A 200 mm x 220 mm timber post is subject to an unknown axial compressive load (F) that is eccentric to both principal axes as shown below. If the axial stress is 2.4 MPa then: 80 mm 200 mm X C 220 mm (a) What is the compressive load? (b) What are the applied moments in the x and y directions? (c) What are the moments of inertia in the x and y directions. (d) At what corner does the maximum stress occur? State whether it is tensile or compressiv (e) Calculate the maximum stress at the corner 60 mm FL D
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.
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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.
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