L02_Concept of stress-fall 10

L02_Concept of stress-fall 10 - EAS 209 Fall 2010...

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EAS 209 – Fall 2010 Instructor: Human 8/24/2010 1 02-FDB/Normal Stress/Shear Stress Lecture 2 - Concept of Stress Study of mechanics of materials provides future engineers with the means of analyzing and designing various machines and load bearing structures. Both the analysis and design of a given structure involve the determination of stresses and deformations . This chapter is devoted to the concept of stress. Today’s Objectives: Review concepts of equilibrium learned in Statics Free Body Diagram (FBD) Force triangles Understand concept of normal stress, σ and shear stress, τ Calculate normal stress in bars Calculate shear and bearing stresses in bolted connections Today’s Homework EAS 209 – Fall 2010 Instructor: Human 8/24/2010 2 02-FDB/Normal Stress/Shear Stress Review of Equilibrium The structure below consists of a boom and rod joined by pins (zero moment connections) Construct Free-Body Diagram: Detach the structure from supports and apply the loads and reaction forces. Solve for reactions : four unknown forces, three equations of equilibrium The structure is not statically indeterminate because both AB and BC are two-force members
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EAS 209 – Fall 2010 Instructor: Human 8/24/2010 3 02-FDB/Normal Stress/Shear Stress Definition two-force member: a member that has pins or hinge supports at both ends and carries no load in- between . For a two-force member the internal force is directed along the member. If we recognize that both the rod and boom are two-force members, we can solve for F AB and F BC by considering equilibrium at joint B F AB =40 kN (compression) F BC =50 kN (tension) 0 30kN 4 5 3 40kN 50kN B BC AB AB BC F F F F F = = = = = r Sign convention: Tension is +ve (force points away from the joint) Compression is –ve (force points towards the joint) For the joint to be in equilibrium, the force triangle must close EAS 209 – Fall 2010 Instructor: Human 8/24/2010 4 02-FDB/Normal Stress/Shear Stress Note: use force triangle whenever you know the orientation of all three forces, and the magnitude of one.
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