8.9 A bending member with a rectangular cross section has dimensions, as defined in Fig. 8.13(a),...

 

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8.9 A bending member with a rectangular cross section has dimensions, as defined in Fig. 8.13(a), of b = 40 and t = 20mm, and a through-thickness edge crack of length a is present. The beam is made of 7475-T7351 aluminum and is subjected to a bending moment of M = 900N-m. a. If the crack length is a = 4.0mm, what is the stress intensity factor K? What is the safety factor against brittle fracture? b. Repeat (a) fora crack length of 20 mm. 8.10 For the same bending member with an edge crack as in Prob. 8.9, proceed as follows: a. What is the critical crack length for fracture? b. What crack length can be allowed if a safety factor of 3.0 against brittle fracture is required? c. For the crack length found in (b), what is the safety factor against fully plastic yielding? Figure 8.13 IL F 5 4 3 2 - K-FSgJma 6M Sg = bt (a) F= Expressions for any = alb: (b) F= 0.2 Values for small alb and limits for 10% accuracy: (a, b) K=1.12S na tan 0.4 2 a = ab P/2 cos P/2 (a) (b) h/b=2 0.6 (a/b 0.4) 0.923 +0.199 (1-sin 2 1.99-a (1-a) (2.15 - 3.93a+2.7a) (1+2a) (1-a)/2 0.8 Ph M= 2 (h/b=2) 1.0 (large h/b) 8.9 A bending member with a rectangular cross section has dimensions, as defined in Fig. 8.13(a), of b = 40 and t = 20mm, and a through-thickness edge crack of length a is present. The beam is made of 7475-T7351 aluminum and is subjected to a bending moment of M = 900N-m. a. If the crack length is a = 4.0mm, what is the stress intensity factor K? What is the safety factor against brittle fracture? b. Repeat (a) fora crack length of 20 mm. 8.10 For the same bending member with an edge crack as in Prob. 8.9, proceed as follows: a. What is the critical crack length for fracture? b. What crack length can be allowed if a safety factor of 3.0 against brittle fracture is required? c. For the crack length found in (b), what is the safety factor against fully plastic yielding? Figure 8.13 IL F 5 4 3 2 - K-FSgJma 6M Sg = bt (a) F= Expressions for any = alb: (b) F= 0.2 Values for small alb and limits for 10% accuracy: (a, b) K=1.12S na tan 0.4 2 a = ab P/2 cos P/2 (a) (b) h/b=2 0.6 (a/b 0.4) 0.923 +0.199 (1-sin 2 1.99-a (1-a) (2.15 - 3.93a+2.7a) (1+2a) (1-a)/2 0.8 Ph M= 2 (h/b=2) 1.0 (large h/b)