(Solved): Q.5 A simply supported beam is subjected to a uniformly distributed load \( ( ...

???????

Q.5 A simply supported beam is subjected to a uniformly distributed load \( (\boldsymbol{U D L}) \) of \( \boldsymbol{w} \mathrm{kN} / \mathrm{m} \) and a concentrated load of \( 15 \mathrm{kN} \) at mid-span as shown in Figure Q.5(a). Its cross section of the beam is shown in Figure Q.5(b) below. (a) Determine the moment of inertia \( \boldsymbol{I}_{x x} \) of the beam about the x-x axis. \( 6.35 \times 10^{\wedge} 7 \mathrm{~mm}^{\wedge} 4 \) (3 marks) (b) Express the support reactions and the maximum bending moment \( \boldsymbol{M}_{\max } \) in terms of \( \boldsymbol{w} \mathrm{kN} / \mathrm{m} \). Hence, draw the bending moment diagram. (6 marks) \( \mathrm{VA}=\mathrm{VB}=7.5+3 \mathrm{w} \mathrm{kN} \quad \) Max \( \mathrm{M}=22.5+4.5 \mathrm{w} \mathrm{kNm} \) (c) If the maximum permissible bending stress of this beam is \( 250 \mathrm{~N} / \mathrm{mm}^{2} \), determine the uniformly distributed load of \( w \mathrm{kN} / \mathrm{m} \) that can be carried by the beam. (5 marks) \( 23.22 \mathrm{kN} / \mathrm{m} \) (d) Sketch the bending stress distribution across the section of the beam under the maximum bending stress. (4 marks) (e) Under the loading \( \boldsymbol{w} \) obtained in (c) and the point load of \( 15 \mathrm{kN} \), determine the maximum shear stress induced in the beam. (7 marks) \( 18.971 \mathrm{~N} / \mathrm{mm} 2 \) Lisure yoving Figure Y. ?(D) (Not to scale)