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(BQ) Part 2 book "Theory and problems of strength of materials" has contents: Stresses in beams, elastic deflection of beams double integration method, elastic deflection of beams method of singularity functions, statically indeterminate elastic beams, special topics in elastic beam theory, plastic deformations of beams, columns, combined stresses, members subjected to combined loadings, theories of failure. | Chapter 8 Stresses in Beams TYPES OF LOADS ACTING ON BEAMS Either forces or couples that lie in a plane containing the longitudinal axis of the beam may act upon the member. The forces are understood to act perpendicular to the longitudinal axis and the plane containing the forces is assumed to be a plane of symmetry of the beam. EFFECTS OF LOADS The effects of these forces and couples acting on a beam are fl to impart deflections perpendicular to the longitudinal axis of the bar and b to set up both normal and shearing stresses on any cross section of the beam perpendicular to its axis. Beam deflections will be considered in Chaps. 9. 10 and 11. TYPES OF BENDING If couples are applied to the ends of the beam and no forces act on the bar then the bending is termed pure bending. For example in Fig. 8-1 the portion of the beam between the two downward forces is subject to pure bending. Bending produced by forces that do not form couples is called ordinary bending. A beam subject to pure bending has only normal stresses with no shearing stresses set up in it a beam subject to ordinary bending has both normal and shearing stresses acting within it. Fig. 8-1 NATURE OF BEAM ACTION It is convenient to imagine a beam to be composed of an infinite number of thin longitudinal rods or fibers. Each longitudinal fiber is assumed to act independently of every other fiber i.e. there are no lateral pressures or shearing stresses between the fibers. The beam of Fig. 8-1 for example will deflect downward and the fibers in the lower part of the beam undergo extension while those in the upper part are shortened. These changes in the lengths of the fibers set up stresses in the fibers. Those that are extended have tensile stresses acting on the fibers in the direction of the longitudinal axis of the beam while those that are shortened are subject to compressive stresses. 177 178 STRESSES IN BEAMS CHAP. 8 NEUTRAL SURFACE There always exists one surface in the beam containing fibers that
