problem 1: The rigidly jointed frame shown in Figure has bending stiffnesses such that EI_{AB} = 1000kNm^{2}and EI_{BC} = EICD = 1600kNm^{2}.
A) Determine the joint rotations at B and C.
B) Hence, plot a bending moment diagram for the frame stating principal values.
C) Sketch a displaced shape for the frame.
problem 2: Determine the critical load (W_{crit}) to cause elastic instability of the rigidly jointed frame shown in figure below. The frame members have constant bending stiffnesses (EI) as indicated on the figure, where E is the modulus of elasticity and I is the second moment of area.
problem 3. For the collapse loads indicated in figure below, find the required plastic moment of resistance (M_{p}). The frame members have varying plastic moments of resistance as indicated on the figure.
problem 4: The two-storey frame shown in Figure below is such that the self-mass may be considered to be located at the beam levels and the beams may be presumed to be rigid. The self-mass (m) at each beam level and column stifnesses (EI) are indicated on the figure, where E is the modulus of elasticity and I is the second moment of area. Determine the natural circular frequencies and natural modes of vibrations of the frame and provide sketches of these.