Method of Join

7/27/2019 Method of Join

http://slidepdf.com/reader/full/method-of-join 1/45

ZURAIDAH BINTI AHMADPEJABAT B, JKA, PUO

http://mindasarjana.!"#sp"t.$"m

http://mindasarjana.blogspot.com/

http://mindasarjana.blogspot.com/



CC601- STRUCTURA% ANA%&SIS '

CHAPTER 1: ANA%&SIS O(STATICA%%& DETERMINATE 'D PIN

JOINTED TRUSSES

%ECTURE: 6 HOURS

TUTORIA%: ) HOURS



• 1.0 ANALYSIS OF STATICALLY DETERMINATE 2D PIN-JOINTED

TRUSSES.

• 1.1 Und*rstand th* app!i$ati"n "+ m*th"d "+ j"ints and m*th"d "+

s*$ti"ns in d*t*rminin# th* +"r$*s in trss*s

• 1.1.1 E-p!ain tp*s "+ trss*s.

• 1.1.' Di++*r*ntiat* *t**n d*t*rminat* and ind*t*rminat*

trss*s.

• 1.1.) E-p!ain t*nsi"n m*m*rs and $"mpr*ssi"n m*m*rs.

• 1.1.0 Stat* th* sm"! +"r t*nsi"n and $"mpr*ssi"n m*m*rs.

• 1.1.1 E-p!ain th* m*th"d "+ j"ints.

• 1.1.6 E-p!ain 2*r"-+"r$* m*m*rs.

• 1.1.3 E4a!at* th* trss m*m*rs +"r$*s sin# th* m*th"d "+

j"ints.

• 1.1.5 E-p!ain th* m*th"d "+ s*$ti"ns.

• 1.1.6 Estimat* th* trss m*m*rs +"r$*s sin# th* m*th"d "+

• S*$ti"ns.



D*+initi"n:• A trss is a str$tr* that $"nsists "+

1. A!! strai#ht m*m*rs

'. C"nn*$t*d t"#*th*r ith pin j"ints). C"nn*$t*d "n! at *nds "+ th* m*m*rs

0. And a!! *-t*rna! +"r$*s 7!"ads 8 r*a$ti"ns9 mst

* app!i*d "n! at th* j"intsN"t*:

E4*r m*m*r "+ a trss is a ' +"r$* m*m*r.

Trss*s ar* assm*d t" * "+ n*#!i#i!* *i#ht7$"mpar*d t" th* !"ads th* $arr9



1.1.1 Tp*s "+ trss*s

a truss is a str$tr* $"mprisin# "n* "r m"r*trian#!ar nits $"nstr$t*d ith strai#htm*m*rs h"s* *nds ar* $"nn*$t*d at j"intsr*+*rr*d t" as n"d*s.

E-t*rna! +"r$*s and r*a$ti"ns t" th"s* +"r$*s ar*$"nsid*r*d t" a$t "n! at th* n"d*s and r*s!t in+"r$*s in th* m*m*rs hi$h ar* *ith*r t*nsi!* "r$"mpr*ssi4* +"r$*s.

M"m*nts 7t"r*s9 ar* *-p!i$it! *-$!d*d *$as*,and "n! *$as*, a!! th* j"ints in a trss ar*tr*at*d as r*4"!t*s.

http://en.wikipedia.org/wiki/Architectural_structure

http://en.wikipedia.org/wiki/Vertex_(geometry)

http://en.wikipedia.org/wiki/Tension_(physics)

http://en.wikipedia.org/wiki/Compression_(physics)

http://en.wikipedia.org/wiki/Torque

http://en.wikipedia.org/wiki/Revolute_joint

http://en.wikipedia.org/wiki/Revolute_joint

http://en.wikipedia.org/wiki/Torque

http://en.wikipedia.org/wiki/Compression_(physics)

http://en.wikipedia.org/wiki/Tension_(physics)

http://en.wikipedia.org/wiki/Vertex_(geometry)

http://en.wikipedia.org/wiki/Architectural_structure



• A p!anar trss !i*s in a sin#!* p!an*. P!anar

trss*s ar* tpi$a!! s*d in para!!*! t" +"rmr""+s and rid#*s.

http://en.wikipedia.org/wiki/Plane_(mathematics)




• A p!anar trss !i*s in a sin#!* p!an*. P!anar

trss*s ar* tpi$a!! s*d in para!!*! t" +"rmr""+s and rid#*s.

•A spa$* +ram* trss is a thr**-dim*nsi"na!+ram*"r; "+ m*m*rs pinn*d at th*ir *nds.

A t*trah*dr"n shap* is th* simp!*st spa$*

trss, $"nsistin# "+ si- m*m*rs hi$h m**t at+"r j"ints.


http://en.wikipedia.org/wiki/Space_frame

http://en.wikipedia.org/wiki/Tetrahedron

http://en.wikipedia.org/wiki/Tetrahedron

http://en.wikipedia.org/wiki/Space_frame




Di++*r*ntiat* *t**n d*t*rminat*

and ind*t*rminat* trss*s.

This is a n*$*ssar $"nditi"ns +"r stati$a!! d*t*rmina$.

This is n"t s++i$i*nt $"nditi"n.

S" *4*n i+ a trss satis+i*s th* a"4* r*!ati"n it ma n"t

* d*t*rminat*. Bt i+ it is d*t*rminat* than it satis+i*s

th* a"4* r*!ati"n.

M<'n-r : stati$a!! d*t*rminat*

M='n-r: nsta!*M> 'n-r: stati$a!! ind*t*rminat*



*-amp!*

• 'n < m?r

• m<1

• r<)

• n<0• 'n <'-0 < 5

• m?r <1 ?) <5



*-amp!*

• 'n < m?r

• m <11

• r<)

•n<6• 'n <'- 6 < 15

• m?r <11 ?) < 15

m < m*m*r

r < r*a$ti"ns

n < j"ints



External forces:

"%"ads" a$tin# on "r str$tr*.

N"t*: this in$!d*s "r*a$ti"n" +"r$*s +r"m th* spp"rts as *!!.

Internal forces: ("r$*s that d*4*!"p ithin *4*r str$tr* that ;**p th*di++*r*nt parts "+ th* str$tr* t"#*th*r.



E-p!ain t*nsi"n m*m*rs and

$"mpr*ssi"n m*m*rs.



Stat* th* sm"! +"r t*nsi"n and

$"mpr*ssi"n m*m*rs.

• Tp* "+ int*rna! +"r$*s Sm"!s

1. T*nsi"n ?4* 7T9

'. C"mpr*ssi"n -4* 7C9



Truss Analysis – Method of Joints :

• M*th"d "+ j"int is a str$tra! ana!sis m*th"d t" d*t*rmin* th* int*rna! +"r$*s "+ m*m*rs in a trss. Thism*th"d is d*ri4*d as*d "n th* *i!irim $"nditi"ns at j"ints. It is asi$a!!, a sp*$ia! $as* "+ *i!irim "+$"n$rr*nt 7int*rs*$tin#9 +"r$*s. In this $as* r"tati"na! "r m"m*nt *i!irim is r*adi! satis+i*d at th* j"int.Th*r*+"r* in th* m*th"d "+ j"int +"r p!an* trss th*r* ar* "n! t" *i!irim *ati"ns r*ir*d:

• Procedure for method of joints:• S*!*$t a j"int ha4in# at !*ast "n* ;n"n +"r$* and at m"st t" n;n"n +"r$*s 7*$as* * ha4* "n! t"

*i!irim *ati"ns9. I+ th* j"int is !"$at*d at th* spp"rt, * ma n**d t" +irst d*t*rmin* *-t*rna! r*a$ti"ns atth* trss spp"rts.

• Dra th* +r**-"d dia#ram 7(BD9 +"r th* s*!*$t*d j"int. Ma;* sr* that a!! ;n"n and n;n"n +"r$*s ar*a$$"nt*d +"r. ("r th* n;n"n +"r$*s, th* dir*$ti"n "+ th* +"r$*s n**d t" * assm*d. M r*$"mm*ndati"n is t"a!as assm* that th* n;n"n +"r$*s ar* in t*nsi"n. N*#ati4* 4a!* +r"m th* ana!sis m*ans that th* a$ta!

+"r$* dir*$ti"n is r*4*rs* and th* m*m*r is in $"mpr*ssi"n.• Ori*nt th* - and a-*s s" that th* +"r$*s $an * *asi! r*s"!4*d int" th*ir - and $"mp"n*nts.

• App! th* *i!irim *ati"ns and s"!4* +"r th* n;n"n m*m*r +"r$*s and $h*$; th*ir dir*$ti"ns.

• C"ntin* th* sam* pr"$*ss t" an"th*r j"int nti! a!! int*rna! m*m*r +"r$*s in a trss str$tr* ar* s"!4*d.

• As " $an s**, th* m*th"d "+ j"int is strai#ht +"rard and n"t di++i$!t. &" jst n**d t" * smart in s*!*$tin# th*s**n$* "+ j"ints ,n**d t" * s"!4*d *$as* th* ma-imm n;n"n +"r$*s that $an * s"!4*d sin# this m*th"dis t". Ths s"m*tim*s m*th"d "+ j"ints $ann"t * app!i*d +"r a parti$!ar j"int *$as* it has m"r* than t"

n;n"n +"r$*s. In this $as* ,n"rma!! * s"!4* it +irst s"!4in# its n*i#h"rh""d j"ints.• Ths th* m*th"ds "+ j"int is asi$a!! a m*th"d t" d*t*rmin* th* int*rna! +"r$*s in th* m*m*rs "+ trss str$tr*

satis+in# th* *i!irim $"nditi"ns "+ +"r$*s at *a$h j"int "+ th* trss.



E-p!ain th* m*th"d "+ j"ints.

• I+ a trss is in *i!irim, th*n *a$h "+ its

j"ints mst * in *i!irim.• Th* m*th"d "+ j"ints $"nsists "+ satis+in# th*

*i!irim *ati"ns +"r +"r$*s a$tin# "n *a$h j"int.

@ (- <0; @(<0

C id h h T



M*th"d "+ j"ints• C"nsid*r th* trss sh"n. Trss

ana!sis in4"!4*s:

• 7i9 D*t*rminin# th* ETERNA%

r*a$ti"ns.

• 7ii9 D*t*rminin# th* INTERNA% +"r$*s

in *a$h "+ th* m*m*rs 7t*nsi"n "r$"mpr*ssi"n9.

• R*$a!!:

•External forces:

• "%"ads" a$tin# on "r str$tr*.

• N"t*: this in$!d*s "r*a$ti"n" +"r$*s

+r"m th* spp"rts as *!!.

• Int*rna! +"r$*s: ("r$*s that d*4*!"pithin *4*r str$tr* that ;**p th*

di++*r*nt parts "+ th* str$tr*

t"#*th*r.



7i9 E-t*rna! r*a$ti"n



7ii9 Int*rna! ("r$*s



J"int B

∑f y=0; CD + 20 = 0

CD = -20N !Com"ression]



J"int C

@ (- < 0;

-BC AC C"s 010

? 10 < 0AC < 10/C"s 010 < 10.10N

9 Decem#er 201$: Method of Joint



9 Decem#er 201$: Method of Joint

Recall• Wh*r*:

• m < n". "+ m*m*r

•r < n". "+ r*a$ti"ns

• j < n". "+ j"int

• m<'j-r : stati$a!! d*t*rminat*

• m='j-r: nsta!*

• m> 'j-r: stati$a!! ind*t*rminat*

• N". "+ r*dndan$ < m + r -2j• = Degree of indeterminate

• = Degree of Freedom



E-amp!* '. D*t*rmin* th* d*#r** "+ +r**d"m "+ th*

str$tr*. B sin# th* m*th"d "+ j"ints, d*t*rmin* th*

+"r$* in *a$h m*m*r "+ th* trss.'1;N

D C

BA

10;N

0m

0m

0m

719 D*#r** "+ (r**d"m< m- 'j ? r

• m<1

• r<)• j<0

• D"(<m-'j ?r

•D"( < 1

-7'-09?)

• D"(< 0

• - N" r*dndan$

• - Stati$a!! d*t*rminat*



E-amp!* ). B sin# th* m*th"d "+ j"ints, d*t*rmin*

th* +"r$* in *a$h m*m*r "+ th* trss.'1;N

D C

BA

10;N

0m

0m

0m

7'9 E-t*rna! R*a$ti"ns

@(-<0

• B- < 0

• @M<0

• A709?10709<0

• A < -10;N

• @(<0• A ?B-'1-10 <0

• -10 ?B -31 <0

• B <1'1;N

A B

B-



7'9 Int*rna! +"r$*s

• @(<0

• AD C"s010 10 <0

•AD < 3

0.3

1;N 7t*nsi"n9

• @(-<0

• AB ? AD C"s010 < 0

• AB < -10;N 7$"mpr*ssi"n9

10;N

AB

AD

J"int A

(r** "d Dia#ram

J"int B

(r** "d Dia#ram

• @(-<0

• BC C"s010 - AB < 0

• BC C"s010 7-109 < 0

• BC < -30.31;N 7$"mpr*ssi"n9

• @(<0

• BD ?BC C"s010 ? 1'1 <0

• BD ? 7-30.319 C"s010 ?1'1< 0• BD < -31;N 7$"mpr*ssi"n9

1'1 ;N

AB

BCBD



7'9 Int*rna! +"r$*s

• @(-<0

• CD ? CB C"s010 < 0

• CD ? 7

-3

0.3

19

C"s01

0

<0

• CD < 10;N 7t*nsi"n9

10;N

CB

CD

J"int C(r** "d Dia#ram

Int*rna! +"r$*s

E ! ) D i h d + + d + h



E-amp!* ). D*t*rmin* th* d*#r** "+ +r**d"m "+ th*


+"r$* in *a$h m*m*r "+ th* trss.

719 D*#r** "+ (r**d"m< m- 'j ? r

• m<1)

• r<)• j<5

• D"(<m-'j ?r

• D"( < 1)-7'-59?)

• D"(< 0

• - N" r*dndan$




E-amp!* ). R*a$ti"n +"r$*s at spp"rts

• @(-<0• G- ?17)9 ?117)9 < 0

• G- ? 60 <0

• G-< -60;N• @M#<0

• H709-117)?6?69-17)?6?69<0

• H< 60;N

• @(<0

• G? H <0

• G ? 60 <0

• G <-60;N

Gy

Gx

%y



E-amp!* ). Int*rna! +"r$*s

G

y

Gx

%y

E-amp!* 0 D*t*rmin* th* d*#r** "+ +r**d"m "+ th*



E-amp!* 0. D*t*rmin* th* d*#r** "+ +r**d"m "+ th*

str$tr*. B sin# th* m*th"d "+ j"ints, d*t*rmin*

th* +"r$* in m*m*r AB, AE, CD, DG.

• D*#r** "+ (r**d"m< m- 'j ? r

• m<11

• r<)• j<3

• D"(<m-'j ?r < 11-'-3?)• D"(< 0

• - N" r*dndan$




719 E-t*rna! r*a$ti"n

• @(<0

• A- 0 71'.19 <0

• A <10;N

• @Ma<0

• E-7'.19-1'.17'?0?69<0

• E- < 60;N

• @(-<0

• A- ?E- < 0

• A- ? 60 <0

• A-< -60;N

A

A-

E-



7'9 Int*rna! +"r$*s

• @(<0

• 10 -1'.1 AE <0

• AE < )3.1;N 7t*nsi"n9• @(-<0

• AB -60 < 0

• AB <60;N 7t*nsi"n9

10;N

60;N

1'.1;N

AE

AB

J"int A

(r** "d Dia#ram

J"int D(r** "d

Dia#ram

• @(<0

• -DGSinӨ -1'.1 <0

• -DG7'.1/6.19-1'.1 < 0

• DG< -)'.1;N 7C"mpr*ssi"n9

• @(-<0

• DC ? DGC"sӨ < 0

• DC ? 7-)'.1976/6.19 <0

• DC< )0;N 7T*nsi"n9

1'.1;N

DG

DCӨ DE<76'?'.1'91/'

DE < 6.1m

E-amp!* 1: D*t*rmin* th* d*#r** "+ +r**d"m "+ th*




+"r$* in *a$h m*m*r "+ th* trss.10;N A B C

0m

D E ( G

'0;N )0;N

'm 'm 'm





















'm

10;N1;N

0m 0m

E-amp!* 6



E-amp!* 6.

719 D*#r** "+ (r**d"m< m- 'j ? r

• m<1

• r<)

• j<0

• D"(<m-'j ?r

• D"( < 1-7'-09?)

• D"(< 0

• - N" r*dndan$


10;N1;N

0m0m

'm

E ! 6



E-amp!* 6.

7'9 E-t*rna! R*a$ti"ns

• @(<0

• A -1-10 <0

• A < 11;N

•@Ma<0

• B-7'9< 1709 ? 10759

• B- < 10;N

• @(-<0

• A- ? B- < 0

• A- ? 10 <0

• A- < -10;N

10;N1;N

0m0m

'm

A-

A

B-

J"int DDA

DC

10;N

• @(<0

• DA SinӨ 10 <0

• DA7'/C659-10 <0

• DA < 01.');N 7t*nsi"n9• @(-<0

• DC ? DA C"s Ө < 0

• DC?DA75/C659<0

• DC < -00;N 7$"mpr*ssi"n9

AD<7''?5'91/'< C65

Өα



7'9 Int*rna! +"r$*s

• @(<0

• AB <0

• @(-<0

•B

C ? 1

0 <

0

• BC < -10;N 7$"mpr*ssi"n9

10;NBC

AB

J"int B

(r** "d Dia#ram

J"int C

(r** "d Dia#ram

• @(<0

• CA Sinα < 1

• CA7 '/C'09 <1

• CA < 11.15 ;N 7t*nsi"n9• @(-<0

• CB?CA C"s α <CD

• CB?11.15 70/C'09 < -00

• BC < -10;N 7$"mpr*ssi"n9 - pr"4*n

1 ;N

CB CD

CAAC<7''?0'91/'< C'0



E-p!ain 2*r"-+"r$* m*m*rs

10;N BC

AB

• @(<0

• AB <0 2*r" +"r$* m*m*r

• @(-<0

•B

C ? 1

0 <

0

• BC < -10;N 7$"mpr*ssi"n9

@(-<0

BC < 0

BC is a 2*r" +"r$* m*m*r

I th +i !d + i i h i f # + t 7

http://en.wikipedia.org/wiki/Engineering_mechanics




• In th* +i*!d "+ *n#in**rin# m*$hani$s, a zero force mem#er r*+*rs t" a m*m*r 7asin#!* trss s*#m*nt9 in a trss hi$h, #i4*n a sp*$i+i$ !"ad, is at r*st: n*ith*r int*nsi"n, n"r in $"mpr*ssi"n. In a trss a 2*r" +"r$* m*m*r is "+t*n +"nd at pins

7an $"nn*$ti"ns ithin th* trss9 h*r* n" *-t*rna! !"ad is app!i*d and thr** "r+**r trss m*m*rs m**t. R*$"#ni2in# asi$ 2*r" +"r$* m*m*rs $an *a$$"mp!ish*d ana!2in# th* +"r$*s a$tin# "n an indi4ida! pin in a phsi$a!sst*m.

• NOTE: If the pin has an external force or moment applied to it, then all of the

members attached to that pin are not zero force members UNLESS the external force acts in a manner that fulfills one of the rules below:

• I+ "n! t" m*m*rs m**t in an n!"ad*d j"int, "th ar* 2*r"-+"r$* m*m*rs.

• I+ thr** m*m*rs m**t in an n!"ad*d j"int "+ hi$h t" ar* in a dir*$t !in* ith"n* an"th*r, th*n th* third m*m*r is a 2*r"-+"r$* m*m*r.

• I+ t" m*m*rs m**t in a !"ad*d j"int and th* !in* "+ a$ti"n "+ th* !"ad $"in$id*sith "n* "+ th* m*m*rs, th* "th*r m*m*r is a 2*r"-+"r$* m*m*r.

• Reasons for &ero-force mem#ers in a truss system

• Th*s* m*m*rs $"ntrit* t" th* stai!it "+ th* str$tr*, pr"4idin# $;!in#pr*4*nti"n +"r !"n# s!*nd*r m*m*rs nd*r $"mpr*ssi4* +"r$*s

• Th*s* m*m*rs $an $arr !"ads in th* *4*nt that 4ariati"ns ar* intr"d$*d in th*n"rma! *-t*rna! !"adin# $"n+i#rati"n

Id*nti+ th* 2*r" +"r$* m*m*r +r"m th* trss *!"


http://en.wikipedia.org/wiki/Truss

http://en.wikipedia.org/wiki/Structural_load

http://en.wikipedia.org/wiki/Tension_(mechanics)

http://en.wikipedia.org/wiki/Compression_(physical)

http://en.wikipedia.org/wiki/Force

http://en.wikipedia.org/wiki/System

http://en.wikipedia.org/wiki/Moment_(physics)

http://en.wikipedia.org/wiki/Joint_(building)

http://en.wikipedia.org/wiki/Line_of_action

http://en.wikipedia.org/wiki/Line_of_action

http://en.wikipedia.org/wiki/Joint_(building)

http://en.wikipedia.org/wiki/Moment_(physics)

http://en.wikipedia.org/wiki/System

http://en.wikipedia.org/wiki/Force

http://en.wikipedia.org/wiki/Compression_(physical)

http://en.wikipedia.org/wiki/Tension_(mechanics)

http://en.wikipedia.org/wiki/Structural_load

http://en.wikipedia.org/wiki/Truss




Id*nti+ th* 2*r" +"r$* m*m*r +r"m th* trss *!".

Gy

Gx

%y

• M*m*r AC

• M*m*r GH• Th* 2*r" +"r$*

m*m*r $arr n"int*rna! +"r$*.



• M*m*r AD

• M*m*r BC




'm

10;N1;N

0m 0m


M*m*r AB





M*m*r ABM*m*r BG

M*m*r DI

M*m*r DE

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Method of Join