Deflections by Integration of the substitute the expression of M(x) into the deflection equation then integrating to satisfy d'y M(x) (i) boundary conditions dx² EI (ii) continuity conditions (iii) symmetry conditions to obtain the slope 0 = Bending-Moment Equation and the deflection y of the beam this method is called method of successive integration VA=0 VB=0

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.

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?