Chapter 4.b(Method of Section)

8/16/2019 Chapter 4.b(Method of Section)

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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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Chapter 4.b(Method of Section)

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