https://www.youtube.com/watch?v=8aFVZZ87k3E

• Initially we start with this structure with a pinned node at A and a horizontal roller at D
• A force of 100N is applied at C
• lengths AC and CD are equal

Method of joints

• equilibrium states that there has to be a net of 100N in the positive y direction
• symmetry shows the net reaction force will be distributed 50/50 on A and D in a

• we start at node A since it has the most constraints.

• we can seem that the only vertical contribution can come from beam AB.

• so we add the blue line creating a triangle with vertical component = 50N and then solve for the force along the blue force and the green force

• we know there has to be an equal and opposite force at B and C, so we add s second blue and green force

• we choose C since there is more info.

• add opposing purple force of 100N

• add opposing green forces of 75N

• we can draw another blue as the only beam contributing vertically to node D
• we can use Pythagoras to find the value of the blue force.
• not very surprising but it is the same as the left side even tho we used a different method. WOW…

• finally, we can now see which beams are under Tension or Compression by the direction of their associated reaction forces

Finding Stress (σ)

Stress is defined as the internal force per unit area that resists the applied force. For a beam under tension, the formula for stress is:

$\sigma = \frac{F}{A}$

• σ: Stress (in Pascals, Pa or N/$m^2$)
• F: Tension force applied to the beam (in Newtons, N)
• A: Cross-sectional area of the beam (in $m^2$)