Architectural Structures

Trusses

Trusses support load much like beams, but for longer spans. As the depth and thus dead weight of beams increases with span they become increasingly inefficient, requiring most capacity to support their own weight rather than imposed live load. Trusses replace bulk by triangulation to reduce dead weight.

1Unstable square panel deforms under load. Only triangles are intrinsically stable polygons

2Truss of triangular panels with inward sloping diagonal bars that elongate in tension under load (preferred configuration)

3Outward sloping diagonal bars compress (disadvantage)

4Top chords shorten in compression

Bottom chords elongate in tension under gravity load

5Gable truss with top compression and bottom tension

3-5 BACKGROUND Basic Concepts

Warren trusses

Pompidou Center, Paris by Piano and Rogers

Prismatic trusses

IBM Sport Center by Michael Hopkins

(Prismatic trusses of triangular cross section provide rotational resistance)

Space trusses

square and triangular plan

Note:

Two way space trusses are most effective if the spans in the principle directions are about equal, as described for two-way slabs above. The base modules of trusses should be compatible with plan configuration (square, triangular, etc.)

3-6 BACKGROUND Basic Concepts

Funicular structures

The funicular concept can be best described and visualized with cables or chains, suspended from two points, that adjust their form for any load in tension. But funicular structures may also be compressed like arches. Yet, although funicular tension structures adjust their form for pure tension under any load, funicular compression structures may be subject to bending in addition to compression since their form is rigid and not adaptable. The funicular line for tension and compression are inversely identical; the form of a cable becomes the form of an arch upside-down. Thus funicular forms may be found on tensile elements.

1Funicular tension triangle under single load

2Funicular compression triangle under single load

3Funicular tension trapezoid under twin loads

4Funicular compression trapezoid under twin loads

5Funicular tension polygon under point loads

6Funicular compression polygon under point load

7Funicular tension parabola under uniform load

8Funicular compression parabola under uniform load

3-7 BACKGROUND Basic Concepts

Vertical structures

Vertical elements

Vertical elements transfer load from roof to foundation, carrying gravity and/or lateral load. Although elements may resist only gravity or only lateral load, most are designed to resist both. Shear walls designed for both gravity and lateral load may use gravity dead load to resist overturning which is most important for short walls. Four basic elements are used individually or in combination to resist gravity and lateral loads

1Wall under gravity load

2Wall under lateral load (shear wall)

3Cantilever under gravity load

4Cantilever under lateral load

5Moment frame under gravity load

6Moment frame under lateral load

7Braced frame under gravity load

9 Braced frame under lateral load

3-9 BACKGROUND Basic Concepts

Shear walls

As the name implies, shear walls resist lateral load in shear. Shear walls may be of wood, concrete or masonry. In the US the most common material for low-rise apartments is light-weight wood framing with plywood or particle board sheathing. Framing studs, spaced 16 or 24 inches, support gravity load and sheathing resists lateral shear. In seismic areas concrete and masonry shear walls must be reinforced with steel bars to resist lateral shear.

1Wood shear wall with plywood sheathing

2Light gauge steel shear wall with plywood sheathing

3Concrete shear wall with steel reinforcing

4CMU shear wall with steel reinforcing

5Un-reinforced brick masonry (not allowed in seismic areas)

8Two-wythe brick shear wall with steel reinforcing

3-11 BACKGROUND Basic Concepts

Cantilevers

Cantilevers resist lateral load primarily in bending. They may consist of single towers or multiple towers. Single towers act much like trees and require large footings like tree roots to resist overturning. Bending in cantilevers increases from top down, justifying tapered form in response.

1Single tower cantilever

2Single tower cantilever under lateral load

3Twin tower cantilever

4Twin tower cantilever under lateral load

5Suspended tower with single cantilever

6Suspended tower under lateral load

3-12 BACKGROUND Basic Concepts

Moment frames

Moment frames resist gravity and lateral load in bending and compression. They are derived from post-and beam portals with moment resisting beam to column connections (for convenience refered to as moment frames and moment joints). The effect of moment joints is that load applied to the beam will rotate its ends and in turn rotate the attached columns. Equally, load applied to columns will rotate their ends and in turn rotate the beam. This mutual interaction makes moment frames effective to resist lateral load with ductility. Ductility is the capacity to deform without breaking, a good property to resist earthquakes, resulting in smaller seismic forces than in shear walls and braced frames. However, in areas with prevailing wind load, the greater stiffness of shear walls and braced frames is an advantage, The effect of moment joints to resist loads is visualized through amplified deformation as follows:

1Portal with pin joints collapses under lateral load

2Portal with moment joints at base under lateral load

3Portal with moment beam/column joints under gravity load

4Portal with moment beam/column joints under lateral load

5Portal with all moment joints under gravity load

6Portal with all moment joints under lateral load

7High-rise moment frame under gravity load

8Moment frame building under lateral load

I Inflection points (zero bending between negative and positive bending

Note:

deformations reverse under reversed load

3-13 BACKGROUND Basic Concepts