Bending resistant structures include cantilever, moment frame, framed tube, and bundled tube structures. They resist lateral load by combed axial and bending stresses. Since bending stress varies from tension to compression with zero stress at the neutral axis, only half the cross section is effectively engaged. This makes them less stiff than shear walls or braced frames, but it provides greater ductility to absorb seismic energy in the elastic range, much like a flower in the wind. On the other hand, bending resistance implies large deformations that may cause damage to non-structural items. Bending resistant structures are sometimes combined with other systems, such as braced frames or shear walls, for greater stiffness under moderate load; but moment frames provide ductility under severe load, after the bracing or shear walls may fail.
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VERTICAL SYSTEMS Bending Resistant
Cantilever
Cantilever structures consist of towers that rise from the foundation. They resist gravity load in compression and lateral load in bending and shear, similar to moment frames.
Cantilevers are subject to global bending of the entire tower, whereas moment frames are subject to localized bending of columns and beams joint by moment resistant joints.
The global bending of cantilever towers increases from minimum on top to maximum at the base; whereas the local bending of beams and columns in moment frames varies at each level from positive to negative.
Cantilever towers may be very slender walls, hollow boxes, or solid columns. But compared to shear walls which resist lateral load primarily in shear, cantilevers resist primarily in bending. The most common materials are reinforced concrete and wood poles of pole houses. Floors may also cantilever from the towers. Cantilevers need large foundations to resist overturn moments. Cantilever systems of multiple towers may have joint foundations that tie the towers together for better stability.
1 Single tower cantilever with cantilever floors 2 Single tower cantilever under lateral load
3 Twin tower cantilever with joined footing for improved stability 4 Twin tower cantilever under lateral load
5 Single tower cantilever with suspended floors 6 Single tower suspension cantilever under lateral load
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VERTICAL SYSTEMS Bending Resistant Pirelli tower, Milan (1956-58)
Architect: Ponti, Fornaroli, Rosselli, Valtolina, Dell Orto Engineer: Arturo Danusso, Pier Luigi Nervi
Facing Milan’s central station across a major urban plaza, the 32-story Pirelli tower rises prominently above the surrounding cityscape. A central corridor, giving access to offices, narrows toward both ends in response to reduced traffic. The reinforced concrete structure features two twin towers in the midsection for lateral resistance in width direction and triangular tubes at both ends for bilateral resistance. The towers and tubes also support gravity load. The gravity load of the towers improves their lateral stability against overturning. The central towers are tapered from top to base, reflecting the increasing global moment and gravity load. The towers are connected across the central corridors at each level by strong beams that tie them together for increased stability. In plan, the central towers are fan-shaped to improve buckling and bending resistance. The tubular end towers of triangular plan house exit stairs, service elevators, and ducts.
Concrete rib slabs supported by beams that span between the towers provide column-free office space of 79 and 43 ft (24 and 13 m). The plan and structure give the tower its unique appearance, a powerful synergy of form and structure.
Floor plan: 18 x 68 m (59 x 223 ft)
Height: 127 m (417 ft))
Typical story height: 3.9 m (12.8 feet) Height/width ratio 7
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VERTICAL SYSTEMS Bending Resistant Hypo Bank, Munich (1980)
Architect: Bea and Walter Betz
The design objective for the Hypo Bank headquarter was to create a landmark for Munich and a unique architectural statement for the bank. Built 1980, the 22 story bank has 114m height. The structure consist of four tubular concrete towers that support a platform which supports 15 floors above and 6 floors suspended below. The suspended floors had been built from top down simultaneous with upper floors being built upwards.
Four towers combined with a platform form a mega-frame to resist gravity and lateral loads. The four towers include exit stairs in prestressed concrete tubes of 7m diameter and 50 to 60 cm wall thickness. A fifth tower of 12.5m diameter, houses eight elevators and mechanical equipment. The support platform consist of prestressed site-cast concrete of 50cm thick concrete slabs on top and bottom, joined by 1.5m rib walls that are tied around the towers. The formwork for the platform was assembled on ground and lifted 45 m by 12 hydraulic jacks.
The office space consists of three triangular units, joined by a T-shaped center. Two-way beams for office floors are supported by columns above the platform and suspended below. Three sub-grade levels include parking, security control, and loading stations.
Floor plan: 7 m ( 23 ft) diameter towers
Height: 114 m (374 ft)
Height/width ratio 16 per tower
1 Typical upper floor supported by columns above the platform 2 Story-high platform forms a mega frame with four towers 3 Typical lower floor suspended from the platform 4 Isometric view of building
5 Roof plan
6 Typical office floor framing 7 Support platform framing 8 Typical floor plan layout
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VERTICAL SYSTEMS Bending Resistant 1 Commerzbank Düsseldorf (1965)
Architect: Paul Schneider-Esleben
This 12-story bank building is located at the boundaries between the old and new banking district of Düsseldorf, linked by a pedestrian footbridge to an older building of the bank. The 12-story building above a 2-story podium was initially designed to allow a drive-in bank at street level. A free-standing service core supports the pedestrian bridge and makes the link to the office floors. A second stair and bathroom core is located at the far end of the building, providing undivided and flexible office space. The curtain wall façade is designed and manufactured using vehicular technology of insulating sandwich panels. The structure consists of reinforced concrete. Two rows of square cantilever columns support cantilever beams and concrete floor slabs. The interior core helps to resist lateral load in length and width directions, but the exterior core at the other end of the building resist lateral load in width direction only.
Floor plan: 16 x 32 m (52 x 104 ft) Height: 44 m (144 ft)
Typical story height 3 m (9.8 ft) Height/width ratio 10 per cantilever 2 Lend Lease House Sydney (1961)
Architect: Harry Seidler
This 15-story office tower with north-south orientation of its length axis has movable exterior blinds for sun control. They give the facade an ever-changing appearance. On sunny mid-days, they are horizontal for optimal sun protection.
On cloudy days, in lowered position, they tend to darken the inside rooms. The orientation provides inspiring views to the Sydney harbor and a nearby botanical garden. A two-story showroom with mezzanine floor is located on the ground floor, above a four-story underground parking garage. The office floors feature elevators, stair and bathrooms on one end and an exit stair at the opposite end, providing flexible office floors. Mechanical equipment is in a roof penthouse. The structure consists of reinforced concrete. Two rows of wall-shape cantilever columns support cantilever slabs. The cantilever columns resist both gravity and lateral loads.
Floor plan: 12 x 30 m (39 x 98 ft) Height: 38 m (125 ft) Height/width ratio 4.7 per twin cantilever
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VERTICAL SYSTEMS Bending Resistant
Moment frame
Moment frames consist of one or more portals with columns joint to beams by moment resistant connections that transmit bending deformation from columns to beam and vice-versa. Beams and columns act together to resist gravity and lateral loads in synergy and redundancy. Bending resistance makes moment frames more ductile and flexible than braced frames or shear walls. The ductile behavior is good to absorb seismic energy, but increases lateral drift, a challenge for safety and comfort of occupants, and possible equipment damage.
Moment frames provide optimal planning freedom, with minimal interference of structure.
Office buildings that require adaptable space for changing tenant needs, usually use moment frames. To reduce lateral drift in tall buildings, dual systems may include bracing or shear walls, usually at an interior core where planning flexibility is not required.
Given the high cost of moment-resistant joints, low-rise buildings may provide only some bays with moment resistant frames. The remaining bays, with pin joints only, carry gravity load and are laterally supported by adjacent moment frames.
Moment frame behavior can be visualized by amplified deformations. The connection of column to beam is usually perpendicular and assumed to remain so after deformation.
Under lateral load, columns with moment joints at both ends assume positive and negative bending at opposite ends, causing S-shapes with inflection points of zero bending at mid-span and end rotation that rotates the ends of a connected beam. By resisting rotation, beams help to resist lateral load. Similarly, a beam subject to bending under gravity load will rotate the columns connected to it and thus engage them in resisting the gravity load. Columns with moment-resistant joints at both ends deform less than columns with only one moment joint. Deformations under gravity and lateral loads are visualized in the diagrams, with dots showing inflection points of zero bending stress.
1 portal with hinged joints unable to resist lateral load 2 Moment joints at base, hinge joints at beam, large drift 3 Moment joints at strong beam, hinge joints at base, large drift 4 Moment joints at base and strong beam, drift reduced to half 5 Hinged base, moment joints at beam, beam forms inflection point 6 Gravity load, hinged base, beam moment joints, 2 beam inflection points 7 Lateral load, all moment joints, inflection points at beam and columns 8 Gravity load, all moment joints, inflection points at beam and columns 9 Multi-bay frame deformation under lateral load
10 Multi-bay frame deformation under gravity load A Inflection point of zero bending stress
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