Plane Strain: The Direct Determination of Stress . Fig 2, 3^ The stresses due to this loading are as follows :P Tra a 1 tan ^ tan ^ • -f x y y . i x y tan y / yy o ira a L \ / tan~^ __ x-^a — U y y ^ y y ^ ay(x^b)(a;—-5)^4-|^^._: r (33) -xy Tra T. ,2 J 120 Mr, S. D. Carothers. (16) There is no difficulty in obtaining from the foregoing the results foitriangular loading of maximum intensity P as shown in fig. y Fig 3. JC The stresses are yy xy- P iraih—a) fe(tan ^—^tan^-—-j + ^^tMtan ^^—tan \ y y I V y y ah tan~^ -—- — tan^ ? -f by log — ? ;/—i \ y y / (a?—a)2-f3/ //rj»—. f) I* —I- Qj + ^w/
Plane Strain: The Direct Determination of Stress . Fig 2, 3^ The stresses due to this loading are as follows :P Tra a 1 tan ^ tan ^ • -f x y y . i x y tan y / yy o ira a L \ / tan~^ __ x-^a — U y y ^ y y ^ ay(x^b)(a;—-5)^4-|^^._: r (33) -xy Tra T. ,2 J 120 Mr, S. D. Carothers. (16) There is no difficulty in obtaining from the foregoing the results foitriangular loading of maximum intensity P as shown in fig. y Fig 3. JC The stresses are yy xy- P iraih—a) fe(tan ^—^tan^-—-j + ^^tMtan ^^—tan \ y y I V y y ah tan~^ -—- — tan^ ? -f by log — ? ;/—i \ y y / (a?—a)2-f3/ //rj»—. f) I* —I- Qj + ^w/ log ^ ^ ^^^ ^ r^* + 3/ Traih^a) fe/tan ^ 2/ tan 1.::—_) -I- . (34) 2/ —a&ftan 1 Jj~~ C tan y ^y iraQy—oC) 1) i tan ^ ic ^ tan^ .1 a X y a tan ^ -^ — tan v y As these results are of some practical importance, the stresses could beexpressed more simply by writing 6 =^ tain~^xjy, #i = tan*^(;«—a)/^/, and02 = tan-^ (^-~^)/3/j where 6, 6i, and 02 are measured from the planes ^ = 0^,X = (Xj and X :=^b respectively, and are positive on the side on which x increasesand negative on the other side. Plane Strain: the Direct Determination of Stress. 121
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