# 238 Finding the resultant of trapezoidal loading

**Problem 238**

The beam AB in Fig. P-238 supports a load which varies an intensity of 220 N/m to 890 N/m. Calculate the magnitude and position of the resultant load.

**Solution 238**

$F_1 = 6(220) = 1320 \, \text{ N}$

$F_2 = \frac{1}{2}(6)(670) = 2010 \, \text{ N}$

$R = F_1 + F_2 = 1320 + 2010$

$R = 3330 \, \text{ N}$

$Rd = 3F_1 + 4F_2$

$3330d = 3(1320) + 4(2010)$

$3330d = 12000$

$d = 3.6 \, \text{ m}$

Thus, R = 3330 N downward at 3.6 m to the left of A. *answer*