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Engineering Mechanics :Engineering Mechanics :STATICSSTATICS
Lecture #09By,
Noraniah KassimUniversiti Tun Hussein Onn Malaysia
(UTHM),
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STRUCTURAL ANALYSIS – THE METHOD OF SECTIONS
Learning Topic:
• Applications
• The Method of Sections
Today’s Objectives:
Students will be able to determine:
1. Forces in truss members using the
method of sections.
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READING QUIZ
1. In the method of sections, generall a !cut" passes through nomore than ##### members in which the forces are un$nown.
A% 1 &% '
(% ) *% +
'. If a simple truss member carries a tensile force of T along its
length, then the internal force in the member is ###### .
A% tensile with magnitude of T'&% compressi-e with magnitude of T'
(% compressi-e with magnitude of T
*% tensile with magnitude of T
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APPLICATIONS
ong trusses are often used to construct bridges.
The method of /oints re0uires that man /oints be analed before we can determine the forces in the middle part of the
truss.
Is there another method to determine these forces directl2
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THE METHOD OF SECTIONS
In the method of sections, a truss is di-ided into two parts b
ta$ing an imaginar !cut" 3shown here as a4a% through the truss.
Since truss members are sub/ected to onl tensile or compressi-eforces along their length, the internal forces at the cut member will
also be either tensile or compressi-e with the same magnitude.
This result is based on the e0uilibrium principle and 5ewton6s
third law.
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STEPS OF ANALYSIS
1. *ecide how ou need to !cut" the truss. This is based on:
a% where ou need to determine forces, and, b% where the total
number of un$nowns does not e7ceed three 3in general%.
'. *ecide which side of the cut truss will be easier to wor$with 3minimie the number of reactions ou ha-e to find%.
). If re0uired, determine the necessar support reactions b
drawing the F&* of the entire truss and appling the 84of48.
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STEPS OF ANALYSIS (Continued)
+. *raw the F&* of the selected part of the cut truss. 9e need to
indicate the un$nown forces at the cut members. Initiall we
ma assume all the members are in tension, as we did when
using the method of /oints. pon sol-ing, if the answer is positi-e, the member is in tension as per our assumption. If the
answer is negati-e, the member must be in compression. 3;lease
note that ou can also assume forces to be either tension or
compression b inspection as was done in the figures abo-e.%
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STEPS OF ANALYSIS (Continued)
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EAMPLE
Given: oads as shown on the
roof truss.
Find: The force in members
*8, *, and M.
Plan:
a% Ta$e a cut through the members *8, *, and M.
b% 9or$ with the left part of the cut section. 9h2
c% *etermine the support reaction at A. 9hat are the2
d% Appl the 8of8 to find the forces in *8, *, and M.
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EAMPLE (continued)
Analing the entire truss, we get Σ F= > A= > ?. &
smmetr, the -ertical support reactions are
A@ > I@ > ) $5
B M* > C ) 3D% B 3D% B 1' 3+% B FM 3 ?
FM > )D.+ $5 3 T %
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EAMPLE (continued)
BΣ M > C) 31'% B 31'% B 1' 3D% B 1' 3+% C F*8 3 +√1E%3% > ?
F*8 > C)E.11 $5 or )E.1 $5 3(%
→ B Σ F= > )D.+ B 3+√1E% 3C)E.11% B 3+√+1% F* > ?
F* > C).D+ $5 or ).D+ $5 3(%
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CONCEPT QUIZ
1. (an ou determine the forcein member 8* b ma$ing the
cut at section a4a2 87plain
our answer.
A% 5o, there are + un$nowns. &% @es, using Σ M* > ? .
(% @es, using Σ M8 > ? .
*% @es, using Σ M& > ? .
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CONCEPT QUIZ (continued)
'. If ou $now F8*, how will ou determine F8& 2
A% & ta$ing section b4b and using Σ M8 > ?
&% & ta$ing section b4b, and using Σ F= > ? and Σ F@ > ?
(% & ta$ing section a4a and using Σ M& > ?
*% & ta$ing section a4a and using Σ M* > ?
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IN CLASS TUTORIAL (GROUP PRO!LEM SOL"ING)
Given: oading on the
truss as shown.
Find: The force in
members &(, &8,
and 8F.
Plan:
a% Ta$e a cut through the members &(, &8, and 8F.
b% Anale the top section 3no support reactions%.
c% *raw the F&* of the top section.
d% Appl the e0uations of e0uilibrium such that e-er
e0uation ields answer to one un$nown.
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PRO!LEM (continued)
B → ΣF= > < B 1? C F&8 cos + ?
F&8 > '1.' $5 3T%
B Σ M8 > C ?
F(& > < $5 3T%
B Σ M& > C < 3D% C 1? 3+% C < 3+% C F8F 3+% > ?
F8F
> C '< $5 or '< $5 3(%
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ATTENTION QUIZ
1. As shown, a cut is madethrough members H, &H
and &( to determine the
forces in them. 9hich section
will ou choose for analsis
and wh2
A% Jight, fewer calculations.
&% eft, fewer calculations.
(% 8ither right or left, same
amount of wor$.
*% 5one of the abo-e, too
man un$nowns.
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ATTENTION QUIZ
'. 9hen determining the force in
member H in the pre-ious
0uestion, which one e0uation of
e0uilibrium is best to use2
A% Σ M > ?
&% Σ MH > ?
(% Σ M&
> ?
*% Σ M( > ?
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HOME#OR$ TUTORIAL
K1 34)?% :
The Home bridge truss is sub/ected to the loading shown. *etermine theforce in members *8, 8, and H, and state if the members are in
tension or compression.
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HOME#OR$ TUTORIAL (continued)
K' 34))% :
The roof truss supports the -ertical loading shown. *etermine the forcein members &(, (L, and L and state if these members are in tension
or compression
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HOME#OR$ TUTORIAL (continued)
K) 3
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