Problem

Solve Problem 15.17 if the beam is made of 2024-T851 aluminum alloy.A rectangular section...

Solve Problem 15.17 if the beam is made of 2024-T851 aluminum alloy.

A rectangular section beam has a depth 2c = 150 mm, width t = 25 mm, and length L = 2.0 m. The beam is loaded as a simply supported beam with a concentrated load P at the center. A notch is machined into the beam on the tension side opposite the point of application of P. The depth of the notch was increased by fatigue loading until a = 15 mm. The beam is made of 17-7PH precipitation hardening steel heat-treated to yield the properties indicated in Table 15.1.

a. Determine whether or not plane strain conditions are satisfied for the beam.
b. Determine the fracture load P.

Table 15.1:

TABLE 15.1 KIC Critical Stress Intensity Factor (Fracture Toughness)a

Material	σu[MPa]	Y [MPa]		Minimum values for B, a, t [mm]
Alloy Steels
A533B	—	500	175	306.0
2618 Ni Mo V	—	648	106	66.9
V1233 Ni Mo V	—	593	75	40.0
124 K 406 Cr Mo V	—	648	62	22.9
17-7PH	1289	1145	77	11.3
17-4PH	1331	1172	48	4.2
Ph 15-7M0	1600	1413	50	3.1
AISI 4340	1827	1503	59	3.9
Stainless Steel
AISI 403	821	690	77	31.1
Aluminum Alloys
6061-T651	352	299	29	23.5
2219-T851	454	340	32	22.1
7075-T7351	470	392	31	15.6
7079-T651	569	502	26	6.7
2024-T851	488	444	23	6.7
Titanium Alloys
Ti-6AI-4Zr-2Sn-0.5Mo-0.5V	890	836	139	69.1
Ti-6AI-4V-2Sn	852	798	111	48.4
Ti-6.5AI-5Zr-1V	904	858	106	38.2
Ti-6AI-4Sn-1V	889	878	93	28.0
Ti-6AI-6V-2.5Sn	1176	1149	66	8.2