1 MEM202 Engineering Mechanics - Statics MEM 7.2 Plane Trusses Examples for Method of Joints
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesExamples for Method of Joints
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesExamples for Method of Joints
Vehicle weight = mg = 9810 N
A: AB, AEB: BC, BEE: CE, EFC: CD, CFD: DxF: Fx, FyReactions not crucial
Reactions must be obtained first
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesExamples for Zero-Force Members
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesExamples for Zero-Force Members
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesMethod of Sections
Method of joints is more convenient when the truss is relatively simple and forces in all members are needed.
1F 2F1R 2R
Force = ?Method of sections is more convenient when the truss is relatively complex and forces in only a few members are needed.
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesMethod of Sections
Force = ?
1. If necessary, draw a free-body diagram of the entire truss and determine the reactions (if r = 3).
2. Divide the truss into two parts by passing an imaginary section through member(s) whose member forces are needed. Draw a free-body diagram for each part.
0
0
0
=
=
=
∑∑∑
M
F
F
y
x
0
0
0
=
=
=
∑∑∑
M
F
F
y
x3. Set up equilibrium equations for either free-body diagram and solve them to obtain the unknown member forces.
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesMethod of Sections
DGI
FGD
CDG
TM
TM
TM
⇒=
⇒=
⇒=
∑∑∑
0
0
0
FGDGCDy
x
TTT
M
F
F
,,
0
0
0
⇒
⎪⎪⎭
⎪⎪⎬
⎫
=
=
=
∑∑∑
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesMethod of Sections
K-Truss
CDF
FGD
TM
TM
⇒=
⇒=
∑∑
0
0
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesMethod of Sections
BA
EC
HF
KI
NL
O
T
R
W
U
D
G
J
M
P S
V
Q
Reactions at A and BSection 1: AC, BE Section 2: CF, EHSection 3: IF, HK Section 4: LI, KN
Joint V: VL, VT Joint W: WN, WUJoint R: RO, RT Joint S: SQ, SUJoint T: TL, TO Joint U: UN, UQJoint O: OL, OP Joint Q: QN, QPJoint P: PL, PN Joint L: LMJoint N: NM Joint M: MI, MKJoint I: IJ Joint K: KJJoint J: JF, JH Joint F: FGJoint H: HG Joint G: GC, GEJoint C: CD Joint D: DA, DBJoint A: AB Joint B: Check
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MEM202 Engineering Mechanics - Statics MEM
7.3 Space Trusses
222222
22
2222
32132
32132
3232
2323
2323
++
−+−=
++
−−−=
=+
−−=
+
−=
+
+=
kjiTFkjiTF
jTFkiTF
jiTFjiTF
CDCDBDBD
BCBCADAD
ACACABAB
rrrr
rrrr
rrrr
r
rrr
rrr
kAjAiAA zyx
rrrr++= kCjCC zy
rrr+=
kBB z
rr=
rjmjm −=−= 3or 63( )lb 30cos30sin125 kjPrrr
oo −=
0=+++ ADACAB FFFArrrr
0=+++ BDDCAB FFFBrrrr
0=+++ CDBCAC FFFCrrrr
0=+++ CDBDAD FFFPrrrr
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MEM202 Engineering Mechanics - Statics MEM
7.2 Plane TrussesForces in Straight and Curved Two-Force Members
αr
ααα sincossin TrTdMTVTP ====00 === MVTP
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