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Evalúa Chile en el Siglo XX
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material producido por MINEDU, Primera Unidad 2017 - del nivel primario de 1° a 6° grado
material producido por MINEDU, Primera Unidad 2017 - del nivel primario de 1° a 6° grado
Quiz 1 Semana 3 Calcul 2 6 de 6Descripción completa
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Activity 2.1.6 Step-by-Step Truss Truss System Introduction Truss systems are essential components within structural systems ranging from residential construction to large scale civil engineering projects such as bridges. Regardless of the system application, trusses are designed to utilize material strength, reduce costs, and support a determined load. Engineers must be able to understand how loads act on a truss structure and within the structure to ensure design feasibility and safety. Activity 2..! will guide you through the step"by"step process of calculating reaction forces and member forces within a truss system.
Equipment • • •
#traight edge $alculator %encil
Procedure &n this activity you will calculate reaction and member forces for the truss system illustrated below. To ensure proper calculations and free body diagrams, it is essential that you follow each step in the procedure.
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age
Calculate Eternal !eaction "orces x and y Reaction Force at Pin A and Y Reaction Force at Roller Roller C
raw raw a free free body body diagr diagram am for the the entire truss structure illustrated above. Make sure to include all known and unknown angles, forces, and distances. Calculate and determine all angles using trigonometry and geometry. - o/ 0 .1 nits3
Algebra hints4 sin θ 0 567 cos θ 0 A67 tan θ 0 56A a2 8 b2 0 c2
2 $alculat $alculate e reactio reaction n forces forces at the the roller roller and and pin pin connecti connections. ons. a.
)ist )ist sta static e9uili uilibr briu ium m e9uatio tions. #int$ : ;< 0 (
b.
%T&ey all involve summations'
: ;= 0 (
: > A 0 (
)ist )ist all all ?no ?nown wn and and un?n un?now own n forc forces es act actin ing g and and rea react ctin ing g on the the trus truss s structure. Label direction of force wit an arrow. i.
;orces in the direction A<
ii.
;orces in the y direction A=
iii. ;ormula review4
=
$=
=
E=
(oment ;orces + etermined from Pin A
$= @ (
"((( @
"1(( @ B
"21( @1
( ) "d
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age 2
c.
se se the the mome moment nt stat static ic e9ui e9uili libr briu ium m e9u e9uat atio ion n act actin ing g upo upon n pin A to solve for !Cy.
:> A 0 (
( 0 $= -(3 "(((-3 "1((-B3 "21(-13
E9uation
#ubstitution
( 0 $= -(3 "BB1( BB1( 0 $= -(3
!Cy 0 BB1 lb
#implification d.
#olution
#olv #olve e for for un? un?now nown rea react ctio ion n for force ce in the the / dir direc ecti tion on - !A3. !se te sum of forces in te x direction direction e"uilibrium e"uation. A< 0 ( : ;< 0 (
!A 0 ( lb
E9uation e.
#ubstitution
#olution
#olv #olve e for for un?n un?now own n rea react ctio ion n forc forces es in the the y dire direct ctio ion. n. !se te sum of forces in te y direction direction e"uilibrium e"uation.
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age
f.
raw raw a fre free e bod body y dia diagr gram am for for the the ent entir ire e trus truss s syst system em ill illus ustr trat ated ed on on pag page e . . Make sure to include your calculated su##ort reactions $% &ox ' .( units).
Calculate Individual Truss (ember "orces
$alc $alcul ulat ate e mem membe berr for force ces s A* and A+. a.
raw raw th the fr free body diag iagram for joint int A. Make sure to include all known and known and unknown angles and angles and forces (including x and y vector components). components) . Do not include lengths. lengths .
b.
se #57 $A7 T5A to e/press A* and A*y in terms of A*. i.
#in ᶿ 0 5 6 7 E9uation
$alculate A* #in D1 0 ;A / 6 ;A #ubstitution
A* 0 ;A @ #in D1
#olution
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age D
ii.
$alculate A*y
$os ᶿ 0 A 6 7
$os D1 0 ;A = 6 ;A
E9uation c.
A*y 0 ;A @ $os D1
#ubstitution
#olution
)ist al all ?n ?nown an and un un?nown fo forces. Label direction of force wit an arrow. i.
;orces in the direction
( lb
- ;A @ #in D1 3 ;A
ii.
;orces in the y direction CB1 lb
d.
- ;A @ $os D1 3
se se sta stati tic c e9u e9uil ilib ibri rium um e9ua e9uati tion ons s to to sol solve ve for for A* and A+. i.
#olve for A* by calculating y direction static e9uilibrium.
F;= 0 (
;A @ $os D1 0 "CB1
E9uation
CB1 8 - ;A @ $os D13 0 ( #ubstitution
#implification A* 0 BG.1! lb
;A 0 -"CB13 6 -$os D13
#implification ii.
#olution
#olve for A+ by calculating direction static e9uilibrium.
"BG.1! @ #in D1 0 ";A #ubstitution + &nsert calculated A value e.
#implification
A+ 0 CB1 lb
#olution
pdate the joint A ,ree body diaram with calculated forces for A* and A+. ' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age 1
D $alculate C+ and CE. a.
raw the free body diagram for oint C. Make sure to include all known and known and unknown angles and angles and forces (including x and y vector components). components) . Do not include lengths. lengths .
b.
se #57 $A7 T5A to e/press CE and CEy in terms of CE. i.
$alculate CE #in D1 0 ;$E < 6 ;$E
#in ᶿ 0 5 6 7
CE/ 0 ;$E @ #in D1
E9uation ii.
#ubstitution
#olution
$alculate CEy $os D1 0 ;$E = 6 ;$E
$os ᶿ 0 A 6 7
CEy 0 ;$E @ $os D1
E9uation c.
#ubstitution
#olution
)ist al all ?n ?nown an and un un?nown fo forces. Label direction of force wit an arrow. i.
;orces in the direction ;$E @ #in D1 ;$
ii.
;orces in the y direction ;$E @ $os D1 BB1 lb
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age !
d. se static static e9uil e9uilibri ibrium um e9uatio e9uations ns to solve solve for A* and A+. i. F;= 0 (
#olve for CE by calculating y direction static e9uilibrium. BB1 8 -;$E @ $os D13 0 (
E9uation
#ubstitution
;$E @ $os D1 0 "BB1 #implification
CE 0 (C!.(2 lb
#olution ii. F;< 0 (
#olve for C+ by calculating direction static e9uilibrium. ;$ 8 -;$E @ #in D13 0 (
E9uation
#ubstitution
;$ 0 #in D1 @ (C!.(2
#ubstitution + &nsert calculated $E value e.
;$ 0 ;$E @ #in D1
#implification
C+ 0 BB1( lb
#olution
pdate joint C ,ree-body diaram with calculated forces for CE and C+.
1 $alculate E+ and E* a.
raw the free"body diagram for oint E. Make sure to include all known and known and unknown angles and angles and forces (including x and y vector components). components) . Do not include lengths. lengths .
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age B
b.
se #57 $A7 T5A to e/press E+ and E+y in terms of E+. i.
$alculate E+y
#in ᶿ 0 5 6 7
#in 1! 0 ;E = 6 ;E
E9uation ii.
#ubstitution
#olution
$alculate E+
$os ᶿ 0 A 6 7
$os 1! 0 ;E < 6 ;E
E9uation c.
E+y 0 #in 1! @ ;E
E+ 0 $os 1! @ ;E
#ubstitution
#olution
)ist al all ?n ?nown an and un un?nown fo forces. Label direction of force wit an arrow. i.
;orces in the direction ;E
$os 1! @ ;E BB1 lb
ii.
;orces in the y direction "1(( lb
d.
E9uation
#in 1! @ ;E
se se sta stati tic c e9u e9uil ilib ibri rium um e9ua e9uati tion ons s to to sol solve ve for for E+. i.
F;= 0 (
BB1 lb
$alculate y direction static e9uilibrium. -#in 1! @ ;E3 + 1(( 8 BB1
2B1 8 -#in 1! @ ;E3 0 (
#ubstitution
"2B1 0 "#in 1! @ ;E
#ubstitution
#implification
;E 0 "2B1 6 "#in 1! @ ;E #implification
E+ 0 ".21 lb
#olution
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age G
pdate joint E ,ree body diaram with calculated forces for E+ and E*.
! $alculate *+ a.
raw the free body diagram for oint *. Make sure to include all known and known and unknown angles and angles and forces (including x and y vector components). components) . Do not include lengths. lengths .
b.
se #57 $A7 T5A to e/press *+ and *+y in terms of *+. i. #in
ii.
$alculate *+y ᶿ
0567
#in 1! 0 ; = 6 ;
E9uation
#ubstitution
*+y 0 #in 1! @ ;
#olution
$alculate *+
$os ᶿ 0 A 6 7
$os 1! 0 ; < 6 ;
E9uation
#ubstitution
*+ 0 $os 1! @ ;
#olution
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age C
c.
)ist al all ?n ?nown an and un un?nown fo forces. Label direction of force wit an arrow. i.
;orces in the direction "CB1
#in 1! @ ; ";E
ii.
;orces in the y direction "CB1
$os 1! @ ; (((
d.
se se sta stati tic c e9u e9uil ilib ibri rium um e9ua e9uati tion ons s to to sol solve ve for for *+. i.
F;= 0 ( E9uation
#olve for *+ by calculating y"direction static e9uilibrium. "CB1 8((( 8 -#in 1! @ ;3 0 ( #ubstitution
"21 6 #in 1! 0 ; #implification
"21 0 -#in 1! @ ;3 #implification
*+ 0 (.(1 lb
#olution
e. pda pdate te join jointt * ,ree body diaram with calculated forces for *+ and *E. *ra0 Completed "ree +ody *iaram
B raw a compl completed eted free free body body diagram diagram for for the entire entire truss truss struct structure ure using using all all calculated reaction and member forces.
' 2(2 %roject )ead The *ay, &nc. %rinciples of Engineering Activity 2..! #tep"by"#tep Truss Truss #ystem + %age (
