University:
Massachusetts Institute of Technology
Course:
16.01 | Unified Engineering I, II, III, & IV
Academic year:

2023
Views:

165

Pages:

5
Author:

Alonzo Warren

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 truss-like structures carry loads