Chapter 4.a(Simple Truses)

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Engineering Mechanics :Engineering Mechanics :STATICSSTATICS

Lecture #08By,

Noraniah KassimUniversiti Tun Hussein Onn Malaysia

(UTHM),


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READING QUIZ

$ %ne of the assumptions used when anal"#in& a simple truss is thatthe members are 'oined to&ether b" ((((((((((

$) weldin& ) boltin& *) ri+etin&

,) smooth pins ) super &lue

!n the method of 'oints. t"picall" ((((((((( e/uations of

e/uilibrium are applied at e+er" 'ointA) two 0) three

1) four D) si2


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APPLICATIONS (Contn!"#$

Trusses are also used in a +ariet" ofstructures li5e cranes and the frames

of aircraft or space stations

6ow can we desi&n a li&ht wei&ht

structure that will meet load. safet".

and cost specifications3


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SIMPLE TRUSSES (S"%ton '$

A truss is a structure composed of slender members 'oined to&ether at

their end points

!f a truss. alon& with the imposed load. lies in a sin&le plane

7as shown at the top ri&ht). then it is called a planar truss

A simple truss is a planar truss which be&ins

with a a trian&ular element and can be e2panded b" addin& two members and a 'oint For these

trusses. the number of members 7M) and the

number of 'oints 7J) are related b" the e/uation

M 8 J 9 *


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SIMPLE TRUSSES (S"%ton '$


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ANALYSIS & DESIGN ASSUMPTIONS

hen desi&nin& both the member and the 'oints of a truss. first it is

necessar" to determine the forces in each truss member This is calledthe force anal"sis of a truss hen doin& this. two assumptions are

made:

$ All loads are applied at the 'oints The wei&ht of the truss

members is often ne&lected as the wei&ht is usuall" small as

compared to the forces supported b" the members The members are 'oined to&ether b" smooth pins This

assumption is satisfied in most practical cases where the 'oints

are formed b" boltin& or weldin&

ith these two assumptions. the members act astwo-force members The" are loaded in either

tension or compression %ften compressi+e

members are made thic5er to pre+ent buc5lin&


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THE METHOD OF JOINTS (S"%ton ')$

!n this method of sol+in& for the forces in truss members. the

e/uilibrium of a 'oint 7pin) is considered All forces actin& at the

'oint are shown in a F0D This includes all e2ternal forces

7includin& support reactions) as well as the forces actin& in the

members ;/uations of e/uilibrium 7∑ F 8 =) are

used to sol+e for the un5nown forces actin& at the 'oints


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THE METHOD OF JOINTS (S"%ton ')$


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STEP FOR ANALYSIS

$ !f the support reactions are not &i+en. draw a F0D of the

entire truss and determine all the support reactions usin& thee/uations of e/uilibrium

Draw the free-bod" dia&ram of a 'oint with one or two

un5nowns Assume that all un5nown member forces act in

tension 7pullin& the pin) unless "ou can determine b"

inspection that the forces are compression loads

* Appl" the scalar e/uations of e/uilibrium. ∑ F

8 =. to determine the un5nown7s) !f the answer is

positi+e. then the assumed direction 7tension) is correct.

otherwise it is in the opposite direction 7compression)

, ?epeat steps and * at each 'oint in succession until all the

re/uired forces are determined


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E*AMPLE

Given: @$ 8 == . @ 8 ==

Find: The forces in each member of

the truss

Plan: First anal"#e pin 0 and then pin 1

B → ∑ F 8 9 == 9 F01 sin ,C 9 7, ) F0A 8 =

F0A 8 $, 7T) and F01 8 9 * 71)

B → ∑ F

$,

FA1,

F0D of pin A

,

F01

==

0 ==

F0A

F0D of pin 0

,

*


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ZERO-FORCE MEMBERS (S"%ton '+$

!f a 'oint has onl" two non-collinear

members and there is no e2ternalload or support reaction at that 'oint.

then those two members are #ero-

force members !n this e2ample

members D;. 1D. AF. and A0 are#ero force members

>ou can easil" pro+e these results b"

appl"in& the e/uations of

e/uilibrium to 'oints D and A

Zero-force members can be

remo+ed 7as shown in the

fi&ure) when anal"#in& the

truss


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ZERO-FORCE MEMBERS (Contn!"#$

!f three members form a truss 'oint forwhich two of the members are collinear

and there is no e2ternal load or reaction at

that 'oint. then the third non-collinear

member is a #ero force member

A&ain. this can easil" be pro+en %ne

can also remo+e the #ero-force member.

as shown. on the left. for anal"#in& the

truss further

@lease note that #ero-force membersare used to increase stabilit" and

ri&idit" of the truss. and to pro+ide

support for +arious different loadin&

conditions


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CONCEPT QUIZ

$ Truss A01 is chan&ed b" decreasin& its

hei&ht from 6 to =G 6 idth and load@ are 5ept the same hich one of the

followin& statements is true for the re+ised

truss as compared to the ori&inal truss3

A) Force in all its members ha+e decreased

0) Force in all its members ha+e increased

1) Force in all its members ha+e remained

the sameD) one of the abo+e

6

@

A

01


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CONCEPT QUIZ (continued)

For this truss. determine the number of #ero-force

members

$) = ) $ *)

,) * ) ,

F F

F


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IN CLASS TUTORIAL (GROUP PROBLEM SOLING$

Given: @$ 8 ,= and

@ 8 $==

Find: Determine the force in

all the truss members

7do not for&et to

mention whether the"

are in T or 1)

Plan:

a) 1hec5 if there are an" #ero-force members

b) Draw F0Ds of pins D and 0. and then appl" ;of; at those pins to

sol+e for the un5nowns

Solution:

Members A0 and A1 are #ero-force members


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GROUP PROBLEM SOLING (continued)

Anal"#in& pin D:

↑ B ∑F> 8 9 $== 9 7 $*) FD0 8 =

FD0 8 9 H= 71)

→ B ∑ F


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ATTENTION QUIZ

$ sin& this F0D. "ou find that F01 8 9 ==

Member 01 must be in ((((((((((

A) tension

0) compression

1) cannot be determined For the same ma&nitude of force to be

carried. truss members in compression

are &enerall" made ((((((( as compared

to members in tension

A) thic5er

0) thinner

1) the same si#e

F0D

F01

0

0>


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HOMEOR. TUTORIAL

K$ 7H-) :

Determine the force in each member of the truss and state if themembers are in tension or compression Set @$ 8 I5. @ 8 $=5


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HOMEOR. TUTORIAL (continued)

K 7H-*) :

The truss. used to support a balcon". is sub'ected to the loadin& shownAppro2imate each 'oint as a pin and determine the force in each

member State whether the members are in tension or compression

Set @$ 8 H== 5. @ 8 ,== 5


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HOMEOR. TUTORIAL (continued)

K* 7H-H) :

Determine the force in each member of the truss and state if themembers are in tension or compression Set @$ 8 ,=5. @ 8 =5


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Chapter 4.a(Simple Truses)