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Download e-book for kindle: Advanced Applied Stress Analysis by C.T.F. Ross

By C.T.F. Ross

ISBN-10: 0745800769

ISBN-13: 9780745800769

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Shearing force. the same figure, which is shown shaded. Let the stress on th€ left of the of Fig. 2(b) be o, and the stress on the right of the sub-sub-element be o + do, due to M and M + dM, respectively. From Fig. e. the only way equilibriurn can be achieved is lor a longitudinal horizontal stress to act tangentially along the rectangular face ABCD. It is evident that as this stress acts tangentially along the face ABCD, it must be a shearing stress. Let, sub-sub-element z : shearing stress on the face ABCD Resolving horizontally, "*6*6*: f do * a,t :JldM*y*d,A 1 where, dA:Z*dy dMll but, ':E ' dM dx :f: 1n oo sneanng lorce at x 48 Shear Stresses in Bending and Shear Deflections [ch.

Complementary shearing stresses in a vertical plane. From Fig. 3, it can be seen that these four complementary shearing stresses act together in a vertical plane, and this is why these shearing stresses are'called vertical shearing stresses. 4. : : M* o: o + do : M dM bending moment at AB bending moment at CD bending stress in flange at AB bending stress in flange at CD Consider the equilibdum of an element of the flange, ABCD, in the x direction. From the plan view oI Fig. 4, it can be seen that the apparent unbalanced force in the longitudinal direction on this element rs do x tx(B - Z).

63 Yertical Sh€oring Str€ss At the top of the tlange, J Y'd'{ = o therefore tr:0 t2 NA t Ch. 1), it can be seen that the maximum shear stress, namely t, occurs where $y'dA)lb is a maximum, which in this case is at NA. 2), it can be seen that the horizontal shearing stress va es linearly along the Ilanges of the RSJ, from zero at the free edges to a maximum value iF at the centre. and. 5 A Dlot of the vertical and horizontal shearins stresses is shown in Fie. 18. 18. d horizotrtal shearing stress distributioN MN/m2).

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Advanced Applied Stress Analysis by C.T.F. Ross

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