farm water trough of length 5 m and width 4 m is supported on four timber beams of Douglas Fir.  The self-weight of each timber beam is 18 kg/m while the tank has a mass of 2 tonnes. The imposed  load is due to the tank containing 0.5 m depth of water. Assuming the beams are also 5 m in length  and carry equal load: (a) Calculate the permanent load per metre on each beam. (b) Calculate the imposed load per metre of each beam. From the loads calculated in (a) and (b) determine the ultimate limit state load using E=1.2G+1.5Q  (d) If the density of the timber is 510 kg/cu.m and the width of each beam is 120 mm determine the depth of beam.

A farm water trough of length 5 m and width 4 m is supported on four timber beams of Douglas Fir. 
The self-weight of each timber beam is 18 kg/m while the tank has a mass of 2 tonnes. The imposed 
load is due to the tank containing 0.5 m depth of water. Assuming the beams are also 5 m in length 
and carry equal load:
(a) Calculate the permanent load per metre on each beam.
(b) Calculate the imposed load per metre of each beam.
From the loads calculated in (a) and (b) determine the ultimate limit state load using
E=1.2G+1.5Q 
(d) If the density of the timber is 510 kg/cu.m and the width of each beam is 120 mm determine
the depth of beam.
(e) If the maximum bending stress is 7 MPa is the structure safe. i.e. Is the maximum bending
stress less that the allowable stress. (Assume loads are uniformly distributed on the beams)
(f) What is the factor of safety against bending failure (FS = max allowable stress/actual stress)
(g) If the maximum allowable shear stress is 1.2 MPa what is the factor of safety against shear
failure. (Note maximum shear stress is 1.5 times average shear stress).
(h) Calculate the long term deflection of the beam chosen in (d) based on the serviceability
requirement Sdeflection= G+0.4Q and E = 9 GPa.