# Example 02: Required Diameter of Circular Log Used for Footbridge Based on Shear Alone

**Problem**

A wooden log is to be used as a footbridge to span 3-m gap. The log is required to support a concentrated load of 30 kN at midspan. If the allowable stress in shear is 0.7 MPa, what is the diameter of the log that would be needed. Assume the log is very nearly circular and the bending stresses are adequately met. Neglect the weight of the log.

**Solution**

Maximum shear

$V_{max} = 15 ~ \text{kN}$

$V_{max} = 15 ~ \text{kN}$

$f_v = \dfrac{16V}{3\pi d^2}$

$0.7 = \dfrac{16(15\,000)}{3\pi d^2}$

$d^2 = \dfrac{16(15\,000)}{3\pi (0.7)}$

$d = 190.73 \text{mm}$ *answer*

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