Balsa Bridge- Tension_compression

7/24/2019 Balsa Bridge- Tension_compression

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Statics in BridgesStatics in Bridges



What is a force?What is a force?

A force is a push or pull on an object (compression and tension).A force is a push or pull on an object (compression and tension).



Stationary objects are static.Stationary objects are static.

No net forcesNo net forces No net moments (torques)No net moments (torques)



Are there forces on you now?Are there forces on you now? Gravity is pulling you down.Gravity is pulling you down. The stool is pushing you up.The stool is pushing you up.

orce is compression.orce is compression. !ach leg supports " of the weight!ach leg supports " of the weight

Total forces are #ero (statics).Total forces are #ero (statics).



What forces are on this girl?What forces are on this girl?

Net force is #ero.Net force is #ero. Gravity pulls the girl downGravity pulls the girl down

(weight).(weight). orce in the line isorce in the line is

tension.tension.

$ample calculation%$ample calculation%



Bending is Bad

&'ending% 'eams have very little bending

strength.

&Never design a structure that relies onbending strength to support a load.



Design and construction ideas:

) Triangles are a construction engineers best friend* i.e.

there are no bending moments in triangular elements.

Good design

'ad design (truss strength depends on bendingstrengths of members)



Truss BridgesTruss Bridges

+our bridge will be essentially a truss.+our bridge will be essentially a truss.



In a truss bridge forces are at anIn a truss bridge forces are at anangle.angle.

$ince the bridge isstationary the Net forcemust be #ero.



Beams and loadscom!ression:

'eam in compression

ailure occurs two ways,

) -hen /d 0 1* failure is by crushing2) -hen /d 3 1* failure is by buc4ling

-e are almost always concerned with failure by buc4ling.

d



5ompression% 'uc4ling $trength, 6 (4)d7/2

8f a beam of length and diameter d can supporta

compressive load of *

d

then a beam of length /2 and diameter d cansupport a compressive load of 7.

/2

d7



2d9

and a beam of length and diameter 2d cansupport a compressive load of 9.

d





&8n compression short and fat members are good.

&'igger beams can be fabricated out of smallerbeams* as in a truss.

The fabricated beam will have the same buc4lingstrength as a solid beam* provided the buc4ling/tensionstrengths of the component beams are not e:ceeded.



Tension: "#$%&

'eam under tension

&ailure occurs when tensile strength is e:ceeded.

&;a:imum load is tensile strength times cross%sectional area.&oad capacity does not depend on length.



'se Bridge Designer to calculate loads:

http,//www.jhu.edu/<virtlab/bridge/bridge.htm

Tension members are in =!>

5ompression members are in '?!




&Taller is better, note loads on these two structures.



Which is the better design and why (cont.)?

a) b)

a) b)

C l l t T i &C l l t T i &



Calculate Tension &Calculate Tension &

Compression Values for theCompression Values for the

Balsa BridgeBalsa Bridge Tension:Tension: F=kR F=kR 22

Balsa wood k=19.9 MPaBalsa wood k=19.9 MPa

Compression:Compression: F=F= EEππ33R R 44

4!4!22

Balsa wood E=113" MPaBalsa wood E=113" MPa

E= #o$n%&s mod$l$s 'a meas$re o( )*eE= #o$n%&s mod$l$s 'a meas$re o( )*eri%idi)# o( a ma)erial+ )*e lar%e E is )*e lessri%idi)# o( a ma)erial+ )*e lar%e E is )*e less

)*e ma)erial will de(orm w*en $nder s)ress,)*e ma)erial will de(orm w*en $nder s)ress,



Some !ro!erties of balsa wood(dry)

"or com!arison* cast aluminum (wet or dry):

. ?ltimate tensile strength <1*111psi

2. $tiffness !<1*111*111psi

DensityDensity 150 kg/m150 kg/m33 .0054 lb/in.0054 lb/in22

+om!ressi,e+om!ressi,e

StrengthStrength

12.1 MPa12.1 MPa 1750 lb/in1750 lb/in22

Tensile StrengthTensile Strength 19.9 MPa19.9 MPa 2890 lbs/in2890 lbs/in22

-lastic odulus-lastic odulus+om!ression+om!ression

460 MPa460 MPa 66,700 lb/in66,700 lb/in22

-lastic odulus-lastic odulus

TensionTension

1280 MPa1280 MPa 185,300 lb/in185,300 lb/in22




. >ont forget about the @rd dimension. A good design in the :%yplane* may be a terrible one in the #%direction.

2. lan the total bridge design. !stimate the weight of each ofthe components* so that you will not e:ceed the weight limit (BCgrams).

@. ;a4e a full%si#e pattern of your bridge. 'uild the bridge onthis pattern. This will ensure that all components will assembleproperly (use wa: paper).

7. =ough cut members then sand to the desired length.

C. 5ommon disqualifications,a. angles must be over @1 degrees.b. Gluing cannot go beyond @mm from a joint.c. ;ass of bridge 0BC grams



Types of TrussesTypes of Trusses

-arren/ Neville Truss D Truss

Eowe Trussratt Truss



'se Bridge Builder'se Bridge Builder

-o )o-o )o

*))p:www./*$.ed$0ir)lair)$al*))p:www./*$.ed$0ir)lair)$al

laora)or#laora)or#



StaticsStatics





5antilevered truss%%irth of orth rail bridge



$uspension%%Golden Gate



New =iver gorge%%largest single arched span (BF)

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Balsa Bridge- Tension_compression