Question

replace the loading (figure 1) by an equivalent resultant force and couple moment acting at point o. suppose that determine the resultant force. express your answer in pounds to three significant figures. assume the positive direction is upward. determine the couple moment.

Explanation:

Step1: Analyze the distributed - load

The distributed - load can be divided into two triangular distributed - loads. The area of a triangular distributed - load is given by \(A=\frac{1}{2}bh\), where \(b\) is the base and \(h\) is the height.
For the upper triangular load with height \(h_1 = 9\mathrm{ft}\) and base \(w\), the magnitude of the equivalent force \(F_1=\frac{1}{2}\times9\times w\). For the lower triangular load with height \(h_2 = 9\mathrm{ft}\) and base \(w\), the magnitude of the equivalent force \(F_2=\frac{1}{2}\times9\times w\).

Step2: Calculate the resultant force

The resultant force \(F_R\) of the two triangular distributed - loads is the sum of the equivalent forces of the two triangular loads. Since \(F_1 = F_2=\frac{9w}{2}\), then \(F_R=F_1 + F_2=9w\).

Answer:

\(F_R = 9w\)