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Vertical support is a category of structural systems or elements in architecture and architectural engineering designed to facilitate the vertical dimensions of space and mass,^[1] for example, columns and load-bearing walls.^[2] Along with horizontal spanning systems (like beams^[3]), vertical supports form the core of a building's structure, housing human activities and enabling the creation of habitable environments.^[1]

The primary function of a vertical support is to act as part of a structural system (a "stable assembly" that sustains architectural forms).^[2] As a fundamental component of a structural system, it is responsible for supporting and transmitting applied loads (such as gravity, wind, and earthquake forces) safely to the ground without exceeding the allowable stresses in the members.^[2]

In the context of architectural design, vertical supports function similarly to a skeletal system in a body; they give shape and form to the building while providing support for other building systems and organs.^[4]

Vertical supports are instrumental in establishing the scale of a building's interior. Of the three dimensions of a room, height has a greater impact on perceived scale than width or length; a ceiling height that feels comfortable in a smaller room may feel oppressive in a large assembly space.^[5] As the unsupported height of columns and bearing walls increases, they must become thicker to maintain stability,^[5] which additionally influences the visual scale of the space.

Vertical supports must collect gravity loads from the horizontal spanning systems (trusses, beams, and slabs) and redirect them downward.^[6]

The load imposed on a specific vertical support is determined by its tributary area, which corresponds to the span of the floor or roof structure it carries.^[6] In a regular structural grid:

• Interior columns: carry the gravity loads for one full bay (extending halfway to the nearest column in all directions).^[6]
• Perimeter columns: carry approximately one-half the load of an interior column.^[6]
• Corner columns: carry approximately a quarter of the load of an interior column.^[6]

Skipping a column in the grid transfers its load to adjacent supports.^[6] In multistory buildings, the gravity loads add up as they are transmitted downward through successive floors to the foundation.^[7]

The form and material of vertical supports have evolved significantly throughout history, transitioning from massive elements to lighter skeletal frames.^[8]

Early vertical supports were characterized by high mass:

• Pillars and columns: Neolithic structures, such as those in Banpo, China (c. 5000 BC), utilized thick pillars to support roofs.^[2] The Egyptians mastered trabeated (post-and-lintel) stone construction, exemplified by the Hypostyle Hall at Karnak (1500 BC).^[9] Ancient Greeks perfected the system, with the Parthenon (447 BC) representing the pinnacle of the Doric order in column design.^[10]
• Bearing walls: Until the late-18th century, stone and masonry bearing wall systems came to dominate the vertical support designs.^[11] These systems simultaneously provided support and enclosure, with formal modifications limited to molding or carving the material mass.^[11]

Concrete and masonry walls rely on their bulk for load-carrying capability and can withstand high compression forces, but require reinforcement to resist the tensile stresses.^[12]

The Industrial Revolution introduced high-strength materials that allowed vertical supports to become slender skeletal elements rather than massive walls:^[13] Unlike timber frames, the rigid steel and reinforced concrete designs might get away with no diagonal bracing or shear planes to ensure lateral stability.^[12]

• Cast iron frame: By 1797, Ditherington Flax Mill utilized a structural frame of cast iron columns and beams, becoming the world's first iron-framed building.^[14]
• Steel frames: The Home Insurance Building (1884) utilized a 10-story frame of steel and cast iron to carry the majority of the weight of floors and walls, reducing the reliance on masonry for support.^[15] Steel frames may utilize moment connections for rigidity but require fireproofing to qualify as fire-resistive construction.^[12]

Vertical supports in reinforced concrete have allowed for diverse structural expressions. Concrete frames are typically rigid and qualify as noncombustible construction.^[12]

• Pillars: Modern suspension structures, such as the Olympic Arena in Tokyo (1961), utilize reinforced concrete pillars to anchor steel cables.^[16]
• Ribs: The Sydney Opera House (1973) utilizes precast concrete ribs to form its iconic shell structure.^[17]

In the field of architectural geometry, complex freeform designs require support structures that address the geometric complexity of nodes where multiple beams intersect.^[18]

In large-scale steel gridshells, the connection of beams at a vertex can introduce significant torsion if not geometrically optimized.^[18] A torsion-free support structure is defined geometrically as an arrangement of planar quadrilaterals along the edges of a mesh such that all quadrilaterals meeting at a vertex intersect in a single common line, known as the node axis.^[18] When structural beams are aligned with these quadrilaterals, their symmetry planes pass through the node axis, creating a torsion-free node that is significantly easier to manufacture than a general node.^[18] This principle was utilized for the support structure of the Yas Hotel Abu Dhabi.^[18]

Torsion-free support structures can be derived from parallel meshes (also known as offset meshes).^[18] Two meshes are considered parallel if they share the same combinatorics and their corresponding edges are parallel; the beam structure effectively connects these two layers.^[18] A special case is the conical mesh, where the parallel meshes are at a constant face-to-face distance, allowing for the use of node axes that coincide with the axes of the cones associated with the mesh vertices.^[18]

For structures requiring curved members, the concept of a support structure can be refined through a limit process into a semidiscrete support structure.^[18] This results in support members that form developable strips, which allows for the fabrication of curved beams with rectangular cross-sections by bending flat material rather than complex molding or machining.^[18] This technique was applied to the pavilions at the Eiffel Tower, where the beams follow the principal curvature lines of the reference surface.^[18]

Tensegrity, a term coined by Buckminster Fuller in 1960, refers to structural systems composed of isolated components under compression (struts) inside a continuous net of tension (cables).^[18] This separation allows for lightweight support structures where distinct elements handle specific forces—cables allowing only tension and struts allowing only compression.^[18] The Kurilpa Bridge (2009) is cited as a notable example, being the largest tensegrity bridge in the world.^[18]

The pattern of vertical supports is intrinsically linked to the spatial composition of a design.^[19] Because columns and walls have a greater presence in the visual field than horizontal planes, they are instrumental in defining volumes of space.^[20]

• Columns: A structural frame of columns and beams allows for relationships to be established with adjacent spaces on all four sides of the defined volume.^[20]
• Bearing walls: Using parallel bearing walls creates a directional quality, orienting the space toward open ends. If a space is enclosed on all four sides by bearing walls, it becomes introverted and must rely on openings for connection to adjacent spaces.^[20]

The structural/spatial relationship can be approached in two different ways:

• Correspondence between structural and spatial arrangements: The pattern of supports prescribes the disposition of spaces, or conversely, the spatial requirements dictate the structural rhythm.^[19]
• Flexibility: The structural form is designed as a "looser fit," allowing freedom in the interior spatial layout independent of the vertical supports.^[19]

• Ching, Francis D.K.; Onouye, Barry; Zuberbuhler, Douglas (2009). Building Structures Illustrated: Patterns, Systems, and Design (1st ed.). John Wiley & Sons. ISBN 978-0470187852.
• Ching, Francis D.K.; Onouye, Barry; Zuberbuhler, Douglas (2014). Building Structures Illustrated: Patterns, Systems, and Design (2nd ed.). John Wiley & Sons. ISBN 978-1-118-45835-8.
• Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes (2015). "Architectural geometry" (PDF). Computers & Graphics. 47: 145–164. doi:10.1016/j.cag.2014.11.002.