chapter 3 trusses - موقع المهندس حماده شعبان 3 final2 (2).pdfb + r > 2 j...
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July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
Chapter 3
Trusses
.
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
Trusses
(members) *
(joints) (forces) (joints)
(member) (tension) (compression).
(compression) (tension) *
(members) (joint method) (member)
(section method)
*
.
(joint) (tension) (member) *
(compression) (joint).
.
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
Analysis of Trusses
considering:
b = number of members.
r = number of reactions.
j = number of joints.
:tabilityS
:tructure will be unstable in the following casesS
1) b + r < 2 j
2) b + r 2 j (but all reactions are parallel)
3) b + r 2 j (but all reactions are concurrent)
: of stability) providedeterminacy (D
b + r = 2 j statically determinate
b + r > 2 j statically indeterminate
degree of indeterminacy = b + r 2 j
( )
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
members (zero) truss *
(. )
(only 2 members) (joint) *
(.A, D) ((zero member
(only 3 members) (joint) *
(. C, D) ((zero member ((member
zero members
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
.((members
.((support reactions 1
(. )
(only 2 members) (joint) 2
. 3
(joints) 3 ,2 4
2 - members)) .
.((members ( 4) 5
(tension) ((member 6
(compression) .
. 7
joint method
.
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
((members
. ( truss)
.((support reactions 1
( )
2
members) .)
( ) 3
4
.
((members - 2 5
.
((members 6
.
( section method) ( joint method) 7
. ((members
ethodmection s
, ,
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
a)
statically indeterminate to the 4th degree
b)
statically determinate.
c)
statically indeterminate to the first degree
d)
the left panel is a collapsible component
(6)
parallel are reactions all satisfied
d
be not can F
< r b
j
r
b
r b
j
r
b
r b
j
r
b
r b
j
r
b
x 0
11
6
2
9
9 2 19
9
4
15
8 2 16
8
3
13
10 2 24
10
4
20
unstable
3-2 classify each of the following trusses as statically determinate, statically indeterminate, or unstable.
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
a)
stable, statically determinate.
b)
stable, statically indeterminate to 1.
c)
stable, statically indeterminate to 1.
d)
(r + b) 2 j = 1
stable, statically indeterminate to 1.
6
10
3
12)(
6
9
4
12)(
6
9
4
2)(
8
13
3
j
b
r
jbr
j
b
r
jbr
j
b
r
jbr
j
b
r
3-3 classify each of the following trusses as statically determinate, statically
indeterminate, or unstable. If indeterminate, state its degree.
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :
Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :
neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .
Gy
Gx FGF = 20 kN
FAG = 15 kN Ax
FAB = 10 kN
20 kN
18 kN
7.5kN
FEF
FBC = FCD
15 kN
FCD
FED = 8.33 kN
5 kN
FCD = 6.67 kN
5 kN
10 kN 6.67 kN
FBF
G
A C
F
B
D
FBE = 4.17 kN
FAf = 18 kN 15 kN FAF = 18 kN
;
members *
( C) ( T)
.
. ( , ) *
joint F:
3-8 Determine the force in each member of the roof truss. State if the members
are in tension or compression. Assume all members are pin connected.
56.3o
56.3o
http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/
July 2011
SMS
Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Stre