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 . orts,the dotted line showing its form when deformed under aload. The hinges are supposed immovable, the rib beingfree to turn about them without friction. The dotted lineis the changed form under a load, and the absolute dis-placement of 0 is zero ; but not so its displacement rela-tively to B and Bs tangent BT, for BT has moved to anew position BT. To find this relative displacement con-ceive the new curve o
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 . orts,the dotted line showing its form when deformed under aload. The hinges are supposed immovable, the rib beingfree to turn about them without friction. The dotted lineis the changed form under a load, and the absolute dis-placement of 0 is zero ; but not so its displacement rela-tively to B and Bs tangent BT, for BT has moved to anew position BT. To find this relative displacement con-ceive the new curve of the rib superposed on the old ina way that B and BT may coincide with their original po- 448 MECHANICS OF ENGINEERING. sitions, Fig. 412. It is now seen that Os displacementrelatively to B and B T is not zero but = 0 0n, and has asmall Ax bnt a comparatively large Ay. In fact for thiscase of hinged ends, piers immovable, rib continuous be-tweer them, and deformation slight, we shall write Ax —zero as compared with Ay, the axis Xpassing through OB). 373. Values of the X and Y Projections of Os Displacement Rela-tively to B and Bs Tangent; the origin being taken at 0, f-^8 ^ Fig. 413. Let the co-ordinates of the dif-ferent points E, D, G,etc., of the rib, re-ferred to 0 and anarbitrary X axis, bex and y, their radialdistances from 0 be-ing u (, u for G, uffor D, etc.; in gener-al, u). OEDG is the jl i ^ unstrained form of the i * j rib, (, the form it FlG. 413 would assume if it lay flat on its side on a level platform,under no straining forces), while OnEDGB is its formunder some loading, , under strain. (The superposi-tion above mentioned (§ 372) is supposed already made ifnecessary, so that BT is tangent at B to both forms).Now conceive the rib OB to pass into its strained condi-tion by the successive bending of each ds in turn. Thestraining or bending of the first ds, BG, through the smallangle dip (dependent on the moment of the stress coupleat G in the
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
