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                                                                                              Deflection and Stiffness  195
                                      4–12     Using superposition, find the deflection of the steel shaft at A in the figure. Find the deflection at
                                               midspan. By what percentage do these two values differ?


                                                y
                                                    15 in       24 in
                                                        340 lbf
                                   Problem 4–12
                                                              150 lbf/ft
                                                                          B
                                               O                             x
                                                          A
                                                       1.5 in-dia. shaft

                                      4–13     A rectangular steel bar supports the two overhanging loads shown in the figure. Using superposition,
                                               find the deflection at the ends and at the center.


                                                y
                                                  300                300
                                                           500
                                                  400 N                  400 N
                                   Problem 4–13
                            Dimensions in millimeters.  A          B
                                                                             x
                                               O                         C
                                                      Bar, b = 6, h = 32


                                      4–14     An aluminum tube with outside diameter of 2 in and inside diameter of 1.5 in is cantilevered and
                                               loaded as shown. Using the formulas in Appendix Table A–9 and superposition, find the deflec-
                                               tion at B.


                                                y

                                                          300 lbf     200 lbf
                                   Problem 4–14
                                                     2 ft        2 ft
                                                                             x
                                                O
                                                            A
                                                                       B

                                      4–15     The cantilever shown in the figure consists of two structural-steel channels size 3 in, 5.0 lbf/ft.
                                               Using superposition, find the deflection at A. Include the weight of the channels.


                                                y
                                                           60 in
                                                                         150 lbf
                                   Problem 4–15         5 lbf/in
                                                                             x
                                                O                        A
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