_______________________________________________________________________ PROBLEM (8.18) Two triangular plates are weld together and subjected to biaxial stresses with σ x = -5 MPa and σy = 15 MPa, as depicted in Fig. P8.18. Determine: (a) The normal stress (b) The shear stress σw τw acting perpendicular to the weld. acting parallel to the weld. SOLUTION We have x’ θ = 25 + 90 = 115 σ x = −5 MPa σ y = 15 MPa τ xy = 0 σ x' τ x' y' θ o 5 MPa o 25 y’ x 15 MPa 1 1 (a) σ x ' = (σ x + σ y ) + (σ x − σ y ) cos 2θ 2 2 1 1 = (−5 + 15) + (−5 − 15) cos 230o = 11.43 MPa 2 2 Thus, σ w = σ x ' = 11.43 MPa 1 (b) τ x ' y ' = − (σ x − σ y ) sin 2θ 2 1 = − (−5 − 15) sin 230o = −7.66 MPa 2 τw So τ w = τ x ' y ' = −7.66 MPa Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.