# Solution to Problem 204 Stress-strain Diagram

**Problem 204**

The following data were obtained during a tension test of an aluminum alloy. The initial diameter of the test specimen was 0.505 in. and the gage length was 2.0 in.

Load (lb) | Elongation (in.) | Load (lb) | Elongation (in.) |

0 | 0 | 14 000 | 0.020 |

2 310 | 0.00220 | 14 400 | 0.025 |

4 640 | 0.00440 | 14 500 | 0.060 |

6 950 | 0.00660 | 14 600 | 0.080 |

9 290 | 0.00880 | 14 800 | 0.100 |

11 600 | 0.0110 | 14 600 | 0.120 |

12 600 | 0.0150 | 13 600 | Fracture |

Plot the stress-strain diagram and determine the following mechanical properties: (a) proportional limit; (b) modulus of elasticity; (c) yield point; (d) yield strength at 0.2% offset; (e) ultimate strength; and (f) rupture strength.

# Solution to Problem 203 Stress-strain Diagram

**Problem 203**

The following data were recorded during the tensile test of a 14-mm-diameter mild steel rod. The gage length was 50 mm.

Load (N) | Elongation (mm) | Load (N) | Elongation (mm) |

0 | 0 | 46 200 | 1.25 |

6 310 | 0.010 | 52 400 | 2.50 |

12 600 | 0.020 | 58 500 | 4.50 |

18 800 | 0.030 | 68 000 | 7.50 |

25 100 | 0.040 | 59 000 | 12.5 |

31 300 | 0.050 | 67 800 | 15.5 |

37 900 | 0.060 | 65 000 | 20.0 |

40 100 | 0.163 | 65 500 | Fracture |

41 600 | 0.433 |

Plot the stress-strain diagram and determine the following mechanical properties: (a) proportional limits; (b) modulus of elasticity; (c) yield point; (d) ultimate strength; and (e) rupture strength.

# Solution to Problem 142 Pressure Vessel

**Problem 142**

A pipe carrying steam at 3.5 MPa has an outside diameter of 450 mm and a wall thickness of 10 mm. A gasket is inserted between the flange at one end of the pipe and a flat plate used to cap the end. How many 40-mm-diameter bolts must be used to hold the cap on if the allowable stress in the bolts is 80 MPa, of which 55 MPa is the initial stress? What circumferential stress is developed in the pipe? Why is it necessary to tighten the bolt initially, and what will happen if the steam pressure should cause the stress in the bolts to be twice the value of the initial stress?

# Solution to Problem 141 Pressure Vessel

# Solution to Problem 140 Pressure Vessel

**Problem 140**

At what angular velocity will the stress of the rotating steel ring equal 150 MPa if its mean radius is 220 mm? The density of steel 7.85 Mg/m^{3}.

**Solution 140**

$CF = M \omega^2 \bar x$

$M = \rho V = \rho A \pi R$

$x = 2R / \pi$

Thus,

$CF = \rho A \pi R \omega^2 (2R / \pi)$

# Solution to Problem 139 Pressure Vessel

# Solution to Problem 138 Pressure Vessel

# Solution to Problem 137 Pressure Vessel

# Solution to Problem 136 Pressure Vessel

**Problem 136**

A cylindrical pressure vessel is fabricated from steel plating that has a thickness of 20 mm. The diameter of the pressure vessel is 450 mm and its length is 2.0 m. Determine the maximum internal pressure that can be applied if the longitudinal stress is limited to 140 MPa, and the circumferential stress is limited to 60 MPa.

**Solution 136**

Based on circumferential stress (tangential):