_______________________________________________________________________ PROBLEMS (8.106 through 110) The state of strain at particular points in a structure is given in the table below. Determine the state of strain associated with axes x’ and y’ rotated through the specified angle θ (Figs. P8.106 through P8.110). Use Eqs. (8.35). ------------------------------------------------------------------------------------Problem εx εy εz θ ------------------------------------------------------------------------------------800 μ 1500 μ 30o 8.106 -400 μ 8.107 500 μ 1200 μ -1000 μ -45o 8.108 200 μ 410 μ 100 μ 40o 8.109 -300 μ 420 μ 200 μ 10o -200 μ 240 μ -30o 8.110 -720 μ -------------------------------------------------------------------------------------- SOLUTION (8.106) −400 + 800 −400 − 800 cos 60o + 750sin 60o + 2 2 = 200 − 600(0.5) + 750(0.866) = 550 μ ε y ' = 200 + 300 − 650 = −150 μ ε x' = γ x ' y ' = −( −400 − 800) sin 60o + 1500 cos 60 o = 1789 μ SOLUTION (8.107) 500 + 1200 + 0 − 500sin(−90o ) 2 = 850 + 500 = 1350 μ ε y ' = 850 − 500 = 350 μ ε x' = γ x ' y ' = −(500 − 1200) sin( −90 o ) + 0 = −700 μ Continued on next slide 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. SOLUTION (8.108) 200 + 410 200 − 410 cos80o + 50sin 80o + 2 2 = 305 − 18 + 49 = 336 μ ε y ' = 305 + 18 − 49 = 274 μ ε x' = γ x ' y ' = −( 200 − 410) sin 80 o + 100 cos 80 o = 224 μ SOLUTION ( 8.109) −300 + 420 −300 − 420 cos 20o + 100sin 20o + 2 2 = 60 − 338 + 34 = −244 μ ε y ' = 60 + 338 − 34 = 364 μ ε x' = γ x ' y ' = −( −300 − 420) sin 20 o + 200 cos 20 o = 246 + 188 = 434 μ SOLUTION ( 8.110) −720 − 200 −720 + 210 cos(−60o ) + 120sin(−60o ) + 2 2 = −460 − 130 − 104 = −694 μ ε y ' = −460 + 130 + 104 = −226 μ ε x' = γ x ' y ' = −( −720 + 200) sin( −60 o ) + 240 cos( −60 o ) = −330 μ 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.