Application of the trusses1

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Structural members commonly used are I-sections, channels, angles, bars, andspecial shapes which are fastened together at their ends by welding, rivetedconnections, or large bolts or pins.

FIG 8.1. shows a typicalframing system for a roofsupported by planetrusses. In this case, twoor more trusses areconnected at their joints bybeams, termed purlins, toform a three-dimensionalframework. The roof isattached to the purlins,which transmit the roofload (weight of the roofand any other load due tosnow, wind, etc.) as wellas their own weight to thesupporting trusses at thejoints.

FIG. 1.1. Roof Trusses. Plum High School. Large Bow Truss and Supporting Truss

Assumptions for Analysis of Trusses1

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The analysis of trusses is usually based on the following simplifying assumptions:

1) All members are linear and connectedonly at their ends/nodes by frictionlesshinges in plane trusses (pin-connected)and by frictionless ball-and-socket jointsin space trusses,

2) All loads and support reactions areapplied only at the joints,

3) The weight of truss members is usuallyneglected,

4) Secondary stress is neglected at thejoints,

5) The centroidal axis of each membercoincides with the line connecting thecenters of the adjacent joints.

The reason for making theseassumptions is to obtain an IDEALTRUSS, whose members aresubjected only to axial forces!!!

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Because of these assumptions, each trussmember will act as a two-force member,and therefore the force acting at each end ofthe member will be directed along the axisof the member.

If the force tends to elongate the member, itis a tensile force (T), if it tends to shortenthe member, it is compressive force (C).

In general, the members of a truss are slender and can support little lateralload. Therefore, all loads, must be applied to the various joints, and NOT tothe members themselves.

Assumptions for Analysis of Trusses

Hence, the members of a real truss, besideselongating or shortening, also tend to bend. Bendingstresses, however, are often small in comparison tothose resulting from tension or compression. In awell-designed truss, these bending stresses (calledsecondary stresses) are less than 20% of thetensile or compressive stresses and are usuallyignored in preliminary design.

Members under Compression1

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BUCKLING: Elastic (Euler) buckling Inelastic buckling

BUCKLING MODES: Overall buckling

- Flexural buckling- Torsional buckling- Torsional-flexural buckling

Local buckling

ELASTIC (EULER) BUCKLING1

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EFFECTIVE LENGTH FACTORS:

Different end conditions give different lengths for equivalent half-sine wave

Compression members:

Moment of inertia Radius of gyration Effective length Slenderness ratio (L/r)