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                 202    Mechanical Engineering Design
                                           y
                                                 l/2          l/2

                              Problem 4–64
                                           A     2I 1    B    I 1   C    x

                                                                      F


                                 4–65     Use Castigliano’s theorem to verify the maximum deflection for the uniformly loaded beam 7 of
                                          Appendix Table A–9. Neglect shear.
                                 4–66     Use Castigliano’s theorem to verify the maximum deflection for the uniformly loaded cantilever
                                          beam 3 of Appendix Table A–9. Neglect shear.
                                 4–67     Solve Prob. 4–15 using Castigliano’s theorem.

                                 4–68     Solve Prob. 4–52 using Castigliano’s theorem.
                                 4–69     Determine the deflection at midspan for the beam of Prob. 4–63 using Castigliano’s theorem.
                                 4–70     Using Castigliano’s theorem, determine the deflection of point B in the direction of the force F
                                          for the steel bar shown.





                                                         15 in
                                             O
                                               1  -in dia.
                              Problem 4–70     2                   A
                                                               7 in
                                                      B
                                                        4
                                                          3
                                                             F = 15 lbf

                                4–71*     Solve Prob. 4–41 using Castigliano’s theorem. Since Eq. (4–18) for torsional strain energy was
                                          derived from the angular displacement for circular cross sections, it is not applicable for section
                                          BC. You will need to obtain a new strain energy equation for the rectangular cross section from
                                          Eqs. (4–15) and (3–41).
                                 4–72     Solve Prob. 4–42 using Castigliano’s theorem.
                                4–73*     The cantilevered handle in Prob. 3–84 is made from mild steel. Let  F y = 250 lbf and
                                          F x = F z = 0. Using Castigliano’s theorem, determine the vertical deflection (along the y axis) at
                                          the tip. Repeat the problem with shaft OC simplified to a uniform diameter of 1 in for its entire
                                          length. What is the percent error from this simplification?
                                4–74*     Solve Prob. 4–50 using Castigliano’s theorem.
                                 4–75     Solve Prob. 4–51 using Castigliano’s theorem.
                                 4–76     The steel curved bar shown has a rectangular cross section with a radial height h = 6 mm, and a
                                          thickness  b = 4 mm. The radius of the centroidal axis is  R = 40 mm. A force  P = 10 N is
                                          applied as shown. Find the vertical deflection at B. Use Castigliano’s method for a curved flexural
                                          member, and since R/h < 10, do not neglect any of the terms.
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