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3-8) SOME PARTICULAR SOLUTIONS OF THE EQUATIONS dv ^«* r«, dw ^ , Pj ^w 5w 5«; dv dw dw dy dz dx dz By dx = (w — n) {a h -\- c) -\- -\- 2na — n){h — n)(c + a) Pz = {m-\-n)c-^{m — n){a-\-h) =^{m-\-n)a-\- {m 'P 2= {m -\- n)h -\- {m S, • • ^ <3-9) '' Therefore Thus ^ ^' ^ = + * + '''a^ = "'a^ = *'^ = ^^^" 29 -\- c) . . 1 1) . 14) and are constant everywhere. 2) give X=0, so that the body forces are Y=:0, Z:==0, Then zero. the only forces on the body is bounded by faces perpendicular to the axes there must be pulls across these faces of amounts P^, Pg, Pg, per unit area.

Although the strength and other elastic properties of a body are THE EMPIRICAL BASIS OF ELASTICITY 45 usually unaltered by stresses within the elastic limit there are circumstances in which this is not true. When a body is subjected for some time to rapidly alternating forces the properties of the material may be very much changed. Experiments show that such a body may be broken by a stress far below that at which it would have iDroken before the application of the alternating force. repeated application and removal of a load, rapidly, 47.

Fracture ultimately maximum 44 stress in takes fig. Factor of safety. In actual engineering practice possible, by the theory of it is elasticity, usual to calculate, as nearly as the greatest stress to which any piece of material in a structure will be subjected, which stress is called the working stress, and the fraction ultimate stress working is stress The ultimate called the factor of safety of that particular piece. stress used in the calculation is, of course, the ultimate stress of a which has been tested.

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Applied elasticity by J Prescott


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