MRS SITI KAMARIAH BINTI MD SA’AT SCHOOL OF BIOPROCESS ENGINEERING

ANALYSIS OF STATICALLY

DETERMINATE TRUSSES

MRS SITI KAMARIAH BINTI MD SA’ATSCHOOL OF BIOPROCESS ENGINEERING

Topic Outcomes

Common Types of Trusses

• Truss: composed of slender members joined together at their end points

• Connections: bolt or weld the ends of the members to a common plate called gusset

• Planar trusses is often used to support roof or bridges


• Roof Trusseso Used as part of an industrial building frameo Roof load is transmitted to

the truss at the joints by means of a series of purlins

o To keep the frame rigid, knee braces are sometimes used at the supporting column


• Roof Trusses


• Bridge Trusseso Load on the deck is transmitted to the stringers floor beams

joints of supporting side trusso Top & bottom cords of these side trusses are connected by top

& bottom lateral bracing resisting lateral forceso For a long span truss, a roller is used at one end for thermal

expansion


• Bridge Trusses


• Assumptions for Designo Members are joined together by smooth pinso All loadings are applied at the joints

• Due to the 2 assumptions, each truss member acts as an axial force member (2-force member)

Classification of Coplanar Trusses

• Three types: Simple , Compound or Complex Truss• Simple Truss

o The simplest framework that is rigid or stable is a triangle


• Compound Truss: connecting 2 or more simple trusseso Type 1: Connected by a common joint & baro Type 2: Joined by 3 barso Type 3: Main + secondary


• Complex Trusso A complex truss is one that cannot be classified as being either

simple or compound

Trusses: Determinacy &

Stability• Determinacyo Comparing no. of unknowns and no. of equilibrium eqnso No. of unknowns = no. of members (member forces) b+

no. of external support reactions ro Each joint provides 2 equilibrium eqns

For j joints, there are 2j eqns

0 and 0 yx FF

unstable 2

tablestable/uns ateindetermin statically 2

edeterminat statically 2

jrb

jrb

jrb


Stability• Stabilityo A truss can still be unstable even if it is statically determinate

or statically indeterminate o Stability has to be determined through inspection or by force

analysis

unstable 2

tablestable/uns ateindetermin statically 2

edeterminat statically 2

jrb

jrb

jrb

All stable structures should have ONE unique solution! All forces can be determined uniquely!


Stability• Stabilityo External Stability

• A structure is externally unstable if all of its reactions are concurrent or parallel


Stabilityo Internal Stability• The internal stability can be checked by careful inspection of the

arrangement of its members• A simple truss will always be internally stable• If a truss is constructed so that it does not hold its joints in a fixed

position, it will be unstable

P

L L L

L

2P/3 P/3


Stabilityo Internal Stability• To determine the internal stability of a compound truss, it is

necessary to identify the way in which the simple truss are connected together

• The truss shown is unstable since the inner simple truss ABC is connected to DEF using 3 bars which are concurrent at point O


Stabilityo Internal Stability• For complex truss, it may not be possible to determine its stablility• The instability of any form of truss may also be noticed by using a

computer to solve the 2j simultaneous eqns for the joints of the truss

• If inconsistent results are obtained, the truss is unstable

Example 3.1

Classify each of the trusses as stable, unstable, statically determinate or statically indeterminate. The trusses are subjected to arbitrary external loadings that are assumed to be known & can act anywhere on the trusses.

Externally stableReactions are not concurrent or

parallelb = 19, r = 3, j = 11 b + r =2j = 22

Truss is statically determinateBy inspection, the truss is internally stable

Solution

© 2009 Pearson Education South Asia Pte Ltd

Structural Analysis 7th EditionChapter 3: Analysis of Statically Determinate Trusses

Externally stableb = 15, r = 4, j = 9b + r = 19 >2j

Truss is statically indeterminateBy inspection, the truss is internally stable

Solution



Externally stableb = 9, r = 3, j = 6b + r = 12 = 2j

Truss is statically determinateBy inspection, the truss is internally stable

Solution



Externally stableb = 12, r = 3, j = 8b + r = 15 < 2j The truss is internally unstable

The Method of Joints

• Satisfying the equilibrium eqns for the forces exerted on the pin at each joint of the truss

• Applications of eqns yields 2 algebraic eqns that can be solved for the 2 unknowns

Example 3.2Determine the force in each member of the roof truss as shown. State whether the members are in tension or compression. The reactions at the supports are given as shown.

Zero-Force Members

• Analysis can be simplified if zero-force members can be identified first

• These zero-force members may be necessary for the stability of the truss during construction & to provide support if the applied loading is changed

• The zero-force members of a truss can generally be determined by inspection of the joints & they occur in 2 cases.

Zero-Force Members

• Case 1o The 2 members at joint C are connected together at a right

angle & there is no external load on the jointo The free-body diagram of joint C indicates that the force in each

member must be zero in order to maintain equilibriumo Any other zero-force members?

Zero-Force Members

• Case 2o Zero-force members also occur at joints having a geometry as

joint Do Any other zero-force member?

Example 3.4Indicate all the members of the truss that have zero force.

The Method of Sections

• If the force in GC is to be determined, section aa will be appropriate

• Also, the member forces acting on one part of the truss are equal but opposite

• The 3 unknown member forces, FBC, FGC & FGF can be obtained by applying the 3 equilibrium eqns

Example 3.5Determine the force in members CF and GC of the roof truss. State whether the members are in tension or compression. The reactions at the supports have been calculated.

Reflection: What Have You Learnt?

• Truss structure• Determinacy and stability• Solution• Zero-force member

EXERCISE1. 3-22. 3-83. 3-94. 3-105. 3-116. 3-187. 3-248. 3-419. 3-42Discuss in tutorial class

QUIZ 1

THANK YOU

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MRS SITI KAMARIAH BINTI MD SA’AT SCHOOL OF BIOPROCESS ENGINEERING