Practice Question: Forces in Truss Members (Tension & Compression)
NCEES Civil PE Specification Design and Details of Structures–Component Design and Detailing: Systems
Problem
A symmetrical truss is shown in the figure and support reactions are provided.
Determine the force in member CG of the truss.
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% Students Correctly Answered:
44.8%
Solution
Method of Joints and Method of Sections can be used to determine the forces in truss members. Method of Section is more convenient to determine the forces in any specific portion of truss. So, by applying Method of Section;
A section z-z is shown in figure:
From geometry of truss, angles can be determined:
\[∠GHD'→tanθ=\frac{L_{GD'}}{L_{HD'}}\]\[∠GHD'→tanθ=\frac{1}{5}\]\[∠GHD'→θ=11.3^o\]Now, we know that
\[∠GHD'=∠COH\]\[∠COH→tanθ=\frac{L_{HC}}{L_{{OC}}}\]\[tan11.3^o =\frac{4}{L_{OC}}\]So, \[L_{OC}=20\ ft\]And, \[L_{OA}=15\ ft\]\[∠COH→θ=11.3^o\]Taking sum of moments at “O”
\[∑M_O=0\]FHG, FCD, and horizontal component of FCG are passing through point “O.
In other words, perpendicular distances between point "O" and FHG, FCD & FCGx is zero (0).
