# Example 01: Spacing of Screws in Box Beam

**Problem**

A concentrated load *P* is carried at midspan by a simply supported 4-m span beam. The beam is made of 40-mm by 150-mm timber screwed together, as shown. The maximum flexural stress developed is 8.3 MPa and each screw can resist 890 N of shear force.

- Determine the spacing of screws at
*A*. - Determine the spacing of screws at
*B*. - Determine the spacing of screws if screws at
*A*and*B*are equally spaced.

**Solution**

$I = \sum \dfrac{bd^3}{12} = \dfrac{190(190^3)}{12} - \dfrac{110(110^3)}{12}$

$I = 96\,400\,000 ~ \text{mm}^4$

$f_b = \dfrac{Mc}{I}$

$8.3 = \dfrac{M(190/2)(1000^2)}{96\,400\,000}$

$M = 8.422 ~ \text{kN}\cdot\text{m}$

$M = \dfrac{PL}{4}$

$8.422 = \dfrac{P(4)}{4}$

$P = 8.422 ~ \text{kN}$

$V_{max} = 0.5P = 4.211 ~ \text{kN}$

**Spacing of Screws**

$s = \dfrac{RI}{VQ}$

Part 1: Spacing of screws at *A*

$s = \dfrac{890(96\,400\,000)}{4\,211(450\,000)} = 45.28 ~ \text{mm}$

Use *s* = 45 mm *answer*

Part 2: Spacing of screws at *B*

$s = \dfrac{890(96\,400\,000)}{4\,211(330\,000)} = 61.78 ~ \text{mm}$

Use *s* = 60 mm *answer*

Part 3: Spacing of screws if all are equally spaced

$s = \dfrac{890(96\,400\,000)}{4\,211(450\,000)} = 45.28 ~ \text{mm}$

Use *s* = 45 mm *answer*