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2009+5-2+StructuralAnalysis

# 2009+5-2+StructuralAnalysis - Introduction to Solid...

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Statics:The Next Generation Mehta & Danielson Lecture Notes for Section 6.4 1 SJTU Introduction to Solid Mechanics -Vm211 TRUSSES–THE METHOD OF SECTIONS (Section 5.4) Objectives : Students will be able to determine forces in truss members using the method of sections. SJTU Introduction to Solid Mechanics -Vm211 APPLICATIONS Long trusses are often used to construct bridges. The method of joints requires that many joints be analyzed before we can determine the forces in the middle part of the truss. Is there another method to determine these forces directly? SJTU Introduction to Solid Mechanics -Vm211 THE METHOD OF SECTIONS In the method of sections, a truss is divided into two parts by taking an imaginary “cut” (shown here as a-a) through the truss. SJTU Introduction to Solid Mechanics -Vm211 THE METHOD OF SECTIONS Since truss members are subjected to only tensile or compressive forces along their length, the internal forces at the cut member will also be either tensile or compressive with the same magnitude. This result is based on the equilibrium principle and Newton’s third law . SJTU Introduction to Solid Mechanics -Vm211 STEPS FOR ANALYSIS 1. Decide how you need to “cut” the truss. This is based on: a) where you need to determine forces, and, b) where the total number of unknowns does not exceed three (in general). SJTU Introduction to Solid Mechanics -Vm211 STEPS FOR ANALYSIS 3. If required , determine the necessary support reactions by drawing the FBD of the entire truss and applying the EofE. 2. Decide which side of the cut truss will be easier to work with (minimize the number of reactions you have to find).

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Statics:The Next Generation Mehta & Danielson Lecture Notes for Section 6.4 2 SJTU Introduction to Solid Mechanics -Vm211 PROCEDURE (continued) 4. Draw the FBD of the selected part of the cut truss. We need to indicate the unknown forces at the cut members. Initially we assume all the members are in tension, as we did when using the method of joints. Upon solving, if the answer is positive, the member is in tension as per our assumption. If the answer is negative, the member must be in compression. SJTU Introduction to Solid Mechanics -Vm211 PROCEDURE (continued) 4. Please note that you can also assume forces to be either tension or compression by inspection as was done in the figures above. SJTU Introduction to Solid Mechanics -Vm211 PROCEDURE (continued) 5. Apply the equations of equilibrium (EofE) to the selected cut section of the truss to solve for the unknown member forces.
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2009+5-2+StructuralAnalysis - Introduction to Solid...

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