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 b
determine the couple moment.
express your answer in kilopound - feet to three significant figures. assume the positive direction is counterclockwise.

( mr ) o =
kip·ft

incorrect; try again; one attempt remaining
previous answers
view available hint(s)

Explanation:

Step1: Calculate the resultant force of the triangular - distributed load

The triangular - distributed load has a maximum intensity \(w = 55\ lb/ft\) and a length \(L=9\ ft\). The resultant force of a triangular - distributed load is \(F=\frac{1}{2}wL\). For each triangular load, \(F=\frac{1}{2}\times55\times9 = 247.5\ lb\), and the location of the resultant of a triangular - distributed load from the vertex is \(\frac{2}{3}L\).

Step2: Calculate the moment of the triangular - distributed loads about point O

The two triangular - distributed loads act at a distance \(d_1=\frac{2}{3}\times9 = 6\ ft\) and \(d_2 = 9+\frac{1}{3}\times9=12\ ft\) from point O. The moment of a force \(F\) about a point is \(M = F\times d\). The moment due to the first triangular load \(M_1=F\times d_1=247.5\times6 = 1485\ lb - ft\), and the moment due to the second triangular load \(M_2=F\times d_2=247.5\times12 = 2970\ lb - ft\).

Step3: Calculate the total couple moment about point O

The total couple moment \((M_R)_O\) is the sum of the moments of the two triangular - distributed loads. \((M_R)_O=(1485 + 2970)\ lb - ft=4455\ lb - ft\). Convert to kilopound - feet: \((M_R)_O=\frac{4455}{1000}=4.46\ kip - ft\) (rounded to three significant figures).

Answer:

\((M_R)_O = 4.46\ kip - ft\)