Stresses of Hollow Circular Tube Used as a Pole | CE Board Problem in Structural Engineering and Construction

Date of Exam

November 2018

Subject

Structural Engineering and Construction

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

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Part (1): [ B ]
Part (2): [ D ]
Part (3): [ A ]

Solution

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$V_{max} = 600(12) = 7200 ~ \text{N}$

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

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

Part (1)

$Q = \frac{1}{2}\pi (136.5^2) \cdot \dfrac{4(136.5)}{3\pi} - \frac{1}{2}\pi (127.5^2) \cdot \dfrac{4(127.5)}{3\pi}$

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

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

$f_v = 1.928 ~ \text{MPa}$ ← answer

Part (2)

$f_b = \dfrac{Mc}{I} = \dfrac{43,200(1000)(136.5)}{65,105,640.45}$

$f_b = 90.57 ~ \text{MPa}$ ← answer

Part (3)

$\delta_{\text{due to force } P} = \delta_{\text{due to uniform load}}$

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

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

$P = 2700 ~ \text{N}$ ← answer

Category

Strength of Materials

Mechanics of Materials

Circular Pole

Maximum Shear Stress

Maximum Flexural Stress

Maximum Bending Stress

Cantilever Deflection

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