Question

A W410 × 60 steel beam (see Appendix B) is simply supported at its ends and carries a concentrated load of P = 300 kN at the center of a 6.0-m span. The W410 × 60 shape will be strengthened by adding two cover plates of width b = 250 mm and thickness t = 16 mm to its flanges, as shown. Each cover plate is attached to its flange by pairs of bolts spaced at intervals of s = 200 mm along the beam span. The allowable average shear stress in the bolts is τallow= 94 MPa, and bending occurs about the zcentroidal axis. Determine the minimum required diameter for the bolts.

In order to find this please do the following steps.

1.) Determine the moment of inertiaI_z,top of the top cover plate about the z centroidal axis of the cross-section, and the moment of inertia I_z,bot of the bottom cover plate about the z centroidal axis of the cross-section.

2.) Determine the moment of inertia I_z of the entire cross-section, including cover plates, about thez centroidal axis.

3.) Calculate the maximum magnitude of the internal shear force in the beam.

4.) Calculate of the first moment of area Q that is associated with the upper cover plate.

5.) Determine the maximum shear flow q that must be transmitted through the two bolts that hold the top cover plate in place.

6.) Determine the minimum bolt cross-sectional area.

7.) Determine the minimum bolt diameter.

Answer 1