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)

p

ax

ayby

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.