Problem 1007 | Flexural stresses developed in the wood and steel fibers | Strength of Materials Review at MATHalino

Problem 1007
A uniformly distributed load of 300 lb/ft (including the weight of the beam) is simply supported on a 20-ft span. The cross section of the beam is described in Problem 1005. If n = 20, determine the maximum stresses produced in the wood and the steel.

Solution 1007

Click here to expand or collapse this section

Maximum moment will occur at the midspan
$M_{max} = \dfrac{w_oL^2}{8} = \dfrac{300(20^2)}{8}$

$M_{max} = 15\,000 ~ \text{lb}\cdot\text{ft}$

From Solution 105:

$\bar{y} = 7.1 ~ \text{in}$

$I_{NA} = \frac{3487}{3} ~ \text{in}^4$

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

At the extreme wood fiber ($c = \bar{y}$)
$f_{bw} = \dfrac{M_{max} \, \bar{y}}{I_{NA}}$

$f_{bw} = \dfrac{15\,000(7.1)(12)}{\frac{3487}{3}}$

$f_{bw} = 1099.51 ~ \text{psi}$ answer

At the extreme steel fiber ($c = 10.5 - \bar{y}$)
$\dfrac{f_{bs}}{n} = \dfrac{M_{max}(10.5 - \bar{y})}{I_{NA}}$

$\dfrac{f_{bs}}{20} = \dfrac{15\,000(10.5 - 7.1)(12)}{\frac{3487}{3}}$

$f_{bs} = 10\,530.54 ~ \text{psi}$ answer

Problem 1007 | Flexural stresses developed in the wood and steel fibers

Navigation

Recent comments