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Static and Strength of MaterialsChapter 4-Structures-Part II
Mehdi Tale Masouleh
November 8, 2013
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
p
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
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ax
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Finally, I corrected it
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Québec BridgeVive le Québec libre
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Québec Bridge
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Plane TrussesTruss connections and supports
For connection:1 Welded2 Riveted3 we assume all as pin joints4 Pass through the same
pointFor large trusses at one ofthe supports:
1 A roller2 A rocker3 Some kind of slip joint4 Why!? (This could be
your exam question)
Like Quebecois, Never Give Up!3 times collapsedQuebec Bridge
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of Joints
1 A truss can be regarded asa group of pinestwo-forces members
Follow theses steps1 If the support reactions are not
given, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
ax
ayby
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
ax
ayby
∑fx = 0∑fy = 0∑m = 0
}Findaxayby
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
A
B
F
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
y
R1
AF
ABTension
Compression
x
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
R1
AF
AB
∑fx = 0
∑fy = 0
θ
AF = r1cos θ
AB = ABsin θ
y
x
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
A
B
F
C
D
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
ay
CD
CB
∑fx = 0
∑fy = 0
θc
CD =ay
cos θc
CB = ax + CD sin θc
y
xax
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
A
B
F
C
D
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
A
B
F
C
D
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
A
B
F
C
D
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesMethod of JointsFollow theses steps
1 If the support reactions are notgiven, draw a FBD of theentire truss
2 From the above FBD determineall the supports reactions usingthe equations equilibrium.
3 Draw the FBD of a joint whereat least one known load existsand where not more tan twounknowns force are present.
4 Write the two equilibriumconditions.
5 Repeat step 2 & 3 for eachjoint.
p
A
B
F
C
D
E
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses-Method of JointsZero-forces Members
1 Zero-forces members can beremoved from the analysis
2 First case:The joint has only twonon-collinear membersThere is no external load orsupport reaction at that joint
3 Second case:Three members form a truss jointTwo of the members are collinearThere is no external load orsupport reaction at that jointThe third non-collinear memberis a zero force member
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses-Method of JointsZero-forces Members
1 Zero-forces members can beremoved from the analysis
2 First case:The joint has only twonon-collinear membersThere is no external load orsupport reaction at that joint
3 Second case:Three members form a truss jointTwo of the members are collinearThere is no external load orsupport reaction at that jointThe third non-collinear memberis a zero force member
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses-Method of JointsZero-forces Members
1 Zero-forces members can beremoved from the analysis
2 First case:The joint has only twonon-collinear membersThere is no external load orsupport reaction at that joint
3 Second case:Three members form a truss jointTwo of the members are collinearThere is no external load orsupport reaction at that jointThe third non-collinear memberis a zero force member
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses-Method of JointsZero-forces Members
1 Zero-forces members can beremoved from the analysis
2 First case:The joint has only twonon-collinear membersThere is no external load orsupport reaction at that joint
3 Second case:Three members form a truss jointTwo of the members are collinearThere is no external load orsupport reaction at that jointThe third non-collinear memberis a zero force member
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses-Method of JointsZero-forces Members
1 Zero-forces members can beremoved from the analysis
2 First case:The joint has only twonon-collinear membersThere is no external load orsupport reaction at that joint
3 Second case:Three members form a truss jointTwo of the members are collinearThere is no external load orsupport reaction at that jointThe third non-collinear memberis a zero force member
FAE = FACFAB = FAD
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of TrussesInternal and external redundancy,(For your exam as true or false)
A statically indetermine truss.1 External2 Internal
m + 3 = 2jNecessary condition (Quiz)If m + 3 > 2j , more members thanindependent equations, staticallyindeterminate internally withredundant members.if m + 3 < 2j , deficiency of internalmembers, the truss is unstable andwill collapse under load.
p
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses
Internal and external redundancy, Some examples
m = 19, j = 11, then22 = 22. The truss isstatically determine bothexternally and internally.m = 19j = 6, then 12 = 12.The truss is staticallydetermine both externallyand internally.
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses
Internal and external redundancy, Some examples
m = 19, j = 11, then22 = 22. The truss isstatically determine bothexternally and internally.m = 19j = 6, then 12 = 12.The truss is staticallydetermine both externallyand internally.
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses, Methods of Sections
Illustration of the method
First the external FBDAssume an imaginary sectionDivide it into two partsDraw the FBD of each partWrite the equilibrium conditions foreach part
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses, Methods of Sections
Illustration of the method
First the external FBDAssume an imaginary sectionDivide it into two partsDraw the FBD of each partWrite the equilibrium conditions foreach part
Ay
Dx
Dy
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses, Methods of Sections
Illustration of the method
First the external FBDAssume an imaginary sectionDivide it into two partsDraw the FBD of each partWrite the equilibrium conditions foreach part
A
B CD
E F
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses, Methods of Sections
Illustration of the method
First the external FBDAssume an imaginary sectionDivide it into two partsDraw the FBD of each partWrite the equilibrium conditions foreach part
A
B CD
E F
I II
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses, Methods of Sections
Illustration of the method
First the external FBDAssume an imaginary sectionDivide it into two partsDraw the FBD of each partWrite the equilibrium conditions foreach part
AC
D
E FEF
BE
BC
EF
BE
BC
Dx
Dy
III
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses, Methods of Sections
Illustration of the method
First the external FBDAssume an imaginary sectionDivide it into two partsDraw the FBD of each partWrite the equilibrium conditions foreach part
AC
D
E FEF
BE
BC
EF
BE
BC
Dx
Dy
III
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses, Method of Joints
Some examples
Find CG and CF .m + 3 = 2j!The order of joint: A,B,Gand CAt joint G the coordinateframe is along AF
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Trusses, Method of Joints
Some examples
Ax = 0Find the zero force member
Statics and Strength of Materials-Tale Masouleh-Part IINovember 8, 2013
Analysis of Space Trusses, Not Subject of Exam.Some examples
A space truss is thethree-dimensionalcounterpart of the planetruss.Statically balanced spacetruss
1 m + 6 = 3j necessary butnot sufficient! Why.
2 m + 6 = 3j staticallyindeterminate internallywith redundant members.
3 m + 6 < 3j Deficiency ofinternal members, subjectto collapse.