building a popsicle (rbl)

8/3/2019 Building a Popsicle (RBL)

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Building a Popsicle-Stick Bridge

The goal: to build the strongest possible bridge to take a matchbox car, usingwooden popsicle sticks.

Constraints: The bridge must span a 55cm gap

No more than 100 popsicle sticks may be used

The sticks may not be cut

Only white glue may be used

Construction paper may be used for the deck only

The test load is applied to a 4cm-wide section at the top of the arch.

The test jig looks like this:

(Well-built bridges can support over 200kg - the weight of two adults)Structural Analysis

A bit of thought, or modelling with a computer-aided design program, shows thatthe bridge can be reduced to a simple triangle. The force required to break a well-constructed bridge is orders of magnitude greater than any other forces acting on it,such as its own weight, the weight of the toy car, "wind load" etc.


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This is not the case for a real bridge, of course, which must be designed for avariety of vehicle loads, wind loading, snow or ice buildup, earthquakes and so on.Also, because of the power law (mass increases as the cube of the size, whilestrength increases as the square of the size), small structures are much muchstronger than their full-size counterparts.

A bit of simple physics (or CAD software) will put numbers to the forces. Simpleanalysis treats the sides as rigid bars, and the corners as free pivot points. Onelower corner is fixed to the support, while the other is allowed to slide. The base of

the triangle is in tension, while the sides are in compression. The higher thetriangle, the less tension in the base. The limiting case for an infinitely hightriangle is zero tension in the base, and half the test weight in compression in eachside.If the triangle is made lower, the forces increase. In the limit of a zero-heighttriangle, they become infinite.


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Forces in Simple Triangle: 200kg weight on apex

Stresses in trianglular element, from "Felt" software. Red is under tension, blue isin compression.

So the optimal shape to minimize the forces on the bridge is an infinitely hightriangle. Two problems - we have only 100 sticks, and the test jig is less than 40cmhigh.


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The bridge is contructed of two compression elements and one tension element. Abit of experiment reveals that failure of a tension element is typically due toshearing of an overlap joint, while failure of a compression element is typicallydue to buckling.

Design of a tension element for the base is relatively simple - a series of sticksoverlapped a suitable amount performs well. Design of a compressive element ismore difficult. The element must resist buckling, and must be designed so that thestress is distributed evenly across the individual sticks. This may be acheived in

part by careful assembly - the element should be perfectly straight, and all thesticks should align exactly at the ends so that they all touch the supports.

In real life, elements are often created with a complex cross-section in order toresist buckling. Three of the most common shapes are the I-beam, box section, andtube. Most real-world structures are made of these shapes.

For the stick bridge, the requirement to not cut sticks makes it difficult to createthese common sections, though it is possible (though not the tube, of course).

Instead, stiff elements may be made by laminating together pairs of sticks. Thisalso guards against weakness in individual sticks - depending on the supplier, somesticks may have grain diagonally across the stick. Since wood will split along thegrain, this makes them much weaker. In this case, pairs of sticks should belaminated so that the grains cross each other.


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When these designs are tested, providing the joints are well made and sufficientlyoverlapped, the element will typically fail by buckling. Once the element starts to

buckle, failure is progressively more rapid. As the sticks depart from perfectalignment, the inside of the curve becomes more stressed than the outside, takingthe inside sticks beyond their breaking strength. The joint may becomedelaminated, a stick may split along the grain, or a stick break across the grain.

To prevent buckling, it is necessary to make the element stiffer. This can be doneby making it thicker, but the finite number of sticks puts a limit on this. Anothertechnique that may be used is the stayed mast, borrowed from sailboat design.

In a sailboat, there are one or more masts (shown below on its side) which areunder compression and subject to sideways force from the sail (this force can bemany tons in strong winds). To stiffen the mast, steel cables are used together with"spreaders" to convert bending in the mast into tension in the cables which is moreeasily resisted.

This concept may be used in the stick bridge, to resist bending of the compressivemembers by staying them against the bottom tension member. This idea is shownin the third design.

Construction

Typically, bridge elements are built first, then glued together to make two or moretrusses, The trusses are then joined with cross members, and finally the paper deckis glued on. Since at each step the glue must dry, it is important to allow enoughtime for all the steps. At least 3 days is required, and typically much more.

When glueing elements, better results will be obtained if the sticks are clampedwhile the glue dries. Since you want to glue many elements at the same time, you
http://andrew.triumf.ca/andrew/popsicle-bridge/triangle3.pnghttp://andrew.triumf.ca/andrew/popsicle-bridge/triangle3.png


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need a lot of clamps. Fortunately, good spring clamps can be obtained at a "dollarstore". For single joins, clothes pegs may be used.

For laminating, pieces of thick metal or wood and steel G-clamps allow many pairsof sticks to be laminated at once. Pairs of sticks may be arranged in two layers

between the metal plates to give e.g. 24 pairs in 2 layers. It is important to makesure the sticks are exactly aligned and do not slip when pressure is applied.

It is important that the final elements should be exactly straight, or they willbuckle. This means they must be glued together against a straight edge such as along piece of wood. Elements must be measured carefully and overlaps glued to

bring them to the designed length.

For final assembly, a setsquare should be used to make sure that the bridge isexactly vertical and that the top load-bearing elements are exactly flat andhorizontal. Any deviation - one stick protruding slightly, for instance - willconcentrate stress under load and be a point of failure. Since sticks cannot be cut,any small errors in alignment may be corrected by adding glue. The load-bearing

points at the bottom corners and apex can be set up on flat metal plates (which theglue won't stick to) and glue added to build up the round end of the sticks to give aflat bearing surface.

The bridge should be constructed to spread the load equally to all elements. Justthinking about it helps - imagine what happens when the weight is applied, andeach stick starts pushing on the next to transfer the load to the base. Are there anysticks that aren't doing anything ? Any sticks that are doing more than their fairshare of work ?

Testing

Testing your design is a good idea - it helps eliminate poor designs early beforeyou have spent too much time on them. Also, it's fun. The Richmond APEG test jiguses a car jack, cable and springs to pull evenly on the load plate, with anelectronic load cell to measure the force. My test jig uses a set of bathroom scalesand two threaded rods. Pieces of 2x4 are used for the cross-pieces. The uppercrosspiece had to be reinforced with a metal plate as sticks would be driven intothe soft wood when testing joints in pairs of sticks. Force is applied by turning thenuts on the screwed rods with a pair of wrenches.

Caution - wear safety glasses and keep fingers clear. Though the stored energy inthe jig is much less than in the springs of the APEG tester, forces will still exceed100kg and elements may break suddenly.

Photos

Laminating pairs of sticks - G-clamps and metal plates

Laminating pairs of sticks

clamping while glue dries - spring clamps with swivel pads for evenpressure

test jig - also used for final assembly
http://andrew.triumf.ca/andrew/popsicle-bridge/7.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/71.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/72.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/73.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/7.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/71.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/72.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/73.jpg


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"testing" the bridge

first design

second design

third design (concept)

third design (photo) 676lbs, 1st place 2008 APEG open category, PrinceGeorge BC

Testing the first design (Video)

Richmond/Delta APEG.BC

Model Bridge Designby Garrett Boon

FElt (open source system for finite element analysis; Linux)

Andrew Daviel [email protected]

March 2004 edited 2011
http://andrew.triumf.ca/andrew/popsicle-bridge/75.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/76.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/77.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/triangle3.pnghttp://andrew.triumf.ca/andrew/popsicle-bridge/000_2448c.JPGhttp://video.triumf.ca/cgi-bin/ramgen/real8/bridge5.rmhttp://www.apeg.bc.ca/services/branches/rd.htmlhttp://www.garrettsbridges.com/popsicle-stick-bridges.htmlhttp://sourceforge.net/projects/felt/http://andrew.triumf.ca/andrew/popsicle-bridge/75.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/76.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/77.jpghttp://andrew.triumf.ca/andrew/popsicle-bridge/triangle3.pnghttp://andrew.triumf.ca/andrew/popsicle-bridge/000_2448c.JPGhttp://video.triumf.ca/cgi-bin/ramgen/real8/bridge5.rmhttp://www.apeg.bc.ca/services/branches/rd.htmlhttp://www.garrettsbridges.com/popsicle-stick-bridges.htmlhttp://sourceforge.net/projects/felt/


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i

The popsicle stick bridge is a classic science demonstration and competition. Every year many

students world-wide build bridges made soley from popsicle sticks and glue, to see which

designs can hold the most weight.

We built one, using maybe 140 sticks, give or take a few. Not expecting it to hold much weight,

we were surprised by how strong it ended up being! (results in last step)

Step 1Design your bridge
http://www.instructables.com/file/FEJRSKPFT7PUCE9/http://www.instructables.com/file/FEJRSKPFT7PUCE9/


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i

There are many ways to build bridges, both real bridges and popsicle stick bridges. Do some

research, be creative, and remember - triangles are strong.

A triangle spreads out weight and is much more stable than a simple rectangle or square

support. Be sure to incorporate lots of triangles into your bridge design. More popsicle sticks

doesn't necessarily mean a stronger bridge.

In fact, according to the internet, "If there is a single most important shape in engineering, it is the

triangle. Unlike a rectangle, a triangle cannot be deformed without changing the length of one of

its sides or breaking one of its joints. In fact, one of the simplest ways to strengthen a rectangle is

to add supports that form triangles at the rectangle's corners or across its diagonal length. A

single support between two diagonal corners greatly strengthens a rectangle by turning it into two

triangles."[link]

My design consists of two main bottom supports, and two across the top, and then a lot of

triangles across the sides, the top and bottom, and going from the bottom of one side to the topof the other. Very similar to the one in the diagram.

Draw your design on paper, and estimate the number of sticks you will need.

Be creative with your design!
http://www.instructables.com/file/FI644AFFTRJ72S4/http://www.teachersdomain.org/resource/phy03.sci.phys.mfe.triarch/http://www.instructables.com/file/FI644AFFTRJ72S4/http://www.teachersdomain.org/resource/phy03.sci.phys.mfe.triarch/


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immediately, but your bridge will not hold as much weight if you test it before the

glue has cured. Be sure to take pictures of your popsicle bridge and send them to

me! I would absolutely love to see photos of the bridges you have made. In fact, I

have a photo contest going on for the month of January, so be sure to check that

out.

How to Make a Sturdy Popsicle Stick BridgeBy Julia Salgado, eHow Contributor

updated August 05, 2011

Print this article

For young engineers, building a Popsicle stick bridge is an ideal way to test the theories of physicsand engineering in a safe and methodical environment. Building these lightweight models will allowyou to work through different ideas and different theories as to what structures are most efficient atbearing weight. The shape of the triangle resists compressive force to such an extent that a relativelysmall and lightweight triangle will be able to bear far more weight than other shapes of equal size.Consequently a successful Popsicle stick bridge will incorporate triangles into the design, utilizing thetensile strength of the basic shape.

Related Searches:

Bridge Fell Out

Building Arch

Difficulty:

Moderate

Instructions

Things You'll Need

Wood glue

40 Popsicle sticks

1.

1
http://www.ehow.com/print/how_10035784_make-sturdy-popsicle-stick-bridge.htmlhttp://www.ehow.com/search.html?rs=1&s=Bridge+Fell%20Out&skin=corporate&t=allhttp://www.ehow.com/search.html?rs=1&s=Bridge+Fell%20Out&skin=corporate&t=allhttp://www.ehow.com/search.html?rs=1&s=Building+Arch&skin=corporate&t=allhttp://www.ehow.com/print/how_10035784_make-sturdy-popsicle-stick-bridge.htmlhttp://www.ehow.com/search.html?rs=1&s=Bridge+Fell%20Out&skin=corporate&t=allhttp://www.ehow.com/search.html?rs=1&s=Building+Arch&skin=corporate&t=all


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Lay a Popsicle stick flat on the work surface. Spread wood glue on half of one side ofanother stick and lay that stick glue side down on the first stick, so that half of the newstick overhangs the end. Spread more wood glue on half of one side of a third stickand slide that under the overhanging end of the second stick. The ends of your thirdand first stick should just be touching. Continue laying and gluing sticks in this wayuntil you have a chain of six sticks in a row.

2

Repeat this process to make another chain of six sticks, then make two more chainsof four sticks each. Lay a chain of six next to a chain of four to create the two parallelsides of a trapezium. Connect the two chains by placing a diagonal Popsicle stick ateach end and gluing it into place. Create a triangle by placing another diagonalPopsicle stick beside where the first stick joins the four-stick chain and gluing it intoplace so that it connects to the six-stick chain. Do the same at the other end of thechain.

3

Where the second diagonal joins the six-stick chain, place another diagonal Popsiclestick to rejoin the four-stick chain at roughly the middle of the bridge. Complete thistriangle with a final diagonal Popsicle stick. Repeat this whole process on the otherpair of chains to create two sides of the bridge.

4

Stand the two sides of the bridge up and ask assistants to support them in a verticalposition. Glue a Popsicle into place connecting the two six-stick chains, keeping themapart by just under the length of a Popsicle stick. Add another Popsicle stick at theother end to keep the two sides parallel. Support the two sides with vertical aides. Apiles of books will suffice.

5

Glue more horizontal Popsicle sticks across the top of the structure, beginning at bothends and adding one in the middle. Two triangles should then be made withhorizontal Popsicle sticks joining the two four-stick chains; then a single diagonal

Popsicle stick should be glued into place connecting two of the corners at each end ofthe structure.

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Short Pratt Truss Bridge UpdatedByGarrett Boon posted/modified on November 6, 2011
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This is the updated design of my Short Pratt Truss Bridge made from popsicle

sticks. The only difference from the original was the addition of 4 more popsicle

sticks in key areas. I doubled up the angled sticks on each end, and made the

lateral bracing into an X shape rather than a zig-zag pattern.

This bridge used 50 popsicle sticks, weighed 75 grams, and held 200 pounds. Its

efficiency score was 1212, which is the highest out of any popsicle stick bridge I

have ever built.

Pratt Truss Popsicle Stick Bridge

Side Close Up

Angle View
http://www.garrettsbridges.com/photos/popsicle-bridges/short-pratt-truss-bridge-updated/attachment/img_5819/http://www.garrettsbridges.com/photos/popsicle-bridges/short-pratt-truss-bridge-updated/attachment/img_5778/http://www.garrettsbridges.com/photos/popsicle-bridges/short-pratt-truss-bridge-updated/attachment/img_5776-2/


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Angle View

Portal View for the Popsicle Bridge

Design Analysis

The Pratt Truss was designed by Thomas and Caleb Pratt in 1844. It became

popular for railway bridges because it made good use of iron. The Pratt has many

variations, most with their own unique name. For instance, the Baltimore,

Pennsylvania, and the Parker are all based off the Pratt.
http://www.garrettsbridges.com/photos/popsicle-bridges/short-pratt-truss-bridge-updated/attachment/shorttrussbd/http://www.garrettsbridges.com/photos/popsicle-bridges/short-pratt-truss-bridge-updated/attachment/img_5821-2/http://www.garrettsbridges.com/photos/popsicle-bridges/short-pratt-truss-bridge-updated/attachment/img_5820-2/


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Pratt Truss

How the forces are spread out

Here are two diagrams showing how the forces are spread out when the Pratt Truss

is under a load. The first shows the load being applied across the entire top of the

bridge. The second shows a localized load in the center of the bridge. In bothcases the total load = 100. Therefore, you can take the numbers as a percentage of

the total load.

Pratt Truss With Centered Load

Pratt Truss with Spread Load

These diagrams bring up several interesting things. Notice that the two end

diagonal members do not change. Also, there is little change on the bottom chordbetween the two pictures. However, there is drastic changes on the internal truss
http://www.garrettsbridges.com/design/pratt-truss/attachment/prattspreadload/http://www.garrettsbridges.com/design/pratt-truss/attachment/prattcenterload/http://www.garrettsbridges.com/wp-content/uploads/2010/12/pratttruss.gif


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members. The centered load dramatically increases the amount of force that is

applied to the internal members of the bridge. Also, the forces are increased on

the top chord of the centered loaded bridge.

This seemingly insignificant change in how the bridge is loaded makes a big

difference in how your model bridge will perform. If you have the ability to change

and set how your bridge is loaded, Id shoot for spreading the load across the

entire span. This pretty much goes for any model bridge design, not just the Pratt

Truss.

Pratt Truss for model bridges

The Pratt Truss is one of my favorites. I have used it often for my model bridges,

including balsa, basswood, and popsicle sticks. It is easy to construct, and is a solid

choice for a model bridge design.

Additional Resources

Pictures of real Pratt Bridges

History of Truss Design

Menghitung Momen Gaya dalam Statika Bangunan

01:37 GONDELLS 6 comments

HMM nyari2 ARTIKEL BUAT NGISI Tentang Mekanika Rekayasa1

Mata Kuliah yang paling aku sukai yang Membicarakan tentang gaya2.. yang

berpengaruh pada suatu bidang..

Berhasil menemukan Modul Pembelajarannya tapi yang ku temuin dibuat

oleh temen2 dari TIM FAKULTAS TEKNIK

UNIVERSITAS NEGERI YOGYAKARTA

Judul modul ini adalah Menghitung Momen Gaya dalam Statika Bangunan

merupakan bahan ajar yang digunakan sebagai panduan praktikum peserta diklat Sekolah

Menengah Kejuruan (SMK) untuk membentuk salah satu bagian dari kompetensi

Menghitung Statika Bangunan
http://bridgehunter.com/category/tag/pratt-truss/http://mysite.du.edu/~jcalvert/tech/machines/bridges.htmhttp://belajar-teknik-sipil.blogspot.com/2010/03/menghitung-momen-gaya-dalam-statika.htmlhttp://bridgehunter.com/category/tag/pratt-truss/http://mysite.du.edu/~jcalvert/tech/machines/bridges.htmhttp://belajar-teknik-sipil.blogspot.com/2010/03/menghitung-momen-gaya-dalam-statika.html


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Sebagian isinya..:

Pembebanan (loading) pada Konstruksi Bangunan telah diatur pada Peraturan Pembebanan

Indonesia untuk gedung (PPIUG) tahun 1983. Oleh karena itu supaya lebih mendalam

diharapkan peserta diklat membaca peraturan tersebut, karena dalam uraian berikut hanya

diambil sebagian saja.

Ada 5 macam pembebanan yaitu :

a. Beban mati (berat sendiri konstruksi dan bagian lain yang melekat)

b. Beban hidup (beban dari pemakaian gedung seperti rumah tinggal,

kantor, tempat pertunjukkkan)

c. Beban angin (beban yang disebabkan oleh tekanan angin)

d. Beban gempa (beban karena adanya gempa)

e. Beban khusus (beban akibat selisih suhu, penurunan, susut dan

sebagainya)

Berdasarkan wujudnya beban tersebut dapat diidealisasikan sebagai (1) beban terpusat, (2)

beban terbagi merata, (3) beban tak merata (beban bentuk segitiga, trapesium dsb). Beban-

beban ini membebani konstruksi (balok, kolom, rangka, batang dsb) yang juga

diidealisasikan sebagai garis sejajar dengan sumbunya. Beban terpusat adalah beban yang

titik singgungnya sangat kecil yang dalam batas tertentu luas bidang singgung tersebut

dapat diabaikan. Sebagai contoh beban akibat tekanan roda mobil atau motor, pasangan

tembok setengah batu di atas balok, beton ataupun

baja dsb. Satuan beban ini dinyatakan dalam Newton atau turunannya kilonewton (kN). Lihat

gambar 1.


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Beban merata adalah beban yang bekerja menyentuh bidang konstruksi yang cukup luas

yang tidak dapat diabaikan. Beban ini dinyatakan dalam satuan Newton/meter persegiataupun newton per meter ata u yang sejenisnya lihat gambar 2.

Beban tidak merata dapat berupa beban berbentuk segitiga baik satu sisi maupun dua sisi,

berbentuk trapesium dsb. Satuan beban ini dalam newton per meter pada bagian ban yang

paling besar lihat

gambar 3.
http://1.bp.blogspot.com/_t7rNlHc4Y64/S41dSuXjIPI/AAAAAAAAAN8/D9ZjaSQ2C_0/s1600-h/Graphic2.jpghttp://2.bp.blogspot.com/_t7rNlHc4Y64/S41dK4h_avI/AAAAAAAAAN0/KlzDNjspbM0/s1600-h/Graphic1.jpg


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Berikut ini dicuplikkan beberapa beban bahan bangunan menerut PPIUG 1983 halaman 11.

1. Baja beratnya 7850 kg/m3,

2. Batu gunung beratnya 1500 kg/m3

3. batu pecah beratnya 1450 kg/m3,

4. beton beratnya 2200 kg/m3,

5. beton bertulang beratnya 2400 kg/m3,

6. kayu kelas 1 beratnya 1000 kg/m3 dan

7. pasangan bata merah 1700 kg/m3.

Contoh perhitungan beban :

Hitunglah beban yang bekerja pada balok beton bertulang ukuran 30 cm x 60 cm yang

ditengah-tengahnya terdapat tembok pasangan setengah batu lebar 15 cm yang dipasang

melintang dengan ukuran tinggi 3 m, panjang 4 m.

Jawaban :

Berat sendiri balok = 0.3 m x 0.6 m x 2400 kg/m3

= 432 kg/m (kg/m gaya)

Gravitasi bumi = 10 kg/ms2 maka beban menjadi 4320 N/m = 432 kN/m

Berat tembok sebagai beban terpusat sebesar :
http://3.bp.blogspot.com/_t7rNlHc4Y64/S41dgnMxttI/AAAAAAAAAOE/dAN5Ve9w7Dw/s1600-h/Graphic3.jpg


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= 0.15 m x 3 m x 4 m x 1700 kg/m3

= 3060 kg (kg gaya) = 30600 N = 30.6 kN

Secara visual dapat dilihat pada gambar 4.

Pada konstruksi bangunan beban yang diperhitungkan bukan hanya beban mati

seperti yang telah diuraikan di atas, tetapi dikombinasikan dengan beban hidup yang disebut

dengan pembebanan tetap, bahkan ada kombinasi yang lain seperti dengan beban angin

menjadi pembebanan sementara. Bila pada contoh di atas, balok digunakan untuk

menyangga ruang rumah tinggal keluarga, maka menurut PPIUG halaman 17 besarnya

beban hidup sebesar 200 kg/m2. Bila luas lantai yang dipikul balok sebesar 2 m tiap panjang

balok (dalam contoh di atas beban lantai tidak dihitung) maka beban karena beban hidup

adalah 200 kg/m2 x 2 m = 400 kg/m (kg gaya/m) = 4000 N/m = 4 kN/m. Dengan demikian

beban tetap yang bekerja pada balok adalah 4,32 + 4 = 8,32 kN/m yang secara visual dapat

dilihat

pada gambar 5.

Dilihat dari persentuhan gaya dan yang dikenai gaya, beban dapat dibedakan sebagai

beban langsung dan beban tidak langsung. Beban langsung adalah beban yang langsung
http://1.bp.blogspot.com/_t7rNlHc4Y64/S41dsLUF1uI/AAAAAAAAAOU/CggW6vLdjk4/s1600-h/Graphic5.jpghttp://3.bp.blogspot.com/_t7rNlHc4Y64/S41dl0XgM7I/AAAAAAAAAOM/B_z5qmDzJM0/s1600-h/Graphic4.jpg


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mengenai benda, sedang beban tidak langsung adalah beban yang membebani benda

dengan perantaraan benda lain (lihat gambar 6 ).

a. Pengertian Gaya

Gaya dapat didefisinikan sebagai sesuatu yang menyebabkan benda (titik materi)

bergerak baik dari diam maupun dari gerak lambat menjadi lebih lambat maupun lebih

cepat. Dalam teknik bangunan gaya berasal dari bangunan itu sendiri berat

benda di atasnya atau yang menempelnya, tekanan angin, gempa, perubahan suhu

dan pengaruh pengerjaan. Gaya dapat digambarkan dalam bentuk garis (atau

kumpulan garis) yang memiliki dimensi besar, garis kerja, arah kerja dan titik tangkap.

Satuan gaya menurut Sistem Satuan Internasional (SI) adalah Newton dan turunannya (kN).

Akan tetapi ada yang memberi satuan kg gaya (kg). Bila gravitasi bumi diambil

10 m/detik2 maka hubungan satuan tersebut adalah 1 kg gaya (atau sering ditulis 1 kg)

ekuivalen dengan 10 Newton. Pada gambar 8 dijelaskan pengertian gaya tersebut.

b. Kesetaraan gaya

Kesetaraan gaya adalah kesamaan pengaruh antara gaya pengganti (resultan)

dengan gaya yang diganti (gaya komponen) tanpa memperhatikan titik tangkap gayanya.
http://3.bp.blogspot.com/_t7rNlHc4Y64/S41d_wfY5OI/AAAAAAAAAOk/jeeWptfc5dA/s1600-h/Graphic7.jpghttp://2.bp.blogspot.com/_t7rNlHc4Y64/S41dxCYS9KI/AAAAAAAAAOc/OrIW7GKjyRs/s1600-h/Graphic6.jpg


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Dengan demikian pada suatu keadaan tertentu, walaupun gaya sudah setara atau

ekuivalen, ada perbedaan pengaruh antara gaya pengganti dengan yang diganti.

Pada prinsipnya gaya dikatakan setara apabila gaya pengganti dan penggantinya

baik gerak translasi maupun rotasi besarnya sama. Pada gambar 9 gaya P yang bertitiktangkap di A dipindahkan di B dalam garis kerja yang sama adalah setara (dalam arti efek

gerak translasi dan rotasinya) tetapi hal ini dapat berpengaruh terhadap jenis gaya yang

dialami benda, pada waktu titik tangkap gaya di A mengalami gaya tekan, sedang pada

waktu di B benda mengalami gaya tarik.

c. Keseimbangan Gaya

Keseimbangan gaya adalah hampir sama dengan kesetaraan gaya bedanya pada

arah gayanya. Pada kesetaraan gaya antara gaya pengganti dengan gaya yang diganti arah

yang dituju sama, sedang pada keseimbangan gaya arah yang dituju berlawanan, gaya

pengganti (reaksi) arahnya menuju titik awal dari gaya yang diganti (aksi). Pada gambar 10

divisualisasikan keseimbangan gaya.

Dengan kata lain keseimbangan gaya yang satu garis kerja dapat dikatakan bahwa

gaya aksi dan reaksi besarnya sama tapi arahnya berlawanan.

Pada statika bidang (koplanar) ada dua macam keseimbangan yaitu keseimbangan

translasi (keseimbangan gerak lurus) dan keseimbangan rotasi (keseimbangan gerak

berputar).
http://2.bp.blogspot.com/_t7rNlHc4Y64/S41epfa1ikI/AAAAAAAAAO0/I2eseqEIBQQ/s1600-h/Graphic9.jpghttp://3.bp.blogspot.com/_t7rNlHc4Y64/S41elTS22HI/AAAAAAAAAOs/5_ODINKer-M/s1600-h/Graphic8.jpg


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Untuk mencapai keseimbangan dalam statika disyaratkan ? Gy = 0 (jumlah gaya vertikal =

0), ?Gx = 0 (jumlah gaya horisontal = 0) dan ?M=0 (jumlah momen pada sebuah titik =0)

d. Pengertian Momen

Momen gaya terhadap suatu titik didefisinikan sebagai hasil kali antara gaya dengan

jaraknya ke titik tersebut. Jarak yang dimaksud adalah jarak tegak lurus dengan gaya

tersebut. Momen dapat diberi tanda positif atau negatif bergantung dari perjanjian

yang umum, tetapi dapat juga tidak memakai perjanjian umum, yang penting bila arah

momen gaya itu berbeda tandanya harus berbada. Pada gambar 11 diperlihatkan momen

gaya terhadap suatu titik.

Di samping momen terhadap suatu titik ada juga momen kopel yang didefinisikan sebagai

momen akibat adanya dua buah gaya yang sejajar dengan besar sama tetapi arahnya

berlawanan.

Gambar 12 menunjukkan momen kopel tersebut.

Momen dapat digambar dalam bentuk vektor momen dengan aturan bahwa arah vektor

momen merupakan arah bergeraknya sekrup yang diputar oleh momen. Lihat gambar 13.
http://2.bp.blogspot.com/_t7rNlHc4Y64/S41exyNHy3I/AAAAAAAAAPE/BNkbHxN8jfQ/s1600-h/Graphic11.jpghttp://4.bp.blogspot.com/_t7rNlHc4Y64/S41es92taRI/AAAAAAAAAO8/L6bzGiERdsg/s1600-h/Graphic10.jpg


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e. Momen Statis

Menurut teori Varignon momen pada suatu titik dikatakan statis bila besarnya momen gaya

pengganti (resultan) sama dengan gaya yang diganti.

? Contoh :

Gaya P1 dan P2 dengan jaraklmempunyai resultan R. Tentukan letak R agar momen di titik

A statis.

? Jawab :
http://1.bp.blogspot.com/_t7rNlHc4Y64/S41e1fF0rlI/AAAAAAAAAPM/oH4T8yYPfcg/s1600-h/Graphic12.jpg


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Misal jarak R dengan P1 (titik A) = a, maka untuk memenuhi momen

statis di A adalah : momen resultan = jumlah momen komponen.

f. Menyusun Gaya yang Setara

Istilah lain menyusun gaya adalah memadu gaya atau mencari resultan gaya. Pada

prinsipnya gaya-gaya yang dipadu harus setara (ekuivalen) dengan gaya resultannya

1) Menyusun Gaya yang Kolinier

2) Menyusun Dua Gaya yang Konkuren

3) Menyusun Beberapa Gaya Konkuren

Juga dikasih tau cara mencari besar dan arah resultan. Dengan cara Analisi dan Grafis..
http://3.bp.blogspot.com/_t7rNlHc4Y64/S41e7A9HmaI/AAAAAAAAAPc/Btspwy49GVg/s1600-h/Graphic14.jpghttp://1.bp.blogspot.com/_t7rNlHc4Y64/S41e5uorJDI/AAAAAAAAAPU/qa5BGt_6Cc8/s1600-h/Graphic13.jpg

building a popsicle (rbl)

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