# 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 |

**Answer Key**

Part (2): [ D ]

Part (3): [ A ]

**Solution**

$M_{max} = 600(12)(6) = 43,200 ~ \text{N}\cdot\text{m}$

$I = \dfrac{\pi}{64}(273^4 - 255^4) = 65,105,640.45 ~ \text{mm}^4$

Part (1)

$Q = 313,753.5 ~ \text{mm}^3$

$f_v = \dfrac{VQ}{Ib} = \dfrac{7200(313,753.5)}{65,105,640.45(18)}$

$f_v = 1.928 ~ \text{MPa}$ ← *answer*

Part (2)

$f_b = 90.57 ~ \text{MPa}$ ← *answer*

Part (3)

$\dfrac{PL^3}{3EI} = \dfrac{wL^4}{8EI}$

$\dfrac{P}{3} = \dfrac{600(12)}{8}$

$P = 2700 ~ \text{N}$ ← *answer*