Chapter10b

Chapter10b - Mechanics & Materials 1 Mechanics &...

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Unformatted text preview: Mechanics & Materials 1 Mechanics & Materials 1 FAMU-FSU College of Engineering Department of Mechanical Engineering Chapter 10 Chapter 10 -- continued continued Axial Loading Axial Loading Composite Bars in Tension or Composite Bars in Tension or Compression Compression Any tensile or compressive member which consists of two or more bars or tubes in parallel , usually of different materials, is called a compound bar. A composite bar is one made of two materials, such as steel rods embedded in concrete. The construction of the bar is such that constituent components extend or contract equally under load . Example:Indeterminate Structure Example:Indeterminate Structure Two components of different materials are arranged concentrically and loaded through rigid end plates as shown. Determine the force carried by each component. Equilibrium : In this case the load is shared in some unknown proportions between two parts so that F 1 + F 2 = F Geometry of deformation (compatibility): If the unloaded lengths, l, are initially the same, then they will remain the same under load; hence 1 = 2 = h Stress-strain relations: For a simple unaxial situation, 1 1 1 E = and 2 2 2 E = Solution Solution From equilibrium and stress equations l A E F l A E F 2 2 2 1 1 1 and = = Substituting the equilibrium equation F l A E l A E = + 2 2 1 1 thus 2 2 1 1 2 2 2 2 2 1 1 1 1 1 2 2 1 1 and A E A E A FE F A E A E A FE F A E A E Fl + = + = + = Solution Solution Composite Bars in Tension or Composite Bars in Tension or Compression Compression To illustrate the behavior of such bars consider a rod made of two materials, 1and 2, A 1 , A 2 are the cross-sectional area of the bars, and E 1 , E 2 are values of Youngs modulus. We imagine the bars to be rigidly connected together at the ends; then for the longitudinal strain to be the same when the composite bar is stretched we must have 2 2 1 1 E E = = Composite Bars in Tension or Composite Bars in Tension or Compression Compression where 1 and 2 are the stresses in the two bars. But the total tensile load is Together with the strain equation we obtain 2 2 1 1 A A P + = 1 1 1 1 2 2 1 1 1 1 1 1 E A E A PE E A E A PE + = + = Shearing Stress in Axial Loaded Shearing Stress in Axial Loaded Member Member The bar is uniformly stressed in tension in the x direction, the tensile stress on across-section of the bar parallel to Ox being x . Consider the stresses acting on an inclined cross-section of the bar; an inclined plane is taken at an angle to the yz- plane. Shearing Stress in Axial Loaded Shearing Stress in Axial Loaded Member Member For equilibrium the resultant force parallel to Ox on an inclined cross section is also P= A x At the inclined cross-section, resolve the force A x into two components-one perpendicular, and the other tangential, to the inclined cross-section,....
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This note was uploaded on 12/11/2011 for the course EML 3011 taught by Professor Schwarz during the Spring '09 term at FSU.

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Chapter10b - Mechanics & Materials 1 Mechanics &...

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