4. A cantilever beam is fixed to a wall at one end, subjected to a load...

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4. A cantilever beam is fixed to a wall at one end, subjected to a load P and moment M, as shown in fig. 3. Note that the beam has a number of circular holes and circular notches located on it. The bearn is made of concrete with the following properties: ult-tension=3 MPa, Jult-compression = 25 MPa, E = 30 GPa and t = 10 cm. Also, assume P = 10000 N. (a) Calculate the maximum stress at the holes, as a function of M. (b) Calculate the maximum stress at the notches, as a function of M. (c) Calculate the maximum stress at section A-A, as a function of M. (d) Specify an appropriate failure criterion, and use it to determine the maximum allowable moment M that can be applied before failure. (e) In a drawing, indicate where the bear is likely to fall due to this loading. Scale: 1 square= 10 x 10 cm Note: Table 1 is provided for reference. Figure 3 Solution: (a) max.hole = 47.6M - 263279 Pa. (b) max.notch=310.54M - 3969851 Pa. (c) max A-4 = 93.75M-1187500 Pa. (d) Maximum Principal Stress Failure Theory, M 22 444 N. (e) Failure at top notches. J 4. A cantilever beam is fixed to a wall at one end, subjected to a load P and moment M, as shown in fig. 3. Note that the beam has a number of circular holes and circular notches located on it. The bearn is made of concrete with the following properties: ult-tension=3 MPa, Jult-compression = 25 MPa, E = 30 GPa and t = 10 cm. Also, assume P = 10000 N. (a) Calculate the maximum stress at the holes, as a function of M. (b) Calculate the maximum stress at the notches, as a function of M. (c) Calculate the maximum stress at section A-A, as a function of M. (d) Specify an appropriate failure criterion, and use it to determine the maximum allowable moment M that can be applied before failure. (e) In a drawing, indicate where the bear is likely to fall due to this loading. Scale: 1 square= 10 x 10 cm Note: Table 1 is provided for reference. Figure 3 Solution: (a) max.hole = 47.6M - 263279 Pa. (b) max.notch=310.54M - 3969851 Pa. (c) max A-4 = 93.75M-1187500 Pa. (d) Maximum Principal Stress Failure Theory, M 22 444 N. (e) Failure at top notches. J