In the design of a domestic roof structure, beam are to be simply supported, and carrying forces as shown in Figure 2 below. These beams are to be made of timber that has an allowable bending stress of \sigma _(allow )=7.5MPa and an allowable shear stress of \tau _(allow )=0.6MPa.
i. Draw a free body diagram for the beam in the figure
[3 marks]
ii. Determine the reactions at the two supports
[5 marks]
iii. Draw shear force and bending moment diagrams
[6 marks]
iv. Given that c=(1)/(2) height of the beam, determine the beam dimensions if it is to be rectangular, with a height-to-width ratio of 1.25 .
[6 marks]