12.9-4 Determine the angles 0, and 0, defining the ori- P1 entations of the principal axes through the origin O and the corresponding principal moments of inertia I, and I, for the L-shaped area described in Prob. 12.8-4 (a = 150 mm, b = 100 mm, and t = 15 mm). P2 %3D a

The truss shown in Fig.3 is supported by a roller at C and a hinge at D. Use Castigliano's theorem to calculate the horizontal deflection for point B. E-200 B. kN/mm² and A-800 mm² for all members. s) 15 kN 2 m 20 KN B Th 2 m Fig.3

Determine the slope and deflection at point B of the steel beam shown. The reactions have been computed. E = 29(103) ksi, I = 800 in4.

Determine the deflections at B and C for the beam shown in Fig. 5 using the moment- area method. Also, determine the slope at D. El is constant. E = 20,000 ksi and I = 31500 in.4. 1.5 k/ft A B 30 k ↓ C 6ft 4 ft- +5 ft Fig. 5 D