Composite Beams

 *Example:  (continued) The moment of inertia for the entire “transformed” section    Iyy  =  829.5 in4   Use  σ  =  Mc/Iyy   to calculate the bending stress.   where       c1  =  h3/2 + h2 + h1,   c2  =  h3/2 + h2 ,  c3 =  h3/2   The bending stresses in terms of the base material (3) are as follows:     At the top of the composite beam  σ1  =  Mc1/Iyy =  (100,000)(9/2) / 829.5  =  542.5 psi   At the interface between (1) and (2)  σ2  =  Mc2/Iyy =  (100,000)(7/2) / 829.5  =  421.9 psi   At the interface between (2) and (3)  σ3  =  Mc3/Iyy =  (100,000)(3/2) / 829.5  =  180.8 psi       5.    Finally multiply the stress for material in section (1) by E1/E3 to obtain the actual            bending stress at the top of section (1).           σ1   =  3(542.5)  =  1630 psi   (result for the maximum bending stress in material (1).              and multiply the stress for material in section (1) by E2/E3 to obtain the actual            bending stress at the top of section (2).           σ2   =  (1.5)(421.9)  =  633 psi   (result for the maximum bending stress in material (2).         σ3   =  180.8 psi   (result for the maximum bending stress in material (3) since it is the                                      base material)

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