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 constructing building ...

, the slenderness ratio, or simply slenderness, is an aspect ratio, the quotient between the height and the width of a

building A building, or edifice, is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory (although there's also portable buildings). Buildings come in a variety of sizes, shapes, and fun ...

. In

structural engineering Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and cal ...

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

buckle The 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 tw ...

. 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. The ...

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) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is ...

E

Structural engineer Structural engineers analyze, design, plan, and research 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 safety, technical, economic ...

s generally consider a

skyscraper A skyscraper is a tall continuously habitable building having multiple floors. Modern sources currently define skyscrapers as being at least or in height, though there is no universally accepted definition. Skyscrapers are very tall high-ris ...

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 supported at only 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 canti ...

, 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 tuned ...

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

pencil tower A pencil tower (also known as a skinny skyscraper, pencil-thin tower, super-slender tower, or super-slim tower) is a high-rise building or skyscraper with a very high slenderness ratio that is very tall and thin. There is no universal definition ...

Examples

References

External links