## 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

## Solution to Problem 141 Pressure Vessel

**Problem 141**

The tank shown in Fig. P-141 is fabricated from 1/8-in steel plate. Calculate the maximum longitudinal and circumferential stress caused by an internal pressure of 125 psi.

## 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

**Problem 138**

The strength of longitudinal joint in Fig. 1-17 is 33 kips/ft, whereas for the girth is 16 kips/ft. Calculate the maximum diameter of the cylinder tank if the internal pressure is 150 psi.

## Solution to Problem 137 Pressure Vessel

**Problem 137**

A water tank, 22 ft in diameter, is made from steel plates that are 1/2 in. thick. Find the maximum height to which the tank may be filled if the circumferential stress is limited to 6000 psi. The specific weight of water is 62.4 lb/ft^{3}.

## 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):

## Solution to Problem 135 Pressure Vessel

## Solution to Problem 134 Pressure Vessel

**Problem 134**

The wall thickness of a 4-ft-diameter spherical tank is 5/16 inch. Calculate the allowable internal pressure if the stress is limited to 8000 psi.