Three Member Frame - Pin/Roller Central Bending Moment

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Three Member Frame - Pin/Roller Central Bending Moment formulas

\(\large{ R_A = R_B  = \frac{M_C}{L}  }\)   
\(\large{ H_A = 0  }\)   
\(\large{ M_{max} \;(at \; C)  =  \frac{M_C}{2}   }\)   
\(\large{ \theta \;(at \; C) =  \frac{M_C\;L}{12 \; \lambda \; I}  }\)  

Where:

 Units English Metric
\(\large{ h }\) = height of frame \(\large{in}\) \(\large{mm}\)
\(\large{ H }\) = horizontal reaction load at bearing point \(\large{lbf}\) \(\large{N}\)
\(\large{ I_h }\) = horizontal member second moment of area (moment of inertia) \(\large{in^4}\) \(\large{mm^4}\)
\(\large{ I_v }\) = vertical member second moment of area (moment of inertia) \(\large{in^4}\) \(\large{mm^4}\)
\(\large{ M }\) = maximum bending moment \(\large{lbf-in}\) \(\large{N-mm}\)
\(\large{ \lambda }\)  (Greek symbol lambda) = modulus of elasticity \(\large{\frac{lbf}{in^2}}\) \(\large{PA}\)
\(\large{ A, B, C, D, E }\) = point of intrest on frame - -
\(\large{ \theta }\) = slope of member \(\large{deg}\) \(\large{rad}\)
\(\large{ L }\) = span length under consideration \(\large{in}\) \(\large{mm}\)
\(\large{ R }\) = vertical reaction load at bearing point \(\large{lbf}\) \(\large{N}\)

 

diagrams

 

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Category: Structural Engineering
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