correspond to the bottom chords of the bridge, experience mainly tensile stresses.  The

diagonal struts making up the web can experience either type of stress depending on their

position in the framework relative to the load. Such spaceframes are statically determinate.

That is, their internal forces can be predicted using static analysis techniques.  It is common

practice, however, to construct real life spaceframes using rigid joints for the hubs to reduce

the forces experienced by the members and the amount of deflection the spaceframes

exhibit. Like the rigid gusset plate joints of truss bridges, and the fixed ends of columns and

beams, rigid hubs impart additional bending stresses in the struts which have to be figured

into the load calculations.  Accounting for these perpendicular acting forces in addition to

the axial forces increases the required cross sectional area of the struts, and the amount of

material used for them, compared to spaceframes with flexible joints.  In general the small

benefit achieved by rigid hubs is offset by the increased cost of materials.  Although both

types of structures are referred to here as spaceframes, technically, lattices with flexible

hubs should be referred to as space trusses, and those with rigid hubs as spaceframes.

.

Just as you saw that there is a relationship between the H/S ratio of a truss bridge and the

maximum load it can carry, so too the ratio of the depth of a spaceframe to its span affects

its load bearing capacity significantly.  In the following example, the depth of the unit cell

of the Tri-1 spaceframe is varied.  This involves varying the length of the struts in the inner

and outer layers, as well as the web diagonals.  You can model this with Polymorf by simply

building the unit cells out of either small triangles (ST), or right triangles (RT), or large

triangles (LT), or isosceles triangles (IT) as  shown by the following.

.

side view

tri-1_spaceframe.gif

tri-1_spaceframe.gif

tri-1_spaceframe.gif

tri-1_spaceframe.gif

depth/module = .41

depth/module = .82

depth/module = .82

depth/module = 1.29

top view

tri-1_spaceframe.gif

tri-1_spaceframe.gif

tri-1_spaceframe.gif

a) w/right tri. (RT)

b) w/small tri. (ST)

c) w/large tri. (LT)

d) w/isosceles tri. (IT)

click image to enlarge

Fig. 234 - Tri-1 unit cells with varying depth/module size ratios (cm)     (demonstration  models)

.

As shown by the forgoing models, The length of each strut comprising the grid layers is

referred to as the spaceframe's module size [e.g. cell a) module = 7.18 cm].  And the

distance between the layers is its depth [e.g. cell a) depth = 2.95 cm].  As with A-frame and

truss bridge structures, increasing the depth, or height, of a spaceframe increases the

.

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Page 136 - Building stability - Tri-1 spaceframe

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