For a truss given below, can we solve the force acting on every member? Surprisingly, yes. Here’s how. First, we have to solve the reactions on $H$ and $L$. \begin{align*} \Sigma M_{L} = 3Pa-4Ha = 0 \to& H= {3 \over 4} P \\ \Sigma F_{y} = H+L-P=0 \to& L={1\over4}P \end{align*} Second, let’s get rid of zero-force members. For joint $D$ to be in equilibrium, $F_{DI}$ should be zero because there’s..
Moment of a force about an axis through the origin $O$ can be calculated in two ways: (1) $\vec{M}_{L} = \vec{r_2} \times \vec{F_2}$ (2) $\vec{M}_{L} = \vec{\lambda} \cdot \left( \vec{r} \times \vec{F} \right)$ where $\lambda$ is a unit vector in the direction of $L$, $\vec{F}_{1}$ is a component of $\vec{F}$ normal to the plane $P$, $\vec{F}_{2}$ parallel to the plane $P$, $P$ is a plane perpen..
In statics, moments – or couples – are treated as “free vectors” which means that they can move freely unless the direction of application is changed. It implies that the point of application of moment is meaningless while that of force is not. Therefore, the beams shown below are exactly under the same condition as a point of view of statics. (But not of mechanics of materials! It should be car..