Truss zero force members examples

Class Today

• Print notes and examples

• Trusses

– Definition

– Working with Trusses

– Truss Analysis

• Example Problems

• Group Work Time

http://www.mst.edu/~ide50-3/printable_notes/13_Trusses.pdf
http://www.mst.edu/~ide50-3/printable_notes/13_Trusses_examples.pdf
…these are cool trusses

Norman Foster Sainsbury Centre

Santiago Calatrava Turning Torso

Shigeru Ban Japanese Pavilion

KMR

… be inspired!

3

Renzo Piano Kansai International Airport

Rem Koolhaas The Shenzhen Stock Exchange

KMR

So what are trusses?

http://bridgehunter.com/story/1109/

http://www.americanpoleandtimber.com/img/wood-timber-trusses-park-BIG.jpg

http://www.hndszj.com/eng/uploads/201008101822313.jpg

Trusses are … • Structures designed to support loads:

− Will transmit loads through the joints of the structure

− Will ultimately transmit loads to the foundation

• Cost effective in design because:

− Weight is minimized (weight of members is typically

light compared to loads carried, so it is often

neglected)

− Strength to weight ratio is maximized

Image copyright 2013, Pearson Education, publishing as Prentice Hall

Working with Trusses: Assumptions

• All loads are applied / transmitted at joints

• All members are joined by pin connections

• Consist entirely of two-force members

(review section 5.4)

• Can contain zero-force members

Image copyright 2013, Pearson Education, publishing as Prentice Hall

Zero-force Members

What are zero-force members?

• Structural members that carry no force

Why do we use them?

• Used to provide stability

– During construction

– If (intermittent) loading of the truss changes

• Shortens chord length and increases

buckling capacity of compression members

7

Zero-force Members: Case 1

Zero-force Members: Case 2

10 http://www.tatasteelconstruction.com/static_files/Images/Construction/Reference/

architectural%20studio/elements/Structural%20steel%20trusses/j2.jpg

http://www.tboake.com/SSEF1/rose2.shtml

http://sluggyjunx.com/rr/georgetown_branch/gallery/04_16_0

3_gb_canal_bridges/04_16_03-gb_canal_br-34.jpg

Gusset plate

pin

Joint Connections

Welded

connection http://www.tatasteelconstruction.com/en/reference/teaching- resources/architectural-teaching-resource/elements/connections/connections-

in-trusses

11

http://civildigital.com/wp-content/uploads/2013/09/Rocker-Type-Bearing.jpg

http://www.dot.state.mn.us/historicbridges/bridge-pictures.html

Rocker

support Truss

Supports

Roller supports

Working with Trusses: So what is the objective of an analysis?

• To determine

the support

reactions.

• To determine

the forces

supported by

individual

members of the

truss. 12

13

FBDs of each

pin and each

member.

(exploded view

showing tension

and compression

forces in a truss)

Image copyright 2013, Pearson Education, publishing as Prentice Hall

FBD of

whole

truss

14

Working with Trusses: Analyzing Structural Forces in Truss Members

• Truss members will carry either

– axial tension (T) forces or

– axial compression (C) forces

• There are two methods of evaluating

trusses.

– Method of Joints (static equilibrium of a point)

– Method of Sections (static equilibrium of a

rigid body)

15

Truss Analysis: Method of Joints

Evaluate an individual joint or pin connection.

• Treat each joint as a 2D particle in equilibrium

• Can have a maximum of two unknowns

• Can sum forces in x & y direction

16

Truss Analysis: Method of Sections

Evaluate a section including multiple joints.

• Treat as 2D rigid body in equilibrium

• Must cut through structural members to evaluate the force.

• Maximum of three unknowns (to solve everything)

• Can sum forces in x & y direction

• Can sum moments

17

Method of Approach for Truss

Problems 1. Solve for support reactions if needed.

2. Mark all members on the truss that need to be

solved.

3. Pick the joint / section for which you will draw your

FBD. Make sure you have the appropriate number

of unknowns.

4. ALWAYS assume unknown forces to be in

TENSION.

5. Be sure to designate answers as (T) or (C)

6. In subsequent FBDs, draw known forces in the

direction they actually act.

18

Trusses Free Body Diagram Practice

Draw the correct FBD to

solve for the forces in

members CD, CJ and IJ.

19

Trusses: More FBD Practice Assuming the necessary support

reactions have already been

found, draw the correct FBD to

solve for the forces in members

DE, JM and JH.

20

Trusses: More FBD Practice

Assuming the necessary support reactions have already been

found, draw the correct FBD to solve for the forces in members CD

and DE.

Can trusses have curved

members?

• Two-force members do not have to be

straight…

• The ideal answer is NO, but …

• Yes, if the members are sufficiently stiff

so that moments developed at the

connections are negligible.

• Curved members are not as cost-

effective. 21