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Unformatted text preview: Mechanics & Materials 1 Mechanics & Materials 1 FAMUFSU 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 δ 1 = δ 2 = δ h Stressstrain relations: For a simple unaxial situation, 1 1 1 E = ε σ and 2 2 2 E = ε σ Solution Solution •From equilibrium and stress equations l A E F l A E F δ δ 2 2 2 1 1 1 and = = •Substituting the equilibrium equation F l A E l A E = + δ δ 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 + = + = + = δ 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 crosssectional area of the bars, and E 1 , E 2 are values of Young’s 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 σ σ ε = = Composite Bars in Tension or Composite Bars in Tension or Compression Compression • where σ 1 and σ 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 σ σ + = 1 1 1 1 2 2 1 1 1 1 1 1 E A E A PE E A E A PE + = + = σ σ 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 acrosssection of the bar parallel to Ox being σ x . • Consider the stresses acting on an inclined crosssection of the bar; an inclined plane is taken at an angle θ 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’ σ x • At the inclined crosssection, resolve the force A´ σ x into two componentsone perpendicular, and the other tangential, to the inclined crosssection,....
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 Spring '09
 Schwarz
 Mechanical Engineering, Force, Stress, σs

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