the s t r e n g t h o f y o u r b r i d g e - m o d e l . I f the
bending i s s m a l l when the l o a d i s heavy, i t means t h a t the b r i d g e i s
strong.
LOAD
7
P'
n
drinking
straw
bead _^
h
-f
1
Load t h e b r i d g e u n t i l i t i s j u s t on the p o i n t o f c o l l a p s i n g (but don't
make i t c o l l a p s e ) . Watch c a r e f u l l y how and where the p a r t s deform.
Check
whether these d e f o r m a t i o n s a r e due t o t e n s i o n , t o compression o r t o
bending
(a c o m b i n a t i o n of t e n s i o n and c o m p r e s s i o n ) .
pk
The P L O N - b r i d g e L o a d e d . The b e n d i n g gauge
v i s i b l e i n the enlarged photograph.
is clearly
-54
1.U
IMPROVING YOUR
a. strengthening
the
BRIDGE
bridge.
Try t o s t r e n g t h e n t h e b r i d g e . I t i s most i m p o r t a n t t o s t r e n g t h e n i t at
those p l a c e s where there i s most d e f o r m a t i o n . Think o f ways t o s t r e n g t h e n
these p a r t s , b e a r i n g i n raind what you have l e a r n e d i n the Theory s e c t i o n
about t e n s i o n and compression,
shapes, and the p r i n c i p l e o f moments.
A few s u g g e s t i o n s :
add e x t r a s t r e n g t h e n i n g in t h e middle
As you make each m o d i f i c a t i o n check whether your b r i d g e has r e a l l y become
s t r o n g e r . D i d your theory work? I f n o t , what c o u l d be the reason?
b. deareasing
the bridge's
weight
Even w i t h o u t any l o a d , the b r i d g e - d e c k
weight.
bends a l i t t l e because o f i t s own
That i s why you s h o u l d t r y and make your b r i d g e as l i g h t as p o s s i b l e ,
w i t h o u t , however, a f f e c t i n g i t s s t r e n g t h . Use what you know about the theory
to t h i n k of p o s s i b l e m o d i f i c a t i o n s .
A few s u g g e s t i o n s :
- r e p l a c e bars under t e n s i o n by ropes
- r e p l a c e bars under compression
- leave out unnecessary
by n o n - s o l i d (H-shaped) bars
bars and o t h e r p a r t s
-55-
As you make each m o d i f i c a t i o n check t h a t y o u r b r i d g e has r e a l l y
decreased
i n weight (but not i n s t r e n g t h ! ) . D i d your theory work? I f n o t , what c o u l d
be the reason?
1.5
COMPARING
BRIDGES
Is the b r i d g e which h o l d s the h e a v i e s t load a u t o m a t i c a l l y the b e s t
T h i s would be t r u e o n l y i f we a r e
bridge?
comparing b r i d g e s c o n s t r u c t e d from the
same amount of m a t e r i a l . So i t i s f a i r t o i n c l u d e i n your comparison the
weight of the b r i d g e
itself.
M a t e r i a l s used f o r r e a l b r i d g e s are e x p e n s i v e . That i s why b r i d g e
try
designers
t o b u i l d the s t r o n g e s t p o s s i b l e b r i d g e u s i n g the l e a s t amount o f
material.
A s u a p e n a i o n b r i d g e made High School i n Utrecht.
and l o a d e d - by
s c u d e n c s o f the N i e l s
Stenaen
There i s a s i m p l e method of comparing b r i d g e s t a k i n g i n t o account both
s t r e n g t h and weight:
.,
.
bridge-ratio
determining
maximum l o a d which the b r i d g e can c a r r y
——
7—r—, •,
weight o f the b r i d g e
=
The b r i d g e made from cardboard
40,000N
a r a t i o of
- 20.
2
)
0
the b r i d g e - r a t i o .
0
0
=
...N
=
...N
shown on page 39 i n the Theory s e c t i o n has
N
- Which b r i d g e i s " t h e b e s t " ?
- Are t h e r e any o t h e r i m p o r t a n t
The new b r i d g e - e l e m e n t s
f a c t o r s t o be i n c l u d e d i r the comparison?
o f the M o e r d i j k b r i d g e (see Reading Text 3) are about
the same weight as the o l d ones. Y e t , the new b r i d g e can h o l d many more c a r s .
T h i s means t h a t the b r i d g e - r a t i o i n the new b r i d g e i s b e t t e r than i n the o l d
bridge.
-56-
S u r v e y of t h e PLON u n i t s ( w r i t t e n in D u t c h )
FOR T H E 2nd FORM (AGE
-
13/14)
A f i r s t exploration of physics
Men and metais
Working with water
L i v i n g in a i r
I c e , w a t e r , steam
FOR T H E 3 r d FORM (AGE
14/15)
- Bridges
- Seeing movements
- R e p r o d u c i n g sounds
- P h y s i c s in s o c i e t y : Water f o r T a n z a n i a ,
(also available in e n g l i s h )
- E n e r g y in o u r homes
- P h y s i c s in s o c i e t y : E n e r g y in t h e f u t u r e
- Electrical networks
- C o l o u r and l i g h t
FOR T H E 3 r d FORM ( H A V O / V W O ) A N D T H E '
4th FORM ( M A V O , A G E 15/16)
- T r a f f i c and s a f e t y
V '
- P h y s i c s in s o c i e t y : Stop o r keep movjftg
- Heating and insulating
..,«'
- Switching and controlling
- Machines and e n e r g y
- P h y s i c s in s o c i e t y : N u c l e a r wpapons and/or se
- Forces
- Review f o r f i n a l exam MAVO
- Q u e s t i o n book
FOR T H € 4th FORM HAVO (AGE
-^comparing
- Weather c h a n g e s .
- Music
- Traffic
- E l e c t r i c a l machines
- E n e r g y and q u a l i t y
FOR THE 5th FORM H>
- Matter
- L i g h t sources
- lonizing radiation
r Electronic^'
/
For
manu
15/16)