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6.3 Assumptions for Truss Analysis

The following assumptions are made in order to simplify the analysis of trusses:

I. Truss members are connected together with frictionless pins. (Pin connections are used for very few trusses erected today, and no pins are frictionless. A heavy bolted or welded joint is a far cry from a frictionless pin. )

2. Truss members are straight. ( If they were not straight, the axial forces would cause them to have bending moments).

3. The deformations of a truss under load, caused by the changes in lengths of the individual members, are not of sufficient magnitude to cause appreciable changes in the overall shape and dimensions of the truss. Special consideration may have to be given to some very long and flexible trusses.

4. Members are so arranged that the loads and reactions are applied only at the truss joints.

Examination of roof and bridge trusses will prove this last statement to be generally true, in buildings with roof trusses the beams, columns, and bracing frame directly into the truss joints. Roof loads are transferred to trusses by horizontal beams, called pudins, which span the distance between the trusses. The roof is supported directly by the purlins or it is supported by rafters, or

subpurlins, which run parallel to the trusses and are supported by the purlins. The purling are placed at the truss joints unless the top-chord panel lengths become case it is sometimes economical to place purlins in between the joints

exceptionally long, in which although some bending will be developed in the top chords. ( Some types of roofing, such as corrugated steel, gypsum slabs, and others may he laid directly on the purling. The purlins then have to be spaced at intermediate points along the top chord so as to provide a proper span for the roofing they directly supports. )

6.4 Effect of Assumptions

The effect of the foregoing assumptions is to produce an ideal truss. Whose members have only axial forces. A member with axial force only is subject to a push or pull with no bending present. (Even if all of the assumptions were perfectly true, there would be some bending in a

member caused by its own weight. )

Forces obtained on the basis of these simplifying assumptions are very satisfactory in most

cases and are referred to as primary forces. Structures are sometimes ~alysed without the aid of

some or all of these assumptions. Forces cauTed by conditions not considered in the primary force

analysis are said to be secondary forces.

6．5 Truss Analysis

An indispensable part of truss analysis，a8 in beam analysis， isthesepamtion 0f the tmss into two part8 with an imaginary section．The part of the truss on one 8ideof the section is removed and studied independendy．The loads applied to this free body include the axial f10rces 0f the members that have been cut by the sectio’n and any loads and reaction8 that may be applied

externally．

Application of the equations of statics to isolated free bodies enable8 one to determine the forces in the cut members if the free bodies are carefully selected 80 thatthe 8ection8 do not Dass through too many members whose forces are unknown．There are only three equations of statics。and no more than three unknowns may be determinedfromany one section．

After he or she has analyzed a few trusses，thestudentwillhavelittledifficuIty in m08t case in selecting satisfactory locations for the sections．The studenti8notencouraged t0 remembe specific sections for specific trusses，althoughheorshewillprobablyunconsciously faU int0 suc a habit as time goes by． At this stage the student needs to consider each case individuallv withou reference to other，similar trusses．

It is convenient to work with horizontal and veRicalcomponentsinthecomputation of ferces

oftrussmembers,as in the c。mputati。n。f reacti。ns．The∑日=0 and∑V=Oequations。 statics are generally written on the basis of a pair of axes that are herizontal and venical． Because the forces in truss members are determined successively across a truss，much time will be 8aved if the vertical and horizontal components of forces in inclined members are recorded for u8e in applying the equations to other members．The use of components i8 cleady illu8trated in the example problems of sections that lollow．

6．6 Arrow Convention

The sign COnvrention for ten8ile and COmpres8ive forces( and一re8pectively)has already been mentioned·Arrows are also used throughout the text torepresentthecharacter 0f forces．The armw8 indicate what members are doing to resist the axial forces applied t0tllem by tlle remainder

0f the truss·For example，if a truss is compressing a certain member from each end(- 一 -)。 the member will push back against the compressive forces．convention i8 ued for members in compression．

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