Dimensions for all panels of the truss figure can be generated from the relationship of sides for a 30º-60º-90º triangle (sides: 1,√3,2). All truss panels maintain this triangular geometric relationship as indicated in the student diagram. As long as the truss panels are in proportion to the 30º-60º-90º triangle, the actual truss dimensions are immaterial, and the calculated magnitude of forces will be the same. Summing moments about a support point of the system yields and summing forces, the following support reactions (all force units are kN, “up” and “to the right” are positive)…
Dhoriz = -8.23 (to left)
Dvert = +8.0 (up)
Ehoriz = +8.23 (to right)
For “Method of Joints,” isolate all truss joints including support joints on a separate diagram, and resolve diagonal member internal forces into their respective individual horizontal and vertical components at each joint. Show all reaction forces calculated. Show all applied loads. The goal is to balance the forces at each joint by adding all vertical forces and adding all horizontal forces to maintain joint equilibrium (∑Fv = 0, ∑Fh =0), starting at point A. Proceed to transfer calculated values through the connected member to the next adjacent joint, working toward the support reactions. Every joint shall be in equilibrium.
The diagonal internal forces are calculated using their components just found. In summary, the member loads are…
MEMB T or C Magnitude (kN)
AB T +5.0
BC C -2.16
CD T +5.54
DB T +6.26
AC C -4.33
Please contact me for a more detailed explanation, setup and walkthrough of the joint isolation diagram, and step-by-step joint load calculations.
