Page 180 - Handbook of Civil Engineering Calculations, Second Edition
P. 180

STRUCTURAL STEEL DESIGN               1.163


                              where A vg   gross area of the vertical part of (2)
                                   A ns   net area of the vertical part of (2)
                                   A g   gross area of the horizontal part of (2)
                                   A n   net area of the horizontal part of (2)

                                                                                    2
                                              1
                                        A vg   (1 /2 sq.in.   3 in.)   0.515 in.   3.86 sq.in. (24.9 cm )
                                                                                         2
                                  A ns   (1 /2 in. + 2   3 in.   2 /2   /16)   0.515 in.   2.66 sq.in. (17.2 cm )
                                        1
                                                            15
                                                        1
                                                                               2
                                                 1
                                            A g   1 /2 in.   0.515 in.   0.77 sq.in. (4.96 cm )
                                                                                     2
                                      A n   (1 /2 in. –  /2   /16 in.)   0.515 in.   0.53 sq.in. (3.42 cm )
                                            1
                                                      15
                                                 1
                              2. Determine the design shear strength
                              R n is the greater of
                                                    kips               kips
                                   0.6   3.86 sq.in.   36     + 0.53 sq.in.   56       114 kips (507 kN)
                                                    sq.in.            sq.in.
                                                   kips               kips
                                  0.6   2.66 sq.in.   58     + 0.77 sq.in.   36       120 kips (533.8 kN)
                                                   sq.in.            sq.in.
                                                     R n   120 kips (533.8 kN)
                                               R n   0.75   120 kips   90 kips (400.3 kN)
                              The design shear strength is 90 kips (400.3 kN), based on the governing limit state of
                              block shear rupture.

                              Related Calculations. This procedure is the work of Abraham J. Rokach, MSCE, As-
                              sociate Director of Education, American Institute of Steel Construction. SI values were
                              prepared by the handbook editor.


                              DESIGNING A BEARING PLATE FOR A BEAM
                              AND ITS END REACTION
                              The unstiffened end of a W21   62 beam in A36 steel rests on a concrete support ( f c 
   3
                              ksi) [20.7 MPa], Fig. 50. Design a bearing plate for the beam and its (factored) end reac-
                              tion of 100 kips (444.8 kN). Assume the area of concrete support A 2   6   A 1 (the area of
                              the bearing plate).

                              Calculation Procedure:

                              1. Find the bearing length
                              For the concentrated compressive reaction of 100 kips (444.8 kN) acting on the bottom
                              flange, the applicable limit states are (1) local web yielding and (2) web crippling. (It is
                              assumed that the beam is welded to the base plate and both are anchor-bolted to the con-
                              crete support. This should provide adequate lateral bracing to prevent sidesway web
                              buckling.)
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