# Solution to Problem 583 | Design for Flexure and Shear

**Problem 583**

A rectangular beam 6 in. wide by 10 in. high supports a total distributed load of W and a concentrated load of 2W applied as shown in Fig. P-583. If f_{b} ≤ 1500 psi and f_{v} ≤ 120 psi, determine the maximum value of W.

**Solution 583**

$\Sigma M_{R2} = 0$

$12R_1 = W(6) + 2W(3)$

$R_1 = W$

$\Sigma M_{R1} = 0$

$12R_2 = W(6) + 2W(9)$

$R_2 = 2W$

Based on allowable bending stress:

$f_b = \dfrac{6M}{bd^2}$

$1500 = \dfrac{6(45W/8)(12)}{6(10^3)}$

$W = 2\,222.22 \, \text{ lb}$

Based on allowable shearing stress:

$f_v = \dfrac{3V}{2bd}$

$120 = \dfrac{3(2W)}{2(6)(10)}$

$W = 2400 \, \text{ lb}$

For safe value of W, use **W = 2 222.22 lb**. *answer*

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