Hw ch7
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The document contains solutions to several problems involving stresses in cylindrical tanks and shafts. Problem 7 involves determining stresses in a compressed air tank given its dimensions, wall thickness, internal pressure, and an applied force. Problem 7.120 calculates stresses in a tank given an applied torque, internal pressure, inner diameter, and wall thickness. Problem 7.121 determines the torque required to produce a given maximum normal stress in a tank with known pressure, diameter, and thickness. Problem 7.104 finds the maximum fill height for a water storage tank given the material properties, wall thickness, and a safety factor. Problem 7.85 uses maximum shear stress to find the force that will cause yielding in
Hw ch7
- 1. Solved Problems Problem 7.124: The compressed-air tank AB has a 250mm outside diameter and an 8mm wall thickness. It is fitted with a collar by which a 40-KN force F is applied at B in the horizontal direction. Knowing that the gage pressure inside the tank is 5-MPa. Determine the maximum normal stress and the maximum shearing stress at point K. Solution: Assume: neglect of the collar dimensions. ( ) ( )
- 2. Using Mohr Circle: √ ( ) ,
- 3. Problem 7.120: A torque of the magnitude T= 12 KN. m is applied to the end of a tank containing compressed air under a pressure of 8 MPa. Knowing that the tank has a 180-mm inner diameter and 12-mm wall thickness, determine the maximum normal stress and the maximum shearing stress in the tank. Solution: = 90mm, t=12mm, , Torsion: C1=90mm, C2=102mm, ( ) Using Mohr’s Circle: √ ( )
- 4. Problem 7.121: The tank shown has a 180-mm inner diameter and 12-mm wall thickness. Knowing that the tank contains compressed air under a pressure of 8- MPa, determine the magnitude T of the applied torque for which the maximum normal stress is 75-MPa. Solution: , Torsion: C1=90mm, C2=102mm, ( ) Using Mohr’s Circle:
- 5. Problem 7.104: The unpressurized cylindrical storage tank shown has a 5-mm wall thickness and is made of steel having 450 MPa, ultimate strength in tension. Determine the max h to which it can be filled with water if the factor of safety of 4 is desired. (Specific weight of water=9810 N/m2.). Solution:
- 6. , Solution: ( ) , Using Mohr’s Circle:
- 7. Since,| | , stress point lies in 4th quadratic Equation of 4th quadratic boundary is: R= 34.612 MPa √ ( ) Torsion: C=16-mm,
- 8. Solution: √ ( ) | | Since,| | stress point lies in 4th quadratic Equation of 4th quadratic boundary is: | |
- 9. Solution: ( ) , √ ( ) √ √ √ ( ) ( )
- 10. Problem 7.85: The 44-mm diameter shaft AB is made of a grade of steel for which the yield strength is 250 MPa. Using the maximum shearing stress principle criterion, determine the magnitude of the force P for which yield occurs when T= 1.5 KN. m. Solution: ( ) √ ( ) ………………………………………………………………………….. (1) √ ( ) ……………………………………………………………………………. (2)
- 11. Subtract (2) from (1): √ = 174 MPa, ( )