(Solved): The beam shown in Figure 6-1 is loaded by an unfactored distributed dead load of \( G \) (includin ...

The beam shown in Figure 6-1 is loaded by an unfactored distributed dead load of \( G \) (including self-weight) and an unfactored distributed live load \( Q \). Its cross-section is depicted in Figure 6- 2. The required material data, loading conditions, and geometrical dimensions are listed in Table 6-1. Note that the live load \( Q \) is applied between the supports at positions \( \mathrm{A} \) and \( \mathrm{C} \) only. The question is divided into three parts. The answer to each part should be clearly structured and documented in detail. 6.1 Sketch the shear force and bending moment diagrams for the beam under a short-term serviceability load. To this end, compute the values of the stress resultants (bending moment, shear force) at points \( \mathrm{A}, \mathrm{B} \) (mid-span of the beam), C, and \( \mathrm{D} \) as indicated in Figure 6-1. The dimensions of the beam are given in Table 6-1. (12 Marks) 6.2 Calculate the average effective second moment of area \( I_{e f . a v e} \) for the span \( \mathrm{AC} \) shown in Figure 6-1. Details of the beam's cross-section at locations \( \mathrm{B} \) (mid-span) and \( \mathrm{C} \) are illustrated in Figure 6-2. Assume that the second moment of area for the cracked section is given as: \( I_{c r}= \) \( \alpha I_{g} \), where \( \alpha=0.24 \). Document the details of the calculations of \( I_{g}, M_{c r . t} \) (cracking moment), and \( I_{e f} \cdot(16 \mathrm{Marks}) \) 6.3 Calculate the total deflection \( \Delta_{\text {tot }} \) at the mid-span (location B) for the span \( \mathrm{AC} \) as shown in Figure 6-1. In addition, check whether the total deflection meets the criterion for the limit deflection, i.e., \( \Delta_{\text {tot }} / L<1 / 250 \), where \( L=2 l_{1} \) is the centre-to-centre length of the span. (12 Marks) Figure 6-1 Figure 6-2