2.1 A beam of a ?-shaped cross section is subjected to a concentrated lateral load Q at its mid-span but off-centered as shown in Fig. 2.23. Determine the maximum normal stress ? _max and the maximum shear stress ? _max. Also determine the vertical deflection of point A shown.

Figure 2.23: Centrally loaded beam for Prob. 2.1

2.2 For the box section shown in Fig. 2.24, determine St. Venant torsion constant K _T, location of shear center S( ? ₀, ? ₀) and shear stresses due to shear force V _? applied through the shear center.

Figure 2.24: Box section for Prob. 2.2

2.3 Find the twisting angle ? for the cantilever beam which is subjected to a distributed torque as shown in Fig. 2.25.

Figure 2.25: Beam under distributed torque for Prob. 2.3

2.4 Show that normal strain in general coordinates ?, ? and ? can be expressed by Eq. (2.116), or

Derive equations for ? ₀, ? ? and ? _?.

2.5 Derive Eq. (2.128a) or

Discuss in what condition the relation holds true.

2.6 Show Eq. (2.158) or

Problem 2.1

Deflection at the midspan due to bending,

Rotation angle at the midspan due to torsion

Figure 2.26: Figures for solution to Prob. 2.1

Deflection of point A due to torsion,

Total deflection of point A is

Fig. for...