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Mechanical Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
A cantilever is a projecting structure, such as a beam, that is supported rigidly at one end and carries a load at the other end or along its length. Cantilevers are fabricated in several shapes (Yang et al. 2000; Ansari et al. 2009): rectangular, two-legged, or V-shaped cantilevers (Figure 4.5). The V-shaped cantilever is the predominant shape manufactured and is used currently in AFM. The popular V-shaped cantilever is intuitively thought to be resistant to lateral forces and therefore less prone to twisting than the rectangular beam. But V-shaped cantilevers make calibration of the microscope and interpretation of the data more difficult. The two-leg type cantilever reduces the spring constant. By decreasing the spring constant, a significant performance improvement is achieved, through the corresponding increase in sensitivity. Cantilevers of different shapes (Vashist, Journal of Nanotechnology Online 3: 1–15, 2007.)
Optimization and shaping of indeterminate frame structures
Published in Paulo J.S. Cruz, Structures and Architecture: Bridging the Gap and Crossing Borders, 2019
where P = the load at the tip of the cantilever, L = the span, x = the location along the longitudinal axis, σ = the allowable stress of the material, E = the E-modulus of the material, ∆ = the target displacement and b = the width (constant) of the beam
Cantilevered Building Components
Published in Kyoung Sun Moon, Cantilever Architecture, 2018
Steel is a good material for cantilever structures because it can excellently carry both tensile and compressive forces. In the steel cantilever stairs designed by Lawrence Architecture for a residence in West Seattle, steel treads are cantilevered from reinforced concrete walls. In order to make rigid connections between the reinforced concrete wall and the cantilevered steel treads, steel plates are typically embedded into the reinforced concrete wall. In general, shear studs are welded to the back side of the steel plates and embedded into the concrete wall together with the plates. Once the formwork of the reinforced concrete wall is removed, the embedded steel plates are exposed. Then, the steel tread structures are welded to the steel plates. This is a typical method to make moment connections between wall type reinforced concrete structures and beam type steel structural members.
The philosophical basis of Seeing and Touching Structural Concepts
Published in European Journal of Engineering Education, 2021
Tianjian Ji, Adrian Bell, Yue Wu
Many equations can be used to practice intuitive interpretation and to gain an improved understanding of theory, leading to new meanings and practical applications. For example, second moment of area of a plane cross-section is expressed as: where y is the distance between the neutral axis of the cross-section and the area of an infinitely small area dA. The intuitive interpretation of Equation (1) should be: the further (closer) the material is away from (to) the neutral axis of a section, the larger (smaller) the contribution to the second moment of area of the section. This captures the physical essence of the equation and forms a basis for creatively designing the shape of the cross section of a beam, such as I-section beams for creating a larger I value, and cellular beams for effectively saving material without significantly reducing I value. It can be extended to the design of tall buildings which can be treated as cantilevers in conceptual designs for resisting lateral loading. In other words, shear walls and columns should be arranged as far away as possible from the neutral axis of the building plane.
Rapid evaluation of lateral-torsional buckling of European standard I-section cantilevers
Published in Mechanics Based Design of Structures and Machines, 2023
Stability research has gained increasing importance since economical and technical developments demand the use of ever stronger and ever lighter structures in a wide range of applications of steel and composite structures. The improvements in manufacturing and computer-aided design (CAD) applications, economical factors, and the consideration of construction efficiency have brought along an expansion of the use of ever stronger and ever lighter structures. These continuous developments not only led to changes in methods in the design and building of traditional structures but also enabled the economical use of the material in different fields such as aerospace, automobile industry, and offshore structures. The need for higher strength and lighter weight in all these applications has led to inevitably the structures whose design must be conducted by considering local and overall stability (Mohri, Damil, and Potier-Ferry 2013). Cantilevers are commonly used in steel structures and assembled so that they are subjected to bending about their major axis with the greatest flexural rigidity to use structural material economically. However, lateral-torsional buckling (LTB) is a global stability loss for cantilevers, where a cantilever that is bent about its strong axis may buckle out of a plane by deflecting laterally and twisting as the values of the applied loads reach a limit value called the elastic LTB load. Figure 1 shows the LTB failure mode. In addition to stress and deformation analysis, the LTB failure mode must be considered in design since it may take place long before the bending stress which occurs at the extreme fiber of the section reaches the yield point. The general concept of the LTB has been well explained in various textbooks (Chen and Atsuta 1977; Chen and Lui 1987; Galambos and Surovek 2008; Timoshenko and Gere 1961; Trahair 1993).
Dynamic reliability analysis of a cantilever beam during a deterioration process
Published in Mechanics Based Design of Structures and Machines, 2019
Wei Wang, Yanxun Zhou, Changyou Li, Hao Wang, Yimin Zhang
Cantilever beam structures are widely applied in structural engineering field, including machine tools, wing surfaces, robotic arms, and highway bridges. The load of a cantilever beam is acting on the free end, which means the maximum stress is acting on the fixed end. During cyclic loading process, bending and vibration of cantilever beams cause microcracks and deterioration. To ensure the safety of a beam, dynamic reliability analysis needs to be carried out during the deterioration process.