. The strength of materials; a text-book for engineers and architects. the same radius so that they contact only at theiredges, we see that each plate may be regarded as supportedat its point of contact with the one below it, the load trans- W mitted at its overhanging end being -^ . (See also Fig. 152.) The diagram for each plate comes therefore as shown. In order that the spring may close practically fiat, the curvature of each plate must remain constant after bending, the radius of each plate after bending must be the same. 1 MBut from p. 249 ^ = ^^^ R EI M . •. Since E is constan
. The strength of materials; a text-book for engineers and architects. the same radius so that they contact only at theiredges, we see that each plate may be regarded as supportedat its point of contact with the one below it, the load trans- W mitted at its overhanging end being -^ . (See also Fig. 152.) The diagram for each plate comes therefore as shown. In order that the spring may close practically fiat, the curvature of each plate must remain constant after bending, the radius of each plate after bending must be the same. 1 MBut from p. 249 ^ = ^^^ R EI M . •. Since E is constant ^ is constant. Between b and b, the is constant so that the sectionis constant, but for A B and a b the varies in thetriangular manner shown, so that the section must vary so as to keep ^ constant. This can be done by making the ends triangular in plan,the thickness being constant. Then at any point at distance x from a 12 M = ^\^ M _ 6 6 X rf3•• I ~ Wa: and ^ = 7, by similar As M 6c?3 . •. T =1X7 7/ = constantI WZ 352 THE STRENGTH OF MATERIALS. Fig. 152.—Stresses in Plate Springs. Another way would be to keep the ends square and to varythe thickness as indicated. Then I ^ *jf, M = Y M For -p to be constant d/ SPRINGS d^ X X 353 and if the lap were I ^^— •• ~ r contoured so that the relation held, the necessary conditionswould be satisfied. Now suppose that there are n plates and that all but thetop one are cut longitudinally through the centre and placedas shown in Fig. 152 they would make up the diamond-shaped
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