Cantilever method

Last updated

The cantilever method is an approximate method for calculating shear forces and moments developed in beams and columns of a frame or structure due to lateral loads. The applied lateral loads typically include wind loads and earthquake loads, which must be taken into consideration while designing buildings. The assumptions used in this method are that the points of contraflexure (or points of inflection of the moment diagram) in both the vertical and horizontal members are located at the midpoint of the member, and that the direct stresses in the columns are proportional to their distances from the centroidal axis of the frame. [1] The frame is analysed in step-wise (iterative) fashion, and the results can then be described by force diagrams drawn up at the end of the process. The method is quite versatile and can be used to analyse frames of any number of storeys or floors.

The position of the centroidal axis (the center of gravity line for the frame) is determined by using the areas of the end columns and interior columns. The cantilever method is considered as one of the two primary approximate methods (the other being the portal method) for indeterminate structural analysis of frames for lateral loads. Its use is recommended for frames that are taller than they are wide, and therefore behave similar to a beam cantilevered up from the ground.

See also

Related Research Articles

Structural engineering sub-discipline of civil engineering dealing with the creation of man made structures

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 need to understand and calculate the stability, strength and rigidity of built structures for buildings and nonbuilding structures. The structural designs are integrated with those of other designers such as architects and building services engineer and often supervise the construction of projects by contractors on site. They can also be involved in the design of machinery, medical equipment, and vehicles where structural integrity affects functioning and safety. See glossary of structural engineering.

Cantilever Beam anchored at only one end

A cantilever is a rigid structural element, such as a beam or a plate, anchored at one end to a support from which it protrudes; this connection could also be perpendicular to a flat, vertical surface such as a wall. Cantilevers can also be constructed with trusses or slabs. When subjected to a structural load, the cantilever carries the load to the support where it applies a shear stress and a bending moment.

Structural analysis is the determination of the effects of loads on physical structures and their components. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis employs the fields of applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures.

Truss structure that consists of two-force members only

A truss is an assembly of beams or other elements that creates a rigid structure. In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object". A "two-force member" is a structural component where force is applied to only two points. Although this rigorous definition allows the members to have any shape connected in any stable configuration, trusses typically comprise five or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes.

Beam (structure) structural element capable of withstanding load by resisting bending

A beam is a structural element that primarily resists loads applied laterally to the beam's axis. Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, that in turn induce internal stresses, strains and deflections of the beam. Beams are characterized by their manner of support, profile, equilibrium conditions, length, and their material.

Buckling the sudden change in shape of a structural component under load

In engineering, buckling is the sudden change in shape of a structural component under load such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled.

Seismic retrofit Modification of existing structures to make them more resistant to seismic activity

Seismic retrofitting is the modification of existing structures to make them more resistant to seismic activity, ground motion, or soil failure due to earthquakes. With better understanding of seismic demand on structures and with our recent experiences with large earthquakes near urban centers, the need of seismic retrofitting is well acknowledged. Prior to the introduction of modern seismic codes in the late 1960s for developed countries and late 1970s for many other parts of the world, many structures were designed without adequate detailing and reinforcement for seismic protection. In view of the imminent problem, various research work has been carried out. State-of-the-art technical guidelines for seismic assessment, retrofit and rehabilitation have been published around the world – such as the ASCE-SEI 41 and the New Zealand Society for Earthquake Engineering (NZSEE)'s guidelines. These codes must be regularly updated; the 1994 Northridge earthquake brought to light the brittleness of welded steel frames, for example.

Shear wall structural system composed of braced panels (also known as shear panels) to counter the effects of lateral load acting on a structure

In structural engineering, a shear wall is a vertical element of a seismic force resisting system that is designed to resist in-plane lateral forces, typically wind and seismic loads. In many jurisdictions, the International Building Code and International Residential Code govern the design of shear walls.

Steel frame building technique in which a skeleton frame of vertical steel columns is constructed in a rectangular grid; made the skyscraper possible

Steel frame is a building technique with a "skeleton frame" of vertical steel columns and horizontal I-beams, constructed in a rectangular grid to support the floors, roof and walls of a building which are all attached to the frame. The development of this technique made the construction of the skyscraper possible.

Plastic bending

Plastic bending is a nonlinear behavior particular to members made of ductile materials that frequently achieve much greater ultimate bending strength than indicated by a linear elastic bending analysis. In both the plastic and elastic bending analyses of a straight beam, it is assumed that the strain distribution is linear about the neutral axis. In an elastic analysis this assumption leads to a linear stress distribution but in a plastic analysis the resulting stress distribution is nonlinear and is dependent on the beam’s material.

Portal frame construction method

Portal frame structures are designed to span between supports and rely on fixed joints with moment resisting capacity where vertical supports connect to horizontal beams or trusses. Portal frame structures can be constructed using a variety of materials and methods. These include steel, reinforced concrete and laminated timber such as glulam. The connections between the columns and the rafters are designed to be moment-resistant, i.e. they can carry bending forces. "They were first developed in the 1960s, and have now become the most common form of enclosure for spans of 20 to 60 m"

The Staggered truss system is a type of structural steel framing used in high-rise buildings. The system consists of a series of story-high trusses spanning the total width between two rows of exterior columns and arranged in a staggered pattern on adjacent column lines. William LeMessurier, the founder Cambridge, Massachusetts engineering firm LeMessurier Consultants has been credited in developing this award winning system as part of his research at the Massachusetts Institute of Technology.

Tube (structure) system to resist lateral loads in structural engineering

In structural engineering, the tube is a system where, to resist lateral loads, a building is designed to act like a hollow cylinder, cantilevered perpendicular to the ground. This system was introduced by Fazlur Rahman Khan while at the architectural firm Skidmore, Owings & Merrill (SOM), in their Chicago office. The first example of the tube’s use is the 43-story Khan-designed DeWitt-Chestnut Apartment Building, since renamed Plaza on DeWitt, in Chicago, Illinois, finished in 1966.

Influence line

In engineering, an influence line graphs the variation of a function at a specific point on a beam or truss caused by a unit load placed at any point along the structure. Some of the common functions studied with influence lines include reactions, shear, moment, and deflection (Deformation). Influence lines are important in designing beams and trusses used in bridges, crane rails, conveyor belts, floor girders, and other structures where loads will move along their span. The influence lines show where a load will create the maximum effect for any of the functions studied.

Steel plate shear wall

A steel plate shear wall (SPSW) consists of steel infill plates bounded by boundary elements.

Deflection (engineering)

In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.

Mete Avni Sözen was Kettelhut Distinguished Professor of Structural Engineering at Purdue University, Indiana, United States from 1992 to 2018. he was a father of 56 people.

Moment-resisting frame is a rectilinear assemblage of beams and columns, with the beams rigidly connected to the columns.

In structural engineering and mechanical engineering, generalised beam theory (GBT) is a one-dimensional theory used to mathematically model how beams bend and twist under various loads. It is a generalization of classical Euler–Bernoulli beam theory that approximates a beam as an assembly of thin-walled plates that are constrained to deform as a linear combination of specified deformation modes.

Structural support is a part of a building or structure providing the necessary stiffness and strength in order to resist the internal forces and guide them safely to the ground. External loads that act on buildings cause internal forces in building support structures. Supports can be either at the end or at any intermediate point along a structural member or a constituent part of a building and they are referred to as connections, joints or restraints.

References

  1. S. Ramamrutham. Theory of Structures.