Fundamental Concepts of Strength of Materials: Engineering Book Chapter | IGI Global

×

Receive a 20% Discount on All Purchases Directly Through IGI Global's Online Bookstore.
Additionally, libraries can receive an extra 5% discount. Learn More

Subscribe to the latest research through IGI Global's new InfoSci-OnDemand Plus

InfoSci®-OnDemand Plus, a subscription-based service, provides researchers the ability to access full-text content from over 100,000 peer-reviewed book chapters and 26,000+ scholarly journal articles covering 11 core subjects. Users can select articles or chapters that meet their interests and gain access to the full content permanently in their personal online InfoSci-OnDemand Plus library.

Purchase the Encyclopedia of Information Science and Technology, Fourth Edition and Receive Complimentary E-Books of Previous Editions

When ordering directly through IGI Global's Online Bookstore, receive the complimentary e-books for the first, second, and third editions with the purchase of the Encyclopedia of Information Science and Technology, Fourth Edition e-book.

Create a Free IGI Global Library Account to Receive a 25% Discount on All Purchases

Exclusive benefits include one-click shopping, flexible payment options, free COUNTER 4 and MARC records, and a 25% discount on all titles as well as the award-winning InfoSci^{®}-Databases.

InfoSci^{®}-Journals Annual Subscription Price for New Customers: As Low As US$ 5,100

This collection of over 175 e-journals offers unlimited access to highly-cited, forward-thinking content in full-text PDF and HTML with no DRM. There are no platform or maintenance fees and a guarantee of no more than 5% increase annually.

Flórez-López, Julio, María Eugenia Marante and Ricardo Picón. "Fundamental Concepts of Strength of Materials." Fracture and Damage Mechanics for Structural Engineering of Frames: State-of-the-Art Industrial Applications. IGI Global, 2015. 10-30. Web. 18 Nov. 2018. doi:10.4018/978-1-4666-6379-4.ch002

APA

Flórez-López, J., Marante, M. E., & Picón, R. (2015). Fundamental Concepts of Strength of Materials. In Fracture and Damage Mechanics for Structural Engineering of Frames: State-of-the-Art Industrial Applications (pp. 10-30). Hershey, PA: IGI Global. doi:10.4018/978-1-4666-6379-4.ch002

Chicago

Flórez-López, Julio, María Eugenia Marante and Ricardo Picón. "Fundamental Concepts of Strength of Materials." In Fracture and Damage Mechanics for Structural Engineering of Frames: State-of-the-Art Industrial Applications, 10-30 (2015), accessed November 18, 2018. doi:10.4018/978-1-4666-6379-4.ch002

This chapter presents the concepts of strength of materials that are relevant to the analysis of frames. These are the modified Timoshenko theory of elastic beams (Sections 2.1-2.3) and the Euler-Bernoulli one (Section 2.4). These concepts are not presented as in the conventional textbooks of strength of materials. Instead, the formulations are described using the scheme that is customary in the theory of elasticity and that was described in Chapter 1 (Section 1.1.1) (i.e. in terms of kinematics, statics, and constitutive equations). Kinematics is the branch of mechanics that studies the movement of solids and structures without considering its causes. Statics studies the equilibrium of forces; the basic tool for this analysis is the principle of virtual work. The constitutive model that describes a one-to-one relationship between stresses and deformations completes the formulation of the elastic beam problem. Finally, in Section 2.5, some concepts of the elementary theory of torsion needed for the formulation of tridimensional frames are recalled.

Consider a beam that displaces only in the plane X-Z as shown in Figure 1. The axis X is chosen so that it passes through the centroid of the beam’s cross-section; i.e. X coincides with the centroidal axis of the beam. The fundamental hypothesis of the theory of beams states that a cross-section of the beam moves only as a rigid body.

Figure 1.

Graphical representation of the fundamental hypothesis of the theory of beams

The movement of a cross-section at a distance x of the origin is defined by the matrix of generalized displacements {U(x)}:

(2.1.1) where u(x) is the displacement in the direction of the axis X of the particle in the centroid of the cross-section; w(x) is the displacement of the same point in the direction of the axis Z and β(x) is the rotation of the cross-section.

2.1.2 Generalized Deformations of Planar Beams

Consider now a beam differential element as the one shown in Figure 1; the modification of its shape is characterized by the following matrix of generalized deformations:

(2.1.2) where ε_{n} is the normal strain of the fiber in the centroidal axis; χ is the curvature and γ the distortion or angular strain (see Figure 2). Notice that the curvature χ measures the amount by which the centroidal axis deviates from being straight; the normal strain ε_{n} is related to the elongation of that axis; and the distortion γ measures the modifications in the angle between the centroidal axis and the transversal fibers of the beam differential element.

Figure 2.

Generalized deformations in a beam a) Normal strain b) Curvature c) Angular