SPACE TRUSSES BASICS AND TUTORIALS

A space truss is the three-dimensional counterpart of the plane truss described in the three previous articles. The idealized space truss consists of rigid links connected at their ends by ball-and-socket joints.

Whereas a triangle of pin-connected bars forms the basic non collapsible unit for the plane truss, a space truss, on the other hand, requires six bars joined at their ends to form the edges of a tetrahedron as the basic noncollapsible unit.

In Fig. 4/13a the two bars AD and BD joined at D require a third support CD to keep the triangle ADB from rotating about AB. In Fig. 4/13b the supporting base is replaced by three more bars AB, BC, and AC to form a tetrahedron not dependent on the foundation for its own rigidity.

We may form a new rigid unit to extend the structure with three additional concurrent bars whose ends are attached to three fixed joints on the existing structure. Thus, in Fig. 4/13c the bars AF, BF, and CF are attached to the foundation and therefore fix point F in space.

Likewise point H is fixed in space by the bars AH, DH, and CH. The three additional bars CG, FG, and HG are attached to the three fixed points C, F, and H and therefore fix G in space. The fixed point E is similarly created.

We see now that the structure is entirely rigid. The two applied loads shown will result in forces in all of the members. A space truss formed in this way is called a simple space truss.

Ideally there must be point support, such as that given by a balland- socket joint, at the connections of a space truss to prevent bending in the members. As in riveted and welded connections for plane trusses, if the centerlines of joined members intersect at a point, we can justify the assumption of two-force members under simple tension and compression.

METHODS OF JOINT TRUSS MEMBERS ANALYSIS BASICS AND CIVIL ENGINEERING TUTORIALS

METHODS OF JOINT TRUSS MEMBERS ANALYSIS BASIC INFORMATION
How To Do The Methods Of Joint Truss Members Analysis?


This method for finding the forces in the members of a truss consists of satisfying the conditions of equilibrium for the forces acting on the connecting pin of each joint. The method therefore deals with the equilibrium of concurrent forces, and only two independent equilibrium equations are involved.

We begin the analysis with any joint where at least one known load exists and where not more than two unknown forces are present. The solution may be started with the pin at the left end. Its free-body diagram is shown in Fig. 4/7.

With the joints indicated by letters, we usually designate the force in each member by the two letters defining the ends of the member. The proper directions of the forces should be evident by inspection for this simple case.

The free-body diagrams of portions of members AF and AB are also shown to clearly indicate the mechanism of the action and reaction. The member AB actually makes contact on the left side of the pin, although the force AB is drawn from the right side and is shown acting away from the pin.

Thus, if we consistently draw the force arrows on the same side of the pin as the member, then tension (such as AB) will always be indicated by an arrow away from the pin, and compression (such as AF) will always be indicated by an arrow toward the pin.

The magnitude of AF is obtained from the equation ΣFy = 0 and AB is then found from ΣFx = 0. Joint F may be analyzed next, since it now contains only two unknowns, EF and BF. Proceeding to the next joint having no more than two unknowns, we subsequently analyze joints B, C, E, and D in that order.

Figure 4/8 shows the free-body diagram of each joint and its corresponding force polygon, which represents graphically the two equilibrium conditions ΣFx = 0 and ΣFy = 0. The numbers indicate the order in which the joints are analyzed.

We note that, when joint D is finally reached, the computed reaction R2 must be in equilibrium with the forces in members CD and ED, which were determined previously from the two neighboring joints. This requirement provides a check on the correctness of our work.

Note that isolation of joint C shows that the force in CE is zero when the equation ΣFy = 0 is applied. The force in this member would not be zero, of course, if an external vertical load were applied at C.

It is often convenient to indicate the tension T and compression C of the various members directly on the original truss diagram by drawing arrows away from the pins for tension and toward the pins for compression.

This designation is illustrated at the bottom of Fig. 4/8. Sometimes we cannot initially assign the correct direction of one or both of the unknown forces acting on a given pin. If so, we may make an arbitrary assignment. A negative computed force value indicates that the initially assumed direction is incorrect.

SPACE TRUSSES BASICS AND CIVIL ENGINEERING TUTORIALS

SPACE TRUSSES BASIC INFORMATION
What Are Space Trusses?

A space truss is the three-dimensional counterpart of the plane truss described in the three previous articles. The idealized space truss consists of rigid links connected at their ends by ball-and-socket joints.

Whereas a triangle of pin-connected bars forms the basic noncollapsible unit for the plane truss, a space truss, on the other hand, requires six bars joined at their ends to form the edges of a tetrahedron as the basic noncollapsible unit.

In Fig. 4/13a the two bars AD and BD joined at D require a third support CD to keep the triangle ADB from rotating about AB. In Fig. 4/13b the supporting base is replaced by three more bars AB, BC, and AC to form a tetrahedron not dependent on the foundation for its own rigidity.

We may form a new rigid unit to extend the structure with three additional concurrent bars whose ends are attached to three fixed joints on the existing structure. Thus, in Fig. 4/13c the bars AF, BF, and CF are attached to the foundation and therefore fix point F in space.

Likewise point H is fixed in space by the bars AH, DH, and CH. The three additional bars CG, FG, and HG are attached to the three fixed points C, F, and H and therefore fix G in space. The fixed point E is similarly created.

We see now that the structure is entirely rigid. The two applied loads shown will result in forces in all of the members. A space truss formed in this way is called a simple space truss.

Ideally there must be point support, such as that given by a balland- socket joint, at the connections of a space truss to prevent bending in the members.

As in riveted and welded connections for plane trusses, if the center lines of joined members intersect at a point, we\ can justify the assumption of two-force members under simple tension and compression.

SIMPLE TRUSSES CIVIL ENGINEERING TUTORIALS

SIMPLE TRUSSES BASIC INFORMATION
What Are Simple Trusses?


The basic element of a plane truss is the triangle. Three bars joined by pins at their ends, Fig. 4/3a, constitute a rigid frame. The term rigid is used to mean noncollapsible and also to mean that deformation of the members due to induced internal strains is negligible.

On the other hand, four or more bars pin-jointed to form a polygon of as many sides constitute a nonrigid frame. We can make the nonrigid frame in Fig. 4/3b rigid, or stable, by adding a diagonal bar joining A and D or B and C and thereby forming two triangles.

We can extend the structure by adding additional units of two end-connected bars, such as DE and CE or AF and DF, Fig. 4/3c, which are pinned to two fixed joints. In this way the entire structure will remain rigid.

Structures built from a basic triangle in the manner described are known as simple trusses. When more members are present than are needed to prevent collapse, the truss is statically indeterminate.

A statically indeterminate truss cannot be analyzed by the equations of equilibrium alone. Additional members or supports which are not necessary for maintaining the equilibrium configuration are called redundant.

To design a truss we must first determine the forces in the various members and then select appropriate sizes and structural shapes to withstand the forces. Several assumptions are made in the force analysis of simple trusses.

First, we assume all members to be two-force members. A two-force member is one in equilibrium under the action of two forces only, as defined in general terms with Fig. 3/4 in Art. 3/3.

Each member of a truss is normally a straight link joining the two points of application of force. The two forces are applied at the ends of the member and are necessarily equal, opposite, and collinear for equilibrium.

The member may be in tension or compression, as shown in Fig. 4/4. When we represent the equilibrium of a portion of a two-force member, the tension T or compression C acting on the cut section is the same for all sections.

We assume here that the weight of the member is small compared with the force it supports. If it is not, or if we must account for the small effect of the weight, we can replace the weight W of the member by two forces, each W/2 if the member is uniform, with one force acting at each end of the member.

These forces, in effect, are treated as loads externally applied to the pin connections. Accounting for the weight of a member in this way gives the correct result for the\ average tension or compression along the member but will not account for the effect of bending of the member.

TYPES OF TRUSSES IN STRUCTURES BASICS AND TUTORIALS

TRUSSES TYPES USED IN STRUCTURAL ENGINEERING BASIC INFO
What Are the Different Types of Trusses In Construction?


Trusses. When depth limits permit, a more economical way of spanning long distances is with trusses, for both floor and roof construction. Because of their greater depth, trusses usually provide greater stiffness against deflection when compared pound for pound with the corresponding rolled beam or plate girder that
otherwise would be required.

Six general types of trusses frequently used in building frames are shown in Fig. 7.11 together with modifications that can be made to suit particular conditions.

Trusses in Fig. 7.11a to d and k may be used as the principal supporting members in floor and roof framing. Types e to j serve a similar function in the framing of symmetrical roofs having a pronounced pitch. As shown, types a to d have a top chord that is not quite parallel to the bottom chord. Such an arrangement is
used to provide for drainage of flat roofs.

Most of the connections of the roof beams (purlins), which these trusses support, can be identical, which would not be the case if the top chord were dead level and the elevation of the purlins varied. When used in floors, truss types a to d have parallel chords.

Properly proportioned, bow string trusses (Fig. 7.11j) have the unique characteristic that the stress in their web members is relatively small. The top chord, which usually is formed in the arc of a circle, is stressed in compression, and the bottom chord is stressed in tension. In spite of the relatively expensive operation of forming the top chord, this type of truss has proved very popular in roof framing on spans of moderate lengths up to about 100 ft.

The Vierendeel truss (Fig. 7.11k) generally is shop welded to the extent possible to develop full rigidity of connections between the verticals and chords. It is useful where absence of diagonals is desirable to permit passage between the verticals.

Trusses also may be used for long spans, as three-dimensional trusses (space frames) or as grids. In two-way girds, one set of parallel lines of trusses is intersected at 90 by another set of trusses so that the verticals are common to both sets.

Because of the rigid connections at the intersections, loads are distributed nearly equally to all trusses. Reduced truss depth and weight savings are among the apparent advantages of such grids.

Long-span joists are light trusses closely spaced to support floors and flat roofs. They conform to standard specifications (Table 7.1) and to standard loading. Both Pratt and Warren types are used, the shape of chords and webs varying with the fabricator.

Yet, all joists with the same designation have the same guaranteed load supporting capacity. The standard loading tables list allowable loads for joists up to 72 in deep and with clear span up to 144 ft. The joists may have parallel or sloping chords or other configuration.