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Unformatted text preview: Page 1 M6 Method of Sections
Isolate a section (part) of the truss of interest
 Draw FBD, determine reactions  "cut" truss into sections (through bars)  Replace cut bars by coincident tensile forces  Apply planar equilibrium equations (positive tensile, negative compressive) All as for Method of Joints
 But now can use equilibrium of moments  can now have 3 unknown bar forces in a section EXAMPLE First draw FBD Page 2 + ∑ F1 = 0 → ⇒ HA = 0 ∑ F2 = 0 ↑ + ⇒ VA + VC − 2P = 0 ∑M3 = 0 A+ ⇒ −2P .2l + 4lVC = 0 ⇒ VC = +P ⇒ VA = +P Page 3
We are interested in bar ED. So take an appropriate cut. Closed
surface Must include
reactions
crossing surface
Want to find FED , one equation one unknown
→Take moments about B ∑M (draw in B) B : +2lP − lFED = 0 FED = −2P Page 4
Suppose we had wanted FED Suppose we had wanted FAB Redraw FBD. Is this correct?  Think about cutting members ED  shortens AB  opens Page 5
NOTE: In both methods of joints, method of sections, we solve for the internal forces by isolating part of the structure. Two Tips: • Reduce computation by intelligent choice of method & section to analyze
1 equation, 1 unknown • Check, check & double check as you go
 simultaneous equations Joint Realities Frictionless pins are an idealization of reality. Joints are generally more restrained Nevertheless the idealization of a pin jointed truss can go quite a long way to modeling
how real trusslike structures carry loads ...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
 Fall '05
 MarkDrela

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