PLAIN AND CIVIL: EXAMPLE 6.0.4. APPLICATION OF RESULTANT COUPLE MOMENT FOR COPLANAR FORCES

Saturday 16 March 2019

Determine the required magnitude of F, if the resultant couple moment on the beam is to be zero.

The resultant couple moment is computed by adding all couples in the clockwise rotation and deducting those couples in the counterclockwise rotation.

$M_{R}=M_{CW}-M_{}CCW=0$

Although couples are visible in the given beam, their distances between are still hard to identify. Thus, take the components of the couples.

Analyze the rotation of each couple and simplify the equation.

$M_{R}=0=\left ( -5_{x} \right )\left ( 1m \right )+5_{y}\left ( 3m \right )-F_{y}\left ( 3m \right )+F_{x}\left ( 1m \right )$

$M_{R}=0=\frac{-3}{5}5kN\left ( 1m \right )+\frac{4}{5}5kN\left ( 3m \right )-Fsin30^{o}\left ( 3m \right )+Fcos30^{o}\left ( 1m \right )$

$0.634F=9$

${\color{Red} \mathbf{F=14.20kN\cdot m}}$

RELATED TOPIC:

6.0. COUPLES AND FORCE-COUPLE SYSTEMS

PLAIN AND CIVIL

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Saturday 16 March 2019

EXAMPLE 6.0.4. APPLICATION OF RESULTANT COUPLE MOMENT FOR COPLANAR FORCES

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