consider the beam shown in.\npart a\ndetermine the resultant couple moment acting on the beam. express your…

consider the beam shown in.\npart a\ndetermine 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.\n$(m_{c})_{r}=$ value units

consider the beam shown in.\npart a\ndetermine 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.\n$(m_{c})_{r}=$ value units

Answer

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