Question

Q3. The beam AB, shown in Figure 3a), has the cross-sectional area as shown in Figure 3b).The loaded beam is a “1"-shape steel beam reinforced with a horizontal rectangular-shape wooden beam throughout its length AB (shown in black in Figure 3b). Do the following: (a) Derive the centroid position from the top of the cross-section, y (b) Calculate the second moment of area about axis zz for the overall (steel and wooden component) beam cross-section. The second moment of area of the steel section of the beam about axis zz is Isteel=4.24 x 10-5 (m4)[5 marks] (c) Calculate maximum tensile and compressive bending stresses in the beam at a position8 m away from the support A.[8 marks] (d) Determine the bending stress at the point located 62 mm above the bottom edge of the cross-section (point C), at a distance of 8 m away from the support A. Also calculate the percentage increase of bending stress at this point if the steel beam was not reinforced with the wooden beam as shown in Figure 3b.[5 marks]

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