Trusses

Trusses

also known as pin-jointed frames

made up of slender members with pin-jointed ends

carry loads at joints

members carry only tension or compression

used for supporting roofs and bridge decks

Plane truss:- all members lie in one plane

Space truss:- members lie in different planes

3/7/2013 10:02 AM

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Examples of plane and space trusses

Perfect, Redundant and Deficient Trusses

Triangular truss has three joints and three members

Each new joint is created by adding two extra members and in this way a stable, perfect configuration is maintained

Perfect truss:- has just enough members to resist loads without experiencing excessive

deformation of its shape

Deficient truss:- has less members than those required for a perfect truss.

-cannot retain its shape when loading is applied

Redundant truss:- has more members than those required in a perfect truss

Types of Trusses

Selection of truss type depends on intended use

Pratt, Howe, Warren, K trusses used to support bridge decks & large-span roof systems

Fink truss supports gable-ended roofs

Why do the members slope in different directions?

Actual truss

Determinacy

Basic triangle of truss is statically determinate

Truss built up by addition of 2 members and 1 joint

i.e. number of new members = 2 x number of new joints

Relationship expressed as

For a truss which is statically determinate internally

Statically indeterminate

Unstable

e.g. Test the statical determinacy of the trusses below

NB Sometimes equation satisfied but truss is a mechanism or statically indeterminate

e.g.

m = 9 , j = 6 , 2j 3 = 9 = m

BUT truss is unstable

Analysis of Trusses

Assumptions made:

Member ends are pin-connected

Loads act at the joint

Member cross-sections are uniform

Member self-weight is negligible

Remember: truss members carry only axial loads

Methods of Analysis- Method of Joints

At each joint forces in members and loads act as a concurrent system of forces (forces act at same point) so two equations of equilibrium can be formed

Begin by selecting a joint with only two unknowns and solve for these using equilibrium equations

Move onto the next joint with only two unknown forces and in this way work from joint to joint in the truss until all member forces have been determined

e.g. Find all the forces in the members of the truss shown below. Tabulate the results.

Etc.

Finally

where

Methods of Analysis- Method of Sections

First determine reactions

Draw a straight line which cuts through at most three members whose internal forces are unknown

The two separate portions of the truss should be in equilibrium and constitute a non-concurrent system of forces

Where to use method of sections:

(i) in large trusses where only a few member forces are needed

(ii) where method of joints fails

e.g. Determine the forces in members FH, HG and GI. All triangles are equilaterals of side 4m.