For the rigid frame loaded as shown, determine the reaction components using the Method of Least Work. Consider that the flexural rigidity of AB and CD are twice as that of the beam BC. P B 3 20.0 ‒‒‒‒‒‒‒‒‒‒‒‒ 10m с (3) 3m 7m

A beam is part of the framing system for the floor of an office building. The floor is subjected to both dead loads and live loads. The maximum moment caused by the service dead load is 45 ft-kips, and the maximum moment for the service live load is 63 ft-kips (these moments occur at the same location on the beam and can therefore be combined). a. If load and resistance factor design is used, determine the maximum factored bending moment (required moment strength). What is the controlling AISC load combination? b. What is the required nominal moment strength for a resistance factor of 0.90? c. If allowable strength design is used, determine the required moment strength. What is the controlling AISC lead combination? d. What is the required nominal moment strength for a safety factor of 1.67?

For the beam shown: (a) determine the distance a for which the maximum positive and negative bending moments in the beam are equal; and (b) draw the corresponding shear and bending moment diagrams for the beam.

Compute the nominal shear strength of an M107.5 of A572 Grad 65 steel.