# 2009+10AxialLoad - Introduction to Solid Mechanics-Vm211...

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1 SJTU Introduction to Solid Mechanics -Vm211 Chapter 10 Axial Load Chapter 10 Axial Load SJTU Introduction to Solid Mechanics -Vm211 CHAPTER OUTLINE Saint-Venant’s Principle Elastic Deformation of an Axially Loaded Member Principle of Superposition Statically Indeterminate Axially Loaded Member Thermal Stress SJTU Introduction to Solid Mechanics -Vm211 Most concrete columns are reinforced with steel rods; and these two materials work together in supporting the applied load. Are both subjected to axial stress? APPLICATIONS SJTU Introduction to Solid Mechanics -Vm211 ± Localized deformation occurs at each end, and this effect tends to decrease as measurements are taken further away from the ends SAINT-VENANT’S PRINCIPLE SJTU Introduction to Solid Mechanics -Vm211 ² c-c is sufficiently far enough away from P so that localized deformation “vanishes”. The minimum distance from the end to c-c can be determined. ² At section c-c , stress reaches almost uniform value as compared to a-a , b-b SAINT-VENANT’S PRINCIPLE SJTU Introduction to Solid Mechanics -Vm211 ± General rule : min. distance is at least equal to largest dimension of loaded x- section . ± For the bar, the min. distance is equal to width of bar SAINT-VENANT’S PRINCIPLE

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SJTU Introduction to Solid Mechanics -Vm211 ± Saint-Venant Principle states that localized effects caused by any load acting on the body, will dissipate/smooth out within regions that are sufficiently removed from location of load SAINT-VENANT’S PRINCIPLE SJTU Introduction to Solid Mechanics -Vm211 ± Thus, no need to study stress distributions at that points near application loads or support reactions SAINT-VENANT’S PRINCIPLE SJTU Introduction to Solid Mechanics -Vm211 ± Find relative displacement ( δ ) of one end of bar with respect to other end caused by the concentrated loads at ends and a variable external load distributed along its length ELASTIC DEFORMATION SJTU Introduction to Solid Mechanics -Vm211 ± Applying Saint-Venant s Principle, ignore localized deformations at points of concentrated loading and where x-section suddenly changes ELASTIC DEFORMATION SJTU Introduction to Solid Mechanics -Vm211 Use method of sections, and draw free-body diagram ELASTIC DEFORMATION σ = P(x) A(x) ε = d dx σ = E ε • Assume proportional limit not exceeded, thus apply Hooke’s Law P(x) A(x) = E d dx ( ) d δ = P(x) dx A(x) E SJTU Introduction to Solid Mechanics -Vm211 δ = 0 P(x) dx A(x) E L δ = displacement of one pt relative to another pt L = distance between the two points P(x) = internal axial force at the section, located a distance x from one end = modulus of elasticity for material ELASTIC DEFORMATION
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2009+10AxialLoad - Introduction to Solid Mechanics-Vm211...

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