# Strength of Materials

## Stresses of Hollow Circular Tube Used as a Pole

**Situation**

A 12-m pole is fixed at its base and is subjected to uniform lateral load of 600 N/m. The pole is made-up of hollow steel tube 273 mm in outside diameter and 9 mm thick.

1. Calculate the maximum shear stress (MPa).

A. 0.96 | C. 1.39 |

B. 1.93 | D. 0.69 |

2. Calculate the maximum tensile stress (MPa).

A. 96.0 | C. 60.9 |

B. 69.0 | D. 90.6 |

3. Calculate the force (kN) required at the free end to restrain the displacement.

A. 2.7 | C. 27 |

B. 7.2 | D. 72 |

## Continuous Beam With a Gap and a Zero Moment in Interior Support

**Situation**

A beam of uniform cross section whose flexural rigidity *EI* = 2.8 × 10^{11} N·mm^{2}, is placed on three supports as shown. Support *B* is at small gap Δ so that the moment at *B* is zero.

1. Calculate the reaction at *A*.

A. 4.375 kN | C. 5.437 kN |

B. 8.750 kN | D. 6.626 kN |

2. What is the reaction at *B*?

A. 4.375 kN | C. 5.437 kN |

B. 8.750 kN | D. 6.626 kN |

3. Find the value of Δ.

A. 46 mm | C. 34 mm |

B. 64 mm | D. 56 mm |

## Cross-Sectional Dimensions of Steel Rod to Elongate 1-mm when Subjected to 8,000 kg of Tension Force

**Problem**

A tensile load of 8000 kg elongates a 1-m long square rod by 1 mm. Steel modulus of elasticity is 2 × 10^{6} kg/cm^{2}. What is the dimension of a side of the rod?

A. 5 cm | C. 2 cm |

B. 1 cm | D. 4 cm |

## Strength of Temporary Earth Retaining Wall Made from Wooden Planks

**Situation**

A temporary earth retaining wall consists of wooden plank driven vertically into the ground. The wall is designed to resist 2.4 m height of soil.

Cross-sectional dimensions of the plank = 300 mm wide × 75 mm thick

Allowable bending stress of the plank = 10.4 MPa

Allowable shear stress of the plank = 0.8 MPa

Unit weight of retained soil = 17.3 kN/m

^{3}

Active earth pressure coefficient = 1/3

1. Calculate the maximum flexural stress.

A. 12.7 MPa | C. 8.6 MPa |

B. 14.2 MPa | D. 10.1 MPa |

2. Calculate the maximum shear stress.

A. 1.11 MPa | C. 0.99 MPa |

B. 0.33 MPa | D. 0.77 MPa |

3. Calculate the minimum thickness of the plank to prevent failure.

A. 90 mm | C. 110 mm |

B. 80 mm | D. 100 mm |