Question

replace the loading (figure 1) by an equivalent resultant force and couple - moment acting at point o. suppose that w = 55 lb/ft. part a determine the resultant force. express your answer in pounds to three significant figures. assume the positive direction is upward. part b determine the couple moment.

Explanation:

Step1: Analyze the two - part distributed load

The loading consists of two triangular distributed loads. The area of a triangular distributed load gives the resultant force of that load. The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Calculate the resultant force of each triangular load

For the upper triangular load with base $b = 9$ ft and height $h=w = 55$ lb/ft, the resultant force $F_1=\frac{1}{2}\times9\times55 = 247.5$ lb. For the lower triangular load with base $b = 9$ ft and height $h = 55$ lb/ft, the resultant force $F_2=\frac{1}{2}\times9\times55=247.5$ lb.

Step3: Find the total resultant force

Since both forces act in the same direction (down - ward, but we consider the positive direction as upward in the problem statement, so they are negative), the resultant force $F_R=-(F_1 + F_2)$. Substituting the values of $F_1$ and $F_2$, we get $F_R=-(247.5+247.5)= - 495$ lb. The magnitude of the resultant force is $|F_R| = 495$ lb.

Answer:

495 lb