Question

consider the beam shown in.
part a
determine the resultant couple moment acting on the beam. express your answer to three significant figures and include the appropriate units. assume the positive direction is counterclockwise.
$(m_{c})_{r}=$ value units

Explanation:

Step1: Define couple - moment formula

The couple - moment $M = Fd$, where $F$ is the magnitude of the force and $d$ is the perpendicular distance between the forces of the couple.

Step2: Identify and calculate individual couple - moments

• For the 400 - N force couple: The perpendicular distance between the 400 - N forces is $3 + 2=5$ m. The moment of this couple $M_1=400\times5 = 2000$ N·m (counter - clockwise, so positive).
• For the 200 - N force couple: The perpendicular distance is 0.2 m. The moment of this couple $M_2 = 200\times0.2=40$ N·m (clockwise, so negative).
• For the 300 - N force couple: The perpendicular distance between the 300 - N forces is $3 + 2 = 5$ m. The moment of this couple $M_3=300\times5 = 1500$ N·m (clockwise, so negative).

Step3: Calculate the resultant couple - moment

$M_R = M_1+M_2 + M_3$.
$M_R=2000-40 - 1500$.
$M_R = 460$ N·m.

Answer:

460 N·m