Page 224 - Shigley's Mechanical Engineering Design
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                                                                                              Deflection and Stiffness  199
                                                          y




                                                                                      2 in
                                                           A                       C
                                                                   1-in dia.
                                                                        1  in             F y  3  -in dia.
                                   Problem 4–41                         4      1            4
                                                                               1 in
                                                                               2
                                                                      B                     F x
                                               z                                      F z  D
                                                                                      5 in
                                                                6 in
                                                                                    x


                                      4–42     For the cantilevered handle in Prob. 4–41, let F x =−150 lbf, F y = 0 lbf, F z =−100 lbf. Find
                                               the deflection at the tip along the x axis.
                                     4–43*     The cantilevered handle in Prob. 3–84, p. 140, is made from mild steel. Let  F y = 250 lbf,
                                               F x = F z = 0. Determine the angle of twist in bar  OC, ignoring the fillets but including the
                                               changes in diameter along the 13-in effective length. Compare the angle of twist if the bar OC is
                                               simplified to be all of uniform 1-in diameter. Use superposition to determine the vertical deflec-
                                               tion (along the y axis) at the tip, using the simplified bar OC.
                                      4–44     A flat-bed trailer is to be designed with a curvature such that when loaded to capacity the trailer
                                               bed is flat. The load capacity is to be 3000 lbf/ft between the axles, which are 25 ft apart, and the
                                                                                               4
                                               second-area moment of the steel structure of the bed is I = 485 in . Determine the equation for
                                               the curvature of the unloaded bed and the maximum height of the bed relative to the axles.
                                      4–45     The designer of a shaft usually has a slope constraint imposed by the bearings used. This limit
                                               will be denoted as ξ. If the shaft shown in the figure is to have a uniform diameter d except in
                                               the locality of the bearing mounting, it can be approximated as a uniform beam with simple sup-
                                               ports. Show that the minimum diameters to meet the slope constraints at the left and right bear-
                                               ings are, respectively,

                                                                               1/4                    1/4
                                                                        2                     2
                                                                            2                     2
                                                                    32Fb(l − b )          32Fa(l − a )
                                                                     3π Elξ         d R =    3π Elξ
                                                             d L =

                                                              F
                                                         a         b

                                                                l
                                   Problem 4–45
                                                     y
                                                              F

                                                                              x


                                      4–46     A steel shaft is to be designed so that it is supported by roller bearings. The basic geometry is
                                               shown in the figure from Prob. 4–45, with l = 300 mm, a = 100 mm, and F = 3 kN. The allow-
                                               able slope at the bearings is 0.001 mm/mm without bearing life penalty. For a design factor
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