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The Waddell A- Truss Bridge

Designing and Building

File-Folder Bridges as anIntroduction to Engineering

COL Stephen Ressler, P.E., Ph.D.Department o Ci!il " #e$hani$alEngineering

%.S. #ilitar& A$adem&, West Point



O'(e$ti!es

Learn a'out stru$turalengineering) Through a hands-on 'ridge-

'uilding pro(e$t. Through the use o ree $omputer

sot*are.

Learn a'out the ongoingWest Point Bridge DesignContest.



A T&pi$al Bridge-Building Pro(e$tStudents re$ei!e a pile o Popsi$le

sti$+s and some glue.

Students 'uild a 'ridge, 'ased on... A pi$ture.

A !ague idea o *hat a 'ridge shouldloo+ li+e.

Bridges are *eighed.

Bridges are tested to ailure.

ighest strength-to-*eight ratio *ins.

What do students actually learn from this experie



What The& Dont Learn

A s&stemati$ design pro$ess pre$edes$onstru$tion.

Engineers design Contra$tors 'uild.

The design pro$ess is inormed '& math ands$ien$e.

Design is iterati!e.

Stru$tures are designed to $arr& $ode-spe$i/ed loads sael& and e$onomi$all&. Designed to stand up, not to ail.

Strength-to-*eight ratio is never the o'(e$ti!e.

The Essential Characteristics Of Engineering



Wh& 0ile 0olders1 2ne3pensi!e.

Eas& to $ut, 'end, and glue.

Surprisingl& predi$ta'le stru$tural

'eha!ior.Can 'e used to 'uild)

Tu'es and 'ars.

Conne$tions that are stronger than theatta$hed stru$tural mem'ers.



What is a Truss1 A stru$ture $omposed o mem'ers $onne$ted

together to orm a rigid rame*or+.

%suall& $omposed o inter$onne$ted triangles.

#em'ers $arr& load in tension or $ompression.



Component Parts

Vertical Bottom Chord

Diagonal

End Post

Hip Vertical

Deck

Top Chord

Vertical Bottom Chord

Diagonal

End Post

Hip Vertical

Deck

Top Chord

Support (Abutment)



Standard Truss

Con/gurationsPratt Parker

Double Intersection Pratt

Howe Camelback

K-Truss

Fink

Warren

Bowstring Baltimore

Warren (with Verticals

Wa!!ell "#$ Truss Penns%l&ania

Double Intersection Warren

'attice

Pratt Parker

Double Intersection Pratt

Howe Camelback

K-Truss

Fink

Warren

Bowstring Baltimore

Warren (with Verticals

Wa!!ell "#$ Truss Penns%l&ania

Double Intersection Warren

'attice



T&pes o Stru$tural

#em'ers

Solid odSolid Bar

Hollo! Tube

"Shape

Solid odSolid Bar

Hollo! Tube

"Shape

These shapes are calledcross-sections#



T&pes o Truss

Conne$tionsPinned

Connection

#usset Plate

Connection

$ost modern !ridges use gusset plate connectio



%et&s !uild this !ridge###

Waddel '( Truss) Bridge o*er %in Branch

Cree+



The Design

() mm * () mm Tube

Double! + mm Bar

Double! , mm Bar

DesignRe4uirements) Span:;< $m

Loading:= +g>at midspan)

We&ll tal+ a!out ho it as designedlater###



Our A-Truss Bridge



#aterials "

E4uipment0ile olders

5ello* $arpenters glue

Building 'oard >St&rooam or $or+?

PinsS$issors

#etal ruler@

o''& +nie or single-edge ra8or'lade@

Ru''er $ement@

.e/uire! onl% 0or 1re0abrication o0 structural members



Prea'ri$ation o

#em'ers Cut out 'ars

Cut out and assem'letu'es

Cut out gusset plates

Trim 'ars and tu'es tolength

2luing Fla1

.ubber Cement

2luing Fla1

.ubber Cement



Trim Bars and Tu'es

to LengthBottom Chords. per team/



Trim Bars and Tu'es

to Length0erticals. per team/



Trim Bars and Tu'es

to LengthEnd 1osts. per team/



Set up the Building

Board Pla$e the la&out dra*ing on &our 'uilding 'oard.Each Team $em!er2



Set up the Building

Board Pla$e a sheet o plasti$ *rap o!er the la&out

dra*ing.



Add 9usset Plates Pla$e 9usset Plate A at its $orre$t lo$ation on the

la&out dra*ings.

old it in pla$e *ith t*o pins.



Add 9usset Plates Repeat the pro$ess or 9usset Plates B, C, and D.



Add Bars Appl& a line o glue along the 'ottom edge o 9usset

Plates A, B, and C.

Pla$e a mm 'ar in position as the 'ottom $hordAC.

Stret$h tight and hold in pla$e *ith t*o pins.



Add Bars Appl& glue to 9usset Plates B and D.

Pla$e a mm 'ar in position as the !erti$al mem'erBD.

Stret$h tight and hold in pla$e *ith &our /ngers.ach team should no ha*e two of these su!assem!lies 3

the lower half and the upper half of one truss#



Add Tu'es

Appl& glue to 9usset Plates A and D.

Pla$e a <mm 3 <mm tu'e in position as end postAD.

old in pla$e or a minute until the glue sets.

For the bottom half of the truss one per team/2



Add Tu'es Appl& glue to 9usset Plates C and D.

Pla$e a < mm 3 < mm tu'e in position as end postAD.




Add Tu'es Cut a $m length o < mm 3 < mm tu'e.

Appl& glue to 9usset Plate B.

Pla$e the tu'e !erti$all& on the gusset plate.




The 0inished al-

Truss Allo* all glue (oints to dr&.

d



0or$es, Loads, "Rea$tions0or$e : A push or pull.

Load : A or$e applied to a stru$ture.

Rea$tion : A or$e de!eloped at thesupport o a stru$ture to +eep that

stru$ture in e4uili'rium.

4elf-eight of structure, eight of*ehicles, pedestrians, sno, ind, etc#

Forces are represented mathematicallyas

0ECTO54#



E4uili'rium

#n ob3ect at rest will remain at rest4

1ro&i!e! it is not acte! u1on b% an

unbalance! 0orce5

A $oad%%% %%%and eactions

&e!ton's irst $a!

i d



Tension and

Compression #n unloa!e! member e*1eriences no !e0ormation

Tension causes a member to get longer

Com1ression causes a member to shorten

i d



Tension and

Compression

E6TE57(% FO5CE4 and I7TE57(% FO5CE4$ust !e in e8uili!rium ith each other#

'l h



Assem'le the T*o

al!es Pull out all o the pins on 'oth hal!es o the truss.

Carefully separate the upper hal o the truss rom theplasti$ *rap.

7eep the lo*er hal o the truss on the 'uilding 'oard.

A 'l h T



Assem'le the T*o

al!es

Put glue on the tu'es at A, B, C, and D. Pla$e the upper hal onto the lo*er hal.

Stret$h the 'ars tight and hold until the glue hasset.

A 'l h T



Assem'le the T*o

al!es Allo* all glue (oints on the $ompleted truss to dr&.

St t l A l i



Stru$tural Anal&sis0or a gi!en load, /nd the internal or$es

>tension and $ompression? in allmem'ers.

Wh&1

Pro$edure) #odel the stru$ture)

De/ne supports

De/ne loads

Dra* a ree 'od& diagram.

Cal$ulate rea$tions.

Cal$ulate internal or$es using

#ethod o oints.F

# d l th St t



#odel the Stru$ture

(6 cm

(6 cm (6 cm

# CB

D

massG= +g

G.= +g per truss

D 0 B d



Dra* a 0ree Bod&Diagram

(6 cm

(6 cm (6 cm

# CB

D

massG.= +g

5( 5C

3

&

( ) ( ) N5.24secm81.9kg5.2 2

=== ma F

.9#:7

C l l t R ti



Cal$ulate Rea$tions Total do*n*ard or$e is

.= 6. Total up*ard or$e must

be .= 6.

Loads, stru$ture, andrea$tions are alls&mmetri$al.

5( and 5C must !ee8ual#

S*+P

SCALE SCALE

Centerline

Centerline

S*+P

SCALE SCALE

Centerline

Centerline

S*+P

SCALE SCALE

Centerline

Centerline

S*+PS*+P

SCALE SCALE

Centerline

Centerline

C l l t R ti



Cal$ulate Rea$tions

N3.122

5.24

=== C A R R

#

5(

3

&

(6 cm

(6 cm (6 cm

CB

D

5C

.9#: 7

;.#<7

;.#<7

# th d i t



;.#<7

#ethod o oints 2solate a oint.

#

3

&

(6 cm

(6 cm (6 cm

CB

D

5C

.9#: 7

;.#<7

# th d i t



#ethod o oints 2solate a oint.

Dra* a ree 'od& diagram o the (oint. 2n$lude an& e3ternal loads o

rea$tions applied at the (oint.

2n$lude un+no*n internal or$esat e!er& point *here a mem'er *as $ut.

Assume un+no*n or$es in tension.

Sol!e the E4uations o E4uili'rium or the oint.

;.#<7

#

3

&

F(D

F(B

E6TE57(% FO5CE4 and I7TE57(% FO5CE4$ust !e in e8uili!rium ith each other#

E4uations o



E4uations oE4uili'rium The sum o all or$es a$ting in

the 3-dire$tion must e4ual 8ero.

The sum o all or$es a$ting inthe &-dire$tion must e4ual 8ero.

0or or$es that a$t in a diagonal dire$tion,*e must $onsider 'oth the 3-$omponentand the &-$omponent o the or$e.

;.#<7

#

3

&

F(D

F(B0=∑ x F

0=∑ y F

C t 0



Components o 0or$e

F(D

#3

&

θ

2 magnitude o F(D is represented as theh&potenuse o a right triangle...

Then the magnitudes o F(D/x and F(D/y are

represented '& the lengths o the sides.

#

F(D/y

F(D/x

θ

Trigonometr Re ie



Trigonometr& Re!ie*

H

y

== hypotenuse

opposite

sinθ

H

x== hypotenuse

adjacentcosθ

Thereore)

θ sin H y =

θ cos H x =

3

&

θ

De/nitions)

=

Components o 0or$e



Components o 0or$e

F(D F(D/y

#3

&

#F(D/x

θ= ? θ= ?

Thereore)

θ sin H y =

θ cos H x =

9:o

9:o

( ) AD AD x AD F F F 707.045cos =°=

( ) AD AD y AD F F F 707.045sin =°=

E4uations o



E4uations oE4uili'rium

;.#<7

#

3

&

F(D

F(B

0=

∑ x

F

0=∑ y F

>#> F(D

>#>F(D

0707.0 =++ AD AB F F

0707.03.12 =++ AD F

3.12707.0 −= AD F

N3.17

707.0

3.12−=

−= AD F

AD AB F F 707.0−=

N3.12)3.17(707.0 +=−−= AB F

F(D@;#< 7 >$ompression?

F(B@;.#< 7 >tension?

?

#ethod o



#ethod o oints...Again 2solate another

oint.

3

&

;.#<7

#

(6 cm

(6 cm (6 cm

C

D

5C;.#<7

B

.9#: 7

E4uations o



E4uations oE4uili'rium

3

&

B

.9#: 7

FBD

FBCF(B

0=

∑ x

F

0=∑ y F

05.24 =+− BD F

N5.24+= BD F

[email protected]#: 7 >tension?

0=+− BC AB F F

N3.12+== AB BC F F

FBC@;.#< 7 >tension?

Results o Stru$tural



Results o Stru$turalAnal&sis

;.#< 7

# C

D

;.#< 7

B

.9#: 7

;.#< 7 T/ ;.#< 7 T/

. 9 #

:

7 -

T /

; ? # <

7

- C / ; ? # < 7

- C /

Do these results ma+e

sense?

0inish the Truss



0inish the Truss

Trim oH the e3$ess length on 'oth'ottom $hords >AC? .

Results o Stru$tural



Results o Stru$turalAnal&sis

In our model, hat +ind of mem!ers areused for tension? for compression?

;.#< 7

# C

D

;.#< 7

B

.9#: 7

;.#< 7 T/ ;.#< 7 T/

. 9 #

:

7 -

T /

; ? # <

7

- C / ; ? # < 7

- C /

#aterials Testing



#aterials TestingStrength : The largest internal force

a stru$tural mem'er $an e3perien$e'eore it fails.

0ailure : The $ondition that o$$urs

*hen the internal force e3$eeds thestrength o a mem'er

TE74I%E 4T5E7AT= CO$15E44I0E4T5E7AT=

A &drauli$ Testing



A &drauli$ Testing#a$hine

Our Lo* Budget



Our Lo*-Budget Testing #a$hine

Pi&ot

'oa!ing #rm

7otch

Tem1orar%

8u11ort

BasePost

C-'ine

T-'ine

Felt

Pa!s

Testing Tensile



Testing TensileStrength The test setup.

Testing Tensile



Testing TensileStrengthClamp the test spe$imen to the le!er arm.

Testing Tensile



Testing TensileStrengthSlo*l& add sand to the 'u$+et.

Testing Tensile



Testing TensileStrengthWhen the spe$imen 'rea+s, *eigh the 'u$+et

and $ompute the tensile strength.

The Prin$iple o the



The Prin$iple o theLe!er

L 1

L 2

F 2

F 1

2211 L F L F =

=1

2

21

L

L F F

Results o Tension



Results o Tension Testing Tensile strength depends on)

T&pe o material

Thi$+ness o $ross-se$tion

Width o $ross-se$tion

Tensile strength does not dependson) Length o mem'er

Shape o $ross-se$tionSolid od

Solid Bar

Hollo! Tube

"Shape

Solid od

Solid Bar

Hollo! Tube

"Shape

Pro$ess the



Pro$ess theE3perimental ResultsTest ,ember ,ass o- .eight o- Tensile

&umber .idth Bucket / Sand Bucket / Sand Strength

(mm) (g) (&) (&)

T( + 9+, 0%1 12%3

T( + 99: 0%4 13%1

T( + 9,; 0%5 12%6

T, : (+9< 57%3 78%4

T, : (+,+ 57%8 64%4T, : (=9; 56%3 64%5

T= ; (;;) 54%7 25%6

T= ; (9)9 54%3 21%5

T= ; (;=, 54%8 28%8

Con!ert rom grams to ne*tons

Appl& the Prin$iple o the Le!er to $al$ulate strength

9raph the Results



9raph the Results

)5)

()5)

,)5)

=)5)

+)5)

6)5)

:)5)

) ( , = + 6 : < ; 9

,ember .idth (mm)

T e n s i l e S t r e n g t h ( n e ! t o n s )

Tren! 'ine



Testing Compressi!e



Testing Compressi!eStrengthA $ompression spe$imen at ailure.

Results o



Results oCompression TestingCompressi!e strength depends on)

T&pe o material

Length o mem'er

Width and thi$+ness o $ross-se$tion

Shape o $ross-se$tion

Bar Tu'e

9raph the Results



)

,)

+)

:)

;)

())

(,)

(+)

(:)

(;)

) 6 () (6 ,) ,6

$ength (cm)

C o m

p r e s s i 9 e S t r e n g t h ( n e ! t o n s )

() mm * () mm tubes

9raph the Results

'Best t) cur*e

': condence) cur*e

Stru$tural E!aluation



Stru$tural E!aluation 2s the internal mem'er or$e less

than the strength or ea$h mem'er1

Cal$ulate the 0a$tor o Saet&)

Foce"ntena#

$tength$a%etyo% Facto =

Tensile Strength o



Tensile Strength o#em'er AC

)5)

()5)

,)5)

=)5)

+)5)

6)5)

:)5)

) ( , = + 6 : < ; 9

,ember .idth (mm)

T e n s i l e S t r e n g t

h ( n e ! t o n s )

Tren! 'ine

Dou'led mm 'ar

. 7

0a$tor o Saet& or



0a$tor o Saet& or#em'er AC

Foce"ntena#$tength(F$)$a%etyo% Facto =

1.212.3N2&NF$ == > 1 4(FEG

4tructures are normally designedfor a

F4 of at least ;##

Strength o #em'er



)

,)

+)

:)

;)

())

(,)

(+)

(:)

(;)

) 6 () (6 ,) ,6

$ength (cm)

C o m

p r e s s i 9 e S t r e n g t h ( n e ! t o n s )

() mm * () mm tubes

Strength o #em'erAD

': condence) cur*e

.;#.

( ) ( ) cm2.21cm15cm15 22

=+= AB L

H> 7

0a$tor o Saet& or AD



0a$tor o Saet& or AD

Foce"ntena#$tength(F$)$a%etyo% Facto =

&.417.3N80NF$ == > 1 0E5 4(FEG

(re the end posts excessi*elystrong?

Pla$e the Stru$ture



Pla$e the Stru$tureinto Ser!i$e

The $ompleted 'ridge

Load test *ith = +g o sandsuspended rom midspan

Stru$tural Design



Stru$tural DesignDesign Re4uirements)

Span, loading, a$tor o saet&De$ide on truss $on/guration.

Perorm a stru$tural anal&sis. Rea$tions

2nternal mem'er or$es

Sele$t mem'er si8es 'ased on re4uiredstrength.

Dra* plans. Build the 'ridge.

Test : Can the bridge carrythe required loading safely?

1leasedon&t!rea+

the !ridgeG

The West Point Bridge



The West Point BridgeDesigner Loo+ and eel o a standard CAD pa$+age.

Eas& to $reate a su$$essul design. ard to $reate a highl& $ompetiti!e design.

ighl& su$$essul)

O!er =<,<<< $opies do*nloaded sin$e <<<. T*o ma(or national sot*are a*ards.

0ormall& endorsed as an edu$ational tool '& theAmeri$an So$iet& o Ci!il Engineers.

Runs on Windo*s I= >or later? PC.

The West Point Bridge



The West Point BridgeDesign Contest Started on anuar& J, <<.

Students age ; through grade are eligi'le or

pri8es.

To enter)

%se the West Point Bridge Designer 2004 to design a 'ridge.

%pload the design to our *e'site or automated (udging.

Re$ei!e instant eed'a$+ a'out $ontest standing.

K=,<<< s$holarships or the *inners.

Parti$ipation is free

Summar&



Summar& 0ile-older 'ridges)

A$$urate representation o real 'ridges Mehi$le or learning engineering $on$epts.

Design 'ased on authenti$ appli$ations omath, s$ien$e, and $omputer te$hnolog&.

The West Point Bridge Designer) E3perien$e the engineering design pro$ess.

0ree

The West Point Bridge Design Contest) Please help us ma+e it su$$essul

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