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For the curved beam shown (hook with a total lifting capacity of m= 68 tonnes [1 tonne=1000 kg]): NOTE: Be sure to convert mass (m) to force (P) using the acceleration of gravity (g-9.816 m/s² such that P=mg W M=P*r (where t = 5+1), y=1,₂-1, where r = [ -200 mm m=68 tonnes a) Use the curved beam equations to solve for the maximum, tensile bending stress at section A-A. but max tensile stress is at the inner radius, r. For this case & max tension Ae(r, -y) My Note that o= = |M=P*1, where 13 b) Use the straight beam equation to solve for the maximum tensile bending stress at A-A. My Note that o but maximum tensile stress is at the inner radius, 1₁. For this case & max tension I -(rectangular cross section) bh³ 12 y- and I=. W= 600 mm t=150 mm 12 and Awt (rectangular cross section), e=r-r c) Quantify the difference between the answers from a) and b) [Indicate which is "correct" at A-A] Comment on the correctness of either a) or b) for this case and why.
b) Use the straight beam equation to solve for the maximum tensile bending stress at A-A. My Note that o malgr but maximum tensile stress is at the inner radius, L. For this case & max tension I -(rectangular cross section) M-P, (where -5,5). y = bh³ y and I = 12 12 c) Quantify the difference between the answers from a) and b) [Indicate which is "correct" at A-A] Comment on the correctness of either a) or b) for this case and why. d) Calculate the total maximum tensile stress at the surface. that ol = 0+0, where o = such that A = wt and o, is the correct bending stress P A e) If the material is ductile (A441 HSLA steel) with Syp-414 MPa and Suts-552 MPa, use the appropriate failure criterion to determine the factor of safety in the curve of the hook. Is the design safe?