Beam Bending
Beam bending refers to the deformation of a structural beam under the influence of external loads, causing it to bend or flex. This phenomenon is a fundamental concept in structural engineering and is crucial for designing and analyzing the behavior of beams in various applications. Understanding beam bending is essential for ensuring the structural integrity and safety of buildings, bridges, and other load-bearing structures.
3 Key excerpts on "Beam Bending"
eBook - ePub- William Bolton(Author)
- 2012(Publication Date)
- Routledge(Publisher)
...2 Beams and columns 2.1 Introduction As discussed in chapter 1 in relation to possible forms of loading structures, one basic form involves bending. Thus, for the simple beam bridge in Figure 2.1(a) the load arising from a car crossing it will tend to bend the beam. Figure 2.1 Examples of structures where (a) bending (b) compressive loading occurs As also discussed in chapter 1, another form of loading involves the loading in compression. Such members might be concrete or brick columns supporting the floors or roof of a building (Figure 2.2(b)), the applied loads of the floors or roof above applying compressive loads. This chapter is a discussion of loading due to bending, the various forms it can take, and the stresses that can arise from such bending and also the loading of columns. 2.2 Beams A beam can be defined as a structural member, generally horizontal, to which loads are applied and which cause it to bend. As a result of loads causing one surface of a beam to become longer and the opposite surface shorter, when beams bend they become curved. 2.2.1 Types of beams The following are some examples of types of beams: 1 Cantilever (Figure 2.2(a)) This is a beam which is rigidly fixed at just one end, the other end being free. 2 Simply supported beam (Figure 2.2(b)) This is a beam which is supported at its ends on rollers or smooth surfaces or one of these combined with a pin at the other end. 3 Simply supported beam with overhanging ends (Figure 12.2(c)) This is a simple supported beam with the supports set in some distance from the ends. 4 Built-in beam (Figure 2.2(d)) This is a beam which is built-in at both ends and so both ends are rigidly fixed. Figure 2.2 Examples of beams Where an end is rigidly fixed there is a reaction force and a resisting moment. At a supported end or point there are reactions but no resisting moments. At a free end there are no reactions and no resisting moments...
eBook - ePub- C. T. Sun, Ashfaq Adnan(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
...5 Bending and Flexural Shear 5.1 INTRODUCTION Bending is the most frequently occurring form of load in aircraft structures. As the name implies, a bending load “bends” a structure and, depending on the direction of the lateral forces or bending moments, results in the development of nonuniform tensile and compressive stresses normal to the cross‐section and transverse shear stress parallel to the cross‐section. A shear force–bending moment diagram can be constructed to analyze and visualize the nature of the internal shear forces and bending moments at any location on the structure. The intuitive approach for solving a problem would be using a direct method where the applied bending forces would have been first linked with the internal resultants and stress components. Then, using the stress–strain law, strain components would be obtained. Finally, the associated displacements would be obtained via strain–displacement relations. However, there is no direct method to analytically solve a bending problem. As such, inverse or semi‐inverse methods such as theory of elasticity are often used. The theory of elasticity approach is useful for solids with narrow section or axisymmetric circular sections. An analysis becomes very cumbersome and often intractable when the loading becomes complicated. For thin‐walled sections such as boxed‐beam section or multichannel section, analytical solutions are not possible even for simpler loadings. When loadings are only lateral and deformation is not large, a simpler inverse approach, called Bernoulli–Euler beam theory is used. The main disadvantage of the Bernoulli–Euler beam theory is that this theory is not applicable when transverse shear deformation is important. In such a situation, the Timoshenko beam theory is appropriate. For excessive bending deformation, other methods such as inelastic bending or plastic bending approaches are often used...
eBook - ePubForm and Forces
Designing Efficient, Expressive Structures
- Edward Allen, Waclaw Zalewski(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
...Chapter 18 Bending Resistance in Beams of Any Shape Properties of complex cross-sectional shapes Moment of inertia Composite action Designing bays of steel framing We're designing an 11-story office building that will be framed with structural steel (Figure 18.1). We have reached the stage of preliminary design where we must lay out the frame and determine the sizes of the beams and girders (Figure 18.2). We need to consider the placement of columns in the structural bays, as we discussed in Chapter 15, and we will need to expand our knowledge of the bending resistance of beams from Chapters 16 and 17 to understand how to assign sizes to beams with complex cross-sectional shapes. Figure 18.1 An ironworker guides a wide-flange steel beam toward its position in a building frame. Photo courtesy of Bethlehem Steel Corporation. Figure 18.2 A preliminary floor plan for a small office building. Steel The steel used in structural framing is composed of iron that has been refined so that it contains about three-tenths of 1 percent carbon. This reduction in carbon content produces a metal that is ductile and strong. Today, most steel in the United States is manufactured from recycled steel scrap in electric furnaces. The quality is carefully monitored throughout manufacture to assure that it is very high. Various grades of steel are available in varying strengths, but all structural steels, even those with very high strengths, have the same modulus of elasticity, about 29,000,000 psi. Structural steel is usually designed with an allowable stress in bending of 24,000 psi. Production of Shapes Steel is hot-rolled into structural elements, referred to as shapes, in a steel mill by passing hot steel blanks through a series of specially formed rollers that squeeze the steel into the desired form (Figure 18.3). The hot-rolled shape most commonly used in framing is the wide-flange, a more efficient variation of the now-obsolete American Standard shape often referred to as an I-beam...
