The L shape body is made of two uniform slender bar of mass mi and length L1 and mass m2 and length L2 which is welded at point B and can rotate freely in the vertical plane. This body is released from rest when the bar OB is horizontal as shown. Determine the angular acceleration of the body and the magnitude of the force supported by the pivot at O immediately after release. L2m2 L1,m,

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.