Questions: A precast concrete wall section is temporarily held by two cables, as shown. Knowing that the tension in cable BD is 900 N , determine the moment about point O of the force exerted by the cable B. No need to carry out the calculations - Just set up the moment equation based on force and position vectors.

Solution Steps

The position vector $\vec{r}$ is directed from the point about which the moment is taken (point O) to any point on the line of action of the force. We can use the position vector $\vec{r}_{OB}$ which points from O to B:

$\vec{r}_{OB} = 2.5\hat{j} + 2\hat{k}$ m

The tension in cable BD is 900 N. The force vector $\vec{T}_{BD}$ has a magnitude of 900 N and acts along the direction BD. We can express $\vec{T}_{BD}$ in terms of its magnitude and a unit vector along BD:

$\vec{T}_{BD} = 900 \frac{\vec{BD}}{|BD|} $

$\vec{BD} = 1 \hat{i} - 2.5 \hat{j} - 2 \hat{k}$

$|BD| = \sqrt{1^2 + (-2.5)^2 + (-2)^2} = \sqrt{11.25}$

$\vec{T}_{BD} = 900 (\frac{1\hat{i} - 2.5\hat{j} - 2\hat{k}}{\sqrt{11.25}})$ N

The moment $\vec{M}_O$ of the force exerted by cable B about point O is the cross product of the position vector and the force vector:

$\vec{M}_O = \vec{r}_{OB} \times \vec{T}_{BD}$

$\vec{M}_O = (2.5\hat{j} + 2\hat{k}) \times 900 (\frac{1\hat{i} - 2.5\hat{j} - 2\hat{k}}{\sqrt{11.25}})$ N⋅m

Final Answer: