(Solved): A simply supported T-beam, \( A B \), is subjected to a concentrated load of \( 6 \mathrm{kN} \) a ...

A simply supported T-beam, \( A B \), is subjected to a concentrated load of \( 6 \mathrm{kN} \) at \( \mathrm{C} \) as shown in Figure Q4a. \[ I_{y y}=27.00 \times 10^{6} \mathrm{~mm}^{4}, \quad I_{z z}=8.77 \times 10^{6} \mathrm{~mm}^{4} \] I. Determine the maximum bending moment and the shear force acting on the beam. [4/20 marks] II. If the T-beam is made by connecting two wooden planks and nails, determine the maximum permissible nail spacing to resist the maximum shear force. The shear capacity of a single nail is \( 1.2 \mathrm{kN} \). \( [6 / 20 \) marks \( ] \) III. In addition to the above-mentioned \( 6 \mathrm{kN} \) load, a concentrated load of \( 3 \mathrm{kN} \) is applied at the \( \mathrm{C} \) as shown in Figure \( \mathbf{Q} 4 \mathrm{~b} \) and the load produces bending only about the \( z-z \) axis. Assume that there is no twisting is produced. a. Determine the bending stress at point \( R \) and the state of the stress. b. What is the inclination of the neutral axis to the \( y-y \) axis? [10/20 marks]