architecture Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and construction, constructi ...

, the slenderness ratio, or simply slenderness, is an

aspect ratio The aspect ratio of a geometry, geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangl ...

, the quotient between the height and the width of a

building A building or edifice is an enclosed Structure#Load-bearing, structure with a roof, walls and window, windows, usually standing permanently in one place, such as a house or factory. Buildings come in a variety of sizes, shapes, and functions, a ...

. In

structural engineering Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and joints' that create the form and shape of human-made Structure#Load-bearing, structures. Structural engineers also ...

, slenderness is used to calculate the propensity of a column to

buckle A buckle or clasp is a device used for fastening two loose ends, with one end attached to it and the other held by a catch in a secure but adjustable manner. Often taken for granted, the invention of the buckle was indispensable in securing two ...

. It is defined as

l/k

where

l

is the effective length of the column and

k

is the least radius of gyration, the latter defined by

k^2=I/A

where

A

is the area of the cross-section of the column and

I

is the

second moment of area The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. Th ...

of the cross-section. The effective length is calculated from the actual length of the member considering the rotational and relative translational boundary conditions at the ends. Slenderness captures the influence on buckling of all the geometric aspects of the column, namely its length, area, and

. The influence of the material is represented separately by the material's

modulus of elasticity An elastic modulus (also known as modulus of elasticity (MOE)) is a quantity that describes an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. Definition The elastic modu ...

E

Structural engineer Structural engineers analyze, design, plan, and research List of structural elements, structural components and structural systems to achieve design goals and ensure the safety and comfort of users or occupants. Their work takes account mainly of ...

s generally consider a

skyscraper A skyscraper is a tall continuously habitable building having multiple floors. Most modern sources define skyscrapers as being at least or in height, though there is no universally accepted definition, other than being very tall high-rise bui ...

as slender if the height:width ratio exceeds 10:1 or 12:1. Slim towers require the adoption of specific measures to counter the high strengths of wind in the vertical

cantilever A cantilever is a rigid structural element that extends horizontally and is unsupported at one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cantilev ...

, like including additional structures to endow greater rigidity to the building or diverse types of

tuned mass damper A tuned mass damper (TMD), also known as a harmonic absorber or seismic damper, is a device mounted in structures to reduce mechanical vibrations, consisting of a mass mounted on one or more damped springs. Its oscillation frequency is tune ...

s to avoid unwanted swinging. Tall buildings with high slenderness ratio are sometime referred to as pencil towers.

Examples

References

External links