Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . Fig. 294. of the upper and lower surfaces would meet over the supports(as should be the case to make A=2^). Neglecting theweight of the beam, and placing a single load in middle, itis required to find the equation for safe loading; also theequations of the four elastic curves; and finally the deflec-tion. The solutions of this and the following problem are leftto the student, as exercises. Of course the beam
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Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . Fig. 294. of the upper and lower surfaces would meet over the supports(as should be the case to make A=2^). Neglecting theweight of the beam, and placing a single load in middle, itis required to find the equation for safe loading; also theequations of the four elastic curves; and finally the deflec-tion. The solutions of this and the following problem are leftto the student, as exercises. Of course the beam heregiven is not one of uniform strength. 293. Special Problem. (II). Fig. 295. Kequired the man-ner in which the width of the beam must vary, the heightbeing constant, cross-sections rectangular, weight of beam. Fig. 295. neglected, to be a beam of uniform strength, if the load isuniformly distributed ? FLEXURE. OBLIQUE FORCES. 347 CHAPTEK V. FLEXURE OF PRISMATIC BEAMS UNDEROBLIQUE FORCES. 294 Remarks, By oblique forces will be understoodexternal forces not perpendicular to tho beam, but theseexternal forces will be confined to one plane, called theforce-plane, which contains the axis of the beam and alsocuts the beam symmetrically. The curvature induced bythese external forces will as before be considered veryslight, so that distances measured along the beam will betreated as unchanged by the flexure. It will be remembered that in previous problems theproof that the neutral axis of eaeh cross section passesthrough its centre of gravity, rested on the fact that whena portion of the beam having a given section as one of itsbounding surfaces is considered free, the condition ofequilibrium I (compons. || to beam)=0 does not introduceany of the external forces, since these in the problems re-ferr