CES Mechanics I Lecture 8
Topics:
- Trusses. 6.2
- Method of joints. 6.3.1
- Zero-force members.
- Method of sections: 6.3.3
Isolating a section of a truss (more than one node) results in 3 equilibrium equations. The internal forces in removed members appear as unknowns in those equations. In the best case, equations separate and can be solved individually for individual unknowns.
For the example truss from last lecture, in order to compute the forces in members BC, CH and GH, consider left section of the truss containing nodes ABH.
\sum F_y = 0 \Rightarrow \frac{4}{5} T_{CH} - 8000 + 7500 = 0 \Rightarrow T_{CH} = 625\;\mathrm{N}
\sum M_H = 0 \Rightarrow - 7500 \cdot 6 - T_{BC} \cdot 8 = 0 \Rightarrow T_{BC} = - 5625\;\mathrm{N}
\sum F_x = 0 \Rightarrow T_{GH} - 5625 + \frac{3}{5} 625 = 0 \Rightarrow T_{GH} = 5250\;\mathrm{N}
For the ConcepTest truss, separate the top section (all nodes except DGK), and use following equations:
\sum M_J = 0 \Rightarrow T_{CD} \cdot 4 + 3000 \cdot 4 + 1000 \cdot 6 + 1000 \cdot 3 = 0 \Rightarrow T_{CD} = - 5250\;\mathrm{N}
\sum M_C = 0 \Rightarrow - T_{JK} \cdot 4 + 1000 \cdot 6 + 1000 \cdot 3 = 0 \Rightarrow T_{JK} = 2250\;\mathrm{N}
Note that we could solve for the two unknows we were interested in even though there were 4 unknowns total and only 3 equations.
Corresponding Gross et al. Statik chapters are shown in red.
Key techniques:
- Computing internal reactions in truss members using method of joints.
- Simplifying truss FBDs by identifying zero-force members.
- Computing internal reactions in truss members using method of sections.
ConcepTests (accessible from RWTH domains only):
Additional material (accessible from RWTH domains only):
The method of sections is also called Ritter's method (Rittersches Schnittverfahren) and was developed by August Ritter, one of the first professors at the RWTH, then simply called TH Aachen.
