Problem 1009 | Width of aluminum plate reinforcement for the wood section to resist 14 kN-m moment | Strength of Materials Review at MATHalino

Problem 1009
A timber beam 150 mm wide by 200 mm deep is to be reinforced at the top and bottom by aluminum plates 6 mm thick. Determine the width of the aluminum plates if the beam is to resist a moment of 14 kN·m. Assume n = 5 and take the allowable stresses as 10 MPa and 80 MPa in the wood and aluminum, respectively.

Solution 1009

Click here to expand or collapse this section

$M = 14 ~ \text{kN}\cdot\text{m}$

$I = \dfrac{5b(212^3)}{12} - \dfrac{(5b - 150)(200^3)}{12}$

$I = 3\,970\,053.33b - 3\,333\,333.33b + 100\,000\,000$

$I = 636\,720b + 100\,000\,000$

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

Based on allowable flexural stress of aluminum:

$f_b = 80 / n$

$c = \frac{1}{2}(200) + 6 = 106 ~ \text{mm}$

Thus,
$\dfrac{80}{n} = \dfrac{14(1000^2)(106)}{636\,720b + 100\,000\,000}$

$b = -11.38 ~ \text{mm}$

Based on allowable flexural stress of wood:

$f_b = 10 ~ \text{MPa}$

$c = \frac{1}{2}(100) = 100 ~ \text{mm}$

Thus,
$10 = \dfrac{14(1000^2)(100)}{636\,720b + 100\,000\,000}$

$b = 62.82 ~ \text{mm}$

For stronger section, use $b = 62.82 ~ \text{mm}$ answer

Problem 1009 | Width of aluminum plate reinforcement for the wood section to resist 14 kN-m moment

Navigation

Recent comments